Patent ID: 6314220
Filing Date: 2001-11-06
Classification: G02B,G06K,H04J

Abstract:
A waveguide operative to produce a reflected optical signal having a spectral profile corresponding to a product of a spectral profile of an input optical signal and a predetermined complex-valued spectral filtering function, said waveguide comprising: a plurality of spatially distinct subgratings, each subgrating possessing a periodic array of diffraction elements, wherein the subgratings are situated and configured based on the predetermined complex-valued spectral filtering function, wherein each of said subgratings has an amplitude, spatial phase shift, beginning and ending position, and spatial period (A.sub.i, x.sub.i, x.sub.i.sup.a, x.sub.i.sup.b, and .LAMBDA..sub.i, respectively), wherein the amplitude (A.sub.i) and a phase (-j2.pi.x.sub.i /.LAMBDA..sub.i) of each of said subgratings corresponds to a modulus and an argument, respectively, of a complex parameter .alpha..sub.i, wherein .alpha..sub.i can be expressed as ##EQU4##wherein .upsilon. is frequency, n.sub.0 is average waveguide refractive index, .beta.=2/c, c is the vacuum speed of light, d.sub.i =x.sub.i.sup.b -x.sub.i.sup.a, m.sub.i is a diffraction order of an ith subgrating, F.sub.i (.upsilon.)=(jC/N)sinc(.pi.n.sub.0 d.sub.i [.upsilon..beta.-1/(n.sub.0.LAMBDA..sub.i ]), C is a constant, N is a number of subgratings, T(.upsilon.) is a complex-valued spectral filtering function, and j is a square root of -1.