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Fluorescent sensors based on tapered single-mode optical fibres
Sensors and Achutors B, 17 (1994) 233-240
233
Fluorescent sensors based on tapered single-mode optical fibres Z.M. Hale and F.P. Payne Cambridge Univedy Engheehzg Department, Tnwqington Street, Cambridge CB2 IPZ (UK) (Received October 26, 1992; in revised form June 4, 1993; accepted June 25, 1993)
Abstract An optical sensor is presented that relies on the evanescent field excitation of a pH indicator in the external media. The evanescent field is made accessible through the use of an adiabatically tapered single-mode optical tibre. The level of fluorescence captured into the fibre from the excited indicator is directly related to the pH value. Theoretical calculations of the sensitivity are presented and contrasted to those of multimode fibres. The detection range of the sensor is pH 3-9, demonstrating the suitability of tapered fibre devices as sensors.
Introduction Optical-fibre sensors have been designed to respond to spectral changes in their surroundings. These changes are then related to the level of analyte. This can occur because the optical field is not strictly confined to the fibre core, but has approximately exponentially decaying evanescent ‘tails’ into the surrounding materials, i.e., the cladding and potentially beyond. Many optical-fibre sensors are based on evanescent-wave absorption or fluorescence, i.e., light injected into the fibre interacts with an external dye solution via the evanescent portion of the field. A change in the light-signal output at the other end of the fibre is then recorded either as an attenuation through absorption by the dye, or fluorescence at a longer wavelength captured back into the fibre core. In some devices, the dye is bound in the cladding surrounding the fibre and is excited optically [l, 21. In order to develop an optical fluorescent sensor, the fluorescent indicator and the solution of interest are exposed to the evanescent field. This external optical power can excite molecules of the fluorescent indicator that are sufficiently near the waveguide. Their emitted light can be coupled back into guided modes that propagate along the fibre. The overall sensitivity of this process depends on the modes chosen and the thickness of the cladding [3]. In order to expose as much of the evanescent field as possible, thereby increasing the sensitivity of fibres for detection, part of the cladding has to be removed locally. %o examples of this are illustrated in Fig. 1: polished fibres in Fig. l(a) and tapered ones in Fig. l(b). Many devices studied so far are based on unclad multimode fibres. Higher-order modes in these fibres
0925-4005/94/$07.00 @ 1994 Elsevier Sequoia. All rights reserved SSDI 0925-4005(93)00876-Z
@I Fig. 1. (a) Evanescent field of a polished fibre, LP,, mode. (b) Evanescent field of a fibre taper, LPa, mode.
have the advantage of a large number of reflections per unit length, and consequently a long effective interaction length with the external material. They also allow for sensing from distant locations. Further, optical fibres in general are capable of operating in many geometrical configurations, making them a versatile sensor option. These advantages, together with the benefit of low cost, have encouraged investigations of evanescent wave spectroscopy at the surface of an unclad optical fibre [4]. The use of multimode fibres, however, does entail a number of disadvantages. Theoretical calculations [5] show that the efficiency of the coupling of cladding fluorescence to the guided modes of a multimode tibre depends strongly on the dimensionless waveguide fre-
234
quency, the V number, of the fibre:
where p is the core radius, n, is the refractive index of the core, n2 is the refractive index of the cladding and h is the free-space wavelength of light propagating in the fibre. The evanescent field of a multimode fibre is extremely weak, of the order of 2% of the total power in the fibre for a V of 100 [6]. Fibres with higher V numbers have higher coupling coefficients. This is because they have many modes near cut-off and the evanescent fields of such modes penetrate more deeply into the surrounding cladding [7]. Fluorescence from a dye may be excited by the evanescent field for the guided radiation if the dye is close to the fibre core. The fluorescent light generated must be re-radiated in a manner that allows it to be coupled (or captured) into a guided mode, as portrayed in Fig. 2. As a result, most multimode fibre devices rely on preferential excitation of higher-order modes, either by launching the light off axis, or by means of suitable masks. This in itself can cause problems in maintaining repeatable launch conditions. Lastly, multimode fibres themselves are incompatible with single-mode fibres, and are thereby unable to take advantage of the very highquality single-mode fibre couplers and power splitters now commonly available. As an alternative to unclad multimode fibres, a number of devices have been reported based on polished fibres. In these devices, part of the fibre cladding is removed mechanically to within several microns of the core, resulting in a D-shaped cross section. This exposes the evanescent field to the surrounding medium (Fig. l(a)). The evanescent field of the fibre mode or modes can then interact with a dye solution with spectrochemical properties of interest to the sensor type desired. However, the evanescent field of polished fibres is extremelyweak unless the refractive indexof the external dye solution is very close to that of the fibre (typically to within a few parts per thousand). As a result, polished
devices exhibit extreme sensitivity to changes in external refractive index. Their efficiency is also low because of their very short interaction length. The use of single-mode fibres can avoid the negative aspects of multimode fibres while still retaining the advantages. We have demonstrated this idea by using a monomode tapered optical fibre as a pH sensor. A single-mode fibre is used because modal coupling amongst the higher-order modes of a multimode fibre along the taper results in high losses. Further, the modal field in a single-mode fibre is well defined. In general, biconical tapers consist of a region of the fibre with decreasing diameter followed by an expanding section of equal diameter, as seen in Fig. l(b). Fibre tapers can be constructed quite easily: a portion of the optical fibre is heated, by an oxybutane flame, to the softening point of the silica glass and pulled by applying equal and opposite axial tensions. In this experiment, the tapers were made on the set-up illustrated in Fig. 3. While the fibre is being stretched, the power transmitted through it is monitored. An acceptable taper is a low-loss one (~0.1 dB), which is typically achieved in a slow process. Tbe resultant taper is adiabatic, that is, the diameter changes slowly along the length of the taper. Because of this, the fundamental fibre mode that enters the tapered region does not couple to either cladding or radiation modes [8]. Power guided by the fundamental mode is concentrated in a very small circular cross section at the taper waist with a diameter (in this study) of about 5 pm. A very small power, of the order of milliwatts, can cause a high power density of kW/cm2 [9]. At the taper waist the fibre core is so small that it plays no role in guiding the light. Guiding is achieved by a new effective waveguide consisting of the fibre cladding and the surrounding medium. The local value Uonccbmmatcr
C
1
Lock-in ampIffier Fig. 2. Fluorescence from an excited dye molecule, generating a current element J.
Fig. 3. Configuration for tapering fibrcs: WLS = white light source; C= optical chopper; L= objective lens; M= motor-driven stages; F = oxybutane flame; PD= large-area photodiode.
235
of V is reduced in proportion to the fibre diameter and in very small-diameter tapers (of the order of microns), the fundamental mode field extends into the medium surrounding the cladding. This has been shown experimentally [lo], as well as being predicted theoretically. The level of interaction with the field, as well as the fluorescent indicator used, determines the efficiency with which the fluorescence can be recaptured into the fibre.
In this section we present a detailed theoretical description of the efficiency with which the external fluorescence in the dye solution surrounding the tapered fibre is coupled into the fundamental mode of the taper. We base our analysis on Snyder and Love [ll], who have given a general account of radiative capture into the core of an optical fibre. A corresponding analysis for the case of highly multimoded fibres has been given by Marcuse [5]. For simplicity, we assume that the taper waist is of constant radius p and length L. At the taper waist, the original core of the fibre is so small that it can be neglected, so that the light is guided by a new effective waveguide consisting of the fibre cladding and external medium, as illustrated in Fig. 4. At the taper waist, the pump light excites the dye molecules into the first excited state, from which they fluoresce as an incoherent mixture of radiative dipoles. A dipole at position r, can be represented by a current density J given by J= rrs3(f-fJ
(2)
where 6 is the Dirac delta function. The vector u describes the strength and direction of the dipole, and depends on the detailed dipole moment of the dye molecule. For our purposes we shall assume that all the molecules radiate incoherently and isotropically; then the following ensemble average will apply:
((y.(y.)=&O 1
I
”
3
Equation (3) is derived in the Appendix. To calculate the fluorescence coupled into the fundamental mode of the taper, we need to know the amplitude of the mode excited by the current source in eqn. (2). This is given by Snyder and Love [12] as
where Y refers to either of the two orthogonal polarizations of the fundamental modal field e, with propagation constant /I and normalization N defined so that the power carried by the mode is P,,= la,rN and where the normalization defined so that
of the modal field is
(6) The integral in eqn. (6) is over the entire transverse cross section, and n, is the refractive index of the taper (normally silica). Combining eqns. (2) to (6), and summing over the two polarizations v=x,y, we find that the average power in the fundamental mode excited by a fluorescing dye molecule at radius r, is given by
P=
kNg(~>l~o(rd)12
In eqn. (7) we have neglected the z component of the field; we have also dropped the polarization subscript, since the fundamental mode has the same radial form e, for the x and y polarizations. We now combine eqn. (7) with the distribution n&J of dipoles at radius r, excited by the fundamental pump mode in the taper. This will be expressed in terms of the following parameters: n,, concentration of the dye molecules u,, absorption cross section of the dye molecule it, fluorescent lifetime of the dye molecule rp, quantum efficiency of the dye The density distribution of radiating dye molecules at radius r,, is then given by n&J = +&,)I2
Fig. 4. Idealized taper geometry used in theoretical analysis of fluorescence capture. The taper waist is assumed to bc of length L and of constant radius p. The fibre core is negligible at the . ___^ waist. (NE tigure is not to scale.)
(5)
(8)
where y=n,rtU~APi,,,lk. The incident pump power is Ph, and the modal field of the pump is e,; h is Plan&s constant, c is the speed of light and A is the wavelength of the radiation. Equation (8) comes about because the photon flux is P,,lphoton energy, which is P,,A/hc. To obtain the flux per unit area at radius r,, this must be multiplied by ~&.Jl’. Each dye molecule has an absorption cross section a, and a concentration n,, so that the excitation
236
rate per unit volume of the dye is
(13) The rate of decay from fluorescence is l/rr, which leads to eqn. (8) for the steady-state concentration of excited dye molecules. Multiplying eqns. (7) and (8) and integrating over all molecules, we obtain the following expression for the total fluorescent power captured into the fundamental mode of a taper of length L:
In both eqns. (12) and (13) the integrals are over the region external to the taper radius p. Equation (13) can be evaluated analytically by using the Gaussian approximation [14] for the fundamental mode of a waveguide with radius p: e,(r) =
The integral in eqn. (9) is over the region surrounding the taper, with a radius of p (see Fig. 4). We have also dropped the subscript on r, since it is being integrated over. In order to estimate the efficiency of fluorescent capture we now need the total power radiated by all the dye molecules. The power radiated by one molecule is given by Snyder and Love [13] as
(10)
(m~2,1n eq.4-r2~2r,2)
where ro=p/(210&V)1n and V is as defined in eqn. (1). The Gaussian approximation holds true for V> 1. The integral in eqn. (13) can now be easily evaluated to give this expression for the efficiency: lo& v 17= (kopnl)2v2
(15)
Writing eqn. (15) using the definition of V from eqn. (l), we arrive at the final expression for the efficiency: log, v(Nz4)2
where /r,,=2rr/h and n, is the refractive index of the surrounding dye solution. We can neglect the effect of the presence of the fibre on the total radiation. The total fluorescent power is given by combining eqn. (10) with the density of dye molecules, given by eqn. (8). We then obtain
We define the efficiency of fluorescent capture as the ratio 7 =P,,,/P,,,. From eqns. (9) and (11) this is given by *n m
In our experiment, the refractive index of the dye solution was close to that of the silica taper, so that we may put n, =nP In addition, the pump and fluorescence wavelengths are normally close enough so that we may approximate the modal fields eP and e, as being equal. This allows eqn. (12) to be written in a slightly simpler form:
II=
V4n12
ALA,the numerical aperture of the taper, is given by (n12-n,2)ln. In this form, 7 can easily be seen to be always less than one. Equations (15) and (16) are plotted in Figs. 5 and 6 as functions of V for different values of NA and p/con,. From these curves we can estimate the efficiencies of fluorescent capture for various taper diameters and external dye refractive indices. The smallest tapers used in our experiments had diameters of approximately 0.5 pm. The external dye index was adjusted to 1.44, which, combined with the index of refraction for the cladding of 1.458,corresponded to an NA of 0.23. The fluorescent efficiency (“h)
v Fig. 5. Efficiency as a function of the dimensionless waveguide frequency, V, at different levels of NA (eqn. (16) of main text).
237
efficiency (%) 0.05 0.045 0.04 o.w5 0.03 10
OM5-
15 ‘JQZ “.“_
curves 1
plottedfordifferentvalues of pk,n, 2
3
0.02
20
10
0.015 20
0.01 1.32
1.34
1.36
1.38
1.4
1.42
144
1.46
external index
V5
Fig. 6. Efficiency as a function of the dimensionless waveguide frequency, V, at different levels of &nl (eqn. (15) of main text).
Fig. 7. Efficiencyas a function of external refractiveindex for a 2 pm diameter taper and a wavelengthof 0.526,um.
wavelength was 0.526 pm, yielding an estimated efficiency of 0.2%. For tapers with a 2 pm diameter the corresponding efficiency would be about 0.04%. Results using multimode polished fibres give efficiencies of approximately 10V4 [7]. Similarly, given that the fluorescein dye exhibits a very high quantum yield of 90 f 5% [U-17], with a taper diameter ranging from 2-4 Frn, a typical experimentally derived fluorescent energy taper capture rate was of the order of 10e3 of the input light energy to the dye molecule. Several methods were used for measuring captured fluorescent energy into the taper, including adjusting the pump power to the point at which all input power was absorbed, and measuring the resultant fluorescent energy at the far end of the taper. There is a further more important distinction between the tapered and multimode fibre cases: the much higher optical intensities achievable with a tapered fibre will translate into higher absolute levels of captured fluorescence. We can see this as follows. The total fluorescence will be proportional to the fraction of pump power in the external dye solution. For a multimode fibre with equal excitation of modes, this is 4/3V [18, after correcting a minor error]. For a tapered fibre propagating the fundamental mode, the fraction is 1/V2, as is easily shown from eqn. (14). A typical value for a 200 pm diameter multimode fibre is V=300, whereas for a 2 pm taper Y is about 2.7; in each case we can assume a wavelength of 0.5 pm and an external dye index of 1.44. From this we anticipate the level of fluorescence to be 30 times higher in a taper than in a multimode polished fibre of the same length. Furthermore, most of the pump power is absorbed in a taper. Consequently we conclude that for smalldiameter tapers (about 2 pm), much higher absolute efficiencies are possible compared to multimode fibres. They are also less sensitive to variations in the external refractive index, as shown in Fig. 7. Here we have plotted the efficiency of a 2 pm taper as a function of dye index over the range n = 1.33 (water)-1.44. As
can be seen, the efficiency does not vary by more than a factor of three over the whole index range.
Experimental Materials The indicator, disodium fluorescein, and solvent chosen for our experiments, methanol, as well as pH buffer solutions, were purchased from Fisons Scientific Equipment. For the titration process, glacial acetic acid (17.4 M) and concentrated aqueous potassium hydroxide (100 M) were obtained from Aldrich Chemical Company and Fisons, respectively. The pH levels of the buffers and titration products were verified using a hand-held pH electrode supplied by RS Components with an overall stated accuracy of f0.03 pH units. To ensure a constant external refractive index, appropriate amounts of dimethyl sulfoxide, supplied by BDH Laboratory Supplies, were added and regularly confirmed using a Bellingham and Stanley sugar refractometer.
Apparatus
The single-mode optical fibre used for the sensor was a York Technology SM4.50with a numerical aperture of 0.18 and a cut-off wavelength of 450 nm. The diameter of the nominally circular core was -2 pm. The outer diameter of the fibre was 80 pm, with a cladding refractive index of 1.458. Tapers were fabricated in a manner reported earlier [19] and illustrated in Fig. 3. The resultant tapers used in this study had waist diameters from 0.5 to 10 Frn, as well as typical transmission losses of 0.1 dB. The most optimal diameters were between 2 and 4 pm and had a length of at least 5 mm, which represented a compromise between a sensitive system and a durable one. Narrow tapers tended to break, and wide tapers were not sufficiently sensitive. The tapers were then mounted in a custombuilt dye cell, as shown in Fig. 8, to provide a means of circulating solutions about the taper. The refractive
238
!%oreacence level, arbitraty units
Ll
500
550
575
E
Wavelength, nm /
Fig. 8. Stainless steel die-cast dye cell for tapered fibres: the taper is centred in the cavity and secured by glue; a glass plate is placed over the cell and afiixed with sealant. Solution enters tubing and flows through the cell along fibre taper.
~0
Fig. 10. Fluorescence spectrum of disodium fluorescein in methanol, 1.02X10-* M, measured with fibre taper.
Monochromator
Single
argon-ion
mode
IaSW
Fig. 9. Experimental configuration: titration passes along the taper, mounted in its dye cell. C=optical chopper; L=objective lens; PD = large area photodiode.
index of the solutions ranged from 1.32 to 1.458. Once mounted, the tapers could be easily handled and have been in use for several months. The experimental configuration, shown in Fig. 9, measured output fluorescence level as a function of pH. An argon-ion laser, tuned to the 488 nm line, was used to excite the fluorescent dye around the taper. The indicator in solution released fluorescent energy when excited by the evanescent field of the fibre. The fluorescent emissions from the excited dye molecules were then coupled back into the fundamental guided mode of the taper. The level of these emissions was characterized by using a monochromator. This light was then detected by a large-area photodiode (RS Components, data sheet 12508). Because of the signal levels, intensity measurements were made using lock-in detection (Stanford Research Systems). The lock-in amplifier was linked to a personal computer via an analog to digital data-acquisition card. The fluorescence spectrum found was typical for that of ,bulk absorption, as seen in Fig. 10. Subsequent measurements were then made with the monochromator set at 526 nm, the wavelength of maximum fluorescence. Measurements
A volumetric titration of 100 M potassium hydroxide and 17.4 M acetic acid was carried out to establish a
Volume added 4’ (normalised Utlits)
pH units
Fig. 11. Comparison of volumetric acid-base titration verified by pH meter (solid tine) and fluorescence level in a taper (squares).
baseline for pH level as a function of volume of added base. The amount of acetic acid used was then fixed for all subsequent experiment trials, and the pH levels obtained were verified by the pH meter. This baseline curve, as shown by the solid line of Fig. 11, exhibited the typical sigmoid shape. The data represented by squares in Fig. 11 describe the same titration performed using a tapered fibre with the fluorescein indicator in solution. Approximately fifty sets of data were taken on the described experimental apparatus, which clearly demonstrated the expected curve.
The tapered optical-fibre sensor was found to be very responsive to pH changes. A calibration curve between the level of fluorescent light and pH could be readily determined. However, because the indicator was not a fundamental portion of the sensor, the solutions used had to be pre-conditioned for both refractive index and indicator dye content. A possible cure for this limitation would be to immobilize the indicator in the cladding along the taper. Such ‘active coating’ sensors often provide much higher sensitivity
239
[20]. Many immobilization metbbds are described in the literature. Sol-gel techniques have already been applied with success to optical fibres [l, 211.This would fix both the refractive index and the concentration of the indicator. Further work is under way to apply indicator-doped sol-gel to the taper. In addition, a sensor configuration based on silanization of a taper loop with a radius of curvature of 1 mm is under investigation. In conclusion, we have proposed the use of tapered single-mode fibres as sensing elements in fluorescent sensors. The use of single-mode rather than multimode fibres results in a more stable and repeatable optical launch as well as higher achievable levels of fluorescent capture. We would expect similar advantages when these tapers are applied to absorption sensors.
Acknowledgements We would like to thank Dr H.S. MacKenzie and the referee for helpful comments and discussions. Z.M. Hale would like to thank the United States Air Force Institute of Technology for personal support.
15 LH. Drexhage, in F .D. Schafer (ed.), TopicsinApplicdPhysics, Vol. 1, Dye Losers, Springer, Heidelberg, 1990, p. 161. 16 E.D. Owen, in N.S. Allen and J.F. McKellar (eds.), Phorochemimy of Dyed and PigmentedPolymers,Applied Science Publishers, London, 1980, p. 45. 17 K. Gollnick, T. Franken, M.F.R. Fouda, H.R. Paur and S. Held, Merbromin (mercorochrome) and other xanthene dyes: quantum yields of triplet sensitizer generation and singlet oxygen formation in alcoholic solutions, J. Photochem. Photobiol.. B: Biobev~ 12 (19921 58. 18 D. Gioge, Weakly iiding fibres, Appl. Opr, 10 (1971) 2252-2258. 19 H.S. Mackenzie and F.P. Payne, Saturable absorption in a tapered single-mode optical fibre, Electron Left., 26 (1990) 1744-1745. 20 R.A. Liebennan, Recent progress in intrinsic fiber optic chemical sensing, in R-4. Lieberman and M.T. Wlodarczyk (eds.), SPIE Rx, Vol. 1368, Chemical, Biochemical and Envimnmental Fiber Sensors II, 1990, p. 15. 21 K.T.V. Grattan,G.E. Badmi,A.W.PahnerandA.C.C.Tseung, Use of sol-gel techniques for fibre-optic sensor applications, Sensors and Actuators A, 25-27 (1991) 483487.
Appendix In this Appendix we give the derivation of eqn. (3) in the main text. The Cartesian components of (Ycan be expressed in polar form as
1 B.D. MacCraith, V. Ruddy, C. Potter, B. O’Kelly and J.F. McGilp, Optical waveguide sensor using evanescent wave excitation of fluorescent dye in sol-gel glass, Elecfroon. Lett, 27 (1991) 1247-1248. 2 J.Y. Ding, M.R. Shahriari and G.H. Sigel, Jr., Fiber optic pH sensors prepared by sol-gel immobilisation technique, Electron. Len., 27 (1991) 1560-1562. 3 G. Stewart, .I. Norris, D.F. Clark, M. Tribble, I. Andovic and B. Culshaw, Evanescent-wave chemical sensors - a theoretical evaluation, Int. 1. Optoelecrron.,6 (3) (1991) 227-238. 4 V. Ruddy, B.D. MacCraith and LA. Murphy, Evanescent wave absorption spectroscopy using multimode fibers, J. Apple Phys., 67 (1990) 6070-6074. 5 D. Marcuse, Launching light into fiber cores from sources located in the cladding, 3. Liphtnwe Tech&., 6 (1990) 1273-1279. 6 P.H. Paul and G. Kychakoff, Fiber-optic evanescent field absorption sensors, Appi. Phys. Len., 51 (1987) 12-14. 7 R.A. Lieberman, LL. Blyler and G. Cohen, A distributed fiber optic sensor based on cladding fluorescence, 1. Light~~~ve Technol., 8 (1990) 212-220. 8 E.G. Neumann, Single Mode Fibers: Fundumenfals, Springer, Heidelberg, 1988, p. 305. 9 Ref. 8, p. 86. 10 F.P. Payne and H.S. MacKenzie, Novel applications of monomode fibre tapers, in O.D. Soares (ed.), SPIE Proc., Vol. 1504, Fiber-Optic Metiogy and Standnrdr: Roceedings of the Conference in the Hague, Netherlands, 1991, p. 15. 11 A.W. Snyder and J.D. Love, OpticalWaveguideTheory, Chap man and Hall, London, 1983, p. 442. 12 Ref. 11, p. 444. 13 Ref. 11, p. 451. 14 Ref. 11, p. 338 and p. 341.
ci;=asin
0coscp
cr,=crsinesincp a2 = a cos tl We assume that the direction of Q is distributed isotropically in space. This means that its direction is described by the probability distribution P(0,6p):
qe, (p)= y where
The average (aiaj) is defined by “r ‘;: (aiaj> =J
J aiajP(e,
‘p)
dtJ drp
-0 -0
and a little algebra gives the following: (a&
= (~4
= (a,4
=0
(a~)=(ay2)=(a~)=az/3
The result stated in eqn. (3) then follows.
240
Biographies ZoLiHale received a B.S. in applied and engineering physics from Cornell Universify in 1986, an MBA in multinational operations from St Mary’s University in 1989, and is currently working for a Ph.D. in opticalfibre sensors at Cambridge University. Frank Payne read natural sciences at Cambridge University, graduating in 1975. He remained at Cam-
bridge until 1978 to read for his Ph.D. in physics at the Cavendish Laboratory. He has since held posts at Liverpool and Southampton Universities, and from 1986 has been a lecturer in optical electronics in the Engineering Department at Cambridge University. His research interests are in linear and non-linear propagation in optical fibres and he has published some fifty technical papers.
233
Fluorescent sensors based on tapered single-mode optical fibres Z.M. Hale and F.P. Payne Cambridge Univedy Engheehzg Department, Tnwqington Street, Cambridge CB2 IPZ (UK) (Received October 26, 1992; in revised form June 4, 1993; accepted June 25, 1993)
Abstract An optical sensor is presented that relies on the evanescent field excitation of a pH indicator in the external media. The evanescent field is made accessible through the use of an adiabatically tapered single-mode optical tibre. The level of fluorescence captured into the fibre from the excited indicator is directly related to the pH value. Theoretical calculations of the sensitivity are presented and contrasted to those of multimode fibres. The detection range of the sensor is pH 3-9, demonstrating the suitability of tapered fibre devices as sensors.
Introduction Optical-fibre sensors have been designed to respond to spectral changes in their surroundings. These changes are then related to the level of analyte. This can occur because the optical field is not strictly confined to the fibre core, but has approximately exponentially decaying evanescent ‘tails’ into the surrounding materials, i.e., the cladding and potentially beyond. Many optical-fibre sensors are based on evanescent-wave absorption or fluorescence, i.e., light injected into the fibre interacts with an external dye solution via the evanescent portion of the field. A change in the light-signal output at the other end of the fibre is then recorded either as an attenuation through absorption by the dye, or fluorescence at a longer wavelength captured back into the fibre core. In some devices, the dye is bound in the cladding surrounding the fibre and is excited optically [l, 21. In order to develop an optical fluorescent sensor, the fluorescent indicator and the solution of interest are exposed to the evanescent field. This external optical power can excite molecules of the fluorescent indicator that are sufficiently near the waveguide. Their emitted light can be coupled back into guided modes that propagate along the fibre. The overall sensitivity of this process depends on the modes chosen and the thickness of the cladding [3]. In order to expose as much of the evanescent field as possible, thereby increasing the sensitivity of fibres for detection, part of the cladding has to be removed locally. %o examples of this are illustrated in Fig. 1: polished fibres in Fig. l(a) and tapered ones in Fig. l(b). Many devices studied so far are based on unclad multimode fibres. Higher-order modes in these fibres
0925-4005/94/$07.00 @ 1994 Elsevier Sequoia. All rights reserved SSDI 0925-4005(93)00876-Z
@I Fig. 1. (a) Evanescent field of a polished fibre, LP,, mode. (b) Evanescent field of a fibre taper, LPa, mode.
have the advantage of a large number of reflections per unit length, and consequently a long effective interaction length with the external material. They also allow for sensing from distant locations. Further, optical fibres in general are capable of operating in many geometrical configurations, making them a versatile sensor option. These advantages, together with the benefit of low cost, have encouraged investigations of evanescent wave spectroscopy at the surface of an unclad optical fibre [4]. The use of multimode fibres, however, does entail a number of disadvantages. Theoretical calculations [5] show that the efficiency of the coupling of cladding fluorescence to the guided modes of a multimode tibre depends strongly on the dimensionless waveguide fre-
234
quency, the V number, of the fibre:
where p is the core radius, n, is the refractive index of the core, n2 is the refractive index of the cladding and h is the free-space wavelength of light propagating in the fibre. The evanescent field of a multimode fibre is extremely weak, of the order of 2% of the total power in the fibre for a V of 100 [6]. Fibres with higher V numbers have higher coupling coefficients. This is because they have many modes near cut-off and the evanescent fields of such modes penetrate more deeply into the surrounding cladding [7]. Fluorescence from a dye may be excited by the evanescent field for the guided radiation if the dye is close to the fibre core. The fluorescent light generated must be re-radiated in a manner that allows it to be coupled (or captured) into a guided mode, as portrayed in Fig. 2. As a result, most multimode fibre devices rely on preferential excitation of higher-order modes, either by launching the light off axis, or by means of suitable masks. This in itself can cause problems in maintaining repeatable launch conditions. Lastly, multimode fibres themselves are incompatible with single-mode fibres, and are thereby unable to take advantage of the very highquality single-mode fibre couplers and power splitters now commonly available. As an alternative to unclad multimode fibres, a number of devices have been reported based on polished fibres. In these devices, part of the fibre cladding is removed mechanically to within several microns of the core, resulting in a D-shaped cross section. This exposes the evanescent field to the surrounding medium (Fig. l(a)). The evanescent field of the fibre mode or modes can then interact with a dye solution with spectrochemical properties of interest to the sensor type desired. However, the evanescent field of polished fibres is extremelyweak unless the refractive indexof the external dye solution is very close to that of the fibre (typically to within a few parts per thousand). As a result, polished
devices exhibit extreme sensitivity to changes in external refractive index. Their efficiency is also low because of their very short interaction length. The use of single-mode fibres can avoid the negative aspects of multimode fibres while still retaining the advantages. We have demonstrated this idea by using a monomode tapered optical fibre as a pH sensor. A single-mode fibre is used because modal coupling amongst the higher-order modes of a multimode fibre along the taper results in high losses. Further, the modal field in a single-mode fibre is well defined. In general, biconical tapers consist of a region of the fibre with decreasing diameter followed by an expanding section of equal diameter, as seen in Fig. l(b). Fibre tapers can be constructed quite easily: a portion of the optical fibre is heated, by an oxybutane flame, to the softening point of the silica glass and pulled by applying equal and opposite axial tensions. In this experiment, the tapers were made on the set-up illustrated in Fig. 3. While the fibre is being stretched, the power transmitted through it is monitored. An acceptable taper is a low-loss one (~0.1 dB), which is typically achieved in a slow process. Tbe resultant taper is adiabatic, that is, the diameter changes slowly along the length of the taper. Because of this, the fundamental fibre mode that enters the tapered region does not couple to either cladding or radiation modes [8]. Power guided by the fundamental mode is concentrated in a very small circular cross section at the taper waist with a diameter (in this study) of about 5 pm. A very small power, of the order of milliwatts, can cause a high power density of kW/cm2 [9]. At the taper waist the fibre core is so small that it plays no role in guiding the light. Guiding is achieved by a new effective waveguide consisting of the fibre cladding and the surrounding medium. The local value Uonccbmmatcr
C
1
Lock-in ampIffier Fig. 2. Fluorescence from an excited dye molecule, generating a current element J.
Fig. 3. Configuration for tapering fibrcs: WLS = white light source; C= optical chopper; L= objective lens; M= motor-driven stages; F = oxybutane flame; PD= large-area photodiode.
235
of V is reduced in proportion to the fibre diameter and in very small-diameter tapers (of the order of microns), the fundamental mode field extends into the medium surrounding the cladding. This has been shown experimentally [lo], as well as being predicted theoretically. The level of interaction with the field, as well as the fluorescent indicator used, determines the efficiency with which the fluorescence can be recaptured into the fibre.
In this section we present a detailed theoretical description of the efficiency with which the external fluorescence in the dye solution surrounding the tapered fibre is coupled into the fundamental mode of the taper. We base our analysis on Snyder and Love [ll], who have given a general account of radiative capture into the core of an optical fibre. A corresponding analysis for the case of highly multimoded fibres has been given by Marcuse [5]. For simplicity, we assume that the taper waist is of constant radius p and length L. At the taper waist, the original core of the fibre is so small that it can be neglected, so that the light is guided by a new effective waveguide consisting of the fibre cladding and external medium, as illustrated in Fig. 4. At the taper waist, the pump light excites the dye molecules into the first excited state, from which they fluoresce as an incoherent mixture of radiative dipoles. A dipole at position r, can be represented by a current density J given by J= rrs3(f-fJ
(2)
where 6 is the Dirac delta function. The vector u describes the strength and direction of the dipole, and depends on the detailed dipole moment of the dye molecule. For our purposes we shall assume that all the molecules radiate incoherently and isotropically; then the following ensemble average will apply:
((y.(y.)=&O 1
I
”
3
Equation (3) is derived in the Appendix. To calculate the fluorescence coupled into the fundamental mode of the taper, we need to know the amplitude of the mode excited by the current source in eqn. (2). This is given by Snyder and Love [12] as
where Y refers to either of the two orthogonal polarizations of the fundamental modal field e, with propagation constant /I and normalization N defined so that the power carried by the mode is P,,= la,rN and where the normalization defined so that
of the modal field is
(6) The integral in eqn. (6) is over the entire transverse cross section, and n, is the refractive index of the taper (normally silica). Combining eqns. (2) to (6), and summing over the two polarizations v=x,y, we find that the average power in the fundamental mode excited by a fluorescing dye molecule at radius r, is given by
P=
kNg(~>l~o(rd)12
In eqn. (7) we have neglected the z component of the field; we have also dropped the polarization subscript, since the fundamental mode has the same radial form e, for the x and y polarizations. We now combine eqn. (7) with the distribution n&J of dipoles at radius r, excited by the fundamental pump mode in the taper. This will be expressed in terms of the following parameters: n,, concentration of the dye molecules u,, absorption cross section of the dye molecule it, fluorescent lifetime of the dye molecule rp, quantum efficiency of the dye The density distribution of radiating dye molecules at radius r,, is then given by n&J = +&,)I2
Fig. 4. Idealized taper geometry used in theoretical analysis of fluorescence capture. The taper waist is assumed to bc of length L and of constant radius p. The fibre core is negligible at the . ___^ waist. (NE tigure is not to scale.)
(5)
(8)
where y=n,rtU~APi,,,lk. The incident pump power is Ph, and the modal field of the pump is e,; h is Plan&s constant, c is the speed of light and A is the wavelength of the radiation. Equation (8) comes about because the photon flux is P,,lphoton energy, which is P,,A/hc. To obtain the flux per unit area at radius r,, this must be multiplied by ~&.Jl’. Each dye molecule has an absorption cross section a, and a concentration n,, so that the excitation
236
rate per unit volume of the dye is
(13) The rate of decay from fluorescence is l/rr, which leads to eqn. (8) for the steady-state concentration of excited dye molecules. Multiplying eqns. (7) and (8) and integrating over all molecules, we obtain the following expression for the total fluorescent power captured into the fundamental mode of a taper of length L:
In both eqns. (12) and (13) the integrals are over the region external to the taper radius p. Equation (13) can be evaluated analytically by using the Gaussian approximation [14] for the fundamental mode of a waveguide with radius p: e,(r) =
The integral in eqn. (9) is over the region surrounding the taper, with a radius of p (see Fig. 4). We have also dropped the subscript on r, since it is being integrated over. In order to estimate the efficiency of fluorescent capture we now need the total power radiated by all the dye molecules. The power radiated by one molecule is given by Snyder and Love [13] as
(10)
(m~2,1n eq.4-r2~2r,2)
where ro=p/(210&V)1n and V is as defined in eqn. (1). The Gaussian approximation holds true for V> 1. The integral in eqn. (13) can now be easily evaluated to give this expression for the efficiency: lo& v 17= (kopnl)2v2
(15)
Writing eqn. (15) using the definition of V from eqn. (l), we arrive at the final expression for the efficiency: log, v(Nz4)2
where /r,,=2rr/h and n, is the refractive index of the surrounding dye solution. We can neglect the effect of the presence of the fibre on the total radiation. The total fluorescent power is given by combining eqn. (10) with the density of dye molecules, given by eqn. (8). We then obtain
We define the efficiency of fluorescent capture as the ratio 7 =P,,,/P,,,. From eqns. (9) and (11) this is given by *n m
In our experiment, the refractive index of the dye solution was close to that of the silica taper, so that we may put n, =nP In addition, the pump and fluorescence wavelengths are normally close enough so that we may approximate the modal fields eP and e, as being equal. This allows eqn. (12) to be written in a slightly simpler form:
II=
V4n12
ALA,the numerical aperture of the taper, is given by (n12-n,2)ln. In this form, 7 can easily be seen to be always less than one. Equations (15) and (16) are plotted in Figs. 5 and 6 as functions of V for different values of NA and p/con,. From these curves we can estimate the efficiencies of fluorescent capture for various taper diameters and external dye refractive indices. The smallest tapers used in our experiments had diameters of approximately 0.5 pm. The external dye index was adjusted to 1.44, which, combined with the index of refraction for the cladding of 1.458,corresponded to an NA of 0.23. The fluorescent efficiency (“h)
v Fig. 5. Efficiency as a function of the dimensionless waveguide frequency, V, at different levels of NA (eqn. (16) of main text).
237
efficiency (%) 0.05 0.045 0.04 o.w5 0.03 10
OM5-
15 ‘JQZ “.“_
curves 1
plottedfordifferentvalues of pk,n, 2
3
0.02
20
10
0.015 20
0.01 1.32
1.34
1.36
1.38
1.4
1.42
144
1.46
external index
V5
Fig. 6. Efficiency as a function of the dimensionless waveguide frequency, V, at different levels of &nl (eqn. (15) of main text).
Fig. 7. Efficiencyas a function of external refractiveindex for a 2 pm diameter taper and a wavelengthof 0.526,um.
wavelength was 0.526 pm, yielding an estimated efficiency of 0.2%. For tapers with a 2 pm diameter the corresponding efficiency would be about 0.04%. Results using multimode polished fibres give efficiencies of approximately 10V4 [7]. Similarly, given that the fluorescein dye exhibits a very high quantum yield of 90 f 5% [U-17], with a taper diameter ranging from 2-4 Frn, a typical experimentally derived fluorescent energy taper capture rate was of the order of 10e3 of the input light energy to the dye molecule. Several methods were used for measuring captured fluorescent energy into the taper, including adjusting the pump power to the point at which all input power was absorbed, and measuring the resultant fluorescent energy at the far end of the taper. There is a further more important distinction between the tapered and multimode fibre cases: the much higher optical intensities achievable with a tapered fibre will translate into higher absolute levels of captured fluorescence. We can see this as follows. The total fluorescence will be proportional to the fraction of pump power in the external dye solution. For a multimode fibre with equal excitation of modes, this is 4/3V [18, after correcting a minor error]. For a tapered fibre propagating the fundamental mode, the fraction is 1/V2, as is easily shown from eqn. (14). A typical value for a 200 pm diameter multimode fibre is V=300, whereas for a 2 pm taper Y is about 2.7; in each case we can assume a wavelength of 0.5 pm and an external dye index of 1.44. From this we anticipate the level of fluorescence to be 30 times higher in a taper than in a multimode polished fibre of the same length. Furthermore, most of the pump power is absorbed in a taper. Consequently we conclude that for smalldiameter tapers (about 2 pm), much higher absolute efficiencies are possible compared to multimode fibres. They are also less sensitive to variations in the external refractive index, as shown in Fig. 7. Here we have plotted the efficiency of a 2 pm taper as a function of dye index over the range n = 1.33 (water)-1.44. As
can be seen, the efficiency does not vary by more than a factor of three over the whole index range.
Experimental Materials The indicator, disodium fluorescein, and solvent chosen for our experiments, methanol, as well as pH buffer solutions, were purchased from Fisons Scientific Equipment. For the titration process, glacial acetic acid (17.4 M) and concentrated aqueous potassium hydroxide (100 M) were obtained from Aldrich Chemical Company and Fisons, respectively. The pH levels of the buffers and titration products were verified using a hand-held pH electrode supplied by RS Components with an overall stated accuracy of f0.03 pH units. To ensure a constant external refractive index, appropriate amounts of dimethyl sulfoxide, supplied by BDH Laboratory Supplies, were added and regularly confirmed using a Bellingham and Stanley sugar refractometer.
Apparatus
The single-mode optical fibre used for the sensor was a York Technology SM4.50with a numerical aperture of 0.18 and a cut-off wavelength of 450 nm. The diameter of the nominally circular core was -2 pm. The outer diameter of the fibre was 80 pm, with a cladding refractive index of 1.458. Tapers were fabricated in a manner reported earlier [19] and illustrated in Fig. 3. The resultant tapers used in this study had waist diameters from 0.5 to 10 Frn, as well as typical transmission losses of 0.1 dB. The most optimal diameters were between 2 and 4 pm and had a length of at least 5 mm, which represented a compromise between a sensitive system and a durable one. Narrow tapers tended to break, and wide tapers were not sufficiently sensitive. The tapers were then mounted in a custombuilt dye cell, as shown in Fig. 8, to provide a means of circulating solutions about the taper. The refractive
238
!%oreacence level, arbitraty units
Ll
500
550
575
E
Wavelength, nm /
Fig. 8. Stainless steel die-cast dye cell for tapered fibres: the taper is centred in the cavity and secured by glue; a glass plate is placed over the cell and afiixed with sealant. Solution enters tubing and flows through the cell along fibre taper.
~0
Fig. 10. Fluorescence spectrum of disodium fluorescein in methanol, 1.02X10-* M, measured with fibre taper.
Monochromator
Single
argon-ion
mode
IaSW
Fig. 9. Experimental configuration: titration passes along the taper, mounted in its dye cell. C=optical chopper; L=objective lens; PD = large area photodiode.
index of the solutions ranged from 1.32 to 1.458. Once mounted, the tapers could be easily handled and have been in use for several months. The experimental configuration, shown in Fig. 9, measured output fluorescence level as a function of pH. An argon-ion laser, tuned to the 488 nm line, was used to excite the fluorescent dye around the taper. The indicator in solution released fluorescent energy when excited by the evanescent field of the fibre. The fluorescent emissions from the excited dye molecules were then coupled back into the fundamental guided mode of the taper. The level of these emissions was characterized by using a monochromator. This light was then detected by a large-area photodiode (RS Components, data sheet 12508). Because of the signal levels, intensity measurements were made using lock-in detection (Stanford Research Systems). The lock-in amplifier was linked to a personal computer via an analog to digital data-acquisition card. The fluorescence spectrum found was typical for that of ,bulk absorption, as seen in Fig. 10. Subsequent measurements were then made with the monochromator set at 526 nm, the wavelength of maximum fluorescence. Measurements
A volumetric titration of 100 M potassium hydroxide and 17.4 M acetic acid was carried out to establish a
Volume added 4’ (normalised Utlits)
pH units
Fig. 11. Comparison of volumetric acid-base titration verified by pH meter (solid tine) and fluorescence level in a taper (squares).
baseline for pH level as a function of volume of added base. The amount of acetic acid used was then fixed for all subsequent experiment trials, and the pH levels obtained were verified by the pH meter. This baseline curve, as shown by the solid line of Fig. 11, exhibited the typical sigmoid shape. The data represented by squares in Fig. 11 describe the same titration performed using a tapered fibre with the fluorescein indicator in solution. Approximately fifty sets of data were taken on the described experimental apparatus, which clearly demonstrated the expected curve.
The tapered optical-fibre sensor was found to be very responsive to pH changes. A calibration curve between the level of fluorescent light and pH could be readily determined. However, because the indicator was not a fundamental portion of the sensor, the solutions used had to be pre-conditioned for both refractive index and indicator dye content. A possible cure for this limitation would be to immobilize the indicator in the cladding along the taper. Such ‘active coating’ sensors often provide much higher sensitivity
239
[20]. Many immobilization metbbds are described in the literature. Sol-gel techniques have already been applied with success to optical fibres [l, 211.This would fix both the refractive index and the concentration of the indicator. Further work is under way to apply indicator-doped sol-gel to the taper. In addition, a sensor configuration based on silanization of a taper loop with a radius of curvature of 1 mm is under investigation. In conclusion, we have proposed the use of tapered single-mode fibres as sensing elements in fluorescent sensors. The use of single-mode rather than multimode fibres results in a more stable and repeatable optical launch as well as higher achievable levels of fluorescent capture. We would expect similar advantages when these tapers are applied to absorption sensors.
Acknowledgements We would like to thank Dr H.S. MacKenzie and the referee for helpful comments and discussions. Z.M. Hale would like to thank the United States Air Force Institute of Technology for personal support.
15 LH. Drexhage, in F .D. Schafer (ed.), TopicsinApplicdPhysics, Vol. 1, Dye Losers, Springer, Heidelberg, 1990, p. 161. 16 E.D. Owen, in N.S. Allen and J.F. McKellar (eds.), Phorochemimy of Dyed and PigmentedPolymers,Applied Science Publishers, London, 1980, p. 45. 17 K. Gollnick, T. Franken, M.F.R. Fouda, H.R. Paur and S. Held, Merbromin (mercorochrome) and other xanthene dyes: quantum yields of triplet sensitizer generation and singlet oxygen formation in alcoholic solutions, J. Photochem. Photobiol.. B: Biobev~ 12 (19921 58. 18 D. Gioge, Weakly iiding fibres, Appl. Opr, 10 (1971) 2252-2258. 19 H.S. Mackenzie and F.P. Payne, Saturable absorption in a tapered single-mode optical fibre, Electron Left., 26 (1990) 1744-1745. 20 R.A. Liebennan, Recent progress in intrinsic fiber optic chemical sensing, in R-4. Lieberman and M.T. Wlodarczyk (eds.), SPIE Rx, Vol. 1368, Chemical, Biochemical and Envimnmental Fiber Sensors II, 1990, p. 15. 21 K.T.V. Grattan,G.E. Badmi,A.W.PahnerandA.C.C.Tseung, Use of sol-gel techniques for fibre-optic sensor applications, Sensors and Actuators A, 25-27 (1991) 483487.
Appendix In this Appendix we give the derivation of eqn. (3) in the main text. The Cartesian components of (Ycan be expressed in polar form as
1 B.D. MacCraith, V. Ruddy, C. Potter, B. O’Kelly and J.F. McGilp, Optical waveguide sensor using evanescent wave excitation of fluorescent dye in sol-gel glass, Elecfroon. Lett, 27 (1991) 1247-1248. 2 J.Y. Ding, M.R. Shahriari and G.H. Sigel, Jr., Fiber optic pH sensors prepared by sol-gel immobilisation technique, Electron. Len., 27 (1991) 1560-1562. 3 G. Stewart, .I. Norris, D.F. Clark, M. Tribble, I. Andovic and B. Culshaw, Evanescent-wave chemical sensors - a theoretical evaluation, Int. 1. Optoelecrron.,6 (3) (1991) 227-238. 4 V. Ruddy, B.D. MacCraith and LA. Murphy, Evanescent wave absorption spectroscopy using multimode fibers, J. Apple Phys., 67 (1990) 6070-6074. 5 D. Marcuse, Launching light into fiber cores from sources located in the cladding, 3. Liphtnwe Tech&., 6 (1990) 1273-1279. 6 P.H. Paul and G. Kychakoff, Fiber-optic evanescent field absorption sensors, Appi. Phys. Len., 51 (1987) 12-14. 7 R.A. Lieberman, LL. Blyler and G. Cohen, A distributed fiber optic sensor based on cladding fluorescence, 1. Light~~~ve Technol., 8 (1990) 212-220. 8 E.G. Neumann, Single Mode Fibers: Fundumenfals, Springer, Heidelberg, 1988, p. 305. 9 Ref. 8, p. 86. 10 F.P. Payne and H.S. MacKenzie, Novel applications of monomode fibre tapers, in O.D. Soares (ed.), SPIE Proc., Vol. 1504, Fiber-Optic Metiogy and Standnrdr: Roceedings of the Conference in the Hague, Netherlands, 1991, p. 15. 11 A.W. Snyder and J.D. Love, OpticalWaveguideTheory, Chap man and Hall, London, 1983, p. 442. 12 Ref. 11, p. 444. 13 Ref. 11, p. 451. 14 Ref. 11, p. 338 and p. 341.
ci;=asin
0coscp
cr,=crsinesincp a2 = a cos tl We assume that the direction of Q is distributed isotropically in space. This means that its direction is described by the probability distribution P(0,6p):
qe, (p)= y where
The average (aiaj) is defined by “r ‘;: (aiaj> =J
J aiajP(e,
‘p)
dtJ drp
-0 -0
and a little algebra gives the following: (a&
= (~4
= (a,4
=0
(a~)=(ay2)=(a~)=az/3
The result stated in eqn. (3) then follows.
240
Biographies ZoLiHale received a B.S. in applied and engineering physics from Cornell Universify in 1986, an MBA in multinational operations from St Mary’s University in 1989, and is currently working for a Ph.D. in opticalfibre sensors at Cambridge University. Frank Payne read natural sciences at Cambridge University, graduating in 1975. He remained at Cam-
bridge until 1978 to read for his Ph.D. in physics at the Cavendish Laboratory. He has since held posts at Liverpool and Southampton Universities, and from 1986 has been a lecturer in optical electronics in the Engineering Department at Cambridge University. His research interests are in linear and non-linear propagation in optical fibres and he has published some fifty technical papers.