1. Introduction

Dispersion compensation has been one of the most significant issues for the high-speed optical communication systems. Chirped fiber Bragg gratings (CFBGs) have been of interest in the applications to dispersion compensating devices due to their versatile advantages like fiber compatibility, polarization insensitivity, low nonlinearity, low loss and so on [1–2]. To provide the dispersion tunability of CFBGs, the great efforts based on thermal heater [1]-[2], tapered fiber by etching [3]-[4], stacks of piezoelectric actuators [5], and adhesive package with gradient thickness [6]. The previous methods, however, have the drawback of the center wavelength shift into the longer wavelength. To solve the limitation of the previous methods, a range of the methods to induce the wide tuning range of dispersion without the center wavelength shift have been intensively investigated [7–14]. Using a divided thin-film heater with a peltier element, the tunable dispersion compensator based on a fiber grating was reported [7]. To prevent the center wavelength shift, two heating elements like a thin-film heater and a peltier element were used. However, it has the complex structure and the small tuning range of dispersion. Most of the methods to improve the dispersion controllability of a fiber grating without the center wavelength shift are based on the symmetrical bending method [8]-[14]. To induce the symmetrical bending along a fiber grating, versatile schemes based on moving block [8]-[9], curved fiber gratings attached on a plate [10]-[11], and a rotational stage with pivots [12]-[13] were proposed.

In this letter, a new method to control the chromatic dispersion of uniform FBG is proposed and experimentally demonstrated. Since the symmetric bending of the flexible cantilever beam with the uniform FBG is induced by the interaction between two translation stages and a sawtooth wheel, the tension and compression caused by the symmetrical bending can effectively control the properties of the fiber grating like bandwidth and group delay. We successfully obtain the wide tuning range of chromatic dispersion of the uniform FBG (from 312.6 ps/nm to 35.9 ps/nm) without the center wavelength shift, which is less than 0.02 nm. We also suppress the group delay ripple as low as ~ ±5 ps. And we also demonstrate the application of the proposed tunable dispersion compensation technique to the tunable repetition-rate multiplication and obtain high quality pulses at repetition-rates in the range of 20 ~ 40 GHz from an original 1.8 ps, 10 GHz soliton pulse train.

2. Tunable chromatic dispersion controller based on uniform fiber Bragg rating with symmetrical bending technique and its application to the tunable repetition-rate multiplication

When the linear strain like the tension and compression strain is induced along the length of a fiber grating, the resonant wavelength is shifted into the longer and shorter wavelength, respectively, and the corresponding dispersion parameter (D) is written as

where Δτ is the group delay induced by the strain gradient along the grating, Δλ (=λ _L-λ _S) is the difference of two wavelength reflected at either end of the grating, and λ_p is the center wavelength of the grating. The induced strain gradient (ε) by the symmetrical bending with respect to the variation of translation stage can be written as [8]-[9]

where L is the total length of cantilever beam and d is the distance between the grating axis and neutral axis, which is equal to the half thickness of cantilever beam. It is clearly obvious that the tension and compression strain can be induced in the region where x<L/2 and L/2<x<L, respectively. The uniform FBG is free of strain under x=L/2. Consequently, the chirp ratio of uniform FBG can be changed by the tension and compression strain induced by the symmetrical bending, but the center wavelength is not changed since the effect of tension and compression strain on the center wavelength shift should be compensated mutually. Therefore, the group delay and dispersion can be effectively controlled without the center wavelength shift.

Figure 1(a) shows the experimental setup of the proposed chromatic dispersion-tuning device based on the symmetrical bending technique along the uniform FBG. The proposed method is based on the sophisticated fiber bending technique to induce symmetrically linear strains gradient in the center of the uniform FBG. The proposed chromatic dispersion controller consists of two translation stages, a sawtooth wheel, two pivots, a micrometer, and two cantilever beam holder. The sawtooth wheel is positioned at the middle of fixed stage. Each of two translation stages has a gear, which can convert the linear motion of translation stage into the rotary motion of sawtooth wheel. When the left translation stage is moved by the micrometer, its gear rotates the sawtooth wheel and the right translation stage is moved oppositely by the rotary motion of sawtooth wheel. As two translation stages are moved oppositely by the interaction between two gears and a sawtooth wheel, the position of two pivots on two translation stages is changed oppositely and the symmetrical bending along the flexible cantilever beam can be induced. Consequently the tension and compression strain along the uniform FBG through the symmetrically curved cantilever beam can be induced, which are corresponding to the bending direction. Figure 1(b) shows the induction principle of tension and compression strain along the uniform FBG based on the symmetrical bending. Therefore, the properties of uniform FBG like bandwidth and group delay can be effectively controlled by the tension and compression strain at each side of the FBG without the center wavelength shift.

The flexible cantilever beam is made of a spring steel with the high resistance against fatigue and corrosion. The length and thickness of cantilever beam are 15 cm and 0.2 mm, respectively. The uniform FBG was carefully attached to the cantilever beam using the UV curable epoxy to reduce the phase error along the fiber grating due to the microbending, which can induce additional phase error._ The uniform FBG was apodized by the Blackman profile to reduce the sidelobes and the group delay ripple [12]. Its length and resonant wavelength were 11 cm and 1557.1 nm, respectively.

Figure 2 shows the experimental results of reflection spectra of the uniform FBG with the variation of translation stage. When the left translation stage is moved by the micrometer in the range from 0 mm to 18 mm, the bandwidth of the reflection spectrum of the uniform FBG becomes broad due to the enhancement of tension and compression strain. With the moving distance of left translation stage to 18 nm, the bandwidth of the uniform FBG increased by ~7.5 nm, and its reflectivity decreased by ~5 dB, on average. It is clearly evident that the center wavelength of the uniform FBG is not changed due to the symmetrical bending. As the micrometer moves the left translation stage more and more, the bending curve along the cantilever beam becomes strong, which can increase the amount of tension and compression strain corresponding to the bending direction. A large amount of strain gradient changes the chirp ratio along the uniform FBG and consequently makes its bandwidth be broad without the center wavelength shift. As shown in Fig.2, the center wavelength shift over the whole dispersion tuning range was less than 0.02 nm.

Figure 3 shows the measured group delay of the uniform FBG with the variation of the translation stage. When the left translation stage was moved to 16 mm, the dispersion of uniform FBG was changed by 39.4 ps/nm. Figure 4 shows the measured group velocity dispersion with respect to the variation of translation stage and the theoretical fitting curve using Eqs. (1) and (2). Theoretical result is good agreement with the experimental one. The small difference between two results may be caused by the imperfection in the fabrication of the grating or in curing process and coating material. When the left translation stage was changed from 0 mm to 18 mm, the dispersion of CFBG was controlled in the range from 312.6 ps/nm to 35.9 ps/nm.

Figure 5 shows the experimental results of the group delay ripple as two stages were moved oppositely by the micrometer. We successfully reduced the group delay ripple and the amplitude of group delay ripple was less than ~±5 ps over the whole dispersion tuning range. Since the uniform FBG apodized by the Blackman profile was utilized, the stitching error induced by the imperfection of the phase mask could be removed and the group delay ripple could be suppressed. It is obvious that the uniform FBG is more effective to utilize the tunable chromatic dispersion controller compared with the chirped FBG.

 

Fig. 1. (a) Schematic of the proposed chromatic dispersion controller with the uniform FBG. (b) Symmetrical bending scheme based on two moving stage. Tension and compression strain depending on the bending direction can be induced.

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Fig. 2. Measured reflection spectra with the variation of translation stage. Two translation stages were oppositely moved by the micrometer and a sawtooth wheel. The bandwidth of the uniform FBG was changed in the range from 0.5 nm to 7.5 nm corresponding to the moving distance range of translation stage (0 mm < y < 18 mm).

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Fig. 3. Measured group delay with the variation of translation stage.

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Fig. 4. Measured group velocity dispersion with the variation of translation stage and theoretical fitting curve.

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Fig. 5. Measured group delay ripple with the variation of translation stage.

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Based on the temporal Talbot effect using the proposed tunable dispersions compensation technique, we could obtain tunable repetition at repetition-rates in the range of 20 ~ 40 GHz from an original 1.8 ps, 10 GHz soliton pulse train [14]-[18]. The input pulses with a 1.8 ps temporal width at a repetition rate of 10 GHz are first generated using an active, harmonically mode locked erbium fiber ring laser (EFRL). These pulses were then fed onto the proosed tunable dispersion compensator using a circulator. A polarization controller was employed to stabilize the polarization state of the input pulse and the fiber grating. The reflected output pulses from the tunable dispersion compensator were monitored by an optical spectrum analyzer, a second harmonic generation (SHG) autocorrelator. Figure 6 shows the measured autocorrelation traces of the multiplied output pulse train at various repetition rates of 20 ~ 40 GHztogether with that of the original 10 GHz input pulses from the mode-locked laser. The temporal width of the multiplied pulses was measured to be close to that of the original soliton pulses. Note that some degree of pulse shape distortion of the measured traces is mainly due to the poor performance of our autocorrelator used in this experiment and the group delay ripple of the proposed tunable dispersion compensator, which can induce the unwanted amplitude jitter [18].

 

Fig. 6. Measured autocorrelation traces of the multiplied output pulse train at various repetition-rates of 20 ~ 50 GHz together with that of the original 10 GHz input pulses from the mode-locked laser.

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3. Discussion and conclusion

We proposed and experimentally demonstrated a new and simple chromatic dispersion controller based on the uniform FBG with the symmetrical bending technique. We precisely controlled the dispersion value of uniform FBG by inducing the linear strain gradient based on the proposed tuning device. The symmetrical bending curvature was induced by the interaction between two translation stages with gears and a sawtooth wheel in the middle of fixed stage. The properties of the uniform FBG like bandwidth and group delay could be flexibly controlled by the tension and compression strain corresponding to the bending direction. Accordingly, the dispersion value of the grating was effectively controlled without the center wavelength shift, which was less than 0.02 nm. We successfully suppressed the group delay ripple over the whole tuning range of chromatic dispersion. The amplitude of group delay ripple was less than ~±5 ps. And we also demonstrated the application of the proposed tunable dispersion compensation technique to the tunable repetition-rate multiplication and achieved high quality pulses at repetition-rates in the range of 20 ~ 40 GHz. The proposed dispersion tuning method can be useful for application to the tunable dispersion devices in future optical communication systems.