IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 39, NO. 1, JANUARY 2003 91 Optimization of Refractive Index Sampling for Multichannel Fiber Bragg Gratings Alexander V. Buryak, Kazimir Y. Kolossovski, and Dmitrii Yu. Stepanov Abstract—A comprehensive analysis of multichannel grating op- timization strategies is presented. The central idea is in dephasing of partial gratings with respect to each other. This dephasing al- lows the utilization of ultraviolet-induced refractive index changes with maximum efficiency. The dependence of group delay ripple on optimization strategy, number of channels, and other grating char- acteristics is also briefly discussed. Finally, we discuss further gen- eralization of the dephasing approach to the case of multichannel gratings with nonidentical spectral characteristics. Index Terms—Fiber Bragg grating, multichannel. I. INTRODUCTION S INCE early experiments in the 1970s [1], fiber Bragg grat- ings (FBGs) have become an essential part of fiber optics communications. They are used as filters, strain and tempera- ture sensors, laser source tuners, stabilizers, etc. [2]. We specif- ically emphasize the importance of FBG applications in wave- length-division-multiplexing (WDM) systems which have at- tracted growing attention over recent years because of their ob- vious advantages when upgrading system capacity. Such sys- tems may rely on multichannel Bragg gratings—optical com- ponents that provide a series of wavelength channels with ac- curate inter-channel separations and customized, e.g., identical in-band specifications [3]–[6]. Recently, the problem of multi- channel FBG optimization has been put on the agenda for laser applications [7], [8] and for passive FBG-based devices [9], [10]. Additionally, a conceptually similar problem has attracted considerable attention in radiophysics (see, e.g., [11] and [12]). For FBG applications, the main scope of such an optimization is to reduce the refractive index change required for manufacturing a multichannel FBG. In this work, we significantly extend the analysis of [9], [10] and present a comprehensive description of different optimization strategies. Before going into a detailed description of our findings, we summarize some basic results for FBGs and define our nota- tions. The fundamental system of equations describing light propagation in FBGs is (1) Manuscript received April 19, 2002; revised August 19, 2002. A. V. Buryak is with Redfern Optical Components Pty. Ltd., Eveleigh, NSW 1430, Australia. D. Yu. Stepanov was with Redfern Optical Components Pty. Ltd., Eveleigh, NSW 1430, Australia. He is now with Bandwidth Foundry Pty. Ltd., Eveleigh, NSW 1430, Australia. K. Y. Kolossovski is with the School of Mathematics, University of New South Wales at ADFA, ACT 2600, Australia. Digital Object Identifier 10.1109/JQE.2002.806202 where and are the amplitudes of the forward and backward propagating fields, respectively, is a normalized frequency detuning from the central Bragg reflection frequency, is a local distance along FBG, and is a spatial profile of the FBG coupling coefficient. For a reciprocal and lossless FBG of length (see, e.g., [13] for definitions), we may find complex reflection and transmission coefficients from a transfer matrix , which relates field values at the grating ends (2) and is given by (3) where is the reflection coefficient measured at and is the complex transmission coeffi- cient. Conventional reflection and group delay ( depending on grating side) are related to the complex reflection coefficients as , where is the light wave frequency. Similar relations exist for transmission , group delay in transmission and the complex transmission co- efficient . II. FORMULATION OF THE PROBLEM Before one designs any multichannel grating with equal inter-channel separations and identical in-band specifications, a corresponding single-channel grating design should be constructed. Below we refer to this initial single channel grating as a seeding grating. For any physically viable spectral response in reflection of a single-channel FBG device, a so-called inverse scattering problem should be solved, e.g., by applying a layer-peeling algorithm (LPA) [14]–[16] to system (1). As a result of solving the inverse scattering problem, we obtain a grating design , where is the grating amplitude and is the grating phase. The grating amplitude is normalized to be measured in cm and is related to the FBG effective refractive index modulation amplitude as , where is the FBG period and is the average refractive index. In the literature, FBG grating amplitude and phase are often referred to as apodization and chirp profiles, respectively. In a vast majority of previously reported work on multi- channel gratings, a so-called sinc-sampling approach has been used. In this method, the amplitude (but not the phase) of a given single-channel grating is periodically modulated. For 0018-9197/03$17.00 © 2003 IEEE