Inhomogeneous optical filter design with the use of a Riccati equation

Inhomogeneous optical filter design based upon tapered transmission-line th eory is described by deriving an approximate spectral function from a nonli near Riccati equation, which governs the reflection characteristics of tape red lines. We deal with the problem of discontinuity that may occur at both ends of the filter section, and pursue a solution of the nonlinear differe ntial equation via iterations It is shown that the derived spectral functio n Q(k) is equivalent to an improved Q(k)-function used in the optical appro ach when the phase is not considered. Numerical examples are given to illus trate the role of the phase function to obtain refractive index profiles su itable for design specifications. (C) 1999 John Wiley & Sons, inc.