A formalism is presented for determining the amount of symmetry of optical interconnects in terms of their required number of degrees of freedom. The formalism is based on matrix representation of optical interconnects and shows that the relevant property of the interconnect matrix is its rank. On the basis of this formalism, an optical arrangement is proposed for the implementation of general interconnects. This arrangement exploits the symmetry of the interconnects to increase the space–bandwidth-product capabilities, up to the limit imposed by information theory. Some examples that illustrate the effectiveness of our approach are also given.
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