Design of Talbot array illuminators for planar optics

Markus Testorf, Jürgen Jahns, Nikolay A. Khilo+, Andrey M. Goncharenko+

An array illuminators is an optical device that forms a uniform array of equal intensity spots. Such spots are required, for example, to illuminate 2-D arrays of modulators in optical interconnection systems. Talbot array illuminators use near field diffraction at specially designed phase gratings [1] for this purpose. The ouput spot array is located at rational fractions of the Talbot distance. Here we investigate the performance of a planar- integrated Talbot array illuminator.

The situation we want to analyze is depicted in Fig. 1. A plane wave is reflected off a phase grating under a certain angle . Our goal is to form an intensity spot pattern on the top surface after one double pass of the light wave as indicated in the figure. From the analysis of the Talbot effect for oblique angles of light propagation it appears, that the Talbot distance and thus the location of fractional Talbot planes are different for both lateral coordinates [2]. For a desired shape of the output spots it is either necessary to choose the grating periods, the deflection angle and the propagation distance of the light wave conveniently, or to tolerate a certain derogation of the spots due to the mismatch introduced by off-axis propagation.

Fig. 1: Planar integrated Talbot array illuminator

Other reasons for a derogation of the output pattern are the finite size of the grating and wave aberration which occur due to off axis light propagation. To study all influences simultaneously, we numeri-cally simulated the output patterns of Talbot array illuminators with respect to the angle . For a substrate of thickness mm we found, that more than 90 % of the light energy is diffracted towards the area of the ideal output spots, for angles a between and . Fig. 2 shows the simulated output, where a design for quadratic spots was assumed. Here, the spots are smeared out mainly due to the mismatch of the Talbot distances in x and y.

Fig. 2: Simulated spot array of a planar integrated Talbot array illuminator. Low intensities are enhanced to demonstrate the behavior of aberrations.

+ Dr. Khilo and Prof. Goncharenko are with the Belarussian Academy of Sciences.

[1] A. W. Lohmann, Optik 79, 41-45 (1988).

[2] M. Testorf, J. Jahns, N. A. Khilo and A. M. Goncharenko., "The Talbot effect for oblique angles of light propagation", this report.

[3] M. Testorf, J. Jahns, N. A. Khilo and A. M. Goncharenko, "Design of Talbot array illuminators for planar optics", Opt. Comm. (submitted).