We present a novel method for realizing a slow light with a broadband flat Brillouin gain and low distortion by using an optical frequency comb. We obtained a pump light consisting of 20 discrete line spectra using an optical frequency comb generation technique and a flat SBS gain with a 200 MHz bandwidth. We have realized a large relative pulse delay of 2.46 while suppressing the broadening factor to less than 1.19 for a pulse with a duration of 5.44 ns.
©2008 Optical Society of America
There is great interest in finding a way to control the propagation speed of optical pulses through a medium because it offers the potential to realize all-optical network technologies such as optical buffering, memory, and signal processing. The group velocity of optical pulses can be controlled by using slow light techniques . Most of these techniques utilize nonlinear effects in an optical fiber such as stimulated Brillouin scattering (SBS) [2, 3], stimulated Raman scattering , or parametric amplification . These approaches have many advantages over other slow light techniques because they can utilize fiber-optic components, and this leads to good compatibility with existing telecommunication systems. Of these techniques, stimulated Brillouin scattering (SBS) based slow light has attracted a lot of attention because it does not require a high pump power.
The main problem with SBS based slow light is pulse distortion accompanied by a pulse delay owing to the narrow SBS gain bandwidth (about 40 MHz). This phenomenon causes severe degradation of the signal quality and limits the maximum pulse delay. To overcome this problem, many approaches have been investigated for broadening the SBS gain spectrum, such as expanding the pump spectrum by externally or directly modulating a pump source with a sinusoidal wave  or Gaussian (super Gaussian) noise [7–9]. However, pulse distortion still occurs when the broadened SBS gain spectrum is dependent on frequency or the bandwidth of the SBS gain spectrum is not sufficiently wider than the signal bandwidth, which causes a change in the signal spectrum. Therefore, SBS gain with a broad and flat spectrum is highly desirable if we are to suppress pulse distortion and increase the maximum pulse delay.
To achieve a flat SBS gain, multi-line spectra pump techniques have been reported that involve using multi pump sources  or multi sideband spectra generated by externally modulating a pump light [11–14]. However, fewer than ten line spectra were achieved and the SBS gain bandwidth remained insufficient.
This paper presents a novel method for realizing a broad and flat SBS gain by using an optical frequency comb generated with a LiNbO3 intensity modulator (IM) and a LiNbO3 phase modulator (PM). We investigated a technique for modifying the optical frequency comb spectrum to realize a broad and flat SBS gain and achieved a flat SBS gain with a bandwidth of over 200 MHz. As a result, we achieved a relative pulse delay Δτ/τ i of 2.46 while suppressing the broadening factor τ d/τ i to 1.19, where Δτ is the pulse delay, τ d and τ i are the pulse widths of the delayed pulse and the pulse before applying the time delay, respectively.
2. Optical frequency comb based flat SBS gain
Brillouin scattering is a nonlinear effect caused by the interaction between a lightwave and an acoustic wave in optical fibers. When a pump light with a frequency ν p is injected into an optical fiber, it generates a gain in the vicinity of the frequency ν p-ν B (ν B: Brillouin frequency shift) in the counter-propagating direction. The SBS process also simultaneously induces a group index increase in the vicinity of ν p-ν B. Therefore, when a signal light with a frequency ν p-ν B is injected into optical fibers in the counter-propagating direction with respect to the pump light, the signal gain increases and the propagation speed of the signal light decreases. This phenomenon is called “slow light”. When a signal field is sufficiently weak and the pump is undepleted, the signal field in an optical fiber is derived by 
where E(ν) is the signal field and k(ν) is the complex wave vector which is derived by
where ⊗ denotes convolution, p(ν) is the pump spectrum, g B (ν) is the intrinsic gain spectrum, which has a Lorentzian shape
where g0 and Δν B are the line-center gain factor and the intrinsic SBS gain bandwidth (FWHM), respectively.
To obtain a broad and flat SBS gain, we must inject a pump light with a broad and flat spectrum. However, we can also obtain a flat SBS gain spectrum by using a pump light with flat multi-line spectra that are equally spaced up to Δν B . This technique does not require a large pump power because the pump consists of discrete line spectra, and not a continuous spectrum.
We used an optical frequency comb technique to generate a pump that met the above requirement. An optical frequency comb is a comb-like optical spectrum with equally spaced spectral lines. A spectrally flattened optical frequency comb generation technique employing a CW light source and optical modulators has been developed for the multi-carrier light source in WDM transmission systems [15–17]. We employed this technique to obtain a broad and flat SBS gain in order to suppress the pulse distortion and extend the maximum pulse delay.
Figure 1 shows the optical frequency comb generator we used to obtain a broad and flat Brillouin gain. It consists mainly of an IM and a PM, both of which are driven by a sinusoidal electric wave with a frequency f m [16, 17]. When a CW light is injected into a PM and sinusoidal phase modulation is applied, modulation sidebands are generated with a frequency spacing equal to the modulation frequency. The power of the nth modulation sideband is expressed as
where E 0 is the input signal field, J n is the nth Bessel function of the first kind and Δθ is the modulation index. Δθ is given by
where V pp is the peak-to-peak voltage of the applied sinusoidal wave, and V π is the half-wave voltage of the PM. Although a large power deviation exists among the sidebands generated by the phase modulation, we can flatten the spectrum by inserting an IM before the PM [16, 17]. The settings required for obtaining a broad and flat optical frequency comb are designed to generate 50 % duty cycle pulses in advance and then modulate them with a large modulation index Δθ at the PM . We controlled the amplitude of the sinusoidal wave and direct current (DC) bias voltage applied to the IM to meet the above condition. In this configuration, the frequency spacing of each line spectrum is the same as f m. The number of line spectra is nearly proportional to Δθ, namely the amplitude of the sinusoidal wave applied to the PM.
Thus, we can realize a flat SBS gain by apply the sinusoidal wave with a frequency f m less than Δν B and expand the bandwidth of the SBS gain by increasing Δθ.
3. Experiment and results
Figure 2(a) shows the experimentally obtained spectrum of the flattened optical frequency comb with f m=10 MHz and Δθ=3.7π. We obtained more than 20 line spectra with a 10 MHz spacing. We also show the simulated results in Fig. 2(a), where we used the same parameters of the experiment. The experimental results and simulation results agreed well. Then, we measured the spectrum of the back-scattered light when this pump was injected into a 25 km-long standard single mode fiber (SSMF). Figure 2(b) shows the SBS gain spectrum. A flat SBS gain with a bandwidth of more than 200 MHz was achieved. However, we can see a 15-dB peak at each end of the spectrum, and this results in signal pulse distortion when the signal spectrum overlaps this spectrum region.
Here, we present a novel method for realizing a flat SBS gain spectrum without peaks. To eliminate the peaks, we adjusted the DC bias voltage applied to the IM and changed the spectrum after the IM, which enabled us to realize the changing of the whole spectrum of the optical frequency comb and suppressed the two peaks. Figures 3(a) and 3(b) show the experimentally obtained optical frequency comb and SBS gain spectra, respectively. Although the power of each line spectrum fluctuates as shown in Fig. 3(a), the SBS gain fluctuation is improved from 15 to 2 dB as shown in Fig. 3(b). This is realized because the frequency spacing between the line spectra (10 MHz) is smaller than the intrinsic SBS gain bandwidth Δν B (40MHz), and the SBS gain fluctuation is cancelled out by the overlapping of the multiple SBS gain spectra. As the cancellation is achieved more effectively when f m is small, the SBS gain fluctuation decreases as f m decreases.
Next, we numerically investigated if we can realize the flat SBS gain spectrum for any Δθ in the simulation. Figure 4 shows the calculated results of the SBS gain fluctuation contour map between modulation index Δθ and normalized DC bias voltage V/Vπ for an f m of 10 MHz, where V is the DC bias voltage applied to the IM. We assume that 50 % duty cycle pulses are generated when V=0. The SBS gain spectrum is calculated by convoluting the spectrum of optical frequency comb obtained from Eq. (4) and intrinsic SBS gain spectrum expressed as Eq. (3), where the Δν B=40 MHz and g 0=5×10-11 m/W. The SBS gain fluctuation varies periodically as V changes. As seen in Fig. 4, there exists DC bias voltage which suppress the SBS fluctuation to less than 0.5 dB for any Δθ. For the experimental case of f m=10 MHz and Δθ=3.7π, we can suppress the SBS gain fluctuation and realize flat SBS gain by setting the V/Vπ to 0.12 or 0.88. We also confirmed numerically that, for f m values of 20, 30 and 40 MHz, there is a DC bias voltage range that suppresses the SBS gain fluctuation to less than 4 dB for π<Δθ<10π.
Figure 5 shows the experimental setup we used to realize a low distortion slow light. We used a DFB-LD operating at 1550 nm as both a signal and a pump source. CW light from the DFB-LD was divided into two ports by a 3 dB coupler and the two lights were converted into a pump light (an optical frequency comb) and a signal pulse with a duration of 5.44 ns. We used a 50 km-long SSMF as a slow light medium. To fully utilize the pulse delay effect in the fiber, the SSMF was divided into two 25 km-long SSMFs, and a variable optical attenuator (VOA) 1 was inserted between them. VOA1 was used to reduce the signal power and avoid SBS gain saturation in the latter 25 km-long SSMF. This cascaded configuration enable us to obtain the large pulse delay [10, 18]. The pump light was divided into two and coupled into the two SSMFs. Then, the signal gain shown in Fig. 3(b) was realized in each of the two SSMFs. A second VOA (VOA2) was installed to keep the signal power constant at the photo detector. A frequency shifter consisting of an IM driven by a ν B sinusoidal wave and a narrowband fiber Bragg grating was deployed to shift the signal frequency and match the frequency difference between the pump and signal lights to ν B.
Figure 6 shows the signal pulse waveforms observed by using an oscilloscope with pump powers P p of 0, 32.4, 95.5, and 151 mW, where we used the pump shown in Fig. 3(a). We only give the loss for the signal light at VOA1 when the pump power was 151 mW to avoid the SBS gain saturation in the SMF2. Signal pulse waveforms obtained by the simulation using Eqs. (1) – (3) are also shown in Fig. 6. The signal pulse waveform in the simulation is uniquely determined by four factors, namely, Δν B, pump spectrum p(ν), input pulse waveform, and pulse delay Δτ. In the simulation, we set Δν B at 40 MHz and we used simulated pump spectrum shown in Fig. 3(a), and experimentally obtained values for the other two factors. Figure 7 shows the measured and the simulated results of the broadening factor as a function of the relative pulse delay, which corresponds to replot the results of the Fig. 6. We achieved a maximum pulse delay of 13.4 ns, which corresponds to a relative pulse delay of 2.46, while suppressing the broadening factor to 1.19 in the experiment. From Figs. 6 and 7, we can see that the experimental waveforms of the delayed pulse agreed well with the simulation waveforms.
We expect to expand the SBS gain bandwidth by increasing the line spectrum spacing to Δν B (although strict control of the optical frequency comb spectrum is required) or by increasing the modulation index at the PM. As shown in Eq. (5), the modulation index increases when V pp increases or V π decreases. We can expect our proposed technique using an optical frequency comb to achieve an SBS gain bandwidth of more than a few GHz by using a low V π phase modulator such as that reported in .
We presented a novel method for realizing a broad and flat SBS gain and low distortion slow light by using an optical frequency comb. We obtained a pump light consisting of 20 line spectra by using an optical frequency comb generation technique. We achieved a flat SBS gain with a 200 MHz bandwidth and a relative pulse delay of 2.46 while suppressing the broadening factor to less than 1.19 for a pulse with a duration of 5.44 ns. We can expect the SBS gain bandwidth to be increased by using a low V π phase modulator and increasing the modulation index, which will enable us to apply this method to signal pulses with higher bit rates.
The authors thank M. Shimizu and K. Sakuda for their continuous encouragement.
References and links
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