Analysis of nonquarterwave grating by a modified Fouriertransform method.pdfVIP

Analysis of non-quarter-wave grating by a modified Fourier-transform method Tim K. L. Wong, Lukasz Brzozowski, and Edward H. Sargent When unity reflectance is approached, the Fourier-transform method of calculating the reflectance spectrum of an optical grating modulated by a slowly varying envelope becomes unacceptably inaccurate. The modified Fourier transform method of Bovard Appl. Opt. 29, 24 1990 can achieve complete accuracy for quarter-wave gratings. We report herein the extension of Bovard’s method to non-quarter- wave gratings. We demonstrate the accurate deployment of our simplified modified Fourier-transform method to apodized linear gratings and optically apodized nonlinear gratings. © 2002 Optical Society of America OCIS codes: 070.4340, 070.2590, 060.4370, 230.4320. 1. Introduction refractive-index profile is The synthesis of filters is widely and well understood through Fourier-transform FT methods. An entire p 1 4m 3 4m 1 body of convenient computational methods, as well as r x r0 x 40 x 40 , a shared intuition and vocabulary, surrounds the use m p (1) of methods such as apodization to engineer the spec- trum of a filter. where x is the centered double optical thickness, p This is true in some respect for optical filters, but N2,