  High-speed photonic switching networks can switch optical signals at the rate
of several terabits per second. However, they suffer from an intrinsic
crosstalk problem when two optical signals cross at the same switch element. To
avoid crosstalk, active connections must be node-disjoint in the switching
network. In this paper, we propose a sequence of decomposition and merge
operations, called conjugate transformation, performed on each switch element
to tackle this problem. The network resulting from this transformation is
called conjugate network. By using the numbering-schemes of networks, we prove
that if the route assignments in the original network are link-disjoint, their
corresponding ones in the conjugate network would be node-disjoint. Thus,
traditional nonblocking switching networks can be transformed into
crosstalk-free optical switches in a routine manner. Furthermore, we show that
crosstalk-free multicast switches can also be obtained from existing
nonblocking multicast switches via the same conjugate transformation.
