Optimum nonblocking networks for photonic switching

We systematically minimize the number of elements in a N X N crossconnect consisting of 2 X 2 elements. The derivation covers all cases of interest, including dilated arrangements,vith negligible crosstalk. The relationship between number of elements and important parameters such as crosstalk, depth, and width is obtained. If N is not too large, and if stringent requirements are imposed on loss and crosstalk, then we show that the N X N arrangement is best realized using binary trees. The derivation also applies to arrangements including wavelength routers and channel adding/dropping filters.