## Abstract

A largely tunable chirped fiber Bragg grating (CFBG)-based dispersion compensator with fixed center wavelength is demonstrated. Tunable dispersion ranging from 178 to 2126 ps/nm, corresponding to a large range of 3-db bandwidth from 0.42 to 5.04 nm, is realized by using a 10 cm-long CFBG with an original bandwidth of 1.61 nm. The variation in center wavelength is less than 0.2 nm.

©2003 Optical Society of America

## 1. Introduction

Dispersion compensation is necessary to maintain adequate performance in long haul optical fiber communication systems at a high bit rate of 10 Gbit/s or beyond. Chirped fiber Bragg grating (CFBG)-based dispersion compensators have been widely studied as a simple and low cost solution [1]. They are highly effective and free from nonlinear effects, have low insertion loss, and are tunable in compensation capability to cater for different system requirements. Their main limit, i.e., to be an intrinsical narrow-band component, has been demonstrated to overcome by means of different writing techniques [2,3]. Various techniques have been demonstrated to obtain tunable CFBG-based dispersion compensator using thermal, mechanical, electrical, and magnetic methods, but few of them can fix the center wavelength during the process of tuning [4–9]. It is a great drawback in tunable dispersion compensator since shift of the center wavelength may cause the signal wavelength being located at the edge of the effective band of the CFBG.

We have ever reported a method to chirp a uniform fiber Bragg grating to a great extend (3-dB bandwidth=11.32 nm) nearly without center wavelength shift [10]. It was realized by gluing the grating in a slanted direction onto the lateral side of a simple-supported beam and bending the beam to generate stain gradient along the grating. It’s a good method to produce chirp in gratings with short length, but not competent for long gratings like what are used in dispersion compensators due to its nonlinear feature (which will be described in detail in the following section). In this paper, a modified method is presented and used to fabricate a largely tunable CFBG-based dispersion compensator with fixed center wavelength.

## 2. Design and principle

Figure 1 shows the schematic diagram of the CFBG-based dispersion compensator. A 10 cm-long CFBG is glued in a slanted direction onto the lateral side of a right-angled triangle cantilever beam with length *L*=18 cm, width at the fixed end *b*
_{0}=3 cm, and thickness *h*=0.8 cm. The CFBG, which was deeply written in a H_{2}-loaded single-mode fiber, has a reflectivity higher than 0.999. The original 3-dB bandwidth and center wavelength of the CFBG are 1.61 nm and 1562.5 nm, respectively. The angle between the axis of the CFBG and the central axis of the lateral side of the beam is *θ*=4.5°.

The basic principle of tunable dispersion compensator is the same as described in Ref. [10]. When the cantilever beam is bent by applying a force or displacement on the free end, half of the CFBG is under varying tension whereas the other half is under a varying compression. The strain on the neutral layer of the beam is zero. If the center of the grating is located well to the neutral layer of the beam, there will be no strain effect at the center of the grating. Therefore, the center wavelength of the grating may keep fixed during the process of tuning since the strain at the two halves of the grating is symmetrical. As compared to the method presented in Ref. [10], the main mend is the use of the right-angled triangle cantilever beam as the grating carrier, whereas it was a rectangle simple-supported beam in Ref. [10]. The former is a kind of beam with uniform strength while the later is not. If the small effect of the transverse moment is neglected, curvature (not radius of curvature, as wrong defined in Ref. [10]) on the neutral layer of the beam at a given point of *x* (0<*x*<*L*), can be given by

where *M*(*x*) and *I*(*x*) are the bending moment and the moment of inertia of the beam cross section at *x*, *E* the Young modulus, *F* and *f*, the force and displacement at the free end of the beam, respectively.

The strain-induced variation in Bragg wavelength, *Δλ _{B}* (

*λ*denotes the Bragg wavelength), for any segment of the grating is directly proportional to the local axial strain along the grating (

_{B}*ε*) [10]. Based on the analysis described in Ref. [10], the axial strain along the grating is directly proportional to

_{ax}*κ*and the grating length from the given segment to the cross point of grating and the neutral layer of the beam,

*l*(-0.5

*L*<

_{g}*l*<0.5

*L*), where

_{g}*L*is the total length of the CFBG. Therefore, the final description of variation in Bragg wavelength at a given grating segment with

_{g}*l*can be described as [10]

where *C*(0<*C*<1) is a constant introduced to describe the efficiency of strain transfer from the beam to the grating, and *p _{e}* the effective photoelastic constant (~0.22) of the fiber material. The bandwidth variation thus can be described as

where *A*≅0.5*C*(1-*p _{e}*)

*λ*sin(2

_{Bc}L_{g}*θ*), is a constant.

*λ*is the center wavelength of the CFBG.

_{Bc}It can be seen from the Eq. (1) that the value of curvature is independent of *x*, i.e., *κ* is uniform along the beam. That is the main improvement in our modified method since it is dependent on *x* for the simple supported beam used in Ref. 10, where we assumed it to be independent of *x* for the grating was much shorter than the beam. A uniform curvature in the beam is very important for keeping a linear chirp in the grating as shown by Eq. (2), and a linear chirp means linear time delay and uniform dispersion in the grating. The above equations show that the bandwidth of the grating, i.e., the dispersion of the dispersion compensator, can be linearly tuned by applying force or displacement at the free end of the cantilever beam.

Figure 2 shows the theoretical curvature distribution and Bragg wavelength variation of the method presented in Ref. [10] and in this paper. We assumed that the beam dimension and grating parameters are the same, *C*=0.9, and the curvatures of the beam at the center of the grating is 0.2 m^{-1}. It is obviously shown that the tuning efficiency and linearity of the CFBG are greatly enhanced by using the modified method.

## 3. Results and discussion

Figure 3 shows the measured reflection spectra under different adjustment for the tunable CFBG-based dispersion compensator. The 3-dB bandwidth can be tuned in a large range from 0.42 nm to 5.04 nm with high reflection maintained. A maximum variation in center wavelength of 0.18 nm is observed during the process of tuning, which is mainly caused by the effect of the transverse moment that is neglected in theoretical analysis, and the small offset between the center of the grating and the neutral layer of the beam [10]. Figure 4 shows the 3-dB bandwidth and the variation in center wavelength versus the displacement at the free end of the cantilever beam. The tuning rate calculated by linear fit of the experimental data is 0.45 nm/mm. The *R*-squared value of the linear fit to the experimental data is 0.9991, which shows a good linearity in tuning of bandwidth. The factor of *C*, inferred from the tuning rate and the other experimental parameters, is 0.83, which is much better than that (~0.55) achieved in Ref. [10], showing improved efficiency for strain transfer from the beam to the grating. A micrometer of 10 µm resolution was used to adjust the displacement on the free end of the beam. Consequently high precision control with resolution of 0.0045 nm is achieved for bandwidth, which is corresponding to about 23 ps/nm for resolution of dispersion at bandwidth of 0.42 nm.

To study the dispersion property of the tunable dispersion compensator, the time delay was measured under different adjustment. The results measured with various 3-dB bandwidths of 0.42, 2.05, and 5.04 nm (see Fig. 5) show good linearity as expected and low ripples. The dispersions calculated by linear fit are 2126, 405, and 178 ps/nm, respectively. Given a longer grating, a higher dispersion and larger tuning range can be obtained. Further studies involving system applications of this tunable dispersion compensator, the origin and system effects of polarization mode dispersion arising from fiber bending in the chirped fiber Bragg grating are being carried out.

## 4. Summary

A largely tunable CFBG-based dispersion compensator with fixed center wavelength has been demonstrated. It used a right-angled triangle cantilever beam as the CFBG carrier and to generate uniform strain gradient along the CFBG, resulting in a linearly tunable chirp and dispersion. Tunable dispersion ranging from 178 to 2126 ps/nm, corresponding to a large range of 3-dB bandwidth of 0.42 to 5.04 nm, has been realized by using a 10 cm-long CFBG with an original bandwidth of 1.61 nm. The variation in center wavelength is less than 0.2 nm.

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