IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 16, NO. 8, AUGUST 2004 1867 Efﬁcient Technique for Increasing the Channel Density in Multiwavelength Sampled Fiber Bragg Grating Filters Chinhua Wang, José Azaña, Member, IEEE, and Lawrence R. Chen, Member, IEEE Abstract—We introduce a new class of high channel count mul- tiwavelength comb ﬁlters based on sampled ﬁber Bragg gratings (FBGs). Our approach exploits the spectral fractional Talbot effect in sampled chirped FBGs (S-CFBGs). For speciﬁc conditions be- tween the grating chirp and sampling period, the channel spacing can be reduced compared to the value obtained using conventional sampling techniques. In this way, the channel density can be mul- tiplied without needing to increase the sampling period. Moreover, despite the fact that the grating is chirped, operating under the spectral Talbot regime ensures that the resultant in-band group delay characteristics are similar to those of a sampled uniform pe- riod FBG. Index Terms—Fiber Bragg gratings (FBGs), optical ﬁber de- vices, optical ﬁlters, wavelength-division multiplexing. I. INTRODUCTION F IBER Bragg gratings (FBGs) are essential components for numerous applications in optical communications and ﬁber-optic sensing [1]. While an FBG typically operates on a single channel, techniques can be used to achieve multichannel operation [1]–[9]. This generally involves sampling the grating structure in which the refractive index variation of the “seeding” grating (i.e., grating before sampling) is periodically modulated by an amplitude and/or phase sampling function. The periodic sampling function is characterized by two parameters: the sampling period and the sample length (the ratio deﬁnes the duty cycle of the sampling function). This refractive index modulation results in a reﬂection spectrum consisting of a discrete and periodic series of nearly identical wavelength channels (comb ﬁlter), where the interchannel separation and in-band amplitude and/or phase speciﬁcations can be tailored by ﬁxing the shape and period of the sampling function as well as the seeding grating parameters. In particular, the wavelength Manuscript received January 30, 2004; revised April 6, 2004. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada and in part by the Fonds Québécois de la Recherche sur la Nature et des Technologies. C. Wang is with the Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON M5S 3G8, Canada. J. Azaña is with the Institut National de la Recherche Scientiﬁque-Énergie, Matériaux et Télécommunications, Montreal, QC H5A 1K6, Canada. L. R. Chen is with the Photonic Systems Group, Department of Electrical and Computer Engineering, McGill University, Montreal, QC H3A 2A7, Canada (e-mail: chen@photonics.ece.mcgill.ca). Digital Object Identiﬁer 10.1109/LPT.2004.831276 spacing between adjacent reﬂection bands is ﬁxed by the sampling period according to the following relation: (1) where is the Bragg frequency and is the effective mode index in the ﬁber. The in-band amplitude and phase characteris- tics are those of the seeding grating. The simplest sampled FBG (SFBG) structure is a uniform one (denoted U-SFBG), where the seeding grating is a uniform FBG and uniform amplitude sampling is used [2], [3], [5]. An impor- tant consideration in the design of SFBGs, including U-SFBGs, involves energetic efﬁciency. From (1), it can be immediately inferred that in a conventional SFBG, increasing the number of wavelength channels within a given bandwidth (i.e., reducing the corresponding channel spacing by ) can be achieved only by increasing . However, increasing the sampling period re- duces the effective grating length which, in turn, decreases the peak reﬂectivity for each wavelength channel. As a general rule of thumb, in order to keep the same peak reﬂectivity per channel, an SFBG must have a peak refractive index modulation ap- proximately times larger than that of the shorter sampling period case. The use of interleaved SFBGs [6] or purely phase sampling functions [8] can partially solve this problem (e.g., it has been estimated that for phase-only SFBGs, must be in- creased by a factor of as opposed to ), but at the expense of increasing signiﬁcantly the fabrication complexity. In this letter, we present a new means for increasing the channel density of SFBG-based multiwavelength comb ﬁlters using sampled chirped FBGs (S-CFBGs). II. THEORETICAL PRINCIPLE OF OPERATION Recently, we have shown that the well-known integer and fractional self-imaging Talbot effects [10] can be observed in the spectral domain using one-dimensional photonic bandgap structures and in particular, S-CFBGs [11]. We demonstrated that if speciﬁc conditions between the grating chirp and the sam- pling period are satisﬁed, then a suitable interference between the individual spectrally overlapped wavelength channels can result in a comb-like spectrum with two outstanding features: 1) in contrast to a conventional SFBG, the wavelength spacing is not uniquely ﬁxed by but can be reduced by appropri- ately setting the grating chirp, and 2) despite the fact that the seeding grating is chirped, the discrete reﬂection bands exhibit a group delay characteristic similar to that of a uniform grating. 1041-1135/04$20.00 © 2004 IEEE