Analysis and design of optical lowpass multilayer filters via noncommensurate to pseudocommensurate system transformation

A method has been developed, based on the transformation of a noncommensurate system to a pseudocommensurate system, to enable the optical lowpass multilayer to be designed and analysed along similar lines as the classical commensurate networks. Using this transformation, the insertion loss of an optical multilayer can be expressed in the polynomial form with frequency-varying coefficients. In other words, the poles of an optical multilayer filter migrate in the complex plane as the frequency changes. By equating the insertion loss of the multilayer at the cutoff frequency to that of the Cheby¿¿chev insertion-loss function, optimised (though not optimum) multilayers having Cheby¿¿chev-like performance in the passband, have been designed.