## Abstract

We experimentally demonstrate a simple scheme for the tunable pulse repetition-rate multiplication based on the fractional Talbot effect in a linearly tunable, chirped fiber Bragg grating (FBG). The key component in this scheme is our linearly tunable, chirped FBG with no center wavelength shift, which was fabricated with the S-bending method using a uniform FBG. By simply tuning the group velocity dispersion of the chirped FBG, we readily multiply an original 8.5 ps, 10 GHz soliton pulse train by a factor of 2~5 to obtain high quality pulses at repetition-rates of 20~50 GHz without significantly changing the system configuration.

© 2004 Optical Society of America

## 1. Introduction

Stable sources of high repetition-rate short pulses in the 1550 nm telecommunication wavelength bands are of great importance for the development of future high-speed optical time division multiplexing (OTDM) systems, and all-optical packet switching networks [1]. A range of techniques for the generation of high repetition-rate short pulses have thus been devised and demonstrated so far. For example, active harmonically mode locked fiber lasers [2], the combined use of a fast electro-optic modulator and adiabatic pulse compression techniques [3], mode locked semiconductor lasers [4], soliton compression of frequency beating signals [5], and so on. However, the direct generation of high quality short pulses with a few pico-second duration at a repetition-rate of over 40 GHz is difficult to achieve in practice since it requires the corresponding high-speed electronic components or/and the precise control of optical properties in the laser cavity. One attractive and simple method for the generation of optical short pulses at repletion rates beyond those achievable with the conventional direct generation approaches, is to increase the repetition-rate of a low rate source using all-optical pulse rate multiplication techniques [6,7,8,9]. Several research groups suggested a variety of all-optical methods for pulse rate multiplication and those methods are mainly based on spectral filtering of the input pulse source [6], temporal Talbot effect in a dispersive medium [7,8], or an array of multiple uniform fiber Bragg gratings (FBG’s) with a low reflectivity [9]. The approach based on temporal Talbot effect is likely to be the most promising and simple means among them since we can obtain the desired multiplication factor without pulse distortion by simply controlling the group velocity dispersion (GVD) of the dispersive medium. In this simple and flexible approach the dispersive medium can be either optical fiber [7] or a chirped fiber Bragg grating (FBG) [8], and the maximum multiplication factor is known to be limited by the duty cycle of the input pulse source [10]. Furthermore, a recent advance of the Talbot effect based pulse rate multiplication technology allows for achieving a higher multiplication factor than the limitation by the duty cycle. N. K. Berger *et al*. demonstrated a possibility that overlapping between adjacent pulses in the Talbot effect could still result in both rate multiplication and temporal width compression [11].

In such pulse rate multiplication approaches one important function to be implemented together is flexible tunability of multiplication factor since it can provide a wide range of potential applications for the methods. However, in the previous Talbot effect based pulse rate multiplication demonstrations which mostly employed either a fixed length of fiber or a fixed GVD of a chirped FBG it was not straightforward to achieve the flexible multiplication factor tuning without significant system configuration change [7,8]. Recently C. J. S. de Matos *et al*. proposed an advanced scheme based on the fractional Talbot effect in optical fiber for tunable repetition-rate multiplication, and experimentally demonstrated a 10~30 GHz repetition-rate tuning [12]. However, the complexity of the configuration requiring several optical fibers with tight specifications of length and dispersion could be a limiting factor in terms of practical implementation of a simple and robust device.

In this paper we demonstrate a more practical and simple scheme based on the fractional Talbot effect in a linearly tunable, chirped fiber Bragg grating for the tunable repetition-rate multiplication. The key component in this scheme is our linearly tunable, chirped FBG with no center wavelength shift. The linear group delay and the corresponding GVD of the chirped grating fabricated with the S-bending method using a uniform FBG can be easily tuned by adjusting the bending angle [13]. By tuning the GVD of the chirped FBG we obtain high quality pulses at repetition-rates in the range of 20~50 GHz from an original 8.5 ps, 10 GHz soliton pulse train. Our results imply that both the use of shorter input pulses and the proper tuning of the GVD should result in the further increase of the multiplication factor.

## 2. Experiment and results

Our experimental setup for the proposed chirped fiber Bragg grating based tunable pulse rate multiplication scheme is shown in Fig. 1. The input pulses with an 8.5 ps temporal width at a repetition-rate of 10 GHz are first generated using an active, harmonically mode locked erbium fiber ring laser (EFRL) operating at a wavelength of 1556.5 nm. These pulses were then fed onto a chirped FBG using a circulator. A polarization controller was employed since the chirped FBG showed a small amount of polarization dependence due to the S-bending induced directional strain. The reflected output pulses from the chirped FBG were monitored by an optical spectrum analyzer, a second harmonic generation (SHG) autocorrelator, and a sampling oscilloscope.

In order to obtain a pulse repetition-rate multiplication by a factor M using the temporal Talbot effect in a chirped FBG, the following condition should be satisfied [10].

where *T* is the period of the input pulses and $\frac{{\partial}^{2}\Phi}{\partial {\omega}^{2}}$ is the GVD coefficient of the chirped FBG. N is an arbitrary integer number and $\frac{N}{M}$ should be a noninteger rational number. Using the above equation we performed a simple calculation to estimate the required GVD levels to obtain the multiplication factors of 2~5 assuming *N*=1. The results are summarized in the Table 1.

The linearly tunable, chirped FBG used in this experiment was fabricated with the Sbending method using a uniform FBG embedded onto a thin and highly flexible metal plate [13]. The photosensitive fiber used for our FBG fabrication was boron (B)-Germanium (Ge) codoped silica fiber which was chosen due to its high photosensitivity. We used the UV beam scanning method with a phase mask to fabricate the uniform FBG. The length of the uniform FBG was 11 cm. The thin metal plate with the uniform FBG was fixed onto two small metal supports with both a fixed pivot and a moving pivot, and was then bent into an S-shape by rotating the moving pivots as shown in Fig. 1. Both of the pivots moved through the same angle when the metal plate was bent. This bent metal plate induced a linear strain gradient along the FBG, which led to chirp. By adjusting the rotation angle (θ) of the moving pivot we can thus control the amount of induced chirp and the corresponding gradient of linear group delay without changing the grating center wavelength as shown in Fig. 2(a). As shown in Fig. 2(b) spectral bandwidth of the tunable chirped FBG was observed to increase in proportion to the rotation angle whilst its reflectivity was observed to decrease. The tunable chirped FBG showed a better reflectivity at the longer wavelength band compared to the shorter wavelength band. The operating principle of our linearly tunable, chirped FBG is fully described in Ref. [13]. Figure 3 shows the measured GVD with respect to rotation angle of the moving pivot (θ). The dispersion was observed to be inversely proportional to the rotation angle. By adjusting the rotation angle in the range of 1.5~5°, we could readily obtain the required GVD’s for the 2~5 times pulse rate multiplication as shown in the Table 1. Having this tunable chirped FBG and an input 10 GHz soliton pulse source ready, we were in a position to perform a pulse train multiplication experiment at 20~50 GHz variable repetition-rates.

At first, we performed the autocorrelation measurement to characterize the optical properties of the multiplied output pulses in the temporal domain using a SHG autocorrelator. The measured autocorrelation traces of the multiplied output pulse train at various repetition-rates of 20~50 GHz are shown in Fig. 4(a) together with that of the original 10 GHz input pulses from the mode-locked fiber 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 was mainly due to the poor performance of the autocorrelator used in this experiment although the group delay ripple and the non-uniform reflectivity of the chirped FBG could lead to a small amount of output pulse distortion. Next, the sampling scope measurement using a fast pin diode and sampling oscilloscope of a combined 45 GHz bandwidth, was performed to reconfirm both the functionality and the output pulse quality of our tunable pulse rate multiplication scheme. The other purpose of the sampling oscilloscope measurement was to assess pulse intensity noise that cannot be observed in the autocorrelation measurement. No significant intensity noise was observed at the output pulses. Stable operation of the high quality, tunable pulse rate multiplier was readily achieved as shown in Fig. 4(b).

## 3. Discussion and conclusion

We have experimentally demonstrated the use of a linearly tunable, chirped fiber Bragg grating to obtain all-optical, tunable pulse repetition-rate multiplication based on the fractional Talbot effect. By tuning the GVD of a chirped FBG based on the S-bending method using a uniform FBG, we multiplied an original 8.5 ps, 10 GHz soliton pulse train by a factor of 2~5 to obtain high quality pulses at repetition-rates of 20~50 GHz. Further enhancement of the multiplication factor could be easily achieved by both using shorter input pulses (≪8.5 ps) and tuning the GVD. We believe that the FBG approach should provide a simple and flexible way of manipulating the temporal characteristics of pulses for future high-speed, high-capacity optical communication systems and photonic systems.

## Acknowledgments

The authors thank Y. M. Jhon, and J. W. Choi of KIST for their help in the autocorrelation measurement, and thank M. J. Chu of ETRI for the loan of a 10 GHz erbium fiber laser and associated help. The authors are also grateful to J. Bae of KIST for his help in the S-bending chirped FBG design and fabrication

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