Comment on Optimised implementation of real-time discrete Wigner distribution

3 NELSON, B. P., BLOW, K. J., CONSTANTINE, P. D., DORAN, N. J., LUCEK, J. K., MARSHALL, I. w., and SMITH, K.: ‘All-optical gigabit switching using a nonlinear optical loop mirror’, Elecrron. Lett., 1991. 27, (9), pp. 704-705

and STEGEMAN, G. I.: ‘Picosecond nonlinear polarisation switching with a fiber filter’, Appl. Phys. Lett., 1988, 53, pp. 837-839 5 FELOMAN, s. F., WEINBERGER, U. A., and WINFUL, H. G . : ‘Observation

of polarisation instabilities and modulational gain in a low- birefringence optical fiber’, Opt. Lerr., 1990, 15, pp. 311-313 6 LEFEVRE, H. c.: ‘Single-mode fibre fractional wave devices and pol-

arisation controllers’, Electron. Lett., 1980, 16, pp, 778-780 7 HARMON, R. A.: ‘Polarisation stability in long lengths of monomode

fibre’, Electron. Lett., 1982, 18, pp. 1058-1060

8 WINFUL, H. G.: ‘Self-induced polarisation changes in birefringent optical fibers’, A p p l . Phys. Lett., 1985, 47, pp 213-215

9 DORAN, N. I., FORRESTER, D. s., and NAYAR, B. K.: ‘Experimental investigation of all-optical switching in fibre loop mirror device’, Electron. Left., 1989, 25, pp. 267-268

IO TAI, K., HASEGAWA, A., and TOMITA, A.: ‘Observation of modulation- al instability in optical fibers’, Phys. Rev. Lett., 1986, 56, pp. 135-138

11 SNYDER, A. w., and mm, Y.: ‘Nonlinear fiber couplers: switches and polarisation beam splitters’, Opt. Lett., 1989, 14, pp. 517-519

4 TRILLO. S., WABMTZ, S., FINLAYSON, N., BANYAI, W. C., SEATON, C. T.,

C O M M E N T

OPTlMlSED IMPLEMENTATION

OF

DISTRIBUTION

REAL-TIME DISCRETE WIGNER

Owing to the Hermitian symmetry of the Wigner kernel, the above Letter’ proposed a fast algorithm to compute the dis- crete Wigner distribution (DWD) by an N/2-point F F T

wk(n) = x d ( n ) . xf(-n) = even (n)

+

n = O ,

+

+

CWl

+

However, the last half part of the D W D is not equal to zero as the author claims; it needs to be added and computed as follows : 2 sin 2nklN N 2 k = 1, 2 , . _ . , - - _{1 (4)} N - 1 D W D ( I , 0) = Re [wk(n)] k = 0 ( 5 ) n = o N Re [wk(n)] k = - 2 (6) S.-C. PE1

Department of’Electrica1 Engineering National Taiwan University Taipei, Taiwan, Republic of China

30th April 1991

ELECTRONICS LETTERS 20th June 1991 Vol. 27 No. 13

Reference

1 EILOUTI, H. H., and KHAORA, L. M.: ‘Optimised implementation of real-time discrete Wigner distribution’, Electron. Lett.. 1989, 25,

( I 1). pp. 7 0 6 7 0 7

INTEGRATED ACOUSTO-OPTIC COLLINEAR TE-TM MODE CONVERTORS FOR 0.8pm OPTICAL WAVELENGTH RANGE

Indexing terms. Acousto-optics, Surface-acoustic-wave devices, Convertors, Integrated optics

Low power, narrowband integrated acousto-optic T E - T M mode convertors for the 0 - 8 p m optical wavelength range have been developed. Acoustic drive power of less then lOmW was required for 96% conversion etliciency. The 0.32 nm optical bandwidth corresponding to the acoustlc bandwidth of 138 kHz achieved is the narrowest reported to date for a T E - T M mode convertor.

Introduction: Surface acoustic wave (SAW) controlled inte- grated optical TE-TM mode convertors are used for several applications, e.g. as tunable optical filters in wavelength divi- sion multiplexed fibre optic communication systems,’.’ in narrow-linewidth extended cavity semiconductor lasers as intracavity wavelength filters4 or in the optical spectroscopy,’ or as acousto-optic frequency shifters’ etc. Recently, an unconventional X-Y (X cut, Y propagation) interaction geometry on LiNbO, was proposed, which results in a signifi- cant reduction of the power requirement.’ All TE-TM mode convertors known up to now have been developed for the wavelength range 1.3-I.55pmi.* or earlier with the conven- tional Y-X geometry for the He-Ne wavelength of 0 .633~ 1~1,~ for experimental convenience. The wavelength range in the vicinity of 0.8 pm, for which a large choice of cheap semicon- ductor lasers, LEDs and optical fibres exists has not yet been considered. In this wavelength range, besides the above men- tioned general application areas of the T E - T M mode conver- tors, several sensor applications can be envisaged; one example is the recently proposed acousto-optic gas sensor.6

In the 0.8pm optical range, the phase matching is achieved with shorter acoustic waves (as compared to the 1.3- 1.55pm).4 The smaller penetration depth of the SAWS leads to higher power densities and better overlap with the optical fields and, consequently, significantly lower acoustic power requirements can be expected. Additionally, the bandwidth of the mode conversion, which is directly proportional to the SAW wavelength, will also be narrowed.

We report on the development and investigation of col- linear acousto-optic TE-TM mode convertors for the 0.8 pm wavelength range. Using X-Y LiNbO, samples, we were able

to construct efficient devices with low acoustic power require- ments and with very narrow bandwidth, especially suitable for filter applications.

Fabrication of devices: An integrated optical TE-TM mode

convertor essentially consists of an optical waveguide and a suitably designed interdigital transducer (IDT) for exciting the SAWS necessary to achieve phase matching. The optical channel waveguides were produced with Ti diffusion on 10 x 30”’ LiNbO, samples. O n the surface of the samples 68nm thick and 2.5 and 3pm wide, vacuum evaporated Ti stripes were photolithographically formed. The diffusion was performed for 7 h at 1050°C in 0, atmosphere using a closed platinum box. After polishing the endfaces of the samples, the near-field patterns of the two fundamental modes were investi- gated (at 0.84pm wavelength) showing a pure monomode behaviour and a good overlap of the modal fields.

In a further technological step, the IDT was photolitho- graphically patterned on the surface of the samples. It consist- ed of four pairs of 150nm thick A1 fingers with 2.6pm width, and spacing between the fingers. The aperture of the trans- ducer ( - 1 mm) was equal to 100 SAW wavelengths to mini- 1211