IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 18, NO. 12, JUNE 15, 2006
1371
Periodically Chirped Sampled Fiber Bragg Gratings for Multichannel Comb Filters Xi-Hua Zou, Wei Pan, Bin Luo, Zhang-Miao Qin, Meng-Yao Wang, and Wei-Li Zhang
Abstract—Periodically chirped sampled fiber Bragg gratings (PC-SFBGs) are proposed as multichannel comb filters. A PC-SFBG consists of many chirp periods corresponding to the periodic chirp effect. With the same chirp coefficient released for a linearly chirped SFBG (LC-SFBG), the spectral self-imaging phenomenon is also observed in the PC-SFBG. Compared with a uniform SFBG, the PC-SFBG exhibits a narrower channel spacing and a similar group-delay characteristic in the reflection bands. Meanwhile, the PC-SFBG ensures a more accurate phase-shift condition (or a better tolerance on the chirp coefficient) and higher peak reflectivities than the LC-SFBG. Index Terms—Gratings, optical fiber devices, optical filter, wavelength-division multiplexing.
I. INTRODUCTION
F
IBER gratings are essential components of optical communication systems and fiber-sensing systems. Recently, the increasing demand on the number of wavelength channels has aroused considerable interest in the design and implementation of multichannnel devices based on sampled fiber Bragg gratings (SFBGs). For instance, such gratings can be used as dispersion compensators [1]–[4], add–drop multiplexers [5], and comb filters [6]–[8]. Meanwhile, various techniques have been introduced to improve the performance of these devices. Several devices have been developed via amplitude sampling approaches [1], [6], [9]. To reduce the peak refractive-index modulation, the phase sampling approach and the multiple phase shift technique [4], [10], [11] are proposed. Chirp approaches also have been widely explored. For example, Chen and his colleagues have developed comb filters aided with a chirp in the sampling period or a strong chirp in the grating period [3], [7]. Chen, Azaña, and Wang have presented a series of investigations on the spectral self-imaging phenomenon due to the chirp effect [8], [12], [13]. With a fixed sampling period, the number of channels is efficiently multiplied by the self-imaging effect. In this work, we focus on the chirp effect of SFBGs. Specially, periodically chirped SFBGs (PC-SFBGs) are proposed to design multichannnel comb filters. As compared with a uniform SFBG (U-SFBG), the PC-SFBG shows a narrower channel Manuscript received December 22, 2005; revised April 9, 2006. This work was supported by the National Natural Science Foundation of China under Grant 10174057 and Grant 90201011, by the Key Project of Chinese Ministry of Education under Grant 105148, and by the Foundation of Key Laboratory of Broadband Optical Fiber Transmission and Communication Networks of Chinese Ministry of Education under Grant KF2006. The authors are with the School of Information Science and Technology, Southwest Jiaotong University, Chengdu, Sichuan 610031, China, and also with the Key Laboratory of Broadband Optical Fiber Transmission and Communication Networks of Chinese Ministry of Education (UESTC), Chengdu, Sichuan 610054, China (e-mail:
[email protected];
[email protected];
[email protected]). Digital Object Identifier 10.1109/LPT.2006.877349
Fig. 1.
Schematic diagram of a PC-SFBG.
spacing and a similar group-delay characteristic due to the spectral self-imaging effect. This is equivalent to the phenomenon observed in a linearly chirped SFBG (LC-SFBG) [12], [13]. Moreover, each chirp period of the PC-SFBG is regarded as the whole linear chirp period of the LC-SFBG. This periodic chirp effect results in two outstanding features, a more accurate phase-shift condition and higher peak reflectivities. II. PRINCIPLE As shown in Fig. 1, a PC-SFBG consists of many identical chirp periods with the length of . denotes the number of sampling periods in a chirp period; and are the length of the sampling period and the grating section (sampling length) respectively. The variation of the grating period is periodic over the whole grating and linear over each chirp period, called as the periodic chirp effect. The refractive-index modulation is described as follows. A uniform binary-sampling function, which is not included in the following equations for simplicity, is adopted. For the linear chirp effect, , , and refer to the chirp coefficient, the fundamental grating period, and the local grating period, respectively, (1) Then the refractive-index modulation along axis can be written as
of an LC-SFBG
(2) is the “dc” refractive-index modulation and repwhere resents the phase-shift condition due to (1). As reported for the LC-SFBG [12], [13], if the chirp coefficient is specified as (3), the corresponding phase-shift condition (4) can be derive
1041-1135/$20.00 © 2006 IEEE
(3) (4)
1372
IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 18, NO. 12, JUNE 15, 2006
where and are arbitrary positive integers with that is a noninteger and irreducible number. Compared with a U-SFBG, the LC-SFBG shows a channel spacing reduced by times and a similar group-delay characteristic, namely the spectral self-imaging phenomenon. Note that the product determines the approximating accuracy of (4). If this product is small enough, we can get an excellent phase-shift condition to construct the self-imaging effect. For the PC-SFBG, the refractive-index modulation indicates the periodic chirp effect
(5) where is the total number of chirp periods. Here, both and determine the channel spacing. The most concise relation, which is adopted in this work. ship between and is With the same chirp coefficient (3), we obtain the phase-shift condition of the PC-SFBG
(6) In particular, the phase shifts of the grating samples located at are (7) Obviously, if is an even integer, there always exists an excellent condition for each chirp period (8) where is a positive integer. We take this point as the end of the previous chirp period with and as the beginning of the current chirp period with . Therefore, the similar phase-shift condition of the LC-SFBG, required by the Talbot effect, is also satisfied in the PC-SFBG. Only the maximum phase shift over the whole grating is dramatically reduced in the PC-SFBG. In this way, each chirp period of the PC-SFBG can be regarded as the whole linear chirp period of the LC-SFBG. Consequently, the wavelength spacing of the PC-SFBG is expressed as (9) (10) is the Bragg where is the effective index and wavelength. On the basis of this principle, the corresponding self-imaging effect will be thoroughly analyzed by the transfer matrix method [14] in Section III. III. NUMERICAL SIMULATIONS AND DISCUSSION In our simulations, the detailed parameters of the PC-SFBG (unapodized) are as follows: , nm, , mm, mm, . Only
t
Fig. 2. Reflectivity of the PC-SFBG with different chirp coefficients: (a) = 0 = 3, = 2, (c) (the U-SFBG), (b) = 5, = 2.
M
t
M
t
the chirp coefficient (3) is altered during these simulations. If we specify as 2 (an even integer) to obtain the minimum chirp coefficient, only will change. From Fig. 2, we can analyze the reflection spectra of the PC-SFBG with different chirp coefficients. The reflection peaks of the U-SFBG are shown in Fig. 2(a). As is expected, the wavelength spacing ( 0.8 nm) is determined by the sampling period according to (10). Fig. 2(b) and (c) shows the reflection peaks of the PC-SFBG with chirp coefficients of ( , ) and ( , ), respectively. Clearly, the spacing is reduced to times, compared with that of the U-SFBG. Meanwhile, despite the periodic chirp effect, the corresponding group-delay characteristic in Fig. 3 is similar to that of the U-SFBG in shape. The channel-to-channel average group-delay fluctuations, demonstrated for the LC-SFBG [12], are also observed. In a word, the self-imaging phenomenon is successfully observed in the PC-SFBG, which provides further confirmation for the principle shown in Section II. Additionally, the peak reflectivities of channels drop as the number of channels increases with a fixed length of the PC-SFBG, which is equivalent to the energetic efficiency of the LC-SFBG. In order to keep the same peak reflectivities, reducing the channel spacing by a factor of requires to be increased by approximately [8]. Regarding each chirp period of the PC-SFBG as the whole linear chirp period of the LC-SFBG is the most important characteristic, which provides the PC-SFBG with several outstanding features. First, the phase-shift condition (4) is always accurately achieved because the small value of over each chirp period, making it easier to observe the self-imaging phenomenon. Likewise, this feature translates into a better
ZOU et al.: PC-SFBGs FOR MULTICHANNEL COMB FILTERS
1373
tral self-imaging phenomenon is observed in a PC-SFBG. Compared with an equivalent U-SFBG, the PC-SFBG shows a similar group delay and a narrower channel spacing (reduced by times). In contrast to an LC-SFBG, the phase-shift condition and the peak reflectivities are improved.
ACKNOWLEDGMENT
Fig. 3.
Group-delay characteristic of the PC-SFBG with (
M = 3, t = 2).
The authors would like to thank Dr. X. F. Chen and Dr. J. Azaña for recommendations and sending some literature.
REFERENCES
Fig. 4. Reflectivity of the LC-SFBG with (
M = 3, t = 2).
tolerance on the grating parameters. When the chirp coefficient ( , ) of the PC-SFBG is deviated by 5%, the average 3-dB bandwidth is 0.046 nm and the maximum channel-to-channel fluctuation (from 1546.5 to 1554.5 nm) is about 10%. These results are very close to those released for the LC-SFBG with a deviation of 1.5% [8]. Second, the maximum phase shift of the PC-SFBG is less than that of the LC-SFBG, which ensures higher peak reflectivities for all channels of the PC-SFBG. The comparison between Figs. 2(b) and 4 shows that each peak reflectivity of the PC-SFBG exceeds the corresponding peak reflectivity of the LC-SFBG by 1.1 dB. Moreover, we have discovered that the PC-SFBG is able to partially mitigate the preliminary condition [12]. As an interesting example, the multipeaks aberrations, which appear on some reflection bands (located far from the Bragg wavelength) of the LC-SFBG, are suppressed in the reflection bands of the PC-SFBG. This is useful in broadening the operating wavelength band as the reflectivity uniformity and the extinction ratio can be improved simultaneously by effective approaches, such as apodization techniques. Extensive improvements in the preliminary condition will be demonstrated in our future work. IV. CONCLUSION Multichannel comb filters based on PC-SFBGs are proposed for the first time. According to the periodic chirp effect, the spec-
[1] F. Ouellette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broadband and WDM dispersion compensation using chirped sampled fiber Bragg gratings,” Electron. Lett., vol. 31, no. 11, pp. 899–901, May 1995. [2] W. H. Loh, F. Q. Zhou, and J. J. Pan, “Sampled fiber grating based dispersion slope compensator,” IEEE Photon. Technol. Lett., vol. 11, no. 10, pp. 1280–1282, Oct. 1999. [3] X. F. Chen, Y. Luo, C. C. Fan, T. Wu, and S. Z. Xie, “Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system,” IEEE Photon. Technol. Lett., vol. 12, no. 8, pp. 1013–1015, Aug. 2000. [4] H. Li, Y. Sheng, Y. Li, and J. E. Rothenberg, “Phased-only sampled fiber Bragg gratings for high-channel-count chromatic dispersion compensation,” J. Lightw. Technol., vol. 21, no. 9, pp. 2074–2083, Sep. 2003. [5] H. Lee and G. P. Agrawal, “Add-drop multiplexers and interleavers with broadband chromatic dispersion compensation based on purely phasesampled fiber gratings,” IEEE Photon. Technol. Lett., vol. 16, no. 2, pp. 635–637, Feb. 2004. [6] M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett., vol. 10, no. 6, pp. 842–844, Jun. 1998. [7] X. F. Chen, C. C. Fan, Y. Luo, S. Z. Xie, and S. Hu, “Novel flat multichannel filter based on strongly chirped sampled fiber Bragg grating,” IEEE Photon. Technol. Lett., vol. 12, no. 11, pp. 1501–1503, Nov. 2000. [8] C. Wang, J. Azaña, and L. R. Chen, “Efficient technique for increasing the channel density in multiwavelength sampled fiber Bragg grating filters,” IEEE Photon. Technol. Lett., vol. 16, no. 8, pp. 1867–1869, Aug. 2004. [9] X. H. Zou, W. Pan, B. Luo, W. L. Zhang, and M. Y. Wang, “Accurate analytical expression for reflection-peak wavelengths of sampled Bragg grating,” IEEE Photon. Technol. Lett., vol. 18, no. 3, pp. 529–531, Feb. 2006. [10] A. V. Buryak, K. Y. Kolossovski, and D. Y. Stepanov, “Optimization of refractive index sampling for multichannel fiber Bragg gratings,” IEEE J. Quantum Electron., vol. 39, no. 1, pp. 91–98, Jan. 2003. [11] N. Yusuke and Y. Shinji, “Densification of sampled fiber Bragg gratings using multiple phase shift (MPS) technique,” J. Lightw. Technol., vol. 23, no. 4, pp. 1808–1817, Apr. 2005. [12] J. Azaña, C. Wang, and L. R. Chen, “Spectral self-imaging phenomena in sampled Bragg gratings,” J. Opt. Soc. Amer. B, vol. 22, no. 9, pp. 1829–1841, Sep. 2005. [13] L. R. Chen and J. Azaña, “Spectral Talbot phenomena in sampled arbitrarily chirped Bragg gratings,” Opt. Commun., vol. 250, pp. 302–308, 2005. [14] T. Erdogan, “Fiber grating spectra,” J. Lightw. Technol., vol. 15, no. 8, pp. 1277–1294, Aug. 1997.
