Shuffle-equivalent interconnection topologies based on computer-generated binary-phase gratings

Abstract

Several different shuffle-equivalent interconnection topologies that can be used within the optical link stages of photonic-switching networks are studied. These schemes include the two shuffle, the two banyan, and the segmented two shuffle, which can be used to interconnect two-input, two-output switching nodes. The schemes also include the four shuffle and the four banyan, which can be used to interconnect four-input, four-output switching nodes. (Note: The segmented two shuffle and the four banyan are novel interconnection topologies that were developed to satisfy some of the constraints of free-space digital optics). It is shown that each of these interconnection topologies can be implemented by the use of relatively simple imaging optics that contain space-invariant computer-generated binaryphase gratings. The effects of node type and interconnection topology on the laser power requirements and the optical component complexity within the resulting systems are also studied. The general class of networks nown as extended generalized shuffle networks is used as a baseline for the analysis. It is shown that (2, 1, 1) nodes and (2, 2, 2) nodes connected by two-banyan interconnections can produce power-efficient and cost-effective systems. The results should help identify the architectural trade-offs that exist when a node type and an interconnection topology are selected for implementation within a switching system based on free-space digital optics.

A systematic analysis of equivalence in multistage networks

“…The segmented two-shuffle network is a rather more complex network, proposed by Cloonan et al [11] for use with free-space optical interconnects. This is an example of a three-dimensional (3-D) network, where each switch element is defined by its position in a row and column within each stage.…”

“…Hence, the link address is defined by a triple identifying the row and column occupied by the switch element and the port to which the link is connected. The number of columns (called the segment size in [11]) is . Hence, the number of rows is for a switch.…”

“…Hence, the number of rows is for a switch. The switch illustrated in [11,Figs. 5(b) and 7(c)] features the parameters and .…”

“…for Hence, and observing that must also be a tramline transformation, it must satisfy the following properties: (11) where for This transformation must be bijective if is to be a link permutation. If this property is satisfied, it may be concluded that 3 It is so-called because it is the permutation that results between stage k and the switch outputs if all switch elements downstream of stage k are configured in the "straight-through" position.…”

“…This problem has been addressed many times in the past, using a variety of ad-hoc methods (e.g., [7]- [11]). However, the interconnections between stages in optical multistage switches pose unique problems, such as optical crosstalk in systems based on directional couplers [12] and image rotation in systems featuring polymer fiber-image guides [2].…”