Optimised design of even-order optical low-pass and high-pass multilayer filters by method of coefficient matching

The problem encountered in the optimised design of an even-order low-pass multilayer is twofold: (a) The Cheby¿¿chev polynomial, widely used in multilayer optimisation, is found to be incompatible with the transmittance of even-order multilayer filters. (b) Design by coefficient-matching results in a system of over-determined nonlinear equations with one more equation than the number of unknowns. The problem is solved by generating a new type of optimising polynomial, the coefficients of which are adjusted dynamically to accommodate for the particular filter being designed. The coefficients of the multilayer polynomial and those of the optimising polynomial can be made to converge to effect a perfect match. Multilayers thus designed exhibit an optimised Cheby¿¿chev-like performance in all spectral regions of interest.