Solid state modulators for horizon sensing applications∗

Infrared

Physics, 1971, Vol. 11 pp. 147-193. Pergamon Press. Printed in Great Britain

SOLID STATE MODULATORS FOR HORIZON APPLICATIONS*

SENSING

B. ELLIS Radio Department,

Royal Aircraft Establishment,

Farnborough,

U.K.

(Received 13 April 1971) Abstract-Conventional radiation choppers using rotating discs are potential sources of unreliability in space applications. This report examines a large number of possible alternative modulation techniques, treating several of them in detail. It is concluded that for horizon sensing purposes, using 14-16 pm COZ radiation, the most suitable alternative is a FabryPerot structure in which the plate separation is varied by means of piezo-electric ceramic transducers. Details of thermal com~nsation techniques are also given.

1. INTRODUCTION 1.1 Need for alternative modulators A COMMON method of orienting space vehicles is provided by detecting the 14-14 pm COZ, emission from the atmosphere at the Earth’s horizon, and horizon sensors often employ devices to modulate the intensity of this radiation. Conventional means of periodically interrupting infra-red radiation in order to produce an alternating output generally employ purely mechanical principles. Motor driven discs with alternate segments respectively transparent and opaque are commonly empIoyed in this role in the laboratory, when only moderate interruption frequencies are required. Many alternative methods have been proposed and developed and as a result there exists a considerable literature devoted to the subject of moduiation. Space applications involve other requirements and conditions which make it desirable to seek alternatives to motor driven modulation devices. Some problems with wear and lubrication are encountered and the power consumption of a motor can also be a cause of concern. One possible way of obviating these difficulties, used in the Nimbus IV experiment(l) is to use a vibrating chopper, in which a flexible metal strip may be driven by a piezoelectric element in such a way as to periodically interrupt the beam. While this would appear to avoid the problems associated with motor driven devices there exists the possibility of fatigue. For this reason the present study of possible alternative moduiators, in which macroscopic movement is eliminated, was undertaken. While the horizon sensing application was principally considered, the results should be of more general applicability. A significant part of the work involved an examination of the literature, including that devoted to high frequency modulation, in order to ascertain the extent to which this problem had been tackled by other workers and to see if techniques developed with other ends in mind could be adapted for the present purpose. This account will be devoted to an initial survey of possible solid state modulators (Section 2), followed by a more detailed consideration *This work was carried out for ESRO under ESTEC Contract No. 991/70AA. 147 I.P.-A

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(Section 3) of the several devices which seem to offer most promise for this ap~licatioil. Being largely self-contained, these sections may be read independently. 1.2. Optimum specification for a solid state modulator

A rotating segmented blade is, of course, a relatively simple, well tried device, despite its disadvantages. It follows that any replacement system must either be of known reliability or it must be possible to demonstrate this without unduly extensive testing. ~omprellensive tests on very large numbers of expensive devices would clearly be undesirably costly for a component which is only likely to be used in relatively small numbers. There is thus good reason for tending to favour relatively well tried principles rather than approaches of great novelty. Considerations of reliability also indicate that simple systems are likely to be more suitable than those involving great complexity. It is clearly essential that a modulator offering advantages in a particular aspect (e.g. lower power consumption) should at the very least not be any less reliable than a conventional ‘chopper’. In at least one other respect a properly designed rotating or vibrating blade is extremely satisfactory and the solid state device must strive to be its equal. This is in the matter of modulation efficiency (see Section 1.3), for it is relatively easy to arrange that a conventional ‘chopper’ either passes all the radiation or obstructs its passage completely. It will emerge that this is not so in solid state devices, where either a significant amount of the radiation transmitted is unmodulated or a certain fraction of the incident intensity is lost by absorption, reflection or other processes. In some cases both deficiencies are simultaneously present, for example in systems which require the use of polarisers, where even if a perfect polariser were possible it is inevitable that 50 per cent of the incident radiation is lost (practical potarisers for this application are considered in Appendix 2). Criteria for the assessment of possible modulators were specified by ESTEC and are as follows : 1. Large depth of modulation. 2. Power consumption less than 1 W. 3. Large acceptance angle, preferably f/l ,5 or better. 4. Effective area greater than 1 cm2. 5. Preferably a low voltage device. 6. Modulation frequency up to 1 kHz. 7. High reproducibility of the device. 8. High reliability (compatible with a lifetime of 1yr in orbit, or better). 9. Operating temperature range preferably -20°C to +6O”C. 10, Robustness. I 1. Mininlum stray magnetic fields. 12. Adaptabihty to other wavelength regions (a desirable but not essential feature). In addition, it is clear that neither the weight nor the volume of the modulator should be excessive. For the purpose of the study it was specified that the radiation under consideration, the COs emission in the region of 15 pm, could be taken to occupy the band 14-16 pm. It has been assumed throughout this study that the incident radiation is of uniform intensity over the whole of this band and an effort has been made to indicate where preferential transmission over part of the band may be anticipated. Most of the calculations detailed in subsequent sections assume that the incident radiation is converged to a focus by an f/l lens of ~4 cm dia. that is it is assumed that the absohrte

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maximum limit upon the length of the modulator is in the region of 4 cm, although it is possible that certain parts of the device could, if necessary, surround the detector. An obvious virtue in any device would clearly be the possibility of flexibility in its design so that it could be made in different shapes to suit a variety of circumstances. This possibility scarcely exists for the conventional motor driven discs. What is required for the present purpose of modulation is some means by which radiation at the wavelengths concerned may be absorbed, reflected, scattered or deflected to an extent which may be varied (ideally from 0 to 100%) by changing some parameter in the system. Most of these alternatives have been exploited in some form and the resultant devices are considered below together with some possible schemes which do not appear in the literature. It is first necessary to define the terminology which is to be employed. 1.3 ~e~~j~jon of eflective inoduIation

Mention has already been made of the application to laser communication systems of very fast modulators. In such work a quantity, frequently termed the modulation index, m, is used, being defined by a relation of the form X=X0(1

+mcoswt)cospt

(1)

where ~9is the modulation frequency. Many papers give results in terms of this parameter, which is defined in terms of the amplitude, X,. In some reports (particularly where only very low modulation depths are achieved) it is not at all clear whether it is this definition or some other which is being used. For the present purpose a more useful quantity is IV, defined as that fraction of the intensity incident upon the modulator which is subject to modulation, any unavoidable losses being taken into account (for example, the maximum value of M in a system incorporating a polariser will be SO%), i.e. M = (I,,, - &in)/Iinci&&, where I,,, and &in are the transmitted intensities. In the present discussion this quantity will be used throughout. Any possible losses in the system which may be variable in extent (e.g. due to imperfect blooming of surfaces) will generally be estimated separately. Unless otherwise stated the value of M will apply for uniform radiation filling the band 14-16 pm. In order to minimise confusion M will be referred to as the ‘effective modulation’. Thus, M is defined in terms of the magnitudes of the transmitted intensity and not of the sinusoidal component of intensity at the chopping frequency. Some gain in sensitivity is possible using square wave chopping, since the amplitude of the fundamental is greater than that of the square wave itself (by a factor of 4/n). Well designed mechanical chopping systems take advantage of this point. 2. POSSIBLE

‘SOLID

STATE’

MODULATORS

This section will be concerned with the less promising methods of modulation which have been described or suggested in the literature and also with other possibilities which have not been the subject of publication. Consideration of those methods which have greater potential for horizon sensing application is deferred until Section 3. Some reference is made below to published work, a more comprehensive bibliography has been given by Ellis and Walton.@) All equations will be quoted in rationalised units. 2.1 Free carrier injection One of the first solid state modulators employed this principle(s) the free carriers being injected electrically by forward biasing a germanium p-r? junction. Its operationdepends on the

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B. ELLIS

fact that the presence of free carriers in a semiconducting material gives rise to absorption (see, for example, Ref. 4), the absorption coefficient, being additional to that arising from other loss mechanisms, is given by KF.C. =

Ne3 h2 49 c3n EO prnez

(2)

where N is the concentration of free carriers having an effective mass m* and mobility y; n denotes the refractive index of the medium at wavelength h. A typical geometry for propagation perpendicular to the junction is shown in Fig. 1.

14-E pm rodlotion

-1-l FIG. 1. Forward bias injection modulator. It is possible to use equation (2) to specify an optimum material, having, for example, a low effective mass, for the application. However, other constraints severely limit the choice of material in practice. For the present purpose a relatively large working area is required and it is essential that the absorption in the absence of injected carriers is low. This implies that it must be possible to prepare the material in a form sufficiently pure for the absorption due to residual free carriers to be small, that is the quantity of residual dopant impurities must be small. Further if junction injection is to be used (as is more favourable than optical injection, see below) then it must be possible to preparep-n junctions in the material. Large area devices of the order of 1cm2, as are required here, imply the need for junction areas of the same order and this in turn dictates the use of one of the few materials, the technology of which is highly developed. Perhaps the three most suitable materials would be Si, Ce and CaAs, on the basis of the above arguments. Calculations based upon equation (2), using well established data for the parameters, show that on the assumption that equa1 numbers of electrons and positive holes are injected by forward bias of a p-n junction, the required total increase in carrier density due to injection, is -2-4 x 101ecm-2 for all three of the above materials. The conclusion is presented in this form since the attenuation is given by the product K&d as defined by

Kerfd = i Kp.c.dx (3) 0 where KF.C is the free carrier absorption coefficient for injected holes or electrons, as appropriate, and the integration is over the total thickness, d, of the device. This gives the transmission in the well known form (4:

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for horizon sensing applications

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Thus far it has been tacitly assumed that true free carrier absorption would be entailed in the modulating process. In germanium, however, it is found that the transfer of free holes between the three valence bands increases the absorption at 45 pm by about an order of magnitude and thus the requirements are considerably eased when allowance is made for this effect. To exploit this feature to maximum effect it must be ensured that the injection which occurs on forward bias consists predominantly of positive holes into the n-region. This will be assumed henceforth and it will also be assumed that germanium is the material to be used, since the above advantage is not present for Si or GaAs at 15 pm. In germanium at 15 pm the absorption cross section for a positive hole is 62Aa while for an electron it is 0.5Ae (Kaiser et al.(s)). Incidentally, it may be noted that the absorption cross section for the intervalance band transitions (and including the genuine free hole absorption) quoted above is constant for wavelengths in the range IO-25 pm so that any device developed for the 14-16 pm region may be expected also to function satisfactorily over a wider range of wavelengths. The same is not true for a modulator employing purely free carrier absorption, for which there will exist an optimum design for each operating wavelength, due to the JV dependence given by equation (2). If a continuous excess carrier density, An0 (of either holes or electrons), is maintained at some plane (say x = 0) in a medium which is infmite in extent in the direction perpendicular to this plane, it is well known that the spatial dependence of carrier concentration along OX is given by An0 e-X/L, where L is the carrier diffusion length. In the construction of a modulator in which a low insertion loss is essential it may be necessary to reduce the thickness of the region into which the carriers are injected to such an extent that it can no longer be considered infinite. An equation identical to that used for the infinite medium, derived from simple diffusion considerations, governs the excess carrier density An in this case, PA?l --AAn-0.

(5)

8x2

However, if the recombination rate is taken to be infinite at a contact which occupies the plane x = a, the boundary conditions become

It is then a straightforward

An = An,

at x = 0

An = 0

at x = a.

(6)

matter to show that An = (1 _Ar:2a,L) (e-z/h - e-s@/&ex/L).

Now equation (7) may be integrated over the range O
to give the total number of

When multiplied by the appropriate absorption cross section (cf. equation (2) for the case of true free carrier absorption) this is, of course, equivalent to the integrated absorption coefficient specified in equation (3). For a given required attenuation, given for one region by K,ffa, equation (8) gives the required injection density, Ano.

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B. ELLIS

In order to calculate the power required to maintain such an excess density at x = 0 it is necessary to evaluate the current flow, given by, per unit area

At this stage it is possible to consider the design of a practical modulator which, as cxplained above, will be assumed to be based upon the mechanism of positive hole injection in germanium. Taking, for convenience, the maximum acceptable transmission in the presence of injection (ignoring extraneous losses for the present) as e-2 2: 13.5 “/,, it is found that the total number of positive holes per unit area required to be in the path of the radiation is 3.2 x lO%m-2 (using the data of Kaiser et al. quoted above). Before proceeding it is necessary to consider the geometry of the device. Several factors relating to the optimum thickness of the IT-region into which the holes are injected are governed by the need to minimise free carrier absorption in the device when it is unbiased, that is when maximum transmission is required. Firstly the doping of the n-region should be the minimum consistent with the construction of an adequatep-n junction. This also has the effect of reducing the injection of minority electrons for a given bias voltage so that the injection current (being predominantly due to holes) is used to best effect. A low doping level will also tend to give maximum lifetime for the injected carriers which, as will be seen, is of paramount importance in minimising the power consumption.

FIG, 2. Total number of carriers in beam for injected density no, as a function of a/L (a = distance to contact).

Clearly, the thickness of the n-region should be no greater than is required for anadequate total excess hole density, any extra extent is largely wasted and merely contributes to the losses. It can be seen from equation (8) that the maximum value of N,ff is An,L and that this occurs if a+ (xl. Now the highest possible value of Neff for a given An, is required in order to maximise the efficiency of the device but in view of the above considerations it is necessary to compromise and restrict the extent of thep-region. It may be seen from Fig. 2 that a/L = 3 gives Neff ~1: 0.9 AnoL and this value of a will be used in the following discussion. A more serious consideration affects the design of the p-region. It becomes impracticable to easily inject the required minority carrier densities when these reach similar magnitudes

Solid state modulators for horizon sensing applications

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to the majority carrier concentrations in the injecting region. Thus it is necessary for the doping level in thep-region to exceed the required value of Ano, derived from equation (S), by at least one order of magnitude. Such doping levels are in no way impractical in themselves but since the radiation is required to pass through the p-region, the unavoidable presence of a high concentration of free holes places a severe limitation upon the thickness of that region, With the absorption (86.5 %) in the p-region, due to injection, being given by O-9 AnoL and with p - lOAn, it is evident that the thickness, b, of the p-region must be considerably less than 0.9 L/IO if severe absorption losses in the absence of bias are to be avoided. Taking b = 0*9L/lOO gives a transmission of e-O+ (82%) and since the hole diffusion length in lightly doped germanium is ~0.5mm, giving b - 4.5 pm, this is not impractical. If higher doping levels were to be used, or if the junction is produced by diffusion (so that the surface concentration exceeded that at the junction) the width of the pregion would have to be reduced accordingly. It is now possible to set about the deter~nation of the power consumption of a p-n junction modulator, employing germanium. Using the values of lifetime (T = 50 p set) and diffusion coefficient (D = 47.5 cme/sec) which may be achieved in lightly doped Ge, the hole diffusion length (L2 = 0~) is found to be 490 pm. Thus for Serf = 3.2 x 1015cm-2, as decided above, it is required that Ano = N&O,9L = 7.3 x 1016 cm-s and therefore p 7.3 x 101’ cm-s. As was noted above this is a perfectly reasonable value to achieve in practice. Since it has been assumed that the n-region is of width CI= 3L the average injected hole density is N 2.2 x I@* cm-s. In deciding upon the doping of the n-region it is necessary to bear in mind the points noted above, with respect to the absorption loss. Since the absorption cross section for electrons is l/12 that for holes it is only necessary to keep the donor concentration down to 2 x IOre cm-s to ensure adequate transmission (84.5 %). However, it is critically important to minimise the injected eIectron current, since this contributes directly to the power consumption, while only marginally improving the modulation. Moreover, the current is far higher, for a given injected density, in a region much narrower than a diffusion length (see equation (9)). Since b = 4.5 Pm and taking L = 177 pm in the p-region (T = 12.5 p set and pn = 1000 cma/V set) very low donor concentrations are called for in order to keep An,, and hence ..T,low (noting that if p/10 is injected into the n-region then rz/lOis injected into thep-region) and a value of n = 1 x 1015 cm-s will be assumed. This gives, in addition, improved transmission in the IZregion, 92-5 %. Assuming doping levels of 7.3 x 1Or7 cm-s and 1 x 101s cm-s in thep- and n-regions, it may be shown that for an abrupt junction the ‘built in’ voltage is Yc = 0~37V (at room temperature). Now equation (9) gives the current density, required to sustain the injected hole density, as 11.3A/cm2 and for the injected electrons O-88A/cm2 is needed. Using the standard diode relation it is found that the required forward bias is 0.43V. Hence the total power dissipation when biased is 5.35 W. It is important to realise that since the device is only biased for half a cycle the overall power consumption is only 2.68 W. In summary, forward biased p-n junctions could evidently fulfil the role of solid state modulators as required for horizon sensing purposes, provided that considerable care and control is exercised over their design and man~acture as detailed above. They have the advantages of being small, light, reasonably robust and have no moving parts. Losses, with suitable blooming of the surfaces, could be minimal and ignoring these some 86.5 % of the radiation would be modulated. However, the power consumption in the device would

154

B.

ELLIS

considerably exceed the maximum power specified and, moreover, it is not to be expected that significant losses in the power suppiy (-12A at - 0.4V) could be avoided, At this point it is appropriate to add some comment on optical injection. In principle this could have several advantages and could lead to a device working on much the same lines as those already described. Moreover, the carriers could be excited in pure material so that residual absorption losses could be avoided. Optical injection, however, has many inherent inefficient features. Whether the source used is a solid state ‘lamp’, a conventional tungsten filament, or any other emitting device, it will only emit a small fraction of the power supplied in the form of useful photons. Further, not all of these will be incident on the modulator slice and, of those that are, not all will produce free carriers. The power efficiency of such a device would therefore be considerably inferior to that of the injection modulator and it will thus not be considered further. A number of reports have appeared in which quite high degrees of modulation have been achieved using injection inp-n junctions, @s)(7) In these cases the absorption mechanism used has been basically that described in this section but the radiation has been propagated parallel to the plane of the junction, for distances of 1cm or more. For that part of the beam passing in the vicinity of the junction a very effective of modulation is thus readily achieved. Because the injected carriers recombine within a distance of about a diftitsion length from the junction (a maximum of 0.5 mm in Ge) the useful aperture of such an arrangement is too restricted to warrant further consideration here. In principle, a parallel arrangement of some 20 of these devices could be used but the practical difficulties would be considerable. Several brief reports make mention of an injection modulator for horizon sensing developed by the Honeywell Co.@). Beyond the fact that Ge was used no detail has been given and neither the power consumption nor the effective modulation were specified. 2.2 Reverse biased p-n junction Effectively, the working principle of the reverse biased p-n junction is the converse of the arrangement described in the previous section. Instead of injecting the carriers in order to produce the absorption, they are periodically removed from the path of the radiation. This is achieved by applying reverse bias to thep-n junction, which has the effect of widening the depletion region (in which there are effectively no free carriers). It is readily shown that it is only practical to use this device in the configuration in which the radiation is propagated parallel to the plane of the junction. Suppose, initially, that the radiation is to be propagated perpendicular to the junction as in the forward bias device already described. This ensures that a device of adequate area may be obtained. All other questions, such as the insertion loss of the device may, for the present, be ignored. Two basic requirements have to be met in designing such a modulator and, with the present constraints, they conflict quite seriously. Firstly, it is essential that in the unbiased condition there are a sufficient number of free carriers in the path of the radiation to produce adequate attenuation; this implies a relatively high doping level. Secondly, it is necessary to be able to widen the depletion region considerably with practical values of bias voltage. Unfortunately the Iatter condition requires the region concerned to be light/y doped (for example in Si doped to -lOI* cm-s a depletion region width of -1 mm has been achieved@)). Suppose positive hole absorption in Ge is to.be used and that N,ffti - 3 x 1015 cm-s as is required by the working in Section 2.1. Then, since the depletion width is I, = A/pb (where A is a constant for given bias) an estimate for the doping level, p, may be

Sotid state modulators

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obtained by evaiuating A from known data and equating 10 times the zero bias value of lP with d and Iv,ff with p. (This assumes that the depletion region can be widened by a factor of 10 under bias). An absurdly high value of 1.5 x 1022cm-s is obtained and the corresponding value of d is unrealistically small. It may be concluded that such a device is not practical. Propagation parallel to the junction shows more promise and has been used in practical modulators. For a path length of I cm an acceptor concentration of ~3 x 1015 cm-s is required if the abso~tion in P-type Ge is to be used. Assuming a relatively high n-type doping, say 101s cm-s (giving VO = 0.34V) it is found that at zero bias I, = 4.4 pm. Under reverse bias this may be widened as (V - V# so that for 34V applied, I, = 4.4 pm. Such a device may be practical for use with narrow optical beams, as in laser applications, but is clearly far too small to be of use for the present purpose. Even several devicesused in parallel could not provide an adequate aperture. Reverse biased p-n junction moduiators have been used by Deb and ~haudhuri(lO~ and Renton, among others. 2.3 Strain induced changes in free ear&r absorptiott It has recently been shown@z) that when unixial stress is applied to a semiconductor it is possible to produce considerable anisotropy in the free carrier absorption if certain conditions are fulfilled. It is necessary for the band structure in question to be multivalleyed, that is, at zero strain there must be a number of equivalent extrema in the function relating allowed energy values to the momentum of the free carrier. In practice this almost dictates the use of rz-type material. As long as the stress is not applied in a direction about which the energy extrema are symmetrically disposed, the effect of the stress is to displace (in energy) some of the valleys with respect to the remainder. Specifically in n-type Si, where the energy extrema are in the
156

B. ELLIS

marked anisotropy of the conductio1~ band effective mass. Since the absorption coefficient for one polarisation increases with applied stress the device will only become more transparent for the other polarisat~on, when the stress is apphed. From this it follows that the maximum effect that can be expected is a change from total opacity to a state in which the whole energy content of one polarisation is transmitted, that is at best only 50 ‘A of the incident radiation is transmitted. Unfortunately, it transpires that even if relatively high strains (~3.5 x 10-s) are produced in the material, the total transmission of the sample is typically only changed from 5 T
Basically the me~ha~~srns involved in this process are akin to those described in Section 2.3, the difference being that the dependence on effective mass of the free carrier contribution to the refractive index is utilised in this case. (1%This contribution decreases with the square of wavelength, is proportional to carrier concentration and inversely dependent upon effective mass, At some wavelength (which can be arranged to occur in the vicinity of I5prn by suitable choice of doping level) at which the total refractive index is unity, the reflectivity passes through a minimum, ideally zero, and thereafter rapidfy increases to ~100’A. When this phenomenon is applied to modulation it is envisaged that the reflectivity minimum for one pofarisation would be displaced to shorter wavelengths by ~2 pm by the applied stress, such that the 14-16 pm radiation would then be strongly reffected, Regrettably, it would only be possible to produce such a compIete change for one ~o~ar~sat~on (the other rn~ni~~urn shifts in the opposite direction in wavele~g~, for which the reflectivity increases less rapidly) so that the minimum value of M would be not much higher than 50%. Furthermore, while the reflectivity in principle is zero at the minimum, in practice this is not so and a typical minimum value is 5-10 %* due to the finite spectral bandwidth used, to the finite carrier relaxation time, possible inhomogene~ties in doping and various other causes. In addition, such a device presents somewhat ~onfli&t~ngrequirements since, in order to broaden the reflectivity m~n~murn suf%iently to achieve fow refle~tivjty over the 14 pm-16 pm region, a relatively poor relaxation time (roughly equivalent to low carrier mobility) would be required. Not only does this have the effect of raising the level of the reflectivity at the minimum, it also makes the following increase in reflectivity less steep, so that a larger shift of the minimum is required. An estimate by Wa~ton(l~~shows that a shift of -2 pm in the re~~t~vjty rn~~rnun~ could be produced by a strain of ~10-3, which as noted above, is quite practical ; it must be concluded, however, that values of M exceeding 40% are unlikely and in practice the performance may be poorer. Some additional compli~tion would result from the use of the reflection mode but this is not serious. A benefit of this means of operation is the total absence of other losses ~unwa~lted reflection at the sample surface, absorption in the bulk, etc.).

2.5 Stress ~~~d~ced shift of ~~~~rpt~~~edge Besides having an effect on free carrier properties, as described in Sections 2.3 and 2.4,

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an applied stress (either hydrostatic or u~axial} alters the interband or intrinsic absorption of a semiconducting material. This occurs as a consequence of the relative movement (in energy) of the conduction and valence bands, which is expressed in terms of an appropriate deformation potential (relative shift per unit strain). If such a mechanism were to be employed in a modulator for horizon sensing it would be necessary to choose a material with an absorption edge close to either 14 pm or 16 pm (according to whether the energy gap increased or decreased with strain) and by applying a periodic stress produce a 2 pm shift in its location. By this means the transmission of the material would alternate between low and high values. Two materials suitabfe for this purpose are known to exist, both are alloy systems in which the energy gap may be chosen from very low values upward, by an appropriate selection of alloy composition. Samples with absorption edges in the region 14-16 pm are known to have been made, The alloy systems are PbTe-SnTe and EIgTe-CdTe. Taking the former system as an example aud using deformation potential data for PbTe(rsf which will be sufficient to give an estimate of the necessary strain, it is found that a strain exceeding 4 x 10-s is required to shift the absorption edge from 14-16 pm. It is quite difficult to prepare samples of PbTe-SnTe with low carrier concentrations (in any case the intrinsic carrier concentration at 300°K is ~1017 cm-s) in material with such a low energy gap and thus in order to avoid excessive free carrier absorption it would be necessary to employ thin samples (maybe 100 pm thick or less). Quite severe problems would be encountered in endeavouring to repeatedly create such Iarge strains in a thin sample of such a material. Since it is assumed that cooling to 77°K is impracticable, the poss~bii~ty of using this means of modulation can therefore be dis&oun~. Mention may be made of accounts which have been given of modulators based upon this technique. Some use has been made of ultrasonic disturbances to produce periodically varying strains. In general the accounts relate to shorter wavelengths so that free carrier absorption is no longer a problem (materials having larger energy gaps may be employed) and the modulation is applied to a narrow waveIeng~ region in the vicinity of the energy gap (e.g. in use with a laser). Thus quite small strains are sufficient to produce a very acceptable effective modulation. What makes the method unattractive for horizon sensors is the broad optical bandwidth required.

In materials having narrow energy gaps, such as the alloy systems described above, it is possible for a large density of free carriers to produce a signi~~ant shift of the absorption edge. This arises because the occupancy of energy states by the carriers effectively ‘blocks’ interband transitions to these states. However, at room tem~rature, the relatively high intrinsic carrier concentration would significantly populate the lower energy states (for which the effect is greatest) and it would not be possible to conveniently introduce the additional carrier densities (lOI - 101scm-s) required to displace the absorption edge sufficiently. While p-n junctions can be fabricated in these alloys their effects are imperceptible unless the material is cooled. Optical injection, as noted in Section 2.1, is inefficient. 2.7 Shift of ~~~0~~~~~~ edge ~6the~~~~~~~~e~d Large electric fields applied to se~condueting materials result in a shift of the absorption edge. Under certain conditions the effect is proportional to the square of electric field.

IS8

B. ELLIS

~~nt~~~o~~~~s ~~e~o~~~~~~~~a~~ heresincethis has formed the bas~sofmoduiatorsfor visible and near in&a-red wavelengths. It would be imprac;trcal to adopt this method for the present purpose, however, since the chosen material must of necessity have a low energy gap, which would have to be significantly shifted by the application of the field. It would therefore have a high conductivity making it impossible to sustain the high fieid required. Moss(l4) has suggested that this technique is probably not useful for energy gaps < 1 eV. At short wavelengths use has been made of the high fields present in p-n junctions to produce the required shift of absorption edge. Naturally, such devices are of very small optical aperture. By capitalising upon the non-uniformity of the electric field it is possible to produce deflection devices, which could, in principle, also be used for modulations. A shift in absorption edge necessarily produces a change in refractive index thus a gradation in refractive index results from the non-uniform junction field. This has a prismatic effect, resulting in the deflection of the light beam. No alleviation of the aperture restrictions would result from the use of this mechanism.

Somewhat similar effects to those described at the end of the previous section have been produced without resort to the use of p--pfjunctions. These workers heated a CdS prism by the passage of an electric current, thereby changing its refractive index. Deflections of ~2’ were obtained for an input of -3OW.

If the two optical surfaces of a semiconductor through which 14-16 pm radiation is passed are arranged to have different surface rec~mbinatio~~ velocities then, when free carriers are alternateiy deflected to one surface or the other, the total number of carriers in the path of the beam will vary with time. Such is the basis of a modulator described by Flynn and Schlickmann(ls) in which an alternating current, passed through a germanium sample was deflected by a 3000G magnetic field. Very weak modulation was achieved for a dissipation -1 W and no details of insertion losses (etc.) were given. Quite apart from the problems introduced by the relatively high magnetic fieXd required, this principle would seem to have little potential for use in horizon sensing.

While included here for completeness this device is strictly not adaptable for satellite use since it requires tempe~tures of -4.2% to freeze carriers out into shallow impurity levels. When an electric field sufficient to cause impact ionisation is applied to the sample a dramatic increase in carrier concentration (-6 orders of magnitude) occurs which causes modulation by absorption. Modulation efficiencies (definition lacking) of 30 % at 195 pm and 95 % at 2-15 mm have been obtained by Melngailis and Tannenwald.(17) 2. I 1 ‘Hot carrier’ ~od~l~tio~~ In the presence of a suitably high electric field the distribution of free carriers among the available energy states may become significantly perturbed with consequent effects upon the absorption characteristics. Using the transitions between valence bands inp-type germanium (see Section 2.1) Vasil’eva et al.tl*) found maxima in the modulation efficiency at 2.9 pm and 9.5 pm (M - 50%) with an applied field of 1~V~cn~. It is, however, necessary to cool to -85°K to produce this performan~, an undesirable feature for the present purpose as

Solid state modulators

for horizon sensing applications

159

is the high field requirement. Further, it may be anticipated that high insertion losses would be difficult to avoid. 2.12 Faraday roration modulators

Modulators based on Faraday rotation are well known at shorter wavelengths and the extension to 14-16 pm is merely a matter of choosing an appropriate material. From the widespread use made of Faraday rotation in fundamental studies the relevant data is readily available. Since the Faraday effect is defined as the rotation of ihe plane of polarisation which is experienced by a plane polarised beam when passed through a suitable sample in a direction parallel to an applied magnetic field, it is evident that by varying the degree of rotation (by changing the field) the intensity transmitted by an analyser may be varied, providing the basis of a modulator. Large effective modulations demand Faraday rotations -rr/2 and even with the magnetic fields availabIe in the laboratory, this cannot be achieved without the introduction of an unacceptable loss in intensity. Suppose that the rotation due to free carriers were to be used. The mere introduction of free carriers means additional absorption, indeed the absorption loss given by KF.c.d (see Section 2.1) may be related to the Faraday rotation, 0, by t?

N

QpB

K..c.d

where B is the magnetic induction and p the carrier mobility. Putting KF.c.d = 1 (that is only -36% transmission) shows that even if IOOOGwere available, a mobility (at 300°K) of 3 x lo5 cm2/V set would be required to give B - n/z. This exceeds by much more than an order of magnitude the highest room temperature carrier mobility known. Absorption losses may be avoided if interband Faraday rotation is used. The rotation per unit length of sample is quite small and it is found that prohibitively long samples are required. Using 1000 Gauss in germanium, for example, implies a sample length of 140 cm. Some amelioration of these conditions could be achieved by using multiply reflected beams but it would be insufficient to make this principle practical for space use. Somewhat larger rotations might be obtained from magnetic materials but there appears as yet to be no evidence of a suitably transparent material for use at 14-16 pm. Even if a suitable material is found it must be noted that two polarisers would be required (see Appendix 2), so that the maximum value of M would therefore be 50% and additional losses would be inevitable. Power consumption would also be severe, depending upon the field required and, as noted in Section 1.2, it would be necessary to provide screening for the magnetic field. It is unlikely, therefore, that the Faraday effect modulator could be made compatible with the requirements specified for this application. 2.13 p-n junction in a Fabry-Perot cavity Various means of changing the phase difference between successive beams leaving a Fabry-Perot cavity may be used to vary the transmission and thus provide modulation. One of these, the simple expedient of altering the plate separation, forms the basis of the device considered in detail in Section 3.1. Another possibility is afforded by changing the refractive index of a medium in the cavity. One way in which this might be done is by reverse biasing a p-n junction so that the deple-

160

B. ELLJS

tion region is broadened (see Section 2.2). Since free carriers reduce the refractiveindex, their removal gives an increase, which must be ~50 o/0(averaged over the whole cavity) if efficient modulation is to be achieved (see Section 3. I). In germanium even a loo/, change in n implies an absolute change of 0.4 and this could be produced by the removal of 1.77 x lOI* cm-3 electrons (alternatively 3.18 x 1019cm-3 poritive holes). Now for 15 pm operation the plate separation of a Fabry-Perot cavity, used in the lowest order, is -1.75 pm (assuming the entire volume to be filled with germanium) and thus it would be necessary to widen the depletion region by an amount of this order for the effect to produce even moderate modulation. Calculations show that a reverse bias of 1.5 kV would be required to give such an effect, which is far more than the device would tolerate. No consideration has been given to the inevitable end effects that would occur with such a device or to the question of contacts, which would have to be either transparent or displaced, but in view of the impracticability of the device for present purpose5 these questions will be left in abeyance. It is worth noting that for some applications, for example high resolution spectroscopy in which smaller bandwidths are involved and where scanning Fabry-Perot devices are commonly used, this device might be found to offer advantages, particularly in speed. 2.14 Stark effect modulator High electric fields modify the electronic energy levels in gases and the corresponding absorption frequencies are also displaced. On this principle a modulator for a CO2 laser has been constructed by Landman et aA( Appreciable modulation was achieved with this device using fields of -1 kV/cm and the authors provided a list of gases suitable for use in the range 3-22 pm. However not only was a path length of 1m required (with a narrow optical aperture, -3mm) but also the shift in absorption energy is very small. This while the device may be useful in narrow line width applications it would be unsuitable for such a broadband purpose as horizon sensing. 2.15 Electra-optic effects Probably the most widely used effects for the purpose of modulation, especially in conjunction with laser radiation, are those in which the application of an electric field to a solid or liquid changes the refractive index. Only the effects in solids will be considered below. Two classes of effect are recognised, those depending upon the square of field are termed Kerr Effect and the linear changes constitute the Pockels Effect; the latter, being larger, will be considered here. Use may be made of refractive index changes produced in a direction pe~endicular to the applied field or parallel to the field, the magnitudes being dependent upon the orientation of the crystal which is chosen. Modulation may be achieved by placing an electro-optic material between crossed polarisers and applying an alternating voltage whose peak magnitude gives birefringence sufficient to make the sample a half wave plate. By this means the intensity transmitted may be changed from zero to 100 % (ignoring losses). In practice, since for many applications an intensity output which is linear with the dlive voltage is required, a quarter wave plate is also included and the range of the drive voltage is restricted sufficiently to yield a linear output. Such features are irrelevant to the present consideration, as are the various refinements involving the use of more than one crystal, and the point was noted simply to explain the added complexity of some reported systems. Quite low voltages (~100V) may be used for systems used at visible wavelengths but it must be noted that the change in refractive index required and therefore the voltage, for a

Solid state modulators for horizon sensing applications

161

given electro-optic coefficient, to achieve a h/2 phase difference is (obviously) proportional to wavelength. Moreover, materials having a suitable transparency in the range 14-16 pm, for which the electro-optic coefficients are known, GaAs and CdTe for example, exhibit fairly small effects in this wavelength region. Larger coefficients might, in principle, result from the use of materials with an energy gap closer to 15 pm but the difficulty of obtaining sufficiently high resistivity (cf. Section 2.7) would then occur. It should also be noted that the Pockels Effect depends on the electric3eIrl so that the requirement for a large aperture (-1 cm2) further aggravates the problem of high applied voltages. Data from several sources is available for the electro-optic coefficients of GaAs and CdTe. Using that of Kiefer and Yarivc20) for CdTe at 10.6 pm it is found that the field required to produce a birefringent path difference of h/2 is - 3 x 104V/cm for a specimen length of 1cm. For GaAs the field needed is, if anything, greater. In either case it could be halved, as indicated above, by the addition of a quarter wave plate. Since an aperature of 1 cm2 is required and because sample lengths exceeding 1 cm rapidly become impracticable, it is clear that the voltages required for electro-optical modulation are so high as to prohibit its use in this case. A further disadvantage of this technique is the necessity for two polarisers which means that M cannot exceed 50%. One way in which the voltage requirements of an electro-optic modulator might be drastically reduced is by capitalising on the occurrence of piezo-electric resonances in the sample. Photoelastic contributions to the birefringence can be so large that the drive voltage may be reduced by 3 orders of magnitude(2r) and in GaAs as little as 1V may suffice to give complete modulation of that part of the intensity (40 ‘A) which is transmitted. While this loss may still appear to be unnecessarily severe it should be borne in mind that for many of the systems in which nearly 100% transmission is possible in theory, the practical value of M is not much above 50 % (cf. the Fabry-Perot modulator, Section 3.1). Resonances are a nuisance, of course, in communications applications and it is for this reason that this effect has not been put to greater use. Unfortunately, the resonance frequency may be expected to be high (700 kHz in the O-3 x 0.3 x 1.7 ems device used by Walsh(a1) and ifslow thermal detectors (e.g. bolometers, thermopiles, etc.) are to be used such high modulation frequencies are totally unacceptable. It might well be possible, however, to use such a device in conjunction with a pyroelectric detector if adequate responsivity could be obtained at the resonant frequency. 2.16 Electra-optic material in a Fabry-Perot cavity Similar considerations apply to this modulator as to the use of a p-n junction within a Fabry-Perot cavity, as discussed in Section 2.13. When the electro-optic material is used the object is simply to produce a change in optical path length by changing the refractive index of the material. Some reduction in the voltage requirements is claimed for such a configuration when used to modulate laser radiation for which, as has been noted, small changes in optical path length suffice.( 22-23) Unhappily, this is not the case for a device needed for a horizon sensor and an enormous change in refractive index (-50%) see Sections 2.13 and 3.1) would be required. It is apparent from the discussion of the previous section that this implies the use of fields that are quite out of the question [for CdTe a figure of lOrsV/cm is obtained!). 2.17 Michelson interferometer Several groups have reported the operation of modulators based upon the Michelson

162

B. ELLIS

interferometer, in which one of the mirrors is driven by a piezoelectric transducer in such a way as to alter the optical path length. (24-25) Some other reports relate to the use of clectro-optic cells in one or both arms of a Michelson instrument. Nothing is to be gained by the use of this interferometer rather than the Fabry-Perot for the present purpose and the added complexity of beam splitters together with the greater bulk of the device would be unwelcome features. Tt will not be considered further. 2.18 Devices based on the d@raction grating A simple but unlikely possibility for achieving the desired modulation might be afforded by varying the pitch of a diffraction grating by some means, such as ruling the grating on a piezoelectric material. Elementary calculations confirm that this could not be done in practice. Taking the simple case of transmission grating placed before the focusing lens (i.e. in parallel light) taken to have a 4-cm focal length, and assuming a detector of effective area 1 mm2, it would be necessary for all the radiation in the 14-16 pm band (in a givenorder) to fall on the detector. It is readily shown that this requires a line separation, cl, greater than 100 pm, on the grating. For the same grating it would then be necessary to change d sufficiently to displace the focused image from the detector. Even a strain of 10-l is insufficient to give this movement. There is in addition the possible loss that would arise from the fact that a grating produces a line and not a point image. In principle the disadvantages described can largely be avoided if a plane reflecting surface is periodically converted into a grating. Thus the surface is alternately specularly reflecting and diffracting. Such a device, essentially a membrane in contact with a mesh and which is depressed into the mesh by a periodic electrostatic force, has been described by Preston.@6) It is clear that possible fatigue problems make this approach rather unattractive for 15 /Lrn modulation in the present context. 2.19 Acousto-optic modulators High frequency acoustic disturbances in solid or liquid bodies can cause them to act very much in the manner of a diffraction grating, for electromagnetic radiation propagated in directions roughly perpendicular to the acoustic waves. Diffraction of radiation at normal incidence is described as Raman-Nath scattering and if incidence at the Bragg angle is used it is termed Brillouin scattering. Recently, attention has been given to the application of acousto-optical scattering as a means of providing high speed deflection and modulation devices for use with laser radiation. Bragg angle diffraction will be considered exclusively in the following account since it offers the greater promise for the purpose in hand (twice the deflection angle, for given conditions, is obtained in the Bragg configuration). High acoustic frequencies (>l MHz) are required to give large deflection angles and modulation at low frequencies may be produced by applying low frequency bursts of ultrasonic waves, thus periodically deflecting the focused beam from the detector. Unfortunately, the power required for efficient deflection increases with acoustic frequency and with optical wavelength. Photoelastic data for a number of materials has been compliled by Dixon(27) and it is evident from his paper that the most favourable material for 15 pm operation is GaAs, for which the data relate to acoustic disturbances propagated in a (110) direction. For this configuration the quotient of the power required for complete deflection and the acoustic frequency is 0.24 mW/MHz, for 1.15 pm radiation. Unhappily, this quantity increases as the cube of the optical wavelength, giving 0.53 W/MHz at 15 pm.

Solid state modulators

for horizon

sensingappii~tions

163

While an operating frequency of 1 MHz would, in principle, thus be possible, within the allowed power consumption, it would only yield a deflection of 2 sin-l l;lX/27rvn(where Q is the acoustic frequency, v is the appropriate acoustic velocity and n the refractive index of the material) (see, for example, Ref. 28). Calculations show that this amounts to only about 0.5’. Even if 20MHz could be used (entailing a power dissipation of 1OW) it would stilt require a distance of 40 cm for the lateral displacement to amount to the minimum of I mm that would be needed to deflect the beam from the detector. Still greater power consumption would be experienced in practice since the necessary transducers are unlikely to have an efficiency better than 10%. (For CdS, Foster@g) quotes 6dB loss at 300 MHz rising to 20dB at 16GHz). Acoustic attenuation in the material could also be of some significance. It may thus be concluded that such a device could not be used for 15 pm modulation without excessive power dissipation. 2.20 Muhple rejection modulators Two reports have been published which claim high effective modulations for structures of the form shown in Fig. 3,@**31)Once the radiation has entered the device it is incident Applied voltage

/’ Insuiotin~ film - - -__

. High refractive index material

,/; Incidenf rodiotion

FIG. 3. Multiple reflection modulator.

upon the back surface of the material at an angle greater than the critical angle. It then passes by multiple reflections to the far end of the modulator where it re-emerges. Some complications exist if a convergent beam is used and for the present it will be sufficient to consider only parallel illumination. Electrodes are positioned in close proximity to the reflecting surfaces and insulated from them by thin films of mylar. Both of these are maintained at the same potential and a further contact in the centre of the sample enables a high field to be maintained at the reflecting surfaces. In this way it is well known that it is possible to vary the number of free carriers near the surfaces by varying the electric field, since the field may raise or lower the energy bands near the surfaces. At moderate frequencies (below I kHz) quite high degrees of modulation (up to ~40 %) are claimed for devices using KRS-9) and germanium.(sl) In the latter case the induced free carrier concentration at the surface was derived from measurements of the oscillatory component of the current and a value of N 4.1 x lOrlcm-s was obtained for an applied bias of -500V. It was suggested that the additional absorption due to these free carriers was responsible for the observed modulation. Now it may readily be shown using equation (2) that, even if positive holes cause the absorption, this number of carriers would only produce an attenuation of e : 1 if the effective path length of the radiation in the surface regions was I.P.43

164

B. ELLIS

-4Okm. It is clear that, if the measured induced carrier concentration is correct, the mechanism responsible for modulation cannot be that of free carrier absorption. A third article by the same author(ss) sets out to calculate the attenuations expected in these structures by the application of impedance techniques, Simplifying assumptions are understandably made and the induced carriers are assumed to be uniformly distributed ~roughout a narrow surface region. The result of the calculation is stated to be the reflection coefficient of the interface between that region and the bulk. This is presumably an error since, if it were the case, the considerable reflection from the second surface would be ignored. Apart from an exponential factor which is taken to be unity the resulting expressions (too unwieldy to reproduce here) nowhere include the thickness of the surface layers, merely incorporating the induced conductivity. This is clearly at variance with the suggestion that the mechanism involved is free carrier absorption. As a final check calculations were undertaken using conventional optical formalism. A configuration of the sort treated by Petersc s2) has been discussed by Born and Wolf.@) In the latter treatment the propagation of electromagnetic radiation through a thin conducting medium bounded by two dielectrics is considered in detail. With the slight modifications required to allow for total internal reflection the results are directly applicable to the configuration under discussion. Calculations based upon these results show that at a single reflection the reflectivity is 99,99%, so that even after 100 reflections the overall transmission of the device would be 99 %. The data used in these calculations was that given by Peters@r) who stated that in the Ge modulator some 47 reflections were involved. Assuming that the experimental results are genuine it must be concluded that they cannot be explained by the mechanism postulated. While it is clearly not essential to understand the underlying theory of a useful device it is certainly preferable to do so. At the very least it would be essential to experimentally verify the results claimed before the principle could be applied to horizon sensing. This has, unfortunately, fallen outside the scope of the present work. No details of the insertion losses caused by these modulators have been given and the dimensions of the KRS-5 device were not specified. It would appear that the Ge modulator was some 5cm in length so that the insertion loss at 1Sprn would be quite large (see Section 3.1.2). At 4 pm a value of M = 40% (excluding losses) at low frequencies was reported, with the application of 5OOV.Curiously, the modulation obtained at 10 pm was less thanthat at 4 pm, another feature which implies that the mechanism involved is not free carrier absorption. For the KRS-5 device, used at 9.lprn, the application of only 400V was sufficient to reduce the transmission to virtually zero. In this case increased modulation over that obtained at 5.6 pm was evident at 9.1 pm. No reference to these results is given in the later paper.t3*) 2.21 Gum &ect modulator It has been suggested that the high field domains which are set up when microwave current oscillations are induced in a semiconductor might give sufficiently large changes in the refractive index (by the electro-optic effect, see Section 2.15) to be of use in modulation.@n Very high modulation frequencies could be obtained using a d.c. source. For low frequency operation the d.c, source could be suitably interrupted. No further consideration will be given to this device since its useful aperture would be very small and it has the further disadvantage that it requires the use of two polarisers (see Section 2.15 and Appendix 2).

Solid state modulators for horizon sensing applications 3. PROMISING

MODULATORS

FOR HORIZON

16.5

SENSING

This section covers those means of modulation which at present would appear to offer the most favourable features for 15 pm modulation. Some detail is given of their likely power consumption and greater attention will be paid to losses of optical power in the components of the system. It will become apparent that it is very difficult for a solid state device to approach the 100 % transmission which can be characteristic of mechanical interruption. 3.1 Fabry-Perot cavity with variable plate separation Fabry-Perot etalons are familiar items of laboratory optical equipment, used primarily in high resolution spectroscopy. Various reports have been given of modulation obtained by varying the plate separation or the pressure (or temperature) of the gas in the cavity. In general these produce only small changes in the effective cavity length and are therefore only suitable for use with nearly monochromatic radiation. At least one account of a purely mechanical movement has been given, in which one plate was periodically displaced by a mechanical lever system actuated by a motor driven cam.(ss) For horizon sensing it is envisaged that the movement will be produced by piezoelectric transducers, since these appear to be well suited to the purpose and may give the required displacement with very low power consumption. Two plane parallel plates of reflectivity R, separated by a distance d form a Fabry-Perot cavity. Throughout the following discussion it will be assumed that the plate thickness is very much greater than d and that the refractive index appropriate to the medium between the plates is unity. For the moment it will also be assumed that monochromatic plane parallel radiation of wavelength X is incident at an angle 8. Under these conditions it is well known that the transmission of the system shows a series of peaks when the phase difference, 6, between successive multiply reflected beams is 2~~7 where m is a non-zero integer and 8 is given by

I, the intensity transmitted as a fraction of the incident intensity lo, may be shown to be given by the Airy function, I

10

1 --II_1 + F sins 612

(12)

where F = 4 R/( 1 - R)z. 3.1.1 Application to horizon sensing. At this stage it is as well to state more precisely the aims of the application of this principle to modulation, Firstly, for one particular setting of the plate separation the highest possible transmission of anf/l beam, containing radiation at wavelengths over the whole band 14-I 6 pm, is required. Secondly, at some other setting the lowest attainable transmission of this radiation must be sought. Lastly, some means of accurately and repeatedly transferring from one setting to the other with the expenditure of minimal power is required. For monochromatic radiation these settings would correspond to 6 = 2mrr and (2m - 1)~ respectively. Since, in terms of wavelength, the maximum separation of orders occurs if m = 1 (lowest order) this is probably the most desirable mode of operation. Both of the two departures from the straightforward situation in which Fabry-Perot cavities are described by equation (11) and (12) namely the use of anf/l beam and the

166

B. ELLIS

broad spectral bandwidth, may be described as broadened phase differences (through the dependence of 6 on X and 8, equation (11)). It will be noted from equation (12) for 6 = 2m1~,Z = Z,; what is here required is Z N Z, for 6 = 2m7~i 7*2’/ i.e. the normally sharp transmission peaks must be broadened. It is readily shown from equation (12) that this may be achieved by using reflecting surfaces with a much lower reflectivity than the 98 % or so for those usually employed in this role. However, it must be noted that in place of the virtually zero transmission which is obtained in the region 6 = (2~2 - 1)~ when highly reflecting surfaces are used, a finite transmission occurs if the reflectivity is appreciably lower. Of the two possible approaches to this problem, coating suitably transmitting substrates or using plates of a suitable material, it is the latter which will be considered here. This is primarily because the choice of germanium for the plates affords a reasonable compromise between the conflicting requirements outlined above but it also comes about because the range of possible substrates which are strong, transparent over the range 14-16 pm and not unstable in the atmosphere (giving rise to anxiety over storage and handling before use) is severely limited. Indeed, it would not be unlikely that, were the coating approach to be adopted, the most suitable substrate would be found to be germanium. Pure germanium has a refractive index of 4 at the wavelengths under consideration, so that the reflectivity of a single surface is 36 %. Figure 4, shows the transmission of a FabryGermanium. R: 36% Parallel illuminotlon

’

o X=lSpm

X=l6,um

2rr

!

!

Points coiculoied ossuminq -+ 10% errw in d at extremity of plates

b

7T,4

3W2

Phase

75pm

difference, 5625p

5T/4

T

6 375pm

Plote seporoticn, d Fro.

4. Transmission

of a Fabry-Perot

cavity as a function of phase difference.

Perot cavity formed by two germanium plates as a function of the phase difference 6 for illumination with parallel light, as given by equation (12). This may be interpreted as the transmission as a function of separation for monochromatic light or as the transmission as a function of wavelength for a given separation, as shown by the two abscissa scales. By computing the areas below the curve in Fig. 4 it may be shown that for parallel illumination, having a spectral bandwidth 14-16 pm, the maximum transmission is when the setting is 8 = 2mn for h = 15,um and is 95.5 %. Minimum transmission occurs at 6 = (2m - 1)~ and is 22.2 % so that, ignoring losses for the present, M = 73.3 %. In considering the effects of the convergence of the incident light it must be noted that

Solid state modulators

for horizon sensing applications

167

when uniform parallel radiation is brought to a point focus by a lens the intensity incident at the focal point is a function of the angle of incidence. As shown in Appendix I the intensity incident from the angular range 0 to 0 + 68 as given by Z(@)= Zr .2+

tan 0

sees OS8

03)

where Zr is the intensity per unit area falling upon lens andfis the focal length of the lens. Thus not only is the phase difference, 6, different over the angle of the beam but the fractional intensity having such a phase difference is also a function of the angle. Consequences of this are exhibited in the curves of Fig. 5 which shows the intensity incident as a function of the 15

F

/g!;m

Transmission of

IO

5 . Angle

of

15

incidence,

20

25

8. deq

FIG. 5.Variation of intensity of a convergent beam and its transmission. angle of incidence together with the effect of this on the trans~ssio~ of monochromatic 15 and 16 pm radiation, for a cavity set at 6 = 2mrrfor the centre of the band, that is, 15 pm. By computing the areas below the curves it is found that some 93.8 % of the 15 pm radiation is transmitted while for the 16 pm radiation the fraction is only 75 %. Fortunately, while the phase variations introduced by the finite spectral bandwidth may be of either sign (up to &7*2x), the phase difference due to the convergence of the beam is always negative (with respect to that for the central ray). Thus, while the two effects are additive for 16 pm radiation (assuming the cavity spacing to be set for 15 pm), there is a progressive partial cancellation as h is decreased towards 14 pm and there the fraction transmitted is therefore greater than 93.8%. An approximate assessment of the overall transmission, avoiding laborious calculation, is given by taking the 14-15 pm transmission as 938 % and the 15-16 pm transmission as 4 (93.8 + 75) %, giving the average transmission as 89.1%. Some slight increase in this figure might result from setting the cavity for 6 = 2mn at a wavelength between 15 and 16 pm rather than exactly 15 pm. Such optimisation would be best achieved by experiment.

168

B.

ELLIS

It is evident from Fig. 4 that a spread in S has far less effect in the region 8 =- (202 - l)rr, where minimum transmission is required and the transmitted intensity remains close to 22.2% as obtained in the ideal case. Thus, allowing for the finite spectral bandwidth and the convergence of the beam, the maximum fraction of the incident intensity which is modulated by changing 6 from 2mx to (2m - 1)~ is 89.1-22.2 = 66.9x, ignoring losses. At this point it should be pointed out that the reflectivity (0*36), which has been used in equation (12) to derive Fig. 4 and the above results, strictly applies only for normal incidence. At other angles the reflectivity is dependent upon the polarisation of the radiation (see, for example, Ref. 4). Extreme rays in any/l beam are incident at -26.5” and at this angle the two reflectivities are ~40% and 32 ‘A so that their mean is the 36 */*which has been used. Some error will accrue from the procedure of using the mean value which has been adopted but it is expected to be sufficiently small to be justified by the considerable simplification it has rendered. On the supposition that it is possible to place the modulator in the qLiasi-parallel light before the lens, the above reflectivity difference disappears and so also does the phase variation due to incidence over a range of angles. Such a system would require large Ge plates and entail the production of very flat surfaces over much larger areas. Slight problems, not insurmountable, would be encountered here but the procedure would raise M to 73.3% (disregarding losses). It will be assumed that this small increase is insufficient to justify such action and that the former location is to be used.

3.1.2 Losses iu germanium. Losses may arise from two sources. Firstly, the reflection of the two outer Ge surfaces which, in the absence of blooming, would reduce the transmission to (1 - R)2 = 41%. Secondly, there is minor lattice absorption in Ge in the region 15-16 pm. Blooniing is customarily used to overcome the first problem, typically a Xf4 layer of ZnS is deposited, although more sophisticated multilayers are possible. Procedures for ensuring the adhesion of the layer are well established and would be employed, for example, on any other high refractive index components (e.g. the lens) in the system. Nevertheless, losses are inevitable. Blooming optimised for 15 pm is unlikely to result in transmission (through 2 surfaces) higher than 95 % at that wavelength and rather less may be expected at the 14 pm and I6 pm extremes of the spectral band. Moreover, the use of anf/l beam aggravates this problem since the layer will not be X/4 for a11angles of incidence. Such problems arise, of course, in exactly the same way as with the basic cavity. It must be anticipated that a loss of at least 10 % of the incident radiation is likely to be caused by reflection at the Ge surfaces. A 10 “/, reflection loss reduces M to 60.2 “/,. Lattice absorption in Ge and Si has been measured by Collins and Fan,@@ whose results are shown in Fig. 6. This figure serves both to illustrate one of the reasons for prefer&g Ge to Si as a window in the 14-16 pm band and also to provide the means of estimating the lattice absorption loss in germanium. Using the data of Fig. 6 the absorption loss for uniform intensity in the 14-16 pm band has been calculated and the resulting curve, showing transmission as a function of thickness of germanium (not including reflection losses) is shown in Fig. 7. In view of the requirement for flat polished surfaces and the need for the Ge to be self supporting over 1cm2 in an environment which, at times (during faunch, for example), could be hostile, it is probably unwise to use Ge plates less than 1 mm in thickness. A transmission of 94% is then obtained from Fig. 7 for the 2 plates (the convergence of the beam may be ignored, due to the high refractive index), giving an overall value for M, including

Solid state modulators

for horizon sensing applications

169

losses, of 566 %. Use of @5mm Ce plates would raise this figure to 58-2 % a gain which, in the view of the present writer, is not worth the risk.

3.1.3 Drive req~i~e~e~~~. It was noted in Section 3.1.1 that lowest order operation may be desirable since it gives the greatest wavelength separation of orders. Whatever orderischosen it is necessary, in order to change 8 by - rr at 15 pm, to produce a total movement of 3.75 t*_m. Wave number(Si) 450

600

800

300

400

1000

500

1200

1400

700

600

Wave number (Gel

FIG. 6. Lattice absorption

.$ .-% E

60-

g I-

40-

in germanium and silicon (&er Coltins and Fanr3@).

20-

I 0

Fret. 7. Transmission

0.2

I o-4

I 0.6

I 0.5

I I.0

I I.2

Thickness,

cm

I 1.4

I 1.6

1.8

I CO

of pure Ge in 14-16 pm band (assuming uniform intensity and ignoring reflection loss).

170

B. ELLIS

This is most conveniently achieved by piezoelectric transducers of which the lead zirconate titanate (PZT) ceramics are most suitable. Two alternative modes of operation would seem, in principle, to be feasible and in addition either sinusoidal or square wave drive could be employed. Sinusoidal drive, giving a corresponding variation in 6, would give transmissiotl as a function of time as shown in Fig. 8. It is apparent that this would be quite unsatisfactory

5-

Phase FIG.

8.

Fabry-Perot transmission

of

drive

voltage,

wt

as a function of time for sinusoidal excitation (14-16 ~LIIIbatldwidth, 6 = 0 for 15 pm, parallel beam).

since the peak transmission is attained for a very small fraction of a cycle, a consequence of the relationship between transmission and 6, as shown in Fig. 4. Evidently, square wave drive, rapidly changing the separation of the plates by 3.75 pm is requircd.This provides the added bonus that the amplitude of the Fourier component of the fundamental is greater than that of the square wave transmission, an advantage which may also be obtained using mechanical chopping. Having decided to employ square wave drive, and assuming first order operation, it remains to decide whether the initial setting of the plates should be at 6 = 27~(d = 7.5 pm) or at 8 == 3~/2. Advantages are present for both systems. Tn the former case the initial setting, if precise (and maintained), ensures that maximun~ transn~ission will be obtained and the drive voltage is not:critical since any separation giving 6 - 7 is quite acceptable (see foregoing discussion Section 3. I. 1.) However, the voltage amplitude required is twice that of the second method and moreover, pulses rather than a simple square wave are required. Since the loss factors of PZT ceramics increase at high voltages the power requirements are also likely to be higher. Simpler electronics, half the voltage amplitude and lower power make the square wave, 6 = 3x18, system look the more attractive. Its disadvantages are that more precise voltage control is required, since it must accurately give 8 = 2n on one half cycle and that initial setting up (for maximum transmission) might have to be carried out with some bias applied. Both systems consume very little power and the voltage requirements, using a stack of elements (admittedly, fairly long), are not excessive. Thus, in view of the important advantage that its drive voltage is not critical, it is felt that the former system is probably marginally the better. Sinusoidal drive has been considered in detail by Korolov and Melkhis(37) who show that for a particular choice of operatingpoint and drive amplitude it is possible to avoid harmonics.

Solid state modulators for horizon sensing applications

171

They do not consider the efficiency of the process and the validity of the above comment is unaffected by their conclusions. A range of PZT ceramics are available from several manufact~ers. For convenience the data and nomenclature of the Vernitron company* will be used throughout this report. Several factors are pertinent in choosing the most suitable ceramic from the range and two configurations might be considered, a stack of one or more elements or a single tubular element, These will be considered in turn. Prim~ily, it is important that the coe~cient d33 (&I for the tube) must be as high as possible. This expresses the strain (extension per unit length) obtained along the direction of poling for a given electric field parallel to that direction, in the unloaded condition (which applies in the present case). For the tube the field is applied radially to produce longtitudinal extension. Naturally, the required extension must be achieved without the drive voltage exceeding the depoling field. (Of course the field requirement can be reduced by using a longer stack but there are usually limits to the extent to which this may be done). Thus the depoling field should be high. Lastly, the losses under a.c. drive should be minimal and these may be assessed from the loss tangent figures for the various ceramics. Some consideration must also be given to the Curie temperature since it is essential to avoid heating the ceramic above this point, for example in the course of bonding operations when constructing a stack, if depoling is to be avoided. Values for these parameters, taken from commercial data, are given in Table 1 for various TABLE

I. PROPERTIES OF SOME LEAD

ZIRCONATE-TITANATE CERAMICS*

PZTSA

PZTSH

Units

374 289 -171 -123 24.8 26.1 grr 0.02 OGO4 tan 8’ (low fields) 7 >lO a.c. depoling field a.c. field for tan 6’==0+04 ~4 G: 328 Curie temperature 1700 Relativepermittivity ~3.3 1300

593 -274 19.7 0.02 4 --o-2 193 3400

x lo-10 cm/V X lo-lo cm/V x IO-l3 Vm/N

PzT4 dm

da1

kV/cm kV/cm “C

*Rata from Vernitron Co Ltd. Terminology defined in Section 3.1.3,

ceramics. It is evident that PZT5H would be the least demanding in terms of voltage requirement but in every other respect it is inferior to PZT4, especially with regard to its power factor and the increase in power factor with applied fieId. Some of the fields required for the Fabry-Perot and other devices will in fact be su~ciently high for the increase in power factor to occur. It is therefore clear the PZT4 is the appropriate ceramic for the present application. For a 3.75 pm movement the strain in a stack of length 3+75cm is lo-4 and the data of Table 1 shows that using PZT4 a potential difference of l-3 x WV is required to produce such a strain. Assu~ng that the stack is made up of 19 elements (each roughly 2mm thick) the potential difference per element is only 685 V and for 38 elements (each ~1 mm thick) this is reduced to -342V. Since the elements may be arranged to be electrically in parallel, this represents the voltage requirement of the complete device and is reasonably compatible *Vernitron Co. Ltd., Thornhill,~Southampton SO9 lQX, England.

172

B. ELLIS

with satellite use. Further reduction could be obtained by using a longer stack. It may be noted that the field corresponding to the above voltages is 3.6kV/cm which is well below the depoling field for PZT4 but which is quite close to the field for which the loss tangent is an order of magnitude higher than its low field value. If PZTSH had been used tan a’> 0.2 would have been inevitable and the power consumption would have been excessive. Since the transducer stack is not loaded by any mechanical constraint it may be made quite small in diameter in order to reduce the capacity and hence the power loss. Only the fact that the stack is required to rigidly support the plates demands that the diameter of the elements be maintained at a reasonable size. In practice it is envisaged that two or even three stacks would be used in order to give rigidity (in the latter case to facilitate setting up) and it will henceforth be assumed that each stack has a diameter of -5mm. Using the data of Table 1 (taking the high field value of tan 6’) and the dimensions given above with the simplifying assumption of a sinusoidal voltage of the amplitude stated, it is found that the power consumption at 1kHz is 132mW per stack (with the square wave pulse drive it is likely to be lower, if anything). Thus if three stacks were to be used the total power consumption would be -4OOmW. It should be noted that exactly the same power consumption results from the use of 1 element or a stack of many elements to produce the same displacement. If a tubular transducer is considered it is found that, even for a wall thickness of only 1mm, a potential difference of SOOVis required to produce a strain of 1O-4 in a tube of length 3.75cm. A tube of such length could well become quite an obstruction in a system of focal length 4cm. It might, for example, have to be made of sufficient diameter to accommodate the focusing lens (say internal diameter 3.5cm). If this were to be done the power consumption at 1 kHz (for a 2mm wall thickness) is found to be -1OW (high field value of tan 8) and is only reduced to 6W if tube diameters of 1.7, 1.9cm are used. Since the only advantages of the tube are rigidity and some possible simplicity in construction it is obvious that the use of stacks is preferable for this application. In both cases, proportionately lower power dissipation could be achieved at lower operating frequencies. 3.1.4 General constructionfeatures. One of the most critical features inherent in the use of long transducer stacks is the change in their length which could be brought about by thermal expansion (or contraction). Data is given by the manufacturers which would enable this change in length to be compensated for over some temperature range by construction involving various combinations of metal elements. However, the coefficient of thermal expansion is said to depend upon whether the ceramic is poled or unpoled, whether the heating is the first after poling or not and finally is so strongly temperature dependent that it reverses sign (becoming negative) at 100°C. Clearly, it is far better to achieve the essential compensation by using the ceramic itself. A particularly neat way of achieving this is shown in Fig. 9. Here the drive stacks are split into two nearly equal sections and by suitable combination of the poling directions and applied voltages it is arranged that when the outer stack contracts the inner stack expands, giving an additive effect. Not only does this yield the desired insensitivity to thermal expansion but it also achieves considerable longitudinal compactness, for the device need barely exceed 2cm in length. Lateral expansion of the germanium should strain the supports in a slight and symmetrical fashion and it is not thought likely to give rise to difficulty. It might, however, be a wise precaution to ensure that the base plate upon which the piezo-electric stacks are mounted has an expansion coefficient similar to that of germanium (U = 5.75 x 10-s at 20°C). Nickel (40%) steel, with

Solid state modulators

173

for horizon sensing appii~tions

a = 6 x 1O-6 at 20°C is suitable. Some thought ought also to be devoted to the means by which this supporting plate is constrained. Thermal variations in the piezoelectric coefficient, &s, are also to be expected. Data for dsl is available and by analogy it may be anticipated that the variation in de3 over the range - 20°C to + 60°C is N &-3‘A.The platz separation (and therefore S) would therefore be changed by this amount at the extremes of the temperature range, This is not likely to introduce any serious degradation in performance. It was suggested in the course of the above discussion that the use of three stacks might be desirable. This arises because it is anticipated that some difficulty may exist in the setting Transducer sfacks P,

stacks

(bf Arrong8ment for fine adjustment

(01 Arrangement for thermal compensation FIG. 9.

Fabry-Perot

modulator.

up of a device constructed as shown in Fig. 9. Laboratory models might well be adjusted for parallelism and plate separation by the use of micrometer screws and for satellite use similar arrangements could be made, particularly for the outer plate. Unless suitable locking devices could be devised this procedure is open to the objection that in the rigours of launch the fairly precise alignment required could be destroyed, resulting in degraded performance (however, see Section 3.1.5). Now if three stacks, preferably positioned at the corners of a right angled triangle were used (Fig. 9), the adjustment could be carried out by applying different bias voltages to each stack giving movements akin to those used in mirror mounts. Coarse adjustment could be carried out by screws with lock-nuts. A small disadvantage is the need for providing stabilised bias supplies. Life expectancy considerations are only likely to involve the transducers since the remainder of the system is effectively static. Some comment on this question is made in Section 3.2.8.

3.1.5 ~~ig~~~~~ tdermce. Mention has already been made of the somewhat notorious difficulty of setting up Fabry-Perot etalons which, having high reflectivity mirrors, are to be used for high resolution spectroscopy. Quite stringent tolerances are placed on flatness, uniformity and par~lelism for such work. With such experience in mind it is natural to inquire to what extent similar problems might be encountered with a modulator based upon this

174

B. ELLIS

principle. An expression, giving the transmission for particular distributions of imperfections has been given by de1 Piano and Quesadacss) based upon an earlier report by the same authors. (3%Essentially, the treatment given by these authors assumes that the plates may be considered to be parallel over small elementary lateral distances and that the only feature that need be taken into account is the variation of the separation from element to element, together with the distribution of a given separation over the area of the plates. By this means they were able to give expressions taking account of non-parallelism (constant distribution of separation) and surface irregularities (distribution assumed to be Gaussian). Particularly in the case of non-parallelism the validity of this procedure is not obvious, since elementary areas are just as non-parallel as larger areas. Because non-parallelism is likely to be the dominant problem in a modulator and since it will in fact be shown to be of less critical importance than expected, thereby indicating that minor polishing imperfections may be quite tolerable, it is non-parallelism that will be considered here. It transpires that it is possible, in the present circumstances where the reflectivity is low, to give credibility to the formula of de1 Piano and Quesada.@s) Clearly it is valid to consider the plates to be divided up into elementary areas which, if sufficiently small, may be taken to be plane and mutually inclined at a small angle a. Interference in such conditions is a well known phenomenon and has been treated in a convenient manner by Born and Wolf.(ss) It is there shown that for multiple reflections between surfaces at an angle a the transmitted intensity distribution may be approximated by an Airy function of the form of equation (12) provided that (13) where ri is the refractive index of the wedge which has thickness lz at the point in question (i.e. h is the plate separation in the present case), X is the wavelength in OacUoand p is the number of significant reflections (considered below). If the inequality (13) is simply evaluated to give a it is found that the restriction scarcely exists (ag7”) but in this case there would be a significant change in h over the width of the plates. It is more realistic to consider the situation at the edge of the plates where h +- h + Ah and Ah = al (where the plate width is 21) i.e. to write h in terms of a. On inserting these relations into the inequality (13) the restriction on a may be obtained. First of all it is necessary to decide on the value of p. It is also shown by Born and Wolf@) that the required value ofp is given by RP

2:

_!._ I--.. - R

200’1+3

iw

This ensures that account is taken of a sufficient number of reflections to guarantee that the error in calculating the transmitted intensity, introduced by using only p terms instead of summing an infinite series, is less than I ‘4, Whereas for R = 0.93 it is found that 120 reflections are required, in the present case where R = 0.36 the approximation (14) is satisfied with p = 3.67. This largely accounts for the remarkable latitude in a which results from satisfying the inequality (13). It is found that a4 1.5” is all that is required. All that has been done so far is to justify the use of an Airy function to describe the intensity transmitted by an elementary area of the non-parallel plates. Provided that the inequality (13) is met, however, it is justifiable to follow the procedure of de1 Piano and Quesada@Q) and integrate the Airy function (equation (12)) over the variation in phase

Solid state modulators for horizon sensing applications

175

introduced by the non-parallelism of the plates. This procedure reveals the effect of the non-parallelism on the overall transmission. The result of the integration is

difference

I = __-

lo

h AS(1 + F)i

(1 + F), tan S.t,aal

- tan-l [(l + F)t tan y]]

(15)

where A8 is the maximum variation in phase difference introduced by the non-parallelism and F is as defined in Section 3.1. Quite a large deviation from parallelism of the plates was assumed in order to assess the extent of the problem. A 10% change in 6 was used in equation (151, corresponding to f0.75 pm at the extremes of the plates for nominal separation of 7.5 pm. This is well within the value of a allowed by the above calculations. Somewhat surprisingly, the results show that the effect on the overall transmission is quite negligible at all values of phase difference, as may be seen from Fig. 4 where the calculated values are shown as encircled points. It is evident that alignment is not a critical matter and that relatively large errors may be tolerated both in setting up and in the subsequent working life of the device. As pointed out above this is a direct consequence of the use of low reflectivity surfaces. 3.1.6 Laboratory test. confirmation of the rather agreeable conclusion of the previous section was obtained in a brief laboratory test. Two intrinsic germanium plates were polished flat to N &.t pm and mounted on a simple jig by means of which their separation could readily be adjusted. Micrometer adjustments were provided to facilitate alignment and one plate was mounted on a PZT tubular transducer. Initial alignment was achieved by the simple expedient of inserting 75 pm, ‘feeler’ gauges and the separation of the plates was then reduced as the transmission of monochromatic radiation (h = 11 pm) was monitored. Quite pronounced fringes were immediately apparent and no improvement could be wrought by adjusting the micrometers, transmission ratios of 2 : 1 being achieved (cf. the 3 : 1 or so expected theoretically). In the lowest order position the transducer was used to vary the plate separation, giving the variation in trans~ssion shown in Fig. 10. Some irregularity is evident, this may be attributed to the hasty nature of the experiment. It is felt that such good results coming from a set-up that was far from ideal make the prospect of efficient modulation by this means very encouraging. No figure for the insertion loss of the device were obtained. It should also be noted that large voltages were required to operate the Scm long transducer, agreeing well with the figures deduced in Section 3.1.3. 3.2 Stress induced birefringence Modulated birefringence forms the working principie of the electro-optic devices which are widely used in conjunction with laser radiation and which are described in Section 2.15. Exactly similar basic considerations apply to modulators which use the refractive index changes that may be induced by applied stress. Essentially, the technique is identical to that which has been widely used to reveal built-in strains in transparent materials. A suitable material is placed between crossed polarisers and is subjected to a uniaxial stress in a direction perpendicular to the direction of propagation. In general, the resulting strain produces changes in the refractive index, such that different indices apply for the two polarisations, parallel and perpendicular to the stress. For radiation polarised at 7r/4 to the stress direction it is possible to obtain the effect of a half wave plate at suitabIe values of stress. That is, the

176

8. ELLIS

plane of polarisation is rotated by 7~12and the radiation is thus transmitted by the second polariser. Modulation results when the stress is applied ~riodically. 3.2.1 Application to 14-16 pm operation, Transparency in the range 14-16 pm is the primary requirement for the material to be used in this device, implying the use of insulators or alternatively of semi-conductors which are available in pure form. Most of the available transparent insulating materials, such as the alkali halides, KBr, CsI and CsBr, have undesirable hygroscopic properties and are best avoided if alternative materials give satisfactory

Fobry Peroi etaion for 1st order max

o/--

IO

05

Piezoelectric transducer voltage,

FIG. 10. Experimental

tuned at Ilpm

results with Fabry-Perot

15

i

kV modulator.

performance. Fortunately, it is found that several semi-conductors can develop the required degree of birefringence for applied stresses that are quite realisable in practice. Both the intrinsic and the free carrier properties of a semiconductor may be made to exhibit birefringence (cf. Section 2.3 and 2.4); in the following discussion attention will be exclusively devoted to the intrinsic effects since the absence of free carriers obviates any addi&ional complications arising from the inevitable absorption they would produce. Data for the intrinsic birefringence produced by stresses applied parallel to various crystalline axes has been obtained at near infrared wavelengths (h<2*5 pm) for Si, GaAs and Ge.@e) With the possible addition of CdTe, for which piezobirefringence data is apparently not yet available, these are the most suitable materials to consider for this application. As noted earlier in this report Si is inferior to Ge in transparency over the 14-16 pm region (see Fig. 6). Semi-insulating GaAs might well prove to be more suitable than Ge, since the carrier concentration in this material may be kept sufficiently low to avoid significant free carrier absorption. Published transmission measurements on this material are relatively sparse; however, Walsh@rj gives results for iron doped GaAs (p> 1OsQcm) which shows the absorption coefficient rising from -0.2cm-1 to NO*5cm-1 over the range 14-16 pm. This would give overall transmission only marginally inferior to that of Ge {see Fig. 7). An additional advantage of these materials is their cubic symmetry, which implies that they exhibit no birefringence under zero stress. This greatly simplifies the design of the element to be stressed.

Solid state modulators for horizon sensing appli~tions

177

Since Ce is the most transparent of the materials for which data is available and also because the largest piezobirefringent effect measured by ~gginboth~ et uL(*O)was for Ce with (111) stress, it will be assumed that germanium is to be used for the horizon sensor’s modulator. Although the results cited were only obtained at short wavelengths they were well fitted by established theoretical expressions which provide the means of extrapolation to longer wavelengths. Incidentally, beyond ~3 pm the piezobirefringence is insensitive to wavelength changes, but since a half wave plate is involved, the modulator design will still only apply to a specified wavelength. Of course, the principfe may be used at virtually all wavelengths but will never yield wide band devices. Hi~inbotham e$ uL@O)give results which, for (11 I > stressed Ge, extrapolatea to

where e,,and eL are, respectively, the relative permittivities parallel and perpendicular to the applied stress. It is required that An (-Cc,, - eL)/2n) should give And = h/2 at 15 pm, where d is the sample thickness. This gives the required stress as

Using the known elastic constant data for Gec*Q it may be as~r~ined that such a stress would not give rise to strains which would exceed that required to damage the material. It is convenient, firstly, to formulate the strains along the crystalline (100) axes due to a stress S applied along a (Ill) direction, since the elastic conrtants are given with reference to these axes. Tn the customary notation el

=

sn

:

+

S12 p

+

Al2 4

(10

with similar expressions for es and es, the strains parallel to 0 Y and OZ. Consequent upon the crystal symmetry, ~1s = ~13 and further el = ea = (7sso that the strain in the (Ill > direction is also equal to el, e(311) = 5 @II + 2~12).

07)

Now McSkimin’s data is given in terms of the stiffness tensor Erather than the compliance tensor S as used here. Since $ = E-r the quantities are easily converted@s) with results sit = 9.76 x IO-12ma/N riz = - 2.66 x IO-18 me/Iv. Hence the (I 1I} strain is (S/3) (444 x IO-fs), which, using the birefringence data, may be written, 8.88 x 10-s d-f. This result may now be used in conjunction with other relevant considerations to suggest a suitabie choice for the sample thickness, d. Several factors affect the choice of sample thickness. Clearly, the thicker the sample the lower the strain required to produce the necessary phase shift but this also means that the

178

B.

ELLIS

absorption loss in the material becomes more serious (see Fig. 7). Further, as the sample thickness is increased it is necessary to use larger area piezoelectric transducer stacks to produce the strain, since otherwise these will become loaded to an undesirable extent, as is discussed below. The power dissipation of piezoelectric elements is directly proportional to their area. A certain ~~n~~~~ thickness is a practical requirement to avoid any undue tendency of the sample to tip if the applied stress is slightly unsymmetrical (this could arise if, for example, the sample surfaces were not quite flat). In the light of these requirements d = 0.5 cm seems to be a reasonable choice, giving 86 % transmission (disregarding reflection losses) and not necessitating the use of unduly large piezoelectric elements. Hence the required (11 l} strain is 1.78 x 10-4 and the stress needed to produce this is 4 x IO7 N/ma. 3.2.2 Generation of the stress. Consider the system shown in Fig. I I in which two piezoelectric transducer stacks apply a periodic stress to a sample by means of transverse bars which

i \ Stressed FIG. 11. Disposition of forces in stressed plate modulator.

are assumed to be sufliciently thick to be taken as inelastic. Let the stacks have the same length as the sample and let the force produced when a potential difference is applied be X. This is opposed by internal elastic forces f in the transducer and the resultant, X - J’ = F represents the force applied to the top bar. Hence, since there are two stacks, 2F is applied to the sample. If A is the cross section area of one transducer stack and A that of the sample then f: 5.33=;Ie

A

where e is the strain produced in both the transducer and the sample and $33 is the appropriate elastic constant for the transducer {assumed to be driven parallel to its direction of poling). Using the above value for the required strain in the sample for a stress S = 2F/A, gives _y_

e. -- A’s 2 s33

so

that X _ S.88 x 10-s A -~ = 2 x 107 A N 0.5 533

(1%

Solid state modulators for horizon sensing applications

179

taking d = 0+5cm. Now if the optical faces of the sample are 1 x 1ems, A’ = O.Scms and the above relation gives the stress, X/A, corresponding to the required strain, in terms of the cross section area of the transducer stack. From this relation it is thus possible to decide upon suitable values of A, noting that the area must be sufficiently large to keep the stress (and hence the applied voltage) within reasonable bounds and yet not so large that the capacity (and thus the power consumption) becomes excessive. Now at constant strain the stress is related to the applied electric field by (gssX/A) = E and values of gas are given in Table 1. From the data in this table and bearing in mind the points made in Section 3.1.3 it is readily apparent that PZT4 is the most appropriate ceramic for the purpose (another material PZT2 has a higher value of gas but far poorer high signal properties). Usingsss = 1.55 x lo-11 ms/N the stress developed by a transducer stack of 3cm2 cross section area (w2cm dia.) is found to be 1.48 x 107 N/m2 (corresponding figures for 2cm2 and 1cm2 are 165 x 10’ and 2.15 x 107 N/ms) and the required applied electric field is 3.86 x 103 Y/cm. As may be seen from Table 1, this is comfortably below the depoling field for PZT4. In order to avoid the use of high voltages (3.86kV for 1cm sample length) either much longer transducers or a stack of piezoelectric elements could be used (as suggested in Section 3.1.3). In the interests of compactness, especially in view of the thermal compensation required (as discussed below), the stack is the more attractive alternative. If each stack consists of 10 elements (each 1mm in thickness) a supply of 386V is all that is required. 3.2.3 General const$uctio~. Mention must be made at this juncture of the possibility of difficulties in assembling both the stack and the complete device. Obviously, if any relatively elastic material is incorporated in significant quantities for bonding purposes then the strain will be preferentially taken up in that material rather than in the sample. If, as is envisaged, the assembly and jointing is carried out with the aid of epoxy adhesives it is absolutely essential that they are incorporated only as very thin layers. This difficulty has been recognised and experienced by Mollenauer et ai.t43) who give details of a procedure in which considerable flow of the epoxy takes place at high temperature so that extremely thin layers are ultimately produced. Clearly, while it is comforting to know that these difficulties may be overcome, it is also prudent to reduce the number of joints to a minimum. One way in which this could be done would be to use 5 elements per stack instead of 10, if the increased working voltage thereby entailed, 772V per element, proved to be acceptable. A minor detail, worth noting, is that an even number of elements simplifies construction in that it is then unnecessary to insulate one end of the stack from the other. It should be noted that if, in the course of assembly, temperatures exceeding the Curie temperature (328°C for PZT4) are reached, it may be necessary to repole the ceramics. Other constructional matters of importance are concerned with the question of thermal com~nsation and will be deferred until Section 3.2.5. 3.2.4 Power dissipation. Greatly reduced relative permittivities occur for piezoelectric ceramics in the clamped condition (635 compared to a free value of 1300 for PZT4). In the present case the material is partially clamped and an estimated value of ~3s = 1000 will be used. For 3cme discs each 1 mm thick the capacity is 2.65 x 10-a farad/element giving a total capacity, for both stacks, of 5.7 x lo-* farad. Since the required electric field is -3.86 kV/cm, approaching that for which tan 6’ reaches 0.04 (see Table l), an upper limit on the power consumption will be given by taking the high field value of the loss. At 1kHz the I.P.-C

ISO

B.

E~tis

tot& dissipation is therefore not anticipated to exceed 1~06W. This assessment may be somewhat increased by any loss due to the ebstieity of the adhesive and the use of nonsinusoidal drive (see Sections 3.1.3 and 3.2.7). Lower power consumption would be expected at lower frequencies. 3.2.5 E&cts of ter~lperatureJluctzrations. In this device there are a considerable number of factors which are temperature sensitive, in most cases the effects are fortunately not serious. AI1 the following considerations will apply to the specified temperat~lre range, -20°C to + 60°C. Over this range slight changes in the contpliance parameters of Ge are evident in the data of ~~Skirnin.~4l~ Calculations based on these results show that at each of the two extremes of the temperature range the change in the (I 11>strain of the sample for a given stress woufd be ~1% so that this effect is negligible. It is also to be anticipated that the birefringence of the sample, for a given stress, will be temperature dependent, Higginbotham et ai. attribute the observed birefri~~ge~ce, plausibly, to the strain dependence of the energy gap and of the momentum matrix elements. Now, over the temperature range in question, the direct energy gap in Ge (which is the relevant energy gap to consider since the direct transitions are largely responsible for the refractive index) changes from Q822eV to 0,788eV. Such a change will, in the first order, merely have the effect of displacing the birefringence curve laterally by 0.034eV. Since, as was noted in Section 3.2.1, the birefringence is only extremely weakty dependent upon wavelength at 15 C&M, it may be concluded that this effect may be neglected. It is also unlikely that changes in the matrix elements will cause any significant effect. Some variation in the piezoehztric ~~~~ient gas is to be expected but quantitative information is unfortunately not available. Data is given for the coefhcient gst and may be used to provide a rough estimate of the variation of gss, (See “Piezoelectricity”. Vernitron Co). Over the range 20°C k4O”C the variation anticipated on this basis is roughly Iinear and amounts to Ifi “r;;.The consequences of this upon the transmission are trivial. Serious efforts, however, must be made to compensate for the difference in thermal expansion coefficients between the germanium sample and the piezoelectric transducer stacks. Respectively, these coefficients are -j-575 x 10-e (Ge, 20°C) and +I*7 x 10v6 (PZT4 O”C-5O”C, after thermal cycling). Assuming that the latter figure also applies at -20°C this gives a di~erential expansion coefficient of +4 x 10-e over the range -2O”Ct6O”C. At the extremes of the range the strain introduced is thus 1.6 x 30-a. Since the strain required to produce a half wave phase difference is -1.8 x 10-e (for d = 0*5cm, see Section 3.2.1) the effects of thermal changes are clearly severe. Stilf worse features become apparent when it is recatfed that the expansion coefficient ofPZT4 becomes ne!gative at -100°C (a3 = - 1 x 10-e). Now the assembly procedure (especially that recommended for the stacks by Mollenauer et al. (43) calls for the use of temperatures far in excess of 100°C. Evidently, some cunning in the construction is called for if large unwanted static strains in the device are to be avoided. As regards the constant differential expansion coefficient at temperatures up to 6O”C, this may be adequately countered by inserting compensating materials into each limb, as indicated in Fig. 12, Suitable materials are aluminium ahoy (a - 24 x 10-s) in the transducer arm and brass (u = 18.9 x 10-s) in the sample arm. For a total length of 2cm it would be necessary to use Oe95cm of AI with 1cm of brass. In addition, it is advisable to insert a thin layer of material, having a simifar expansion coefficient to that of Ge, above

Solid state modulators for horizon sensing applications

181

and below the sample. By this means it may be ensured that any lateral differential contraction does not give unwanted birefringence in the Ge. While such tactics effectively combat the problems which may occur in the use of the device they do not eliminate the possibility of strains introduced in the course of assembly. In view of this it is suggested that as an alternative, the simple expedient of placing a dummy PZT4 element above the germanium and similarly inactive blocks of Ge above the ceramic stacks, be adopted. All components should be of equal length. Automatic compensation of

Material to obviate lateral stress (see text)

Stressed j sample (germanium)

stocks

FIG.12. Thermal com~n~tion

in stress plate modulator.

of any effects due to uniform changes in temperature is then guaranteed. No great expense would be incurred in this way since the materials are quite cheap, it should, however, be noted that the dummy components should be of much larger cross section area than the active elements, so as to avoid their being noticeably strained in the course of operation, thereby reducing the efficiency of the device. Thermal expansion of the Ge sample in the direction of propagation will result in the thickness being slightly different from that required for precise #2 operation, but the effect is too small to be of consequence. Two other considerations with respect to temperature changes merit attention. Firstly, the relative pe~ittivity of PZT4 changes somewhat from -20°C to +6O”C. However, the change is only ~3% so that its effect on the power consumption may be disregarded. Secondly, it is assumed that the germanium sample will have anti-reflection coatings and these will have a different expansion coefficient to that of germanium. For ZnS, which is commonly used in this role, a strain of ~1.8 x IO-5 results from a tem~rature change of -40°C. This is an order of magnitude less than that which it is necessary to produce by the applied stress and therefore will not in itself be of importance. 3.2.6 Angular aperture, optical ~~dw~dt~ and the need f~r~iter~. One of the advan~geous features of germanium for this application is its high refractive index. Thus, anf,l beam is refracted to the extent that its angular divergence within the material is only f6.5”. Over a specimen thickness of 0.5cm the phase lag of the extreme rays relative to the central ray is only 12 % and the effect of this on the transmitted intensity at the angular extremes is to reduce the transmission to 93 % of that of the central ray. Averaged over all angles the

182

B. ELLZS

transmission of anf/l beam may be expected to be at least 95 % of that of parallel illumination. Another aspect of the horizon sensing application which leads to a slight spread in the phase lag introduced by the stressed plate is the optical bandwidth, 14-16 pm. In this case the spread is symmetrical, &6.7x but since the variation due to the 12% deviation introduced by the angular aperture has been found to be very small it may be assumed that the use of a 2 pm, optical bandwidth wili not introduce significant losses. Some shght gain in transmission might be gained in a practical device by empirically arranging for it to be a half wave plate at a wavelength slightly off 15 pm, to allow for the spread in phase lag introduced by the use of converging radiation. While the stress plate moduIator is not a wide band device, in the sense that it cannot be applied to other wavelengths without some change in operating characteristics (change in plate material, plate thickness or operating voltage) it must be noted that its optical thickness under stress will be an odd multiple of A/2 for various shorter wavelengths, 5 pm, 3 pm, 2.14 pm,. . . It is thus essential to reject short wavelengths by means of a suitable filter; it may also be desirable to incorporate a long wavelength filter although to a limited extent the germanium itself will perform this function. 3 2.7 Efictitte ~oduIfftio~ and mode qf operut~o~. Quite small losses may be expected from surface reflection from the stress plate sample, provided that the optical surfaces are suitably bloomed. As estimated in Section 3.1.2, for both surfaces this loss might amount to as little as 10%. In the absence of any direct information no comment can be made on the likelihood of such coatings maintaining their adhesion on being continuously subjected to a strain of -2 x 10-4. From the fact that thermal strains of this magnitude are often introduced in this and similar processes (due to deposition onto heated substrates, etc.) it may be inferred that over a limited number of cycles such strains are unlikely to be detrimental. What is uncertain are the consequences of many applications of the strain, applied at rates far in excess of those which occur in thermal protiesses. This point should be checked at an early stage in the development of a stress plate modulator, since it could represent a major difficulty. Some check on the long term effects couId be obtained by operation at very high frequencies although it should be borne in mind that this represents a more severe test due to the increased rapidity of the rate of development of the strain. Apart from the reflection losses, estimated at 10 % of the intensity incident on the plate, the transmission of 05cm of Ge may be expected to be 86 %, as noted in Section 3.2.1. By far the most serious loss arises from the use of the two crossed polarizers. At least 50% of the incident radiation is unavoidably lost in this way and further losses arise from the significant deviations from perfection which are inevitable in practical polarizers at these wavelengths. Details of these losses are given in Appendix 2. As a consequence of the various losses it is expected that the effective modulation as defined in Section 1.3, might reach, M = 0.5 x 0.86 x 0.90 x 0.5 x 100 = 19.4%. Since the transmission of the second polariser follows a (cos a/3)variation, where B is the angle between the direction of maximum transmission of the polariser and the resultant electric vector of radiation leaving the stress plate (the major principal axis of the oscillation in the general case of elliptical polarisation), it follows that, if stress varying sinusoidally with time is applied, the output will not be simply sinusoidal at the frequency of the stress. For this reason it is preferable that the drive to the transducers should follow a square wave

Solid state modulators

for horizon sensing applications

183

pattern, although, as discussed above, this may increase any difficulties experienced with the the adhesion of the antireflection coating. A benefit would be the greater amplitude of the fundamental component with respect to that of the square wave transmitted, as has been noted previously (Section 3.1.3). From the discussion of Section 3.2.6. it is clear that a high degree of stability in the drive voltage is not essential. A change in the phase lag of ~5% has only a small detrimental effect on the transmission and it may be concluded that fluctuations of this order in the drive voltage are of little consequence. 3.2.8 Life expectancy. Apprehensions regarding the durability of the antireflection coatings have been noted above. Clearly, the ability of the Ge plate to withstand the strains involved over a long period of time must also be confirmed before such a device could be confidently used in a satellite with a life expectancy exceeding a year. No evidence on this point is available and it would require some experimental work, although it might be thought to be an unlikely cause of failure in practice. Similar testing of the transducers could be advisable unless suitable data is forthcoming from the manufacturers. Piezoelectric ceramics are widely used for a variety of purposes and the required information probably available. Care should be exercised to ensure that any figures obtained apply to conditions of stress generation rather than to purely displacement applications (cf. Section 3.1.3) or to resonant operation. Silica has been used in the way described here for modulation at short wavelengths, (4s) operating as a Xl4plate for measurements of circular dichroism. Several hundred hours of failure free operation were reported, using the resonance frequency, 16.7 kHz. In this work antireflection coatings were not used. It is likely that this was intermittent rather than continuous working and fused silica is an extremely strong material. Moreover, the stress required for h/4 in the visible is smaller than that for h/2 at 15 pm. Nevertheless, the result is encouraging. Some other considerations on stress plate devices have been given by Kemp.(@) 3.3 Frustrated total reJection Electromagnetic radiation incident at the interface of two semi-infinite nonconducting media from the side which has the higher refractive index nl, is totally reflected if the angle of incidence, d, exceeds the critical angle, given by sin-r n2,h1. Often, the second medium is air, as in the cases which are to be discussed in this section, and n2 2: 1. Some penetration of the electromagnetic field may occur when the second medium is not of infinite extent in the direction of propagation and, in particular, if two media of refractive index n are separated by only a small space it is possible for a significant fraction of the radiation to be transmitted, especially if its angle of incidence only just exceeds the critical angle. Modulation may easily be produced in such a system because the transmission is strong function of the separation of the two media, thus all that is required is means of the varying separation. A modulator for horizon sensing, based on this principle, has been described by Astheimer et al. (45) 3.3.1 ~od~~at~~n in the 14-16 pm band using~~strated total reflection. Theoretical expressions, relating the transmission to the angle of incidence for two media of refractive index n separated by a distance d have been deduced by Hall.(*s) Different results apply to the transmission of the polarisation with electric vector in the plane of incidence (Z’n)and the

184

B.

ELLIS

perpendicular polarisation (Ts). After some rearrangement the form

Hall’s results may be written in

_-P.

T,=

(20)

BC-I-A T8 z _.A__ AIB

(21)

where A=4n”cossi(&sin~iB = ($ - 1)ssinhsu C = [ns sins i - co9 il2 u = 2xd (n2 sin? i -

1) 7

(22)

l)i/X

and X is the wavelength of the radiation in free space. Transmission curves calculated for a refractive index of 4, are shown in Fig. 14, from which it is evident that Tp is a more rapidly varying function of angle of incidence than Ts. For ullpoiarised radiation the overall transmission is $(Tp + T,). In choosing a material for use in a modulator based upon frustrated total reflection the relevant considerations are, transparency in the range 1416 ,um, the availability of the material in quite large sizes and the ease with which it may be appropriately shaped and polished. Arranging for the radiation to be incident at angles exceeding the critical angle is most easily accomplished by shaping the material in the form of right angled prisms whose apex angle exceeds the critical angle. An arrangement of this sort is shown in Fig. 13. Con-

Transducer

stacks

‘,

Compensating

FIG. 13. Frustrated

/

germanlam

blocks

total reflection modulator.

siderably fess material is required if the refractive index is high, since then the prism angle may be kept small. High values of refractive index are also advantageous, if, as in the present case, the incident radiation forms a rapidly converging beam. This is both because the small angle leaves available a greater range of angIes of incidence exceeding the critical angle and also because the cone angle of the radiation is greatly reduced in a medium of high refractive index. These factors, along with the general points noted in foregoing sections (3.1.1 and 3.2.1)

Solid state modulators

for

horizon sensingapplications

185

strongly mitigate for the use of a pure semi~onducting material. Once again germanium proves to be a good choice, since its transparency is superior to that of silicon. Gallium arsenide, in semi-insulating form, would be suitable, despite its lower refractive index (3.4) but is not readily available in sufficiently large pieces. Of the possible alternatives CdTe suffers from the same disadvantage as GaAs and the materials with really high refractive indices (PbTe, n N 5.8, B&Tea, n = 9.2) exhibit too much absorption (due to free carriers) to warrant consideration. It will therefore be assumed that Ge is to be used. Since it is frequently used as the material for long wavelength optical components (including the lenses used in horizon sensors) there is the added advantage that considerable knowledge of its working and shaping is already in existence. Corresponding to the refractive index of 4 is a critical angle of 14” 29’. Now for angles of incidence close to the critical angle quite an appreciable transmission occurs for the polarisation parallel to the plane of incidence, even with values of d/X as high as O-2 (see Fig. 14).

Angle

FIG. 14. Transmission

of

incidence,

deg

of polarised fight through two Ge prisms at different separations.

Thus, if spacings of this order are to correspond to minimum transmission (this is found to be convenient in practice), it is best to avoid angles of incidence close to the critical angle. Once again a high refractive index is beneficial since Tp drops more steeply with increasing i in this case. A minimum angle of incidence of 16” 30’ has therefore been chosen and any/l beam within the germanium is thus incident at angles in the range 16.5” to 29.5”. Since the central ray is incident at 23”, this must be the prism angle. When calculating the overall transmission of the two prisms, as a function of their separation, it is necessary to take account of the distribution of energy over the beam as described in Section 3.1. I and Appendix 1, with the simple angular adjustment necessary to allow for the effects of refraction. By this means the transmission at various separations, summed over the range of incidence angles, weighted to allow for the intensity distribution and averaged over directions of polarisation, has been calculated for the conditions specified and is displayed graphically in Fig. 15. As may be seen from the figure the transmission of 14-16 pm radiation is given to a close approximation by that of the centre of the band, i.e. 15 pm. From this figure it is evident that a very high effective modulation is possible, limited in practice on the one hand by the smallest separation of the prisms which can be achieved in practice and on the other by the ma~tude of the displacement of one prism relative to the

186

B. ELLIS

other which can conveniently and repeatedly be produced. Because the relevant parameter is d/X the requirements are far less severe at 15 pm than they would be at shorter wavelengths. It also follows from the above discussion that, unless the closest spacing of the prisms is chosen to be very small indeed, shorter wavelength radiation will be rejected, progressively more completely as the wavelength is reduced. While some filtering to reject wavelengths just oelow 15 pm will be required it may not be essential at very short wavelengths. Rejection of solar radiation may be expected to be quite high. Conversely, long wavelength filters are essential.

f/l

beam

prism angle230

20 I

I

0

005

01

015

02

d/X

FIG. 15. Transmission

through two Ge prisms separated by distance rl.

Reasonable extreme values of d/X, determined with reference to Fig. 15 are d/X=0*02 and d/h = 0.2, corresponding to d = 0.3 pm and 3 pm. Ignoring losses for the present, this displacement of 2.7 ,um gives M = 80%. Displacements of this order, using lead zirconatetitanate ceramics have already been examined in Section 3.1.3 and found to be quite feasible. No loading of the transducers is required and a stack of 1mm thick PZT4 elements of total length 4cm would require a drive voltage of only 255V, dissipating a mere 212mW (calculated using high field parameters, see Section 3.1.3). 3.3.2 Dimensions of the prisms, tolerance on surfuce~atness. Due to the requirement for maximum transmission it is necessary to minimise the total thickness of germanium in the path of the radiation. A prism angle of 23” and a specified optical aperture of ~1 cm imply an irreducible minimum thickness for the two prisms of 0.42cm and when a minimum of for which the loss due to 2.5mm is allowed at each edge, the thickness becomes -063cm, lattice absorption is, from Fig. 7, 17.8 %. It might be possible to reduce this a little by eliminating the overlap at the edges, which has been included for convenience in mounting and to avoid transmission through edge regions (since preferential erosion of edges is usually unavoidable in polishing processes). However, a thickness of 0.42cm still implies a loss of 12.2%. In a device involving a small separation of 0.3 pm or less it is obviously essential that the surfaces of the hypotenuse faces of the prisms are flat to tolerances of this order. At the worst it could be permissible for the faces to touch in the centre of the area and be separated by 0+3pm near the edges. This is the limitation on edge rounding and corresponds to -& fringe of sodium light from the centre to each edge. It is a relatively modest requirement and

Solid state modulators

for horizon sensing appli~tions

187

should not be difficult to meet; the Ge plates used in the experiment described in Section 3.16 were polished to very nearly this degree of flatness fairly readily. Surface imperfections (polishing scratches, etc.) may be expected to be unimportant in well polished samples. Allowing for a bulk transmission of 82~2% and for possible losses due to imperfect blooming of the two outer Ge surfaces of ~10’A. (cf. Section 3.1.2) gives the effective modulation which may be expected as, 80 x 0.822 x 0.90 = 59~1%. 3.3.3 Alignment and njaintenance of the gap. Alignment is only critical in the transmitting position; when reflecting, any s~l~ciently large separation sufices and it is not required to be uniform. It follows that the stability required of the power supply is not critical (assuming the zero voltage position to correspond to ~nimum separation, which is clearly desirable for convenience in initially setting up the device). Given adequately flat prism surfaces it should be possible, in principle, to achieve the required degree of alignment without undue difficulty. Coarse adjustments could employ screws and locking nuts in the conventional manner and fine adjustment could be provided by a suitable configuration of transducer stacks with appropriate (stabilised) bias supplies (as discussed in Section 3.1.4). Considerably more care is required than for, for example, the Fabry-Perot modulator and setting up would be a fairly painstaking task, requiring the monitoring of transmission at variou~points over the area of the modulator. An error of only O-3 pm in d, giving a minimum separation of 0.6 ,um would reduce M to 44.3%. Quite clearly some care must be taken at all stages of assembly, testing and installation to exclude dust particles of any diameter approaching.0.3 pm,’ since this could have adverse effects on performance, possibly causing, in addition, damage to the polished surfaces. The situation is not helped by the fact that the device will be vibrating, at a frequency which might be as high as 1kHz, so that fairly firmly lodged particles could in time find their way into the modulator gap. Some means of excluding dust coming from the surroundings would clearly be desirable. No tolerance on the prism angle has yet been discussed but it is clear that if the two outer surfaces of the prisms were arranged to be parallel a very severe tolerance on the matching of the prism angles would exist. Fortunately, there is no need for the outer surfaces to be parallel and even a relative angle of lo between these surfaces (giving only 0.25” change in the angle of incidence) could be tolerated without serious consequence. Thus any mismatch in prism angle may be assumed to be taken up by slightly tilting one prism with respect to the other. With this sort of tolerance in prism angle (- i to on each prism) there is no reason why each prism should cost any more than a germanium lens of comparable size. Thus, the cost of the modulator should not be excessive. 3.3.4 E&?&s of changes in temperature. Details have already been given of the rather irregular thermal expansion coefficients of PZT ceramics (Sections 3.1.4 and 3.2.5) and it is recommended that the device of ‘folding’ the ceramic stack be also employed for this modulator. With the maintenance of such a smal1 dimension as O-3 pm being of critical importance it is evident that precise thermal compensation is called for. Assembly may be somewhat complicated by the varying expansion coefficient of the ceramic, if epoxy bonding is used, and the provision of the adjustments discussed in Section 3.3.3 would be essential. i.P.-D

188

3. ELLIS

Even when the longitudinal expansion of the prisms is compensated by the provision of a support for the stacks which expands at the same rate as Ce (Fig. 131, differential lateral expansion could lead to some difficulties. Some care in the detailed design is thus called for and experimental tests at the extremes of the desired temperature range may be desirable. Thermal effects on the piezoelectric coefficient d33 will merely result in slight changes in the distance through which the prism is displaced and the practical consequences are negligible. 3.3.5 Mode of operution. Since the intensity transmitted by the device is a strong function of the distance d, it is essential that for maximum efficiency a pulsed driving voltage is applied to rapidly alternate the position of one prism between the desired extremes. Sinusoidal drive would be noticeably inefficient (cf. Section 3.1.3). 3.3.6 ~eportedfr~strated total reftection ~od~~at5rs. One interesting measurement reported by Astheimer et a1.,(45)who describe modulators working on this principle, showed the variation in the degree of modulation as a function of temperature. For the case reported a radically different construction from that discussed here was employed but it is none the less significant that over the range 2&X!-50°C a 2 : 1 change in iw was recorded. This was attributed to imperfect thermal compensation. It would appear from the account that the ‘folded’ stack approach, recommended here, was not adopted in this case. Various other possible configurations for frustrated total reflection devices have been outlined by Harrick.@‘) 4. SUMMARY

AND

CONCLUSIONS

It was noted in Section 1.2 that there are strong reasons for favouring devices based on well established principles for this application. Thus, of those mechanisms which were found to be worthy of detailed treatment, the choice largely rests between the Fabry-Perot (FP) cavity with variable plate separation, the stressed plate (SP) in which birefringence is induced and the frustrated total reflection device (FTR) described in Sections 3.1, 3.2 and 3.3. Of the alternatives discussed in Section 2 each one suffers from some major disadvantage. Excessive power requirements eliminate free carrier injection, changing the refractive index of a prism, differential surface recombination and also acousto-optical modulators. Poor values of M eliminate (I) stress induced changes in free carrier absorption; (2) the effect of free carriers on the absorption edge; (3) Faraday rotation; and (4) the incorporation of a p-n junction into a Fabry-Perot cavity. Most of the remaining possibilities considered in Section 2 suffer from the disadvantages of poor optical aperture or narrow optical bandwidth. With the elimination of the possibilities considered in Section 2 it is evident that a truly sofid state alternative to the conventional chopper has not been found. All the remaining possibilities (FP, SP and FTR) employ piezoelectric ceramics to produce small movements, having magnitudes in the range 2-4 pm. No special concern need be felt at this magnitude, since all macroscopic movement has been elimated. However, it must be ascertained with all such devices that such movement may be reliably expected to be maintained over long periods of operation and, more important, maintained at a magnitude close to that for which it was designed. Such is the principle consideration of reliability affecting all three devices. Aspects of reliability which are not common to all three are the ability to withstand repeated

Solid state modulators for horizon sensingapplications

189

stress which is essential to the stress plate device and maintenance of alignment in the frustrated total reflection modulator. A clear advantage for the Fabry-Perot arrangement exists in this respect since it has been shown that the alignment of plates of relatively low reflectivity is surprisingly non-critical. None of the three possible modulators gives an effective modulation which even approaches the near 100% which is obtainable with little difficulty using a conventional chopper. An effective loss in useful signal, approaching SO%, must be tolerated if even the better alternatives are selected. These are the frustrated total reflection device (M = 59.1%) and the Fabry-Perot modulator (566%). In this respect the stressed plate compares very unfavourably with these devices, since its effective modulation is a mere 19.4%. This is a direct consequence of the need for two polarisers. All these figures apply for f/l convergent beams with 14-16 pm bandwidth, conditions which are accepted by all the devices without difficulty. Little difference in drive requirements is found for the three devices. Taking 1mm as a reasonable minimum thickness for a transducer element it is found that the required voltages are 386V for the stressed plate, 342V for the Fabry-Perot cavity and 255V for the FTR device. In all cases square pulses of this magnitude with a mark-space ratio of unity give the best form of drive and for no device are there special stability requirements for the drive voltage, f5 % is quite adequate. Estimated power consumptions range from 212mW (FTR) to lG6W (SP, using 2 stacks) and the stress plate is clearly worst in this respect. Operating frequencies up to 1 kHz cause no embarrassment to any of these modulators, although lower frequency operation would give lower power consumption. Apart from the reliability question relating to the repeated application of stress in one device (SP) the modulators are of equal robustness and should be very satisfactory in this respect. Likewise, the specified optical aperture of I cm2 presents no problems for these devices and they may all be expected to compare well with conventional “choppers” in matters of mass and volume. It is likely that the production cost of the solid state devices will not be excessive although it may be anticipated that they will be somewhat more costly than a motor driven modulator, Components for all these modulators should give a total cost in the range $50-200 (including blooming), the precise prisms required for the FTR device giving rise to the greatest cost. Reproducibility in production should not be a problem, provided that the PZTceramics do not show undue variation from sample to sample. If they prove not to be satisfactory in this respect it should be relatively simple to modify the driving voltages. Thermal compensation is essential unless elaborate temperature control can be provided, Due to the irregular behaviour of the PZT ceramics it has been emphasised that compensation is best achieved by using the ceramic itself in ‘folded stacks’. None of the devices can, in general, be used at other wavelengths without some change in design. In the case of the FTR device, use at short wavelengths is largely impractical while for the FP and SP modulators all that is required are slight changes in setting up and in drive voltages. In making a choice between the three alternatives it is quite clear that the Fabry-Perot modulator is superior to its rivals except on two counts. It is very slightly inferior to the FTR device in effective modulation and requires a higher drive voltage. Should the question of drive voltage prove to be a serious objection it could be circumvented by the use of thinner ceramic elements (say Oe5mm) or longer transducer stacks, although the additional bulk of the device would be unwelcome. On grounds of effective modulation alone the stressed

190

B. ELLH

plate modulator may be discounted. The use of polarisers, which causes this deficiency, would also make the whole device occupy a greater volume than its rivals, giving an added disadvantage. This leaves the FTR device which requires more critical alignment than the FP cavity and the maintenance of that alignment for the life of the device. It ma> be more difficult to elimate the effects of temperature changes on the FTR device and it is more costly. It is concluded that of the three devices thought ta be most promising for use as modulators in the horizon sensing systems that which is most suitable is the Fabry-Perot cavity in which the spacing of germanium plates is varied by folded stacks of PZT4 piezoelectric transducers.

APPENDIX

1

Consider the simpfe system in which a converging lens of focal length~~ro~u~s a point focus at P (Fig, 16). Assume that the lens is ifiuminated uniformiy, in a direction parallel to its optical axis. Then, since the A

A

FIG. 16, Notation used for calculating intensity as a function of angle of incidence. projection of rays brought to a focus at P intercepts the path of the rays from which they are derived at points within the lens (Fig. 16) and since the Iens is assumed to be thin these points of interception may be taken to occur at approximately the central plane of the lens (AA’ in Fig. 16). Thereafter, simple geometrical arguments may be used to find the areas on the lens which give rise to rays incident at angles between 6, and e f 68 y=ftan% (A - 11 _~+6y=ftan(%+6e)

- area giving rays which are incident between %and % + 8%is *2794~ = 2xf tan e (f tan (8 + se> - ftan 8)

where since 6% is small 8%N tan 8%. Now neglecting 6%tan % with respect to unity and writing f, as the incident intensity per unit area, I(e)se = 2vfIL tan %see2 888.

APPENDIX

(A - 3

2

Polar&em for 14-16 pm Efficient polarisation at ,- 1.5 pm presents some problems, even in the laboratory. In a horizon sensor it may be still ditikuit to produce a high degree of pofarisation since it may be necessary to ptace one or more polar&s in an f/i converging beam. Virtually all the well developed methods ofpo~arisation are degraded if

Solid state modulators

for horizon sensing applications

191

a significantly non-parallel beam is used, Some easing of the problem would occur if one of the polarisers were to be placed in the nearly parallel radiation before the lens in the optical system but here the aperture is much larger so that this is not always possible. Moreover, the probIems of convergent radiation still apply to any analyser that may be required. Most significance will be attached to the efficiency with which the desired polarisation is transmitted since the polarisation ratio is often of secondary importance (i.e. some transmission of the unwanted polarisation is often of little practical consequence). A 2.1 Re~e~~io~polarisem For light incident at the Brewster angle only one polarisation is reflected and if the refractive index of the reflecting mirror is sufficiently high an efficient polariser may be obtained. If, for example, silicon is used in parallel radiation, 70% of the wanted component is reflected with a polarisation of 98 %. Thus, even in the most favourable circ~tan~s half of the intensity of the wanted component is lost if two Si polarisers are used. It should be noted that the use of Si external to the lens would imply the use of areas - 14cm in dia. (for a 4cm dia. lens). This could be assembled from, say, four large diameter silicon slices. Drastically reduced performance occurs in convergent radiation. For an f/l beam, incident over the range 37”~90”, the fraction reflected is - 62% (no allowance has been made for the distribution of intensity as a function of angle, see Appendix 1) and the polarisation is 84%. Thus only - 38 % of the wanted polarisation would be transmitted by two polar&em Clearly the losses entailed would be severe. A 2.2 ‘Pile of plates' ~o~a~~s~rs Exactly the same principle, Brewster angle reflection, is the basis of the well known ‘pile of plates’ polarisers. Repeated preferential reflection of one component from both surfaces of each plate eventually leaves the transmitted beam strongly polarised. At long wavelengths thin polythene sheets are most convenient for this purpose* and ex~rimental results show that in mildly convergent radiation (--fiS) appro~mately 80 % transmission of the wanted component may be obtained using a stack of 12 sheets each 5 pmin thickness. Greater than 90% polarisation is obtained. Some care in the choice of the thickness of the sheets must be exercised in order to avoid unwanted interference effects, although, if constructive interference occurs at the appropriate wavelengths, enhanced polarisation may be obtained (see, for example, Walton ei ai. 1964). Conversely, if this can be arranged, fewer plates might be required. By this means thetransmissionlossmight be somewhat reduced. In convergent radiation slightly increased losses are inevitable but the effect should be less pronounced than in the silicon reflection device. Thus, a transmission rather in excess of 50% from two polar&s for the wanted component is probably a reasonable assumption. The polarisation would, of course, be somewhat degraded. One polariser could easily be positioned external to the lens, since large aperture stacks may be fabricated without difficulty. Overall, a loss of 50% in intensity due to polarisation, coupled with a further 50% due to polariser deficiencies is the best that can be expected from these polarisers. It should be noted that Brewster angle polarisers require quite a large amount of space. For polythene 1 cm in dia. a longitudinal distance exceeding 1*5cm is needed for each polarizer.

Two forms of this type of polariser have been described.@sB ao) In the former work metallic grids (parallel strips) were deposited on silicon or polythene substrates. Preferential transmission of the polarisation with electric vector perpendicular to the metallic strips occurs to an extent dependent upon their spacing. The wavelengths at which efficient polarisation is obtained are those which exceed the periodic distance of the grid by a factor of about 4 or more. Since a 4 ,rm spacing is the closest that is commercially available it is only just feasible to obtain polarisation by this means over the 14-16 pm band. Data for ~ommerciai devices (AIM Physical Sciences Ltd, Cambridge, England) indicates a transmission of the wanted component - 80% and a polarisation of, perhaps, 70%. Little degradation is to be expected in convergent radiation. Thus, the metal grid polariser could be marginally superior to the other types considered so far. Apertures up to 25cm dia. are available at a cost (1968) of ti6 per pair of polarisers. Needle-like inclusions of such compounds as NiSb in InSb, oriented during growth to lie parallel to a given direction, have been used by Paul et uz’.(s*)in exactly the same way as the evaporated grid polarisers described above. Impressive polarisation figures, even at loam, were obtained but, even with ZnS blooming, the maximum transmission of the wanted component at - 1Spm was - 44%. Two polarisers would therefore have a transmission of 19.4’4. Devices - 1 cm in dia. shoufd be within the bounds of possibility but unless the losses can be reduced the penalty for using two of the polarisers would be severe. *Recent results fm show that polypropylene should also be

considered.

CkarIy, no satisfactory pdariser exists for this appkat-ion. Of those described the ‘piie of plates’ polariser entails the least loss and can be easily and cheaply fabricated with large apertures. Evaporated m&a1 grid polarisem might just give equal performance with the advantage of compactness. They are, however, relatively costly. An overall loss of at least 75 % of the incident intensity will accrue from the use of two polarisers.

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of

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