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One-copy algorithm for optical 2-D shuffles: theory and experiment

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Abstract

A light efficient algorithm is important for any optical computer or optical interconnection system. Here, we discuss a light efficient procedure called the one-copy algorithm which implements various types of shuffle on a 2-D array of channels.1 These optical 2-D shuffles can be used in parallel signal processing, computing, and telecommunication routing systems. We found that for a 2-D array having rm channels (where r is prime and m is even), both 2-D rk-folded and separable shuffles can be achieved using this algorithm in a single stage whenever 1 ≤ k ≤ m/2. The 2-D inverse folded rk shuffle using the one-copy algorithm can be built in a single stage only when k = m/2. On the other hand, the 2-D inverse separable rk shuffle using the one-copy algorithm can be realized in a single stage whenever 1 ≤ k ≤ m/2. Multistage implementations of the one-copy algorithm for any inverse shuffles are possible. The number of stages required in this case is dependent on k,m, and the type of inverse shuffle performed. Experimental results on the holographic implementation of 2-D perfect shuffles for sixty-four channels based on the one-copy algorithm with high light efficiency are presented.2

© 1991 Optical Society of America

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