Array interconnection for rearrangeable 2-D MEMS optical switch

Two-dimensional (2-D) microelectromechanical systems (MEMS) optical switches can be constructed by arranging the MEMS-actuated micromirrors as an array. We consider here the switching capability, routing, and optimization of the rectangular array interconnection on which the capability and efficiency of 2-D MEMS switches depend. The switching capability of a rectangular array is proved analytically. Two routing algorithms, namely, the most-bend routing and the least-bend routing, are developed, which, respectively, maximize and minimize the number of 2 * 2 switches in the "bend" state. A method of counting the number of permutations realizable with a given number of switches in the "bend" state is proposed to evaluate the performance of both routing schemes. The understanding of the underlying interconnection pattern enables us to study the problem of constructing rearrangeable optical switches of arbitrary size.