Optimum nonblocking networks for photonic switching

We systematically minimize the number of elements in a N/spl times/N crossconnect consisting of 2/spl times/2 elements. The derivation covers all cases of interest, including dilated arrangements with 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/spl times/N arrangement is best realized using binary trees. The derivation also applies to arrangements including wavelength routers and channel adding/dropping filters.