Problems arising throughout the (combinatorial) design of 3-D lightwave circuits (3-D LCs) are briefly addressed in the following. (1) The implementation of MxN-gon prism switches. (2) The routing of MxN-gon prism switches and (3) the routing of all-optical 3-D grids. (4) The alternative to (1), the embedding of logical switch architectures onto all-optical 3-D grids and (5) dual switches. (6) The improvement of the switches towards the crossbar and (7) the generalization of all-optical grids to any N 3.

We use d-dimensional shuffle patterns to describe optical frequency division multiplexing. A complexity measure is derived from the geometry of common shuffle patterns and is extended to evaluate d-dimensional shuffle patterns. The least complexity of the generated patterns is determined with respect to the size and the dimension of the data sets. Trade-offs between the dimension of the data sets and the frequency-conversion-based processing of the pattern generation are discussed. A comparison of multiplexing on vectors and arrays is presented. The relation of the complexity analysis to the design of optical frequency division multiplexing systems is briefly discussed.

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The transformations of a two-dimensional shuffle on a 4 × 4 array into a one-dimensional shuffle on a vector of length 16 (and vice versa) are recognized as basic building blocks for the switch-preserving transformation of shuffle patterns of any size. [The switch-preserving transformation means the transformation of one-dimensional shuffles into two-dimensional and d-dimensional shuffles (d ≥ 3) and vice versa without the subdivision of switches.] The switch-preserving transformation of shuffle patterns on large arrays is defined recursively by means of the presented basic building blocks. Thi concept of the transformation is restricted to the two-dimensional symmetric generalized perfect shuffle on arrays with equal sides (squares) being an even multiple of four. (Generalized means arbitrary decomposition of each coordinate, and thus an arbitrary shuffle may be defined; perfect is the counterpart to imperfect and refers to the regularity or absence of failures; symmetric means the same decomposition of the data length for both coordinates.) The relationship of the results to multistage interconnection networks is clarified.

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