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Abstract—We propose a new type of fiber Bragg grating (FBG) with a V-shaped dispersion profile. We demonstrate that such. V-shaped FBGs bring advantages ...
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Design and Fabrication of Fiber Bragg Gratings With V-Shaped Dispersion Profile Elena G. Turitsyna, Xuewen Shu, Sergei K. Turitsyn, Associate Member, IEEE, and Ian Bennion, Member, IEEE

Abstract—We propose a new type of fiber Bragg grating (FBG) with a V-shaped dispersion profile. We demonstrate that such V-shaped FBGs bring advantages in manipulation of optical signals compared to conventional FBGs with a constant dispersion, e.g., they can produce larger chirp for the same input pulsewidth and/or can be used as pulse shapers. Application of the proposed V-shaped FBGs for signal prechirping in fiber transmission is examined. The proposed design of the V-shaped FBG can be easily extended to embrace multichannel devices. Index Terms—Filtering, gratings, optical fiber communications, pulse processing.

I. I NTRODUCTION

F

IBER BRAGG gratings (FBGs) have great and not yet fully explored potential in optical signal control and processing [1]–[4]. Novel fabrication technologies such as, for example, femtosecond radiation point-by-point inscription (see, e.g., [5] and [6] and references therein), open new practical ways to create sophisticated advanced grating structures. The FBG is a powerful tool for performing optical pulse manipulation. In particular, it is well known that fiber gratings can be employed as highly dispersive nonlinear elements for pulse compression [1] and for compensation of the second- or third-order dispersions in fiber communication links [2]–[4]. Dynamic or tunable operations are possible since the transfer function of FBG-based devices can be made adaptive through temperature or stress control [7]. In telecommunications, recent progress in advanced modulation formats draws attention to techniques that are based on signal predistortion to compensate for transmission impairments. For instance, appropriate prechirping of a return-to-zero signal can enhance transmission through the effect of pulse compression in the optical fiber (see, e.g., [8]–[10] and references therein). Generally, precompensation/prechirping now plays an important role in the optimization of the dispersion management of fiber links, helping to suppress nonlinear transmission impairments [8]–[10]. The development of simple and cost-efficient solutions for the appropriate optical signal processing functions is of present interest, as it will be later for telecommunications and for other photonics applications, e.g., laser technologies. Commonly, optical signal prechirping/postcompensation and filtering functions are realized by using two different devices. The possibility to combine in one passive device both amplitude Manuscript received January 17, 2006; revised October 10, 2006. The authors are with the Photonics Research Group, Aston University, B4 7ET Birmingham, U.K. (e-mail: [email protected]; x.shu@aston. ac.uk; [email protected]; [email protected]). Digital Object Identifier 10.1109/JLT.2006.888263

filtering and phase transform functions is very attractive for applications varying from signal processing/control for optical communications to pulse shaping/manipulation in ultrafast optics. Being inherently low cost, FBGs are natural candidates to be considered for this purpose. In this paper, we propose a new type of the FBG with V-shaped dispersion that performs simultaneously the optical filtering and signal-chirping functions. There are two essential ideas behind the proposed V-shaped dispersion profile. The first is that such a profile, in combination with tunability of the central wavelength of the FBG, gives freedom of selection between negative or positive dispersion slope in the device response. This introduces an additional flexibility in using such a device for precompensation or postcompensation of dispersion and/or dispersion slope. Second, using a V-shaped FBG centered at the signal frequency, the left and right parts of the signal spectrum are affected by grating dispersions with opposite slopes, giving new opportunities for signal manipulation. For instance, as will be shown below, in combination with simultaneous signal filtering, this allows for reduction of the signal broadening while creating larger chirp, as compared to normal FBG with constant dispersion. In addition, due to nonparabolic phase response, a V-shaped FBG can act as a pulse-shaping device. Note also that V-shaped dispersion response is an elementary cell of the periodic group delay. Devices with such periodic group delay have been shown to be useful in a range of applications, including dispersion slope compensation [11], tunable dispersion compensation [7], 2R regeneration [12], and reduction of collision-induced timing jitters [13]. In general, signal manipulation functions that are similar to those described in this paper can be achieved by combinations of fiber-based dispersion compensators and optical filters. However, apart from the cost issue, other device combinations generally are less tunable than FBG-based schemes.

II. FBG W ITH V-S HAPED D ISPERSION P ROFILE A. Grating Design and Characteristics Powerful design methods [14], [15], for instance, the discrete layer peeling algorithm, make it possible to synthesize FBGs with desired reflection response and phase characteristics. We take as a target grating response √   HR (δ) = 0.95 exp −(δ/δB )4   × exp −j(β  /2!)L ((c/neff )δ)2   × exp −j(β  /3!)L ((c/neff )δ)3

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Fig. 1. FBG with V-shaped dispersion. (a) Reflection profile. (b) Dispersion profile of three-type gratings. (c) Group delay. (d) Coupling coefficient of the FBG with V-shaped dispersion.

where δ is the detuning parameter between the wavenumber of counter-propagating waves and the reference Bragg wavenumber, δB corresponds to the grating bandwidth (here 100 GHz at −3 dB), β  and β  are the second- and third-order dispersion coefficients for the fiber, L is the link length, c is the speed of light in vacuum, and neff is the average effective refractive index. By varying the values of β  and β  , we can achieve different dispersion profiles of the grating response spectrum, including the desired V-shaped or Λ-shaped profile. The β  coefficient is responsible for the dispersion slope and the β  coefficient for the V- or Λ-peak positions. To obtain the V-shaped dispersion profile of the grating response, we use the different signs of β  coefficient for negative and positive detuning parameters δ (e.g., +β  for positive δ and −β  for negative δ). Fig. 1 shows the reflection profile [Fig. 1(a)], group-delay response [Fig. 1(c), solid line], and the dispersion profile [Fig. 1(b), solid line] of the designed grating. Fig. 1(d) presents the corresponding distributed coupling coefficient of the grating. Thus, the proposed V-shaped dispersion curve design can be implemented in a way similar to conventional gratings without any additional technical problems. Now, we examine the performance of the FBG with a V-shaped dispersion in prechirping of transform limited pulses. We compare here four types of FBGs having exactly the same reflection profile [super-Gaussian, with a bandwidth of 100 GHz at −3 dB, as shown in Fig. 1(a)] but different types of dispersion: constant (two different values), linear (nonzero dispersion slope), and V-shaped, as explained in Fig. 1(b). Two values of the constant dispersion have been chosen for comparison, as shown in Fig. 1(b): first, with the dispersion

value about −30 ps/nm, corresponding to the dispersion of the V-shaped FBG at the bending point as shown in Fig. 1(b) (FBG Const1 in what follows), and the second with the dispersion value about −50 ps/nm, which is close to the average dispersion of the V-shaped FBG over the grating bandwidth (FBG Const2). Group delays of the considered set of gratings are shown in Fig. 1(c). Design of the FBG with V-shaped dispersion is presented in Fig. 1(d). B. Grating Performance To evaluate the gratings performance, we have examined transmission characteristics of gratings using the chirped Gaussian input pulses   2  1 t 2 . (2) A(0, t) = Pin exp −iCt − 2 T0 Here, the standard notation as in [16] is used: Pin is the average input power, C is the chirp of the pulse, and T0 is related to the full width at half maximum (FWHM) by the relation TFWHM = 2(ln 2)1/2 T0 . From (2), we can see that the chirp is related to phase ϕ of the pulse as C = −(1/2)(∂ 2 φ/∂t2 ). Fig. 2 shows power distributions, while Fig. 3 presents a phase derivative over time of an initially unchirped pulse [C = 0 in (2)] at the outputs of the four FBGs described above. First, we note that, as expected, the FBG with nonzero dispersion slope introduces an asymmetry into the signal evolution (dashed line), while those with constant (dotted, and dasheddotted lines) and V-shaped dispersions (solid line) preserve pulse symmetry. Second, it may be seen from Fig. 3 that the

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Fig. 2. Comparison of pulses transmitted through four types of FBGs.

Fig. 4. Comparison of the broadening factors for pulses propagated through (a) different FBGs and (b) chirps acquired.

Fig. 3.

Phase derivative of pulses transmitted through different types of FBGs.

V-shaped FBG produces a larger chirp on the signal while keeping the pulsewidth at the same level, or even below it, compared to the FBGs with constant dispersion. Therefore, in any application that requires to chirp pulse while keeping pulsewidth as minimal as possible, this property of V-shaped grating can be beneficial. For instance, in optical fiber communication, signal prechirping that can substantially improve system performance can be implemented via different means: phase modulation of the input signal or using prechirping fiber. The use of prechirping fiber, indeed, leads to signal chirping. However, it is accompanied by the corresponding pulse broadening. Proposed V-shaped gratings can produce large chirp while suppressing pulse broadening compared to standard FBGs. Fig. 4 quantifies this comparison for various input pulsewidths. It can be seen from Fig. 4 that the FBG with V-shaped dispersion outperforms gratings with constant dispersions. Namely, FBG with V-shaped dispersion produces a larger chirp of the output pulse, while having similar (compared to FBG Const2) or even less (compared to FBG Const1)

Fig. 5.

Transmission system used for evaluation of FBGs’ performance.

pulsewidth broadening factor compared to the grating with constant dispersion. This effect is more pronounced for shorter pulses. C. V-Shaped Gratings as Prechirping Elements To evaluate the performance of the V-shaped FBGs as prechirping elements, without loss of generality, we consider a single-channel SMF/DCF transmission line shown in Fig. 5. Here, the V-shaped FBG and constant dispersion FBG are used as optical prechirping elements. A transmission map consists of four spans of SMF(75 km) + EDFA(15 dB, noise figure NF = 4.5 dB)+DCF (12.75 km) + EDFA(8.2875 dB, noise figure NF = 4.5 dB). The combination of 75 km of single mode fiber (SMF with dispersion of 17 ps/(km · nm), dispersion slope of 0.07 ps/(km · nm2 ), and

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Fig. 7. Q-factor versus cumulative dispersion for V-shaped FBG (dashed line) and FBG with constant dispersion (solid line). Fig. 6. Gaussian pulse of 17 ps (solid line) propagated through V-shaped FBG (dashed line) and through FBG with constant dispersion (dashed and dotted line).

the fiber loss of 0.2 dB/km in the wavelength region near 1.55 µm) and 12.75 km of dispersion compensating fiber (DCF with dispersion of −100 ps/(km · nm), dispersion slope of −0.41 ps/(km · nm2 ), and the fiber loss of 0.65 dB/km in the wavelength region near 1.55 µm) is specially designed to slightly compensate both dispersion and dispersion slope from the transmission through SMF. The cumulative dispersion of the line is 280 ps/nm. The FBGs (with constant dispersion of −260 ps/nm or V-shaped with steep dispersion slope and average dispersion about −280 ps/nm) are placed at the beginning of the line as dispersion precompensation elements. An optical filter with 100-GHz bandwidth is used at the receiver. Fig. 6 shows that a V-shaped grating operates not only as a signal-prechirping element but also as a pulse shaper. For comparison, an output pulse after conventional FBG with the same chirp as after V-shaped grating is shown. V-shaped grating flattens carrier waveform while producing the same chirp as a conventional FBG. Without loss of generality, we consider here the transmission of RZ signal at 40-Gb/s channel rate. Transmission performance was evaluated using a standard Q-factor technique averaged over six runs with 211 − 1 pseudorandom patterns. Measurements of Q-factor values after propagation over four spans (300 km) of the SMF fiber are used for evaluation of the grating performance. Fig. 7 presents simulated Q-factor after transmission (with the Gaussian pulses of 17-ps width and 1-mW input peak power) versus the cumulative line dispersion. It is seen that for this particular link, the V-shaped FBG (dashed line) performs slightly better than the FBG with constant dispersion (solid line). Evidently, there are many situations when V-shaped grating performance will not be that different from conventional FBGs. In this paper, we would like just to attract attention to new design possibilities and to demonstrate that for some applications, the V-shaped grating could be a simple way to further improve the system performance and provide additional system margin.

Considering the application of V-shaped FBGs as optical filters for multiplexing/demultiplexing, it is easy to observe some advantages of such devices over the filters based on FBG with constant dispersion or linear dispersion. By detuning V-shaped FBGs filters around the carrier frequency, one can change the dispersion compensation value (like linear dispersion filters) without worrying much about the sign of the detuning (as opposite to the case of the constant dispersion filters). This property of the FBGs with the V-shaped dispersion profile can be widely used in wavelength-division-multiplexing (WDM) transmission systems. For instance, as it has been demonstrated in [13], using dense WDM at 10-Gb/s channel rate complemented by periodic-group-delay dispersion compensation, that it is feasible to achieve distances of 9000 km with uncorrected (no forward error correction) bit error rates of 10−8 . Potentially, the proposed V-shaped gratings implemented in a multichannel version can serve as such periodic-group-delay compensators. III. E XPERIMENTAL R ESULTS We have fabricated the proposed V-shaped dispersion FBG with the UV direct writing system developed in our laboratory. A frequency-doubled Argon laser at a wavelength of 244 nm and a small portion of uniform phase mask with a period of 1071.278 nm was used in the experiment. The apodization profile and the varied period were realized by appropriately controlling the on/off of an AO-modulator and moving the phase mask/fiber. The structure was written in hydrogen-loaded photosensitive fiber. The annealed grating was finally characterized with the Agilent Chromatic Dispersion Test Set (86073C), with the wavelength resolution and the modulation frequency set at 2.5 pm and 250 MHz, respectively. Fig. 8 shows the reflection coefficient, and Fig. 9 shows the group-delay response of the fabricated FBG and comparisons to the modeling results, respectively. Figs. 8 and 9 demonstrate a good agreement between designed and experimental results. IV. C ONCLUSION We have proposed and fabricated a new type of FBG with V-shaped dispersion characteristic. We have demonstrated that

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Fig. 8. Comparison of the reflection profile of the designed and fabricated FBG with V-shaped dispersion profile.

[3] S. Longhi, M. Marano, P. Laporta, O. Svelto, and M. Belmonte, “Propagation, manipulation, and control of picosecond optical pulses at 1.5 mm in fiber Bragg gratings,” J. Opt. Soc. Amer. B, Opt. Phys., vol. 19, no. 11, pp. 2742–2757, Nov. 2002. [4] K. Hill and G. Meltz, “Fiber Bragg grating technology-fundamentals and overview,” J. Lightw. Technol, vol. 15, no. 8, pp. 1263–1276, Aug. 1997. [5] K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett., vol. 21, no. 21, pp. 1729–1731, Nov. 1996. [6] A. Dragomir, D. N. Nikogosyan, K. A. Zagorulko, P. G. Kryukov, and E. M. Dianov, “Inscription of fiber Bragg gratings by ultraviolet femtosecond radiation,” Opt. Lett., vol. 28, no. 22, pp. 2171–2173, Nov. 2003. [7] X. Shu, K. Sugden, and I. Bennion, “Optically tunable chromatic dispersion controller with coupled-cavity etalon structure,” Opt. Lett., vol. 30, no. 12, pp. 1440–1442, Jun. 2005. [8] F. Favre, D. Le Guen, M. L. Moulinard, M. Henry, G. Michaud, F. Devaux, E. Legros, B. Charbonnier, and T. Georges, “Demonstration of soliton transmission at 20 Gb/s over 2200 km of standard fibre with dispersion compensation and pre-chirping,” Electron. Lett., vol. 33, no. 6, pp. 511–512, Mar. 1997. [9] A. Sano, Y. Miyamoto, S. Kuwahara, and H. Toba, “A 40-Gb/s/ch WDM transmission with SPM/XPM suppression through prechirping and dispersion management,” J. Lightw. Technol., vol. 18, no. 11, pp. 1519–1526, Nov. 2000. [10] S. Cundiff, B. Collins, L. Boivin, M. Nuss, K. Bergman, W. Knox, and S. Evangelides, “Propagation of highly chirped pulses in fiber-optic communication systems,” J. Lightw. Technol., vol. 17, no. 5, pp. 811–816, May 1999. [11] M. Ibsen and R. Feced, “Fiber Bragg gratings for pure dispersion-slope compensation,” Opt. Lett., vol. 28, no. 12, pp. 980–982, Jun. 2003. [12] M. Vasilyev and T. I. Lakoba, “All-optical multichannel 2R regeneration in a fiber-based device,” Opt. Lett., vol. 30, no. 12, pp. 1458–1460, Jun. 2005. [13] L. F. Mollenauer, A. Grant, X. Liu, X. Wei, C. Xie, and I. Kang, “Experimental test of dense wavelength-division multiplexing using novel, periodic-group-delay-complemented dispersion compensation and dispersion-managed solitons,” Opt. Lett., vol. 28, no. 21, pp. 2043–2045, Nov. 2003. [14] R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron., vol. 35, no. 8, pp. 1105–1115, Aug. 1999. [15] J. Skaar, L. Wang, and T. Erdogan, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron., vol. 37, no. 2, pp. 165–173, Feb. 2001. [16] G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. San Diego, CA: Academic, 1995. [17] E. G. Turitsyna, X. Shu, and I. Bennion, “Design and fabrication of fibre bragg gratings with V-shaped dispersion profile for multi-channel signal processing,” presented at the ECOC Conf., vol. 4, pp. 155–156, Sep. 2006, Paper Th3.3.4.

Fig. 9. Comparison of the group delay of the designed and fabricated FBG with V-shaped dispersion profile.

the V-shaped FBG offers advantages in the manipulation of optical signals compared to conventional FBGs with constant dispersion. In particular, it can produce a larger signal chirp with less pulse broadening compared to the corresponding conventional FBG with constant dispersion. Application of the proposed V-shaped FBG for signal prechirping in fiber transmission has been examined. We have observed an operational regime in which the V-shaped grating outperforms a conventional FBG. The proposed design of the V-shaped FBG is not limited by single-channel applications and can be easily extended to embrace more complex multichannel structures [17]. R EFERENCES [1] G. Lenz, B. J. Eggleton, and N. Litchinitser, “Pulse compression using fiber gratings as highly dispersive nonlinear elements,” J. Opt. Soc. Amer. B, Opt. Phys., vol. 15, no. 2, pp. 715–721, Feb. 1998. [2] F. Quellette, “Dispersion cancellation using linearly chirped Bragg,” Opt. Lett., vol. 12, no. 10, pp. 847–849, Oct. 1987.

Elena G. Turitsyna received the M.Sc. degree in mathematics from Novosibirsk State University, Novosibirsk, Russia, in 1983. She is currently with Photonics Research Group at Aston University, Birmingham, U.K. Her main research interests are in optical fiber communications and applications using fiber Bragg gratings.

TURITSYNA et al.: DESIGN AND FABRICATION OF FBGs WITH V-SHAPED DISPERSION PROFILE

Xuewen Shu received the Ph.D. degree in optoelectronics from Huazhong University of Science and Technology, Wuhan, China, in 2000. From August 2000 to August 2001, he was a Visiting Research Fellow with the Photonics Research Group at Aston University, Birmingham, U.K. Then, he spent two years with Indigo Photonics Ltd., U.K., as a Photonics Development Engineer and a Senior Engineer from 2001 to 2003. In August 2003, he rejoined the Photonics Research Group at Aston University, where he is currently employed. He has published several papers in major international journals and conferences and also holds several European and U.S. patents. His research areas include optical communications and optical sensing. Dr. Shu is a member of the Optics Society of America.

Sergei K. Turitsyn (A’04) received the degree from the Department of Physics, Novosibirsk University, Novosibirsk, Russia, in 1982 and the Ph.D. degree in theoretical and mathematical physics from the Institute of Nuclear Physics, Novosibirsk, in 1986. From 1992 to 1998, he was with the Institute for Theoretical Physics I, Heinrich-Heine University Duesseldorf, Duesseldorf, Germany, first as a Humboldt Fellow and later as a Leader of the collaborative projects with Deutsche Telekom. In 1998, he joined the Photonics Research Group, Aston University, Birmingham, U.K., where he is a Professor with the School of Engineering and Applied Science and leads the Theory and Modeling Group. Prof. Turitsyn was the recipient of a Royal Society Wolfson Research Merit Award in 2005.

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Ian Bennion (M’91) has been a Professor of photonics with the School of Engineering and Applied Science, Aston University, Birmingham, U.K., as cofounder of the Photonics Research Group in September 1991. He is presently the Leader of the Group and the Head of the Electronic Engineering Subject Group. Previously, he spent 16 years with Plessey Research Caswell Ltd., later GEC-Marconi Materials Technology Ltd., researching optoelectronic devices and their applications. His most recent research activities have been in the fields of fiber grating technology and its applications, optical sensor technology, biophotonics, highspeed fiber-optic communications, and fiber-optic signal processing. He has published more than 500 journal and conference papers on photonics. Dr. Bennion is a Fellow of the Institution of Electrical Engineers and the Institute of Physics (U.K.) and a member of the Optical Society of America.