Generation and evaluation of d-dimensional (d ≥ 3) optical shuffle patterns

Abstract

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.

Architectural framework for optical frequency division multiplexing systems based on regular space-frequency interconnections

“…Equation (21) has been derived by expressing the maximum skew of the KPS (Appendix A). The maximum number of crossed channels is twice the results for KPS (22) and the structure of (19) remains valid.…”

“…The sum of the skews of shuffles depends on the particular decomposition of the coordinates and in turn on the type of the shuffle [22]. The numbering of the data by d-tuples, their proper organization and their interconnection according to d-dimensional shuffles reduces, e.g., the sum of the skews which is shown in the following.…”

“…For example, the sum of the skews of frequency interconnections expresses the number of channels crossed during the generation of the pattern whereas the maximum skew expresses the tuning range of the laser which generates a pattern [22].…”

“…where the skew is defined for each coordinate and the Euclidian distance formula is applied, and for m-dimensional shuffles [22]. Within Appendix A a formula for dL',i is provided for the KPS of shuffles of mth order which bounds the number of crossed frequency channels during the generation of frequency interconnections.…”

Fundamentals of optical interconnections-a review

“…In this section we mention works that deal with the optical interconnections only, without consideration of the overall computing system architecture [30,31,32,33,34,35,36,37,38,39,40,41]. These studies concentrate primarily on optical systems to image arrays of sources onto arrays of detectors in an efficient manner.…”