Submillimeter wave-guiding on thin dielectric films

Volume 8, number 3

OPTICS COMMUNICATIONS

SUBMILLIMETER

July 1973

WAVE-GUIDING

ON THIN DIELECTRIC

FILMS

M. TACKE and R. ULRICH Max-Planck-Institut fiir FestkiJrperforschung, 7000 Stuttgart, Germany Received 25 May 1973

Tile excitation and propagation of guided submillimeter waves (X = 0.337 mm) is demonstrated on stretched, selfsupporting sheets of polyethylene (PET) and polyterephthalate (PTER). Prism-film couplers serve for input and output. The PTER films show negative birefringence (n o = 1.76, n e = 1.68). An attenuation of 0.25 dB/cm was measured for the TM0 mode on a 12/~m thick PTER fihn.

From the microwave through the submillimeter wave spectral region both tile ohmic losses of metals and the dielectric losses of common insulators increase with frequency. Therefore, in designing submillimeter waveguides [1] one must always compromise between low losses on one hand, and the problems of a wave bound only loosely to an oversized or open guide, on the other hand. The dielectric slab is an open guide which allows adjustment of that compromise to either side, simply by selecting a suitable thickness of the slab. With a thick slab, the field is essentially confined to the interior. Such a guide can negotiate relatively sharp bends without suffering serious radiation losses, but the attenuation of the guide is similar to that of the bulk slab material. In the case of a thin slab (an unsupported dielectric film), however, most of the electromagnetic energy travels outside the dielectric in free space. The attenuation of such a guide is only a small fraction of the attenuation of the bulk film material [2], but the film must be sufficiently smooth and straight. In this work we report on the operation of straight dielectric slab guides at the wavelength X = 0.337 mm of the HCN-laser. The guides have the form of thin, unsupported plastic fihns stretched taut over a metal frame of size 10 X 24 cm 2. Films of polyethylene

(PET) t and polyterephthalate (PTER) + are studied in various thicknesses. The linearly polarized beam of the HCN-laser has an approximately gaussian crosssection with an e --2 power radius of 1 cm. It is coupled into and out of the guides by means of the polyethylene prisms P1 and P2 in fig. 1. Their longest sides measure about 40 mm. Such prism couplers are known from the visible [3,4] ; in the submillimeter range they had recently been used for the coupling to a periodic metallic guide [5]. The dielectric guide and both couplers are mounted on a rotary stage which allows variation of the angle of incidence 0in of the laser beam onto the prism base. The experimental evidence for the excitation and propagation of guided waves on the fihns is twofold: (a) The Golay detector G 1 monitors the intensity of the residual laser beam which has not been coupled into the guide (fig. 1). When the angle 0in is varied by rotating the guide and prisms, the signal at G 1 shows a sharp dip at one angle whose exact position depends on the film material, the film thickness, and the polarization of the laser beam. By careful adjustment of 0in and of the position of prism P1 relative to the input beam and to the guide, the signal from G 1 at this "synchronous angle" [3] can be reduced to less than t SUPRATHEN ® and HOSTAPHAN ® supplied by Kalle AG, D6202 Wiesbaden, Germany.

234

Volume 8, number 3

Is,

OPTICS COMMUNICATIONS

I.

L

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Fig. 1. Experimental arrangement, schematic. Prism P1 is for input, P2 for output. Go, G1, and G2 represents a Golay detector fitted with a large collimating PET lens. This detector can be rotated on a 600 mm long arm around the prism arrangement and permits measuring the directions of the input and output beams. 10% of the intensity at neighboring angles of incidence. The corresponding coupling efficiency of more than 0.90 exceeds the theoretical maximum efficiency of 0.80, valid for a uniform coupling gap [3], because our gap S 1 was slightly tapered and the angle of the taper had been adjusted for maximum depth of the dip [4]. (b) At the same angle of incidence we observe an output beam emerging from prism P2" This beam is measured by Golay detector G 2 which is fixed to the rotary table. The maximum intensity at G 2 occurs when G 1 records the minimum intensity.

w

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PET

From the theory of the prism-coupler [3] it is known that in a coupling position the phase velocity C/np sin 0in of the input field along the prism base is equal to the phase velocity c / N m of the mode excited in the waveguide. Here, c is the velocity of light in free space, np = 1.516 is the refractive index of the prism, and N m the "effective index" of the ruth mode of propagation. Hence we can determine N m = n p sin 0in by measuring the directions of the incident beam and of the two reflected beams G o and G l . The internal direction 0in is then calculated using the prism angle e = 35.05 °. Fig. 2 shows the results of these measurements. In both materials, only the fundamental modes (m = 0) of either polarization have been studied. In the case of PET the measured points lie near the theoretical curves calculated for an isotropic dielectric slab of index n = 1.50. The agreement is only moderate, presumably because of the relatively poor uniformity of the thickness of the PET films. The surface irregularities of these translucent films are visible to the unaided eye. The PTER films, in comparison, have a much smoother surface, i.e., a more uniform thickness. In contrast to the PET films, the dispersion of the PTER films cannot be explained by the assumption of an isotropic dielectric slab. Rather, the PTER films must be birefringent. The film geometry suggests that the c axis of the dielectric tensor of the PTER is

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July 1973

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V o l u m e 8, n u m b e r 3

OPTICS C O M M U N I C A T I O N S

normal to the plane of the film, so that its two other axes lie within this plane. We choose the direction of fabrication (as determined from the supply roll) as the b axis, and the a axis normal to b and c. All measured dispersion points can then be fitted within the experimental uncertainties by n a = n b = 1.76 and n c = 1.68. We conclude that the PTER material behaves optically like a negative uniaxial crystal. The dispersion of the birefringent film in fig. 2 was calculated from the general dispersion formula of a dielectric slab [3, 4] in free space (27T/2t) ~1 IV - 2q~ = rnTr,

J u l y 1973

44/ira and a = 1.5 dB/cm at W = 95/xm, both for the TE 0 mode. On a PTER film of W = 12/xm we have a = 0.25 dB/cm for the TM 0 mode and 2 dB/cm for the TE 0 mode, and at W = 25/ira the attenuation is 1 dB/cm for the TM 0 mode. Whereas on PTER films of IV = 6/3m and 2.5/ira coupling and guidance could be observed, the attenuation was too law to be measured on these films. In order to compare these results among each other and with the bulk absorption ~b of the film materials, we note that the power attenuation of a guide can be written as

(1) a = f l ab + as + ac"

where (27r/X) ~l is the z component of the propagation constant inside the fihn, IV is the film thickness, and 2q) is the phase angle of the internal reflections at the film surfaces.

~1 = [n~ o N2n (na/nc) 2°11/2, = arctan[n2~( N2 - 1)1/2/;i 1] .

(2) (3)

The exponent appearing here is o = 0 for TE and o = 1 for TM polarization; n a and n c are the principal refractive indices of the slab material referring to the axes a and c. Our measurements actually indicated that the thinner PTER films are optically biaxial, because we have observed differences between the effective indices for TE 0 propagation along the a axis and the b axis. The corresponding refractive index difference is very small ( I n a - nbl < 0.001) and was neglected in fitting the dispersion curves. For a 2.5/Jm PTER fihn and at wavelengths in the visible, the birefringence is, however, nmch more pronounced and the film is clearly biaxial. At X = 0.633 ~m, for example, we measured n a = 1.671;n b = 1.634; and n c = 1.491. The uniaxial birefringence may be explained by a preferred in-plane orientation of the benzene rings in the PTER films, and the birefringence by an additional stretching in the a-direction of the films during their fabrication. The wave attenuation of our guides was measured by varying the separation L of the two couplers (fig. 1) in discrete steps and observing the resulting changes of the output signal at G 2. At each position the output coupling gap was readjusted for maximum signal at G 2. In this way the attenuation of the PET films is found as a = 1 dB/cm at a film thickness of IV.= 236

(4)

Here a s denotes the radiation losses due to scattering at irregularities and a c due to curvature. The factor f l gives the reduction of the absorption losses for propagation along the guide as compared to propagation in the bulk film material. By a detailed calculation of the dielectric losses, involving integrations over the wavefunctions of the dielectric slab, one can show that f l may be written a s f l = 2 C W E / n P . Here w E is the average electric energy stored in the dielectric per unit length of the guide, n is the refractive index of the dielectric, and P is the power carried by the guide. Because w E and P are proportional to each other, the above expression for f l is independent of the absolute power level P. The resultingfl is shown in fig. 3 as a function of the film thickness. For very thin films we have f l ~ 1, expressing the fundamental idea of the "microguide" [2]. In the limit W ~ )k the expression f o r f l can be simplified to fl

= 2rr2n( n2-

1)(W/X) 2 n 60.

(5)

This shows that the TM 0 absorption l o S s f l a b is less than the TE 0 absorption loss by a factor n 6, which is practically one order of magnitude or more. The strict computation o f f l gives the somewhat surprising result that for TE modes the factor f l becomes slightly larger than unity when the film thickness exceeds a critical value, which is W(0) ~ 0.5X crit for the TE 0 mode in PTER. This means that a TE m mode guided in a thick film W > w(m) " Crlt suffers a higher absorption loss than a free wave in the bulk film material. The reasons for this phenomenon are that for TE modes the average electric energy w E in

Volume 8, number 3

OPTICS COMMUNICATIONS

July 1973 _ _10 3

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Fig. 3. Calculated reduction factor fz of the absorption losses () and minimum permissible radius Rc of curvature (. . . . ) as functions of the film thickness W. In calculating fl for the PTER film birefringence was neglected and an average film index n = 1.72 was used. Measured attenuations fitted to fl curves ,; values offl derived from measurement of total attenuation o for TM0 and ~ for TE o polarization. The vertical bars represent the experimental error. the dielectric exceeds the magnetic energy w M there, and that the guide is a slow-wave structure, Ugroup < c / N m. In thick films the combination of these two effects outweighs the reduction of the absorption which is due to the fact that only a fraction of the total guided power P travels inside the dielectric. The resulting net effect on f l is only small, however, the m a x i m u m f 1 in fig. 3 b e i n g f l = 1.013. For very thick films, of course, f l -+ 1. A direct comparison of the measured attenuations with fig. 3 is difficult because the bulk absorption c% and the scattering loss c~s are not known. Therefore, we have tentatively ignored the scattering loss, a s = 0, and have determined ~b from the highest ones of the measured attenuation values, using the calculated f l ' The results are c% = 1.9 dB/cm for PET, and ~b = 26 dB/cm for PTER. With these numbers experimental values f l = ~/~b were then determined for the remaining attenuations, and are shown by the open circles in fig. 3. The agreement with the theoretical f l curves is only moderate, indicating that the scattering losses probably do play a role (in PET) and/or that the bulk absorption ~b may be anisotropic (in PTER) or may be different for samples of different thickness. For the application of such guides, e.g. for spectroscopy inside narrow cryostats or magnets, the attenua-

tion c~c due to curvature must be considered, too. Therefore, we have plotted in fig. 3 also the minimum permissible radius of curvature, Rc, as a function of the film thickness. R c was calculated from Marcatili's theory [6] for an attenuation of c% = 0.01 dB/cm. This particular choice of ~c is not critical, because c% increases very drastically if the permissible curvature 1/R c is exceeded just slightly. Whereas the use of the TM 0 mode was advantageous for low absorption loss f l O~b, the other polarization (TE0) is better with respect to low curvature loss. Both these statements are expressions of the fact that the TE 0 mode is bound more tightly to a given film than the TM 0 mode From a comparison of the f l and R c curves of fig. 3 it can be concluded that for a fixed R c the choice of the TM polarization permits an f l which is, in the limit W ~ )t, smaller by a factor n 2 than t h e f 1 for TE polarization. In a preliminary experiment we have also tested a straight dielectric strip line of l m length and 3 X 0.03 mm 2 cross section. The strip was cut from a PET sheet, it was supported by little flaps which had been left standing out from both edges of the strip at regular intervals of 300 mm. The laser beam was coupled into the TM 0 mode by focussing it on one end of the strip, and the output was done similarly by 237

Volume 8, number 3

OPTICS COMMUNICATIONS

butting the other end of the strip directly against the window of the Golay detector. The attenuation of this guide was determined as 0.07 dB/cm by systematically shortening the length of the guide. In summary, we have demonstrated the operation of dielectric slab waveguides at the submillimeter wavelength X = 0.337 mm. The influence of the fihn thickness on the absorption loss and on the permissible curvature was discussed. Such guides may become useful for integrated optical circuits and for spectroscopy in the submillimeter region. We would like to thank D. B6hme for his help with the numerical computations, and W. Dreybrodt for

238

July 1973

making available to us the HCN laser for the present work as well as for the work reported earlier in [5].

References [ 1] D.J. Kroon and J.M. van Niewland, in: Spectroscopic Techniques, by D.H. Martin, Ed., North-Holland Publishing Co., Amsterdam (1967). [2] A.E. Karbowiak, Electronics Lett. 1 (1965) 48. [3] P.K. Tien, R. Ulrich and R.J. Martin, Appl. Phys. Eett. 14 (1969) 291. [4] R. Ulrich, J. Opt. Soc. Am. 61 (1971) 1467. [5] R. Ulrich and M. Tacke, Appl. Phys. Lett. 22 (1973} 251 [6] E.A.J. Marcatili, Bell System Techn. J. 48 (1969) 2103.