1. Introduction

As the dispersion tolerance in 40-Gb/s systems is restricted to ~50ps/nm [1], dispersion compensation is crucial in high-speed optical transmission systems. Meanwhile, the accumulated dispersion varies with factors such as network reconfiguration and environment change (temperature, stress…), etc., leading to system performance degradation. This impairment can be mitigated by various tunable dispersion compensators (TDCs), including virtually imaged phased array (VIPA) [2] and ring resonators [3], etc. Thomas Duthel et al. [4] recently demonstrates a TDC for 40-Gb/s system by use of an all-fiber second-order delay line filter and a tuning range of ±50 ps/nm is realized.

Another option, which we discuss further in this paper, is TDC based on nonlinearly chirped fiber Bragg grating (NLCFBG). NLCFBG is an advisable device for tunable dispersion compensation for its high dispersion variety, and a number of such devices for 10-Gb/s and 40-Gb/s systems have been reported [5–8]. However, these NLCFBGs are fabricated with special nonlinearly chirped phase masks or some mechanical methods with high precision, which are costly and complicated. Hence application of these devices is constrained.

Recently, we have reported a reconstruction-equivalent-chirp (REC) method to design and fabricate NLCFBGs by utilizing a uniform phase mask [9–11], where the nonlinear chirp is simply generated by chirping in the sampling period. Although this method markedly simplifies fabrication, room still exists for relaxed fabrication precision requirement and improved device performance. In this paper, a modified REC (MREC) method is proposed by utilizing a linearly chirped phase mask instead of a uniform one to achieve these goals. In addition, it can be thermally tuned by a uniform thin metal film deposited on the grating. A TDC is designed and fabricated accordingly which demonstrates a ~200ps/nm dispersion tuning range, <14ps peak-to-peak group delay ripple, and about 700mW total power dissipation. Moreover, the group delay ripple, which is one of the key features of TDCs, is not deteriorated as the heating temperature varies. In a 40-Gb/s×5 or 10km conventional single mode fiber (SMF) transmission experiment with carrier suppressed return-to-zero (CSRZ) format, the power penalty is less than 0.7dB at a BER of 10^-10 by using the proposed TDC.

2. Theory and design

For a NLCFBG with given response, its index modulation along the grating length z (as well as the apodization and phase profiles A(z) and φ(z), respectively) can be derived by reconstruction algorithm [12] as

where Λ₀ is the grating period corresponding to center wavelength, and c.c. is the complex conjugate of the first part in the formula. As mentioned in reference [9,10], NLCFBGs described by Eq. (1) can be obtained in the -1^st channel of a sampled FBG through the REC method and a uniform phase mask. The sampling position z_k and corresponding sampling period P_k in the k ^th sample are given by:

respectively. P is a sampling parameter inversely proportional to channel spacing Δλ according to Fourier analysis:

where λ₀ and n are the center wavelength and the efficient index of the grating, respectively. Chirping in the sampling period (induced by variation in P_k along z) leads to nonlinear chirping in the grating period. It is important to note that P must be sufficiently small to prevent overlapping between neighboring channels, according to Eq. (3). Assuming that the desired FBG achieved in the -1^st channel has a 3-dB bandwidth of B, according to REC method [9], the corresponding bandwidth of the -2^nd channel is 2B because the chirp coefficient of the -2^nd channel is twice as large if a uniform phase mask is used. Hence P should be constrained by Δλ < 1.5B to prevent overlapping between the two channels, that is:

It can be seen from (4) that P should be very small if large B is required, and the writing laser beam spot should be small enough and precisely located to prevent neighboring samples from overlapping during fabrication. Consequently, wideband NLCFBGs become difficult to fabricate.

However, this difficulty can be mitigated by utilizing a linearly chirped phase mask instead of a uniform one during grating design and fabrication, while the dispersion is obtained through chirp generated in both the sampling period and phase mask. Consequently, the constraint in P is relaxed, and the grating performance can be improved markedly. Theoretical analysis and calculation results of this MREC method reveal that P can be maximized when the dispersion provided by the linearly chirped phase mask approximately equals to the mean value of the desired maximum and minimum dispersion. In other word, the linear and nonlinear chirps are generated by the phase mask and chirping in the sampling period, respectively. And in this case, the spectrum of the -2^nd channel will not be broadened and has a bandwidth of B. Correspondingly, the sampling position z’_k is decided by:

where C is the chirping coefficient provided by the linearly chirped phase mask. Accordingly, a NLCFBG used for TDC with a tunable dispersion between -60ps/nm and -260ps/nm is designed and demonstrated with the MREC method. The NLCFBG has a third-order chromatic dispersion and its 3-dB bandwidth is 2nm. For comparison, calculated results of the NLCFBG designed with both REC and MREC methods are shown in Figs. 1 and 2. Figure 1(a) shows the apodization profile and sampling period distribution along the grating length by REC method with P=0.2mm to prevent inter-channel crosstalk, according to Eq. (4). The minimum sampling period is 0.15mm. Figure 1(b) shows its insertion loss (reflection) spectrum and group delay curve. It is clear from Fig. 1 that if P is larger than 0.2mm, overlapping between the -1^st and -2^nd channels will occur since the channel spacing decreases as P enlarges, according to Eq. (3). On the other hand, the corresponding curves of a similar NLCFBG (third-order chromatic dispersion and 3-dB bandwidth=2nm) designed by MREC method (C= 0.155nm/cm) are shown in Figs. 2(a) and 2(b), respectively. Here P is increased to 0.57mm without overlapping between neighboring channels. Accordingly, the minimum sampling period is increased to 0.29mm, which is easier to achieve in a precise motorized mechanical system.

 

Fig. 1. Calculated results of a NLCFBG utilizing a uniform phase mask: (a) apodization profile and sampling period distribution along the grating length, (b) reflection spectrum and group delay curve.

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Fig. 2. Calculated results of a NLCFBG utilizing a linearly chirped phase mask: (a) apodization profile and sampling period distribution along the grating length, (b) reflection spectrum and group delay curve.

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3. Experimental results and discussion

The NLCFBG with designed performance shown in Fig. 2 is fabricated by the standard scan-writing technique with a frequency-doubled argon laser. This device is then coated with a uniform thin metal film made up of nickel-phosphorus alloy by conventional chemical plating technique to form a thermally TDC. It has a uniform resistance of 5.02Ω/cm along the whole length (70mm) of the grating, and resistive heating of the metal film will shift the group delay curve without changing its shape. Hence, the dispersion varies at a given wavelength. The uniformity of the metal film is important to avoid, during heating, additional phase modulation and variation in the shape of group delay curve. A uniform metal film can be achieved effectively by keeping a uniform temperature in the plating bath.

Figure 3 illustrates the experimental results of the TDC without heating current (all of the experimental spectra in this paper are measured by Optical Vector Analyzer (OVA Model CTe), made by Luna Technologies Inc., which has a wavelength resolution of 3.2pm and a group delay accuracy of ±0.05ps). The reflection profile and group delay curve are shown in Fig. 3(a). A good agreement with Fig. 2(b) validates the MREC theory and confirms the design. In fact, a flat reflection spectrum with fluctuation less than 1dB in the entire 2nm bandwidth is achieved. Furthermore, the peak-to-peak group delay ripple of the NLCFBG across the whole passband is less than 14ps as shown in Fig 3 (b).

A family of reflection spectra and group delay curves of the TDC under various heating current are shown in Figs. 4(a) and 4(b), respectively. Changing the current does not alter their shapes. At a heating current of 124mA, the group delay curve is shifted by 1.5nm with a power dissipation of 500mW. Relationship between the TDC dispersion and heating current at a given wavelength of 1554.1nm is shown in the inset in Fig. 4(b), while the dispersion reaches -260ps/nm with a heating current of 144mA and power dissipation of 700mW. Figures 4(c) and 4(d) demonstrate the group delay ripple with heating current of 62mA and 124mA, respectively. It can be seen that the peak-to-peak ripple is kept within 14ps. From the comparison between Figs. 3(b), 4(c) and 4(d), one can conclude that the group delay ripple is not deteriorated during the tuning process.

 

Fig. 3. Experimental results of the NLCFBG made with a linearly chirped phase mask: (a) reflection profile and group delay curve, (b) group delay ripple across the passband.

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Fig. 4. Tuning characteristics of the TDC: Impact of heating current I on (a) reflection profile, (b) group delay curve (inset: dispersion at 1554.1nm vs. Heating current I), (c) and (d) group delay ripple.

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To demonstrate the capability of the TDC, a 40-Gb/s optical transmission experiment is carried out (Fig. 5(a)). The center wavelength of the DFB-LD is 1554.1nm, and the signal is externally modulated at 40-Gb/s in a CSRZ format. The SMF has a dispersion of 17ps/nm/km and length = 5 or 10km to change the accumulated dispersion. A variable optical attenuator is employed to adjust the signal power, and the TDC is located after the attenuator to compensate the chromatic dispersion accumulated in SMF. Finally, the signal is sent into a BER tester. The measured BER is shown in Fig. 5(b), while the power penalty after TDC at a BER=10^-10 is less than 0.6dB~ 0.7dB. This power penalty may be caused by the residual chromatic dispersion and/or polarization mode dispersion.

Compared with TDCs obtained by other approaches [5–8], this device has a relatively smaller tuning range (from -60ps/nm to -260ps/nm). However, it is sufficient for the residual dispersion compensation, which is the major purpose of this device; and a larger tuning range could be achieved using this method by increasing the length of the grating. Moreover, this device, with a remarkably small group delay ripple, satisfies many requirements for the real-world applications, such as low-cost, power efficiency, small size and simple fabrication, etc.

 

Fig. 5. Experiment in a 40-Gb/s system for the TDC evaluation: (a) schematic of the 40-Gb/s experimental setup. BERT=BER Tester, TDC=Tunable Dispersion Compensator, VOA=Variable Optical Attenuator, (b) performance of the TDC in 40-Gb/s optical transmission system

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4. Summary

In this paper, a modified reconstructed equivalent chirp method is proposed in the design and fabrication of nonlinearly chirped fiber Bragg gratings. By employing a linearly chirped phase mask instead of a uniform phase mask, precision requirement during fabrication is relaxed and performance improved. A thermally tunable dispersion compensator is demonstrated accordingly, with a tuning range from -60ps/nm to -260ps/nm, a peak-to-peak group delay ripple <14ps, a 3-dB bandwidth≈2nm and total power dissipation around 700mW. Employing this device, the power penalty in a 40-Gb/s×5/10km conventional single mode fiber using CSRZ format is less than 0.7dB. Furthermore, this method demonstrated in this paper would be promising and have potential applications in some relative fields, such as optical signal processing, microwave photonics, etc.