power of the Raman effect could be reduced to around one tenth of that for the standard single-mode fibre.10 Based on calculations, the minimum beam spot size is in the wavelength region of X = 1-5AC.6 The minimum beam spot sizes for fibres A and B are estimated to be 112 /im and 1-28 /im. In addition, high coupling efficiency between these fibres and LDs or SLDs is expected, according to the high-NA value shown in Table 1. Conclusion: This experiment has clarified the possibility to fabricate high-An, small-core single-mode fibres with a low transmission loss. It was also found that these fibres have excellent features including bending, optical power intensity and dispersion. The results obtained suggest that these highAn, small-core single-mode fibres can be applied to nonlinear optical experiments. Detailed experimental results on nonlinear effects and coupling efficiencies will be reported elsewhere. S. SUDO 22nd May 1986 T. HOSAKA H. ITOH K. OKAMOTO NTT Electrical Communications Laboratories Tokai, Ibaraki-ken 319-11, Japan References 1 CROFT, T. D., and RITTER, J. E.: 'LOW loss dispersion-shifted single- mode fibre manufactured by the OVD process'. OFC'85, Tech. dig., 1985, Paper WD2, pp. 94-95 2 YAMAGUCHI, R., NISHIDA, K., ABIRU, T., MIYAMOTO, M., a n d FUKUDA, o.: 'Effect of an additional ring profile on transmission characteristics of 1-55-jon dispersion shifted fibres'. OFC/IGWO'86, Tech. dig., 1986, Paper WF3, pp. 96-97 3 KAWACHI, M., TOMARU, s., EDAHIRO, T., and SUDO, s.: 'Fabrication method of single-mode optical fibre preforms'. US patent 4,345, 928, filed 19 Sept. 1980 normal to the crystal surface arising from the mixing of two counterpropagating surface-acoustic waves (transverse-vertical convolver, TVC). On the other hand, Monks et al.1 reported a new type of convolver using the detection of the bilinear electric polarisation parallel to the crystal surface and perpendicular to the power flow direction of SAWs (transverse-horizontal convolver, THC). In comparison with TVCs, the THC has the advantages that its output electrode structure reduces the possibility of unwanted 'fold-over' convolution from fabrication defects and increases design flexibility. However, a THC on LiNbO3 has some problems in that its efficiency is less than that of the highly efficient Y-Z LiNbO3 TVC and that for the THC there is not such a precise theory as that reported by Ganguly et al.2 for a TVC. In this letter we propose the definition of the figure of merit (M-value) and a practically effective equivalent circuit which have been obtained by the results of precise analysis for the model of a THC. Next, this letter presents the results of calculations about the M-value for a THC with arbitrary crystal orientation and propagation direction on LiNbO3, and shows the existence of a crystal cut and the direction of propagation with large M-value and large electromechanical coupling coefficient K2 of SAWs in LiNbO3. Also, we report experimental results. Figure of merit and equivalent circuit for THC: The definition of the M-value for a TVC2 is not useful for designing a THC3 because it depends on the design parameter of a THC. So, the M-value for a THC should be given by the quantity which shows the electrical nonlinearity of the crystal substrate only and is independent of its design parameter such as frequency and configurations of crystal substrate and electrode to compare some THCs with several crystal cuts and directions of propagation. From this standpoint, we have performed analysis about the model of a THC shown in Fig. \b by 2<JU 4 SH1BATA, N., KAWACHI, M., SUDO, S., a n d EDAHIRO, T.: 'Low-lOSS high-numerical-aperture for optical fibre fabricated by VAD method', Electron. Lett., 1979,15, pp. 680-681 5 BERKEY, G. E.: 'Fabrication of 0-4-N.A. fibres by the outside process'. OFC/IGWO'86, Tech. dig., 1986, Paper TUG3, pp. 36-37 6 HOSAKA, T., SUDO, s., OKAMOTO, K., and HORIGUCHI, M.: 'Investiga- tion of single mode fibres with zero dispersion in 1-5 nm wavelength region'. Paper of technical group, TGOQE 85-137, 1985 (in Japanese) 7 OKAMOTO, K., TAKADA, K., KAWACHI, M., a n d NODA, J.: ' A l l - PANDA-fibre gyroscope with long-form stability', Electron. Lett., 1984, 20, pp.429-430 8 SHIBATA, N., TSUBOKAWA, M., OHASHI, M., a n d KITAYAMA, K.: 'Birefringence properties of a coiled single-mode fibre and its use in a tuned optical amplifier'. CLEO'85, Tech. dig., 1985, Paper THP4, pp. 226-228 9 TAI, K., and TOMITA, A. : '50 x optical fibre pulse compression at 1-319 //m', Appl. Phys. Lett., 1986, 48, pp. 309-311 10 STOLEN, R. H.: 'Fibre Raman laser', Fibre & Integrated Opt., 1980, 3, pp. 21-51 11 MATSUMURA, H., and SUGANUMA, T.: 'Normalisation single-mode fibres having an arbitrary index profile', Appl. Opt., 1980, 19, pp. 3151-3158 THEORETICAL AND EXPERIMENTAL STUDY OF TRANSVERSE-HORIZONTAL CONVOLVER Indexing terms: Ultrasonics, Convolvers The letter presents the results of theoretical and experimental studies for the transverse-horizontal convolver (THC) fabricated on LiNbO 3 . First, the definition of the figure of merit for the THC is proposed and, secondly, the existence of the crystal orientation and the direction of propagation with high efficiency and large electromechanical coupling coefficient for an LiNbO. SAW THC is shown. Introduction: Most SAW convolver designs have been based on the detection of the bilinear electric polarisation field ELECTRONICS LETTERS 31st July 1986 Vol.22 No. 16 Fig. 1 a Commonly used THC b Model of THC used for analysis solving the nonlinear piezoelectric equation of motion subject to appropriate boundary conditions, as Ganguly et al.2 have done for a TVC. Thus we have obtained the following results that the M-value for the THC can be defined by: M = (C/W) (1) where Q'™ is the root mean square of the short-circuit charge stored in the output electrodes, P x and P2 are the powers in the two incident SAWs, / is the beam width of the SAW and b is the integration length determined by the output electrode. From this definition and the analysis of output admittance, we have also obtained an equivalent circuit for the model of the THC, as shown in Fig. 2a, where / s and C are the short-circuit current and the static capacitance of the output electrode, respectively, expressed as Is = = (2) (es33-(es32)2/e\2)j (3) and G is the output conductance which shows the loss arising from the bulk wave generation. However, G is very small in comparison with 2coC. Thus we can finally obtain the equivalent circuit for the model of the THC as shown in Fig. 2b. Although we usually use a THC with the output electrode 835 configuration shown in Fig. la, we can assume the fact that, even in this electrode configuration, the flux of horizontal bilinear electric displacement, which is almost within one , Fig. 2 Equivalent circuit for THC wavelength of SAW of the surface, almost ends in the output electrode at the short-circuit condition. So the abovementioned definition offigureof merit is valid for not only the model of a THC but also the commonly used THC, and the equivalent circuit for the commonly used THC can be obtained by changing the value of the output capacitance of the model of a THC to the measured value of that of the commonly used THC. Using all nonlinear constants of LiNbO3 which had been determined in our laboratoryf we have calculated M-values for THCs about all independent crystal cuts and the propagation directions. It is necessary for a THC to have not only a large M-value but also a large K* of the SAW. Therefore, we have concluded that the propagation directions near the direction of + 5° from the + Z-axis to the — 7-axis on the X-cut plane are optimum for an LiNbO3 steering angle of the SAW is 407°. The wavelength at centre frequency and width of input beams were k = 33-75 /an, corresponding to about 100 MHz, and / = 2 mm, respectively, and the integration length was b = 8 mm. Thus, we have obtained experimental results M = 3-3 ± 0-3 x 10"14(C/W) as plotted in Fig. 3. Discussion: In the preceding Section we showed the existence of the crystal cut and the direction of propagation with large M-value for a THC and large Kj on LiNbO3. Because the definition offigureof merit for a THC differs from that for a TVC,2 to compare this (90°, 90°, 95°) THC with the highly efficient Y-Z TVC as regards efficiency, we have calculated the internal bilinear conversion factor Finr4 about these two types of elastic convolver as a function of frequency as shown in Fig. 4. From this Figure we can find the fact that, at high frequency, the (90°, 90°, 95°) THC and Y-Z TVC of LiNbO3 have almost the same efficiency. Y. CHO K. YAMANOUCHI Research Institute of Electrical Communication Tohoku University Sendai980, Japan References 1 — M -K ^ - ^ ^ $ A 2 , . . it o T o 3< 3 \ X Z / -2 y \ 1 A / ' \J / i i r~\ \ / n 0 XY 30 4 V 90 150 180° 120 X Z .degree Fig. 3 Theoretical and experimental values of figure of merit for THC and K2 of SAW on X-cut ofLiNbO3 THC, as shown in Fig. 3. This crystal cut and propagation direction can be identified through Euler angles of (90°, 90°, 95°). So, in this letter we call the THC with this crystal cut and propagation direction the (90°, 90°, 95°) THC. Experiments: To confirm the above-mentioned fact, we have measured the M-value of the (90°, 90°, 95°) THC whose beam- KINO, G. S., LUDVIK, S., SHAW, H. J., SHREVE, W. R., WHITE, S. J., a n d WINSLOW, D. K.: 'Signal processing by parametric interactions in delay-line devices', IEEE Trans., 1973, SU-20, pp. 162-173 5 LIM, T. c , KRAUT, E. A., and THOMPSON, R. B.: 'Nonlinear materials for acoustic-surface-wave convolver', Appl. Phys. Lett., 1972, 20, pp. 127-128 LASER COUPLING TO SINGLE-MODE FIBRE USING GRADED-INDEX LENSES AND COMPACT DISC 1-3 urn LASER PACKAGE Indexing terms: Optical communications, Optical couplers A 1-3 fim laser in a compact disc package is coupled to single-mode fibre using two graded-index lenses in a nearly confocal scheme. An increase in the alignment tolerance at the lens-lens interface by a factor of six suggests the design for a potentially very low-cost connectorised laser package. The coupling efficiency of approx. 6% (—12 dB) is shown to be adequate for local loop applications. -60 -70 -80 (90°. 90°. 95°) THC -90 YZ TVC 10 10 10 J frequency, MHz Fig. 4 Internal bilinear conversion factor Fint against frequency for (90°, 90\ 95°) THC and Y-Z TVC In this calculation, we have taken the parameters as the integration length b = 30 mm, beam width of SAW / = 2 mm, thickness of substrate d = 0-5 mm and load resistance RL = 50 Q for both types of convolver. The value of the figure of merit for the Y-Z TVC, M = 1-21 x 10~ 4 Vm/W, has been used 5 and, for a (90°, 90°, 95°) THC, we have calculated Fim about the model of the THC shown in Fig. 16 t CHO, Y., and YAMANOUCHI, K. : submitted to J. Appl. Phys. 836 MONKS, T. J., PAIGE, E. G. s., and WOODS, R. a : 'SAW and SSBW convolvers utilising bilinear field in various directions'. Proceedings of ultrasonics symposium, 1983, pp. 402-405 1 \ 60 3 2 \ MONKS, T., PAIGE, E. G. s., and WOODS, R. c.: 'SAW convolvers using the transverse-horizontal bilinear field', Electron. Lett., 1983, 19, pp. 466-467 2 GANGULY, A. K., and DAVIS, K. L. : 'Nonlinear interactions in degenerate surface acoustic wave elastic convolvers', J. Appl. Phys., 1980, 51, pp. 920-926 \ \ 22nd May 1986 Introduction: In new transmission applications such as singlemode distribution in the subscriber loop, very low-cost, highspeed light sources are needed. For the loop environment, these devices must also operate over wide temperature ranges ( —40°C to +85°C). Injection lasers are ideal for the speeds being considered (as high as 560 Mbit/s). Present laser prices, however, are very high due to packaging complexity and yield when selected according to stringent requirements appropriate for long-haul applications. Prices would be reduced significantly if simple packaging schemes could be utilised. Many conventional packaging approaches involve direct fibre-to-laser coupling, or coupling with a single lens element, usually a part of the fibre end. Although high coupling efficiencies (40 to 60%) are achieved, such schemes are very sensitive to lateral displacements, making their use over wide temperature ranges questionable. Alternative, confocal lensing schemes have also been used,1"3 with two or more lens elements. This technique relaxes lateral alignment tolerances by trading off lateral displacement sensitivity for increased angular sensitivity and slightly reduced coupling efficiency. In this letter we examine a confocal arrangement, which, in conELECTRONICS LETTERS 31st July 1986 Vol. 22 No. 16

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