Abstract

Inverse scattering methods may be used to design coupled mode waveguide filters with either codirectional or contradirectional coupling.¹ The response of these and other spatially periodic waveguiding structures is periodic in the frequency domain, a property also exhibited by digital filters. A fundamental problem in digital filter design is to closely approximate the response of a continuous system. In most cases exact replication is impossible, unless an infinite sampling frequency is used, and large amounts of memory are available. Similar problems arise in the design of corrugated waveguide filters, and are associated with finite frequency of the spatial periodicity, and finite coupling lengths. The approximation problem becomes significant when the desired waveguide filter bandwidth is comparable to the optical carrier frequency, a situation which arises when large coupling coefficients are involved, or the coupling region is short. In such situations, significant distortion of the desired spectral response can occur unless the periodicity of the spectral response is accounted for in the design process. Suitable approximation methods from digital filter theory will be shown to improve the performance of coupled mode filters designed by inverse scattering methods.

© 1993 Optical Society of America