## Abstract

We propose and experimentally demonstrate a novel method for tunable dispersion slope compensation. We use two uniform fiber Bragg gratings (FBGs), a spatially designed S-bending stage and 4-port circulator. Two FBGs are mounted on each surface of a metal plate along the calculated quadratic curve. The dispersion slope (DS) can be tuned by adjusting a nonlinear strain along two uniform FBGs without changing second order dispersion as well as the central wavelength. In the experiment, a DS tuning range from -13.9 to -54.8 ps/nm^{2} is achieved with the bandwidth of larger than 2.0 nm.

©2009 Optical Society of America

## 1. Introduction

At bit rates of 160 Gb/s and above, the dispersion slope (DS) gives a limit of transmission distance since typical values of dispersion slope for standard transmission fibers are in the range from 0.04 to 0.1 ps/nm^{2}km [1–3]. Thus tunable dispersion slope compensator (TDSC) is necessary. Among the various dispersion slope compensators, fiber Bragg grating (FBG) based methods have been of interest due to their many advantages of low loss, small size, low optical nonlinearity, and the flexible tuning mechanisms involved. Many methods for FBG-based dispersion slope compensation have been proposed using nonlinearly chirped FBGs [4,5], mechanical tuning of chirped FBGs [6–9], thermal tuning of chirped FBGs [10–13], or specially designed complex FBGs [14]. However, these methods have drawbacks such as complex control system, limited tunability, or a sophisticated structure [6,7]. Moreover, for devices with these configurations, when the dispersion slope is tuned, group velocity dispersion (GVD) or the center wavelength of FBGs will also varies. Thus, additional dispersion compensation with a fixed center wavelength is necessary [4,12].

Previously, we proposed the tunable dispersion and DS compensator using strain-chirped FBG [2]. However, in that scheme, a finite amount of residual group velocity dispersion (GVD) exists with DS and a sophisticated plate with a tapered thickness is needed.

In this paper, we demonstrate a novel pure TDSC using a single tuning element based on the systematic bending method along the fiber without a center wavelength shift. It is based on the technique to induce a quadratic strain on each FBG, respectively with S-bending of a flexible metal plate. Using this method, dispersion slope could be controlled in the range from -13.9 to -54.8 ps/nm^{2} with a bandwidth of larger than 2.0 nm without a center wavelength shift.

## 2. Structure design and operation principle

The proposed pure TDSC consists of a specially designed S-bending stage, a 4-port circulator, a metal beam, and two FBGs as shown in Fig. 1. As for S-bending stage, it includes a rotation stage and two metal plate holders with four pivots [15]. Two uniform FBGs are mounted on the metal beam along the quadratic curve. When we rotate two movable pivots with an angle of *θ*, two metal supporters are oppositely incline to the initial axis with an angle of *φ*, leading to the S-shape bending of the metal beam as shown in Fig. 1(a). An optical signal is launched into the nonlinearly strain induced FBG1 via a four-port circulator, and then is reflected and redirected to the nonlinearly strain chirped FBG2. Since GVD of the two FBGs are the same absolute value but opposite sign, purely DS compensating signal is out from the fourth port of the circulator. Moreover, since the two FBGs are mounted on the single metal plate, no additional temperature control is required to keep the same temperature condition for them.

When a metal beam on which the FBG is mounted is bent in the shape of S as shown in Fig. 1(a), the strain distribution along the length *x* is given as [16],

where *ρ* is the radius of the curvature at the position *x*, d is the thickness of the metal beam, *l* is the length, and *z* is the deflection of the metal beam. Using simple geometric calculations, Eq. (1) can be expressed as

where *θ* is the rotation angle. Above Eq. (2) shows that the tensional and compressive strain can be symmetrically induced with respect to the rotation angle of *θ*.

When the FBGs are mounted on the metal beam with an angle *α* to the *x* axis, the strain can be given by [17]

where *C* is a constant (0 < *C* < 1) depending on the properties of the glue and *f*(*x*) is the function of the curve on which the FBGs are placed. Figure 2(a) and (b) clearly show that the strain field experienced by the FBG 1 and FBG2 is quadratic along the x-axis when the beam is bent in an S-shape. Also their Bragg wavelength distributions *λ _{B}* can be described as the following equation,

where *n* is the effective refractive index of the fiber core and Λ is the period of the grating at point x, and are seen in Fig. 2(a) and (b), respectively. Figure 2(c) and (d) show the calculated group delay of FBG1 and FBG2, respectively as a function of wavelength for different amounts of the S-bending stage rotation.

For FBG1, the induced negative GVD decreases when the rotation angle becomes larger. Similarly, for FBG2, the induced positive GVD decreases with increasing rotation angle. Therefore, for the concatenated module which was built using above two FBGs and a 4-port circulator as shown in Fig. 1(b), total GVD becomes zero and only the dispersion slope is generated with a fixed center wavelength as shown in Fig. 2(e). Therefore, we can obtain a tunable DS compensation with a fixed wavelength with our novel S-bending stage. Here we
assumed the center wavelength of FBG is 1556.8 nm and FBGs are attached on the beam as a curve *f*(*x*) = 0.36*x*
^{2}.

## 3. Fabrication and experimental results of TDSC

In the experiment, FBGs were fabricated by using the phase mask technique. Both FBGs have a 3-dB bandwidth of 0.17 nm, a reflectance of ~95% at Bragg wavelengths of 1556.73 and 1556.89 nm, respectively and a length of 60 mm. First, we drew the calculated quadratic curve on the steel beam for the fiber to be placed accurately along the desired curve. Then, fiber with FBG was carefully bonded on the each surface of the steel beam with thickness of 0.38 mm along a quadratic curve with a function of 0.36*x*
^{2} using ultraviolet (UV)-curable adhesive (3021 from ThreeBond). The thickness of the adhesive was about 200 μm so that FBGs were fully covered with adhesive.

Figures 3(a) and (c) shows the measured reflection spectra and group delay in FBG1 and FBG2, respectively for different rotation angles. In FBG1, the induced negative GVD decreases with increase of rotation angle. Similarly, For the FBG2, when the rotation angle increases, the induced positive GVD decreases. However, in both cases, the induced negative dispersion slope becomes smaller with the increase of rotation angle as shown in Fig. 3(b) and (d).

By cascading these two FBGs via 4-port circulator, the tunable dispersion slope compensator (TDSC) was built. Figures 4(a) and (b) shows the measured time delay and transmission spectra of the TDSC module, respectively. The DS values which are obtained from quadratic fitting to time delay data shown in Fig. 4(a), decreased from -54.8 to -13.9 ps/ nm^{2} as the rotation angle increased from 2.5 to 4.5 degree and the 3-dB bandwidth of the module increased from 2.3 to 5.0 nm. It can be noticed that the measured DS values are different from those of calculation. It may be attributed to the fact that in the calculation we assumed that two FBGs have same Bragg wavelength and the glue constant C=1 in the Eq. (3). However, in the real module, the value of C will be smaller and there are also some deviations from the attaching curve.

Over the DS tuning range from -54.8 to -13.9 ps/ nm^{2}, 3-dB bandwidth of the TDSC was larger than 2 nm and the group delay ripple was less than 20 ps without any appreciable the central wavelength variation. This group delay ripple (GDR) is due to glue non-uniformity and non-apodization of the grating. It can be reduced by minimizing the glue non-uniformity and by improving the FBG fabrication process such as apodization technique and may be averaged out over a large bandwidth at high bit rate signal. Therefore, our proposed TDSC could effectively compensate the dispersion slope just by adjusting the rotation angle of a S-bending stage.

## 4. Conclusion

In this paper, we have demonstrated a novel TDSC by inducing nonlinear strain distribution along two FBGs mounted on each surface of the metal beam. As the signals came through the FBGs, the GVD was cancelled and the DS could be adjusted due to the sign of the induced group delay in each FBG. As the result, the DS was dynamically adjusted in the range from -13.9 to -54.8 ps/nm^{2} with the bandwidth of larger than 2.0 nm with the respect to the rotation angle (2.5° < *θ* < 4.5 °). With improved GDR, the proposed TDSC can be useful in ultra high-speed WDM or OTDM systems.

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