OPTIMAL FINITE-APERTURE FILTERS WITH MAXIMUM EFFICIENCY

A new technique for improving the frequency response of optical filters is described. The technique applies to a wide class of finite-aperture filters, including Bragg-reflector filters, multiplexers, and digital filters. The optimum (mimimax) design that approximates the desired frequency response with the greatest efficiency is derived. Our design is, in general, simpler and more efficient than the well-known Chebyshev approximation in the theory of digital filters. Here we solve the general mimimax problem and treat a special case (a linear filter). Application of our theory to Bragg-reflector filters is given in a forthcoming paper.