## Abstract

At bit rates comparable with the Brillouin shift, i.e. higher than 10 Gbit/s, the signal and the Brillouin backscattered spectra partially overlap. This implies an interaction between different scattering phenomena occurring through out the optical fiber. In particular we believe that an evaluation of how Rayleigh backscattered components of the modulated signal are subjected to Stokes gain is required. This interaction may lead to an increased backscattered power, which in turn will affect Brillouin threshold estimation. We experimentally verified a decrease of Stimulated Brillouin Scattering (SBS) threshold for 10 Gb/s NRZ-OOK signals with respect to theoretical predictions. Simulations carried out with a numerical model of SBS, accounting for Rayleigh contributions, well predict measured backscattered power levels. On the other hand we also experimentally verified that this SBS threshold decrease does not degrade transmission system performance. Indeed, measured BER curves put into evidence a penalty reduction for signal powers just before the saturation regime, which should be usefully taken into consideration in optical systems power budget planning.

©2009 Optical Society of America

## 1. Introduction

In the development of multigigabit long-distance optical repeaterless transmission systems Stimulated Brillouin Scattering (SBS) represents a critical issue as it causes saturation of the average transmitted power and increases noise in the transmitted signal [1–3]. Thus, in order to prevent system performance degradation, power budget plans must account for the necessity to operate under SBS threshold. Though typical definition of SBS threshold is the input power, at which the backscattered Stokes power equals power at the fiber input [4], with the purpose of simplifying the measure, other definition are also employed comparing, for instance, backscattered power with 1% of transmitted power. In view of the correct power budget planning of optical communication systems, there is still a high interest in developing more exhaustive theoretical modeling of the SBS process in order to provide a more accurate evaluation of the SBS backscattered power. Particular attention has been paid to solve the differential coupled equations describing SBS interaction, accounting also for the signal depletion, fiber attenuation and for SBS noise initiation through the *distributed, fluctuating source model*, where the Stokes wave originates from thermally excited spontaneous phonons [5–7]. In this way, more precise relations for CW signal-SBS threshold evaluation has been derived to be used in place of the well-known Smith formula [4,8].

Modulated signal SBS threshold has been proven to be proportional to CW threshold and is strongly dependent on transmitted signal modulation format [8–10]. For the specific case of non-return-to-zero (NRZ) On-Off Keying (OOK) modulation, assuming an average power of the modulated signal equal to the CW power, the SBS threshold is given by [9,10]

*B*is the bit rate. For

*B*high compared to the Brillouin linewidth

*Δν*Eq. (1), irrespectively of

_{B}*B,*predicts a twofold increase in the SBS threshold with respect to the CW case [8–10]. This is consistent with OOK signal carrier containing approximately one-half of the total signal energy. Experiments discussed in literature confirming these theoretical conclusions have been performed at bit rates not higher than 2.5 Gb/s [10,11].

In the present work we have widened the investigation and characterized SBS threshold up to 10 Gb/s. Experimental results at 10 Gb/s have evidenced a SBS threshold decrease of more than 1dB with respect to the 2.5 Gb/s case, which we relate to Rayleigh backscattering interaction with Stokes backscattered spectrum, as confirmed by simulation results of our numerical model. For a more throughout understanding of the impact of this SBS reduced threshold on system performances, BER curves as a function of the transmitted power have also been measured and compared both at 2.5 Gb/s and 10 Gb/s.

## 2. Stimulated Brillouin threshold evaluation

#### 2.1 Setup configuration

The experimental setup exploited to characterize SBS threshold and to evaluate SBS-induced transmission penalties is shown in Fig. 1
. A DFB laser light (λ = 1559 nm), passed through a polarization scrambler to assure complete input polarization randomness, was used as Brillouin pump, both in CW and NRZ-OOK externally modulated with a Mach-Zehnder modulator at bit rates of 2.5 Gbit/s and 10 Gbit/s (PRBS 2^{31}-1). The input power, amplified with an EDFA, was modified by means of a variable optical attenuator (VOA) and monitored through the 1% exit of a coupler. The fiber coil was 48km-long fiber with an effective core area *A _{eff}* = 80μm

^{2}and an average nominal attenuation coefficient

*α*= 0.22 dB/km. An isolator was bonded at the fiber coil end to avoid Fresnel reflection at the fiber-air interface. By means of an optical circulator the average backreflected power was measured as a function of the input power through an optical spectrum analyzer (OSA) employed as a power meter (1-nm resolution), while the transmitted NRZ-OOK signal was characterized in terms of BER versus received power for different launch powers.

#### 2.2 SBS threshold: experimental results

Figure 2 shows the measured backscattered power from the fiber coil as a function of the input power when the transmitted signal is CW (black triangles) and intensity externally modulated at 2.5 Gb/s (squares) and 10 Gb/s (circles). The straight line corresponds to the condition when SBS power is −20dB lower than the input power, here chosen, for experimental convenience, as the definition of SBS threshold. When the signal is 2.5 Gb/s modulated measurements prove, in agreement with theoretical predictions, an approximately 3 dB increase of the SBS threshold with respect to the CW case. As anticipated in the introduction and in contrast with foreseen threshold independence on the bit rate [8–10], repeated measurements at 10 Gb/s show a 1-dB decrease of the SBS threshold at 10 Gbit/s with respect to the 2.5-Gb/s case. Transmitted signal extinction ratio stays unvaried at the two explored bit rate. The reduction of SBS threshold, which corresponds to an increase of the backscattered power, is consistent with an amplification process.

Indeed at 10 Gb/s the bit rate and the Brillouin shift are comparable, the signal and the Brillouin backscattered spectra partially overlap, thus causing an interaction between different scattering phenomena through the fiber. In particular the unpredicted behaviors in Fig. 2 is well explained if we consider that some of the 10 Gb/s OOK signal components fall inside the Brillouin gain spectrum, which is shifted of about 11 GHz from the transmitted signal optical carrier. Brillouin scattering amplifies Rayleigh backscattering of these components, which are not present in the CW case, thus increasing the total backscattered power collected at the fiber input, though not specifically the SBS level. As a consequence the total backscattered power is increased and the measured Brillouin threshold is reduced.

At 2.5 Gb/s these Rayleigh components are far from spectrally overlapping with the Stokes spectrum and the above-described interaction does not occur.

It is worth noting that superimposing a dither (100 kHz with modulation index of 10%) on the signal does not substantially affect our findings, the final effect being an enhanced decrease of the 10 Gb/s threshold with respect to theoretical prediction.

#### 2.3 SBS theoretical modeling for high bit-rate modulated signals

In order to verify our assumption on the origin of the SBS threshold reduction at 10 Gb/s with respect to the 2.5 Gb/s case, we employed the classical theoretical model to evaluate SBS threshold, in which we introduce a term accounting for the contribution of amplified Rayleigh backscattering. The developed model is based on the well-known steady-state equations describing the Brillouin interaction between the pump and Stokes waves [12]:

*P*,

_{p}*P*,

_{S}*g*, A

_{B}_{eff}and

*α*are, respectively, the signal acting as the Brillouin pump, the backscattered Stokes power, the Brillouin gain coefficient [12], the effective fiber core area and the fiber attenuation constant. In Eq. (3)

*P*accounts for those Rayleigh backscattered components of the NRZ-OOK modulated signal that overlap with the Stokes spectrum. In particular,

_{Rayleigh}*P*has been evaluated by integration of the power spectral density of the modulated signal

_{Rayleigh}*P*over the measured 35-MHz Brillouin bandwidth shifted at 11 GHz from the transmitted carrier. In the calculus of

_{p}*P*the Brillouin bandwidth has been assumed almost constant as experimentally verified in the investigated

_{Rayleigh}*P*range.

_{p}*P*is then multiplied by the factors

_{Rayleigh}*α*and

_{R}*S*, which represent, respectively, the Rayleigh scattering loss coefficient in optical fiber and the fraction of scattered radiation captured in the backward direction inside the fiber [13]. The backscattering coefficient

*Sα*has been set to 4.4 10

_{R}^{−5}km

^{−1}, as derived from Rayleigh backscattering measures at low launch power. The signal

*P*is injected at the input of the fiber (z = 0) and propagates over the fiber coil length

_{p}*L*, being subjected to depletion and attenuation according to Eq. (2). Equation (3) describes the growth of a Stokes signal incident at

*z = L*in the backward direction as a result of SBS. In practice no Stokes signal is fed at

*z = L*, but SBS builds up from amplified spontaneous scattering occurring throughout the fiber length [4,12]. In the present work noise initiation of SBS has been modeled following the localized, non-fluctuating source approach [4], which assumes that the summation of all contributions from spontaneous emission along the fiber is equivalent to the injection of a single Stokes photon per mode at the rear side of the fiber. Thus, assuming a single mode supported by the fiber, the effective input Stokes power at

*z = L*has been taken as ${P}_{S}\left(L\right)={P}_{S}^{spon\mathrm{tan}eous}=\hslash {\omega}_{S}{B}_{eff}$where

*B*is the effective bandwidth of the Stokes radiation centered at the Brillouin gain peak

_{eff}*ω = ω*which, in the hypothesis of a Lorentzian gain profile with full width at half maximum Δν, is given by

_{S}In order to estimate differences in predicted SBS thresholds, Eqs. (2,3) have been solved for CW and NRZ-OOK modulated signals both at 2.5 Gb/s and at 10 Gb/s. Backscattered intensities *P _{s}(0)* at the fiber input have been calculated for different power

*P*levels. The numerical model was first calibrated by determining the Brillouin gain coefficient (

_{p}*g*= 2.4 10

_{B}^{−11}m/W) in order to fit experimental data in the CW case, where

*P*is null. Simulated results are reported in Fig. 2. At 2.5 Gb/s the contribution of

_{Rayleigh}*P*is so low that numerical results do not differ from what predicted by Eq. (1), that is a twofold increase of the SBS threshold with respect to the CW case [8–10]. On the other hand, when the amplified Rayleigh contribution in Eq. (3) becomes not negligible, the 1-dB decrease of the SBS threshold at 10 Gb/s with respect to the 2.5-Gb/s case is well foreseen.

_{Rayleigh}The agreement between numerical and experimental results confirms our assumption on the impact of Rayleigh backscattering on SBS threshold when dealing with signal modulated at high bit-rates.

## 3. SBS impact on system BER performances

As a further step we analyzed the impact of this SBS threshold decrease on system performances by carrying out and subsequently comparing BER measurement versus received power at 2.5 Gb/s and 10 Gb/s, for different launch powers, as reported in Fig. 3a
. Launch powers ranging from 5.9 to 11.4 dBm have been explored. Up to 5.9 dBm for both bit rates, BER curves show no penalties with respect to back-to-back. At 10.9 dBm launch power, at 2.5 Gb/s this penalty is 0.5 dB, while the corresponding curve at 10 Gb/s shows evidence of an error floor, with a 1-dB-penalty at 10^{−8}. This error floor is more evident at 11.4-dBm launch power. The interesting launch-power range is around the SBS threshold. At 10.4-dBm launch power, namely when the signal power exceeds 2 dB the 2.5-Gb/s SBS threshold, about 0.5-dB penalties are introduced for 2.5 Gb/s case. At 10 Gb/s, in correspondence of the same launch power, namely 3 dB above the 10-Gb/s threshold, the BER curve shows no penalty with respect to the back-to-back. We can thus affirm that no increase of the SBS-induced noise in the transmitted signal is found at 10 Gb/s at these launch power levels.

To justify this behavior, it is useful to recall that SBS-induced intensity noise originates from the conversion of the phase noise of the optical source caused by the narrowband nonlinear refractive index associated with the Brillouin loss spectrum [14,15]. Thus the SBS-noise induced penalty results from a trade off between the laser source phase noise, which is proportional to the linewidth, and the amount of Brillouin loss spectrum. At 10 Gb/s SBS amplification of Rayleigh backscattered components takes place at the expense of the signal power, thus enhancing the depletion-induced loss spectrum. Yet nowadays laser transmitters have very narrow linewidths thus overall reducing the impact of Rayleigh backscattering amplification in terms of SBS-induced phase-to-intensity noise conversion [14,15]. For instance our transmitter linewidth is 600 kHz.

Additionally in proximity of the SBS threshold Fig. 3a shows an improvement of BER characteristics with respect to the back-to-back, the effect being more evident at 10 Gb/s. To better appreciate this aspect, Fig. 3b plots the 10 Gb/s BER as a function of the fiber launch power, at −7.6-dBm fixed received power, together with the Brillouin backscattered power curve. It can be clearly noticed a reduction of the BER, corresponding to a decade, for signal power values comprised between the SBS threshold (7.5 dBm) and just before the saturation regime.

Selective filtering of the optical carrier induced by the narrow-band SBS [16] can explain this behavior. When only the carrier component exceeds the SBS threshold and sidebands are beyond the Brillouin gain spectral width, just the carrier component is backscattered and the decrease of its power spectral density leads to distortions of the transmitted waveform. This can be clearly appreciated by comparing the two received eye diagrams of a NRZ-OOK 10 Gb/s signal reported in Fig. 3c and Fig. 3d, respectively referring to a fiber launch power P_{launch} below SBS threshold (6.5dBm) and 4dB above SBS threshold (11.5dBm). The eye diagram distortions induced by SBS, as shown in Fig. 3d well agree with those predicted by numerical simulations carried out in [17] and accounting for SBS selective filtering of the optical carrier. This SBS-induced waveform shaping results beneficial and causes a penalty reduction in the transmitted signal with respect to the back-to-back condition.

## 4. Conclusions

In the present work we experimentally verified that for high bit-rate OOK signals, beyond 10 Gb/s, the prediction of a 3-dB increase of the SBS threshold with respect to the CW case fails. In contrast with foreseen SBS threshold independence on the bit-rate, at 10 Gb/s, SBS threshold results only 2 dB higher. We explain this reduction with an increase of backscattered power due to Brillouin amplification of Rayleigh backscattering components of the signal broad spectrum that fall inside the Brillouin gain spectrum. Simulations carried out with a numerical model of SBS, accounting for these Rayleigh contributions, fairly agree with experimental curves, thus confirming advanced assumptions. Measured BER curves demonstrate that, in spite of the SBS threshold reduction, at 10 Gb/s no additional penalty is present with respect to 2.5 Gb/s at same launch power.

Two aspects have been taken into account: SBS-induced noise contribution and SBS selective filtering. The former thanks to nowadays narrow linewidth is not significant though Rayleigh-Brillouin interaction enhances the Brillouin loss spectrum. The latter indeed causes a penalty reduction just before the SBS saturation regime. These unexpected results may prove useful in the frame of power budget planning of optical transmission system, where SBS is a severe limiting factor, as in fiber-to-the-home networks and long distance repeaterless optical links where high power signals are needed.

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