## Abstract

We present a simple method for the stimulated Brillouin scattering (SBS) gain bandwidth reduction in an optical fiber. We were able to reduce the natural bandwidth of 20MHz to around 3.4MHz by a superposition of the gain with two losses produced by the same source. This reduced bandwidth can drastically enhance the performance of many different applications which up to now were limited by the minimum of the natural SBS bandwidth.

© 2011 OSA

## 1. Introduction

Stimulated Brillouin scattering is one of the most dominant nonlinear effects in standard single mode fibers (SSMF) [1]. SBS in a waveguide is an interaction between counter propagating optical waves mediated by an acoustic wave. A narrow bandwidth pump wave, propagating in one direction inside an optical waveguide, can produce a gain and a loss for a frequency shifted counter propagating wave via the acoustic wave. The frequency shift between the pump and the line center of the Brillouin gain is around 11GHz and the bandwidth is around 10–30MHz in a SSMF at a wavelength of 1550 nm. A unique advantage of SBS is it’s very small bandwidth which is important for many different applications like high resolution optical spectrometry [2, 3], Quasi-Light-Storage (QLS) [4, 5], optical microwave filtering [6–8] and narrowband amplifiers [9] for instance. The resolution of the spectrometry and the filtering as well as the storage time of the QLS method depend directly on the minimum bandwidth of the SBS. Hence, a bandwidth reduction can enhance the performance of these methods. The natural SBS bandwidth is defined by the phonon lifetime in the material [10]. Since the phonon lifetime depends on the fiber material, the natural SBS bandwidth determines the smallest achievable bandwidth in Brillouin scattering. For high pump powers the SBS gain bandwidth can be reduced to 11MHz in an AllWave fiber [11] and down to 7.2MHz in a dispersion shifted fiber [12]. A numerical simulation for the statistical properties of a SBS gain above threshold can be found in [13]. However, since the SBS is an amplification process which adds noise to the signal, this cannot be exploited in many applications.

In this article we propose a method for a drastical SBS gain bandwidth reduction far below 11MHz without an increase of the gain. In simulation and experiment we show the reduction down to 3.4MHz by the superposition of the SBS gain with two losses.

## 2. Theory

In SSMF a pump wave generates a gain for counter propagating pulses if they are down shifted in frequency by the Brillouin shift. For up shifted counter propagating pulses the same pump wave generates a loss. These Brillouin gain and loss have a natural full width at half maximum (FWHM) bandwidth of around 10–30MHz. The gain distribution of the SBS mechanism in the fiber for a gain superimposed with two losses can be written as [14]:

*g*

_{0}is the maximum gain,

*g*

_{1}is the maximum loss,

*γ*

_{0}is the half width at half maximum bandwidth of the Brillouin gain and

*δ*is the separation between the losses. By normalizing Eq. (1) with $\Omega \hspace{0.17em}=\hspace{0.17em}\frac{\omega}{{\gamma}_{0}}$; $m\hspace{0.17em}=\hspace{0.17em}\frac{{g}_{1}}{{g}_{0}}$ and $d\hspace{0.17em}=\hspace{0.17em}\frac{\delta}{{\gamma}_{0}}$ it follows:

*δ*of the losses and the ratio

*m*between gain and losses, the overall gain bandwidth can be narrowed. The dependence of the reduced gain bandwidth, normalized to the natural gain versus the loss separation can be seen in Fig. 1(a) for 19 different ratios between gain and loss. The parameter

*m*goes from 0.1 to 1 in steps of 0.05. As can be seen, the gain bandwidth can be narrowed to 50% (Point 1), 20% (Point 2) or even below. This narrowing comes at the cost of a lower gain, as can be seen from Fig. 1(b).

The two reduced gains in comparison to a natural gain can be seen in Fig. 2. Please note that a negative gain means a suppression of the spectral components of the counter propagating signal which fall in this area. For the applications which are based on the narrow band extraction of frequency components this is an additional advantage of the method since it can enhance the SNR or the dynamic range. The reduced 50% gain bandwidth has only 33% of the maximum gain which is achieved without losses and for the 20% bandwidth it is reduced to only 5%.

This reduced gain may have advantages for some applications. Since the SBS is an amplification process, it adds noise to the signal and decreases the signal to noise ratio (SNR). For the 11MHz minimum Brillouin gain bandwidth in an AllWave fiber, high pump powers are needed and hence a high amount of noise is added to the signal. For the proposed method the power of the overall gain and the noise are smaller for reduced bandwidths. However, in some applications this reduced gain can decrease the SNR. But it is also possible to compensate the reduction of the gain by the two losses with higher pump powers. In the above Eqs. only the ratio between the gain and losses is important. However, since the wave which generates the losses is generating two gains as well, the maximum achievable pump power for the losses is defined by the threshold of SBS in the fiber [15]. The gain in the line center of SBS can be written as:

*g*is the peak value of the SBS gain coefficient,

_{p}*P*is the input pump power, and

_{p}*L*and

_{eff}*A*are the effective length and area of the fiber. According to [16] for a low loss uniform fiber the threshold gain is

_{eff}*g*= 19. For Point 1 we have

_{SBSTh}*m*= 0.45 thus, the maximum loss is 45% of the maximum gain. For

*d*= 0.6 the gain is reduced by the losses to 33% of its original value. Thus to achieve the original amplification, the gain has to be enhanced by 3. Therefore to have the same ratio, the losses have to be enhanced by 3 as well. But since the losses are smaller than the gain, the threshold is defined by the gain. So, the amplification can be the same as without losses. For Point 2 the threshold will be defined by the losses. Since the gain is reduced to 5%, it has to be increased by 20 to achieve the same amplification. For the same ratio

*m*the losses have to be increased by 20 as well. Since the losses define the threshold, the maximum amplification of this set up can be 19/20 ≈ 1. However, since the other spectral components are suppressed, this still corresponds to an extraction of narrowband frequency components.

## 3. Experiment and results

In Fig. 3 the experimental setup is shown. The gain and the two losses are produced by the laser diode (LD) on the right side. The LD has a line width of 1MHz at a wavelength of 1550nm. The Mach-Zehnder modulator (MZM4) is driven in the suppressed carrier regime with a sine wave at the frequency of the Brillouin shift *f _{SBS}*, which is 10.855GHz for the used fiber. The two sidebands have a distance of twice the Brillouin shift. Afterwards the signal is splitted via a 3dB coupler. In the upper path the upper sideband is filtered out with a fiber Bragg grating (FBG), so that the lower sideband can be used as the gain pump. In the lower path the upper sideband is used in combination with MZM3 to produce the two losses. MZM3 is driven with a sine wave with a frequency corresponding to the parameter

*δ*in Eq. (1). Afterwards both pump waves, for the gain and the two losses, are independently amplified by an erbium doped fiber amplifier (EDFA) and combined via a coupler. On the left side the setup for scanning the reduced gain can be seen. A fiber laser (Koh) with a line width of 1kHz and a wavelength of 1550nm is modulated via MZM1. The fiber laser is just used for measuring the spectrum of the resulting signal. Therefore, the power of the fiber laser is too low to create a Stokes or Anti-Stokes wave. In order to adapt the fiber laser to the wavelength of LD we modulate the input signal at MZM1 with 8GHz and sweep the modulation frequency ±100MHz in 0.5MHz steps during the scanning process. With MZM2 the reference frequency for the lock in amplifier is modulated to the signal. With a FBG one of the sidebands is filtered out. The other sideband falls in the spectral region where the reduced gain is generated. As propagation medium we used a 20km AllWave fiber (

*L*= 13.38

_{eff}*km*,

*α*= 0.19

*dB/km, A*= 86

_{eff}*μm*

^{2}). The pump waves are coupled into the fiber via a circulator. The backscattered wave is splitted with a 90/10 coupler and then detected with an optical spectrum analyzer (OSA) and a photo diode (PD). The electrical signal from the PD is measured by the Lock In amplifier. For every frequency step the corresponding value for the amplitude is recorded. In comparison to a standard SBS system the complexity of the setup is increased minimally. The additional components are limited to two MZM and filters. If the output power of LD is sufficient, the two EDFAs can be replaced by a tunable coupler which set up the gain/loss ratio

*m*. In the used AllWave fiber we have measured a FWHM gain bandwidth of around 20MHz. For a superposition of gain and losses with the parameters

*m*= 0.45 and

*d*= 0.6 the measured result can be seen in Fig. 4(a). For this measurement the power at the output of the EDFA for the gain was 27dBm and for the losses 23.5dBm. Therefore the gain/loss ratio is

*m*= 0.45. The losses are separated by 12MHz which results in

*d*= 0.6. In accordance with the simulation this corresponds to a gain reduction of 50%. The reduction for the parameters

*m*= 0.55 and

*d*= 0.4 can be seen in Fig. 4(b).

A further bandwidth reduction is possible by a decrease of the distance of the losses. In Fig. 5 the results for *m* = 0.55 and *d* = 0.3 can be seen. For these values, a reduction of the bandwidth down to 3.4MHz was achieved. This equals to a reduction of the overall gain to 17% of the original Brillouin gain bandwidth.

In Fig. 4(b) the results differ a bit from the simulation. Within the measurement the gain bandwidth is not reduced as much as in the simulation. We just achieved a reduction to 40% of the SBS bandwidth and not down to 20% as stated in the simulation. A reason could be that the theory of Eqs. (1) and (2) holds just for small signals. In order to show the suppression by the losses, our signal for Fig. 4(b) had to be with 10dBm quite high.

## 4. Conclusion

In conclusion we have shown that the reduction of the SBS bandwidth is possible by the superposition of a gain with two losses. The SBS bandwidth can be reduced down to 17% of the natural Brillouin gain bandwidth. To compensate the occuring reduction of the maximum gain, higher pump powers are required. The reduced Brillouin gain bandwidth has obvious advantages for applications like the QLS, narrowband filtering or the high resolution spectroscopy based on SBS. Much better results could be achieved with broadened and adapted losses. If the losses could be made rectangular, every bandwidth reduction would be feasible. However this requires further investigation.

## Acknowledgments

The authors would like to acknowledge the financial support of the German Research Foundation (reference number: SCHN 716/6-2). Additionally the authors would like to thank Zeev Zalevsky from Bar-Ilan University for the fruitful discussions which lead to this investigation.

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