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Abstract
We assess the importance of Stimulated Brillouin scattering (SBS) anti-Stokes wave on reflection tolerance in remotely seeded wavelength-division multiplexing passive optical networks (WDM PON). Experimental validation of the extended model for the externally seeded SBS is presented towards assessing the conditions in which the anti-Stokes contribution becomes relevant in the variant scenario of remotely carrier-seeded PON. We identify relevant operating conditions in which the latter can no longer be reliably neglected, and analyze the remote seed power budget implications of such contribution. Considering typical launch powers in PON systems we found that, even for seed launch powers below SBS threshold, non-optimized upstream (US) power spectral density may lead to a considerable anti-Stokes contribution to the SBS gain. In effect, in order to maintain a reference optical return loss (ORL) of 32 dB in such scenario, anti-Stokes wave contribution imposed rigorous remote seed power budget restrictions depending on fiber parameters.
© 2017 Optical Society of America
1. Introduction
Stimulated Brillouin scattering (SBS) in optical fibers, originating from the coupling between photons and acoustic phonons, has been widely studied both from the fundamental and practical aspects. As a consequence, important studies and applications as diverse as optical amplification, sensing and high-speed signal processing have been reported [1–3]. However, in optical fiber communication systems SBS is predominantly perceived as a detrimental effect [4–8]. Typically, SBS modeling efforts towards characterizing those effects only regard the aspects resultant from the interaction between the Stokes and counter-propagating transmission signal, neglecting the anti-Stokes wave contribution as negligible in most studied cases due to the absence of high power external seeding [9–11]. In [2], anti-Stokes was included in the theoretical consideration providing an extended model for SBS, however, in the scenario of fiber optical sensing where main experimental focus was on the effects of linewidth. In scenarios that combine high optical power with bidirectional propagation, however, the contribution of anti-Stokes may impact the performance in a way that is yet to be assessed.
In wavelength division multiplexing (WDM) passive optical networks (PON), particularly the variants relying on bi-directional propagation in the optical distribution network (ODN), SBS mitigation is typically required [6, 8, 12]. The issue was in part addressed by G.989.2 standard for the next generation (NG)-PON2, establishing the minimum of 32 dB of optical return loss (ORL) in ODN [13, 14]. For other PON scenarios under evaluation and not yet standardized, thus, an ORL at least equal to that of NG-PON2 must be considered. In particular, the scenario of remotely seeded bidirectional WDM PON with centralized light source raised attention for its potential of reducing the cost and increasing the deployment feasibility [15]. In such scenario, continuous wave (CW) seed carriers, generated at the optical line terminal (OLT), are launched into the feeder fiber for the purpose of remodulation at the optical network unit (ONU) and generation of the upstream (US) data [6, 16–22], as shown in Fig. 1. Due to the double loss it suffers in ODN, the US signal is critically exposed to the impairment caused by the interference with distributed backscattered light. Previous works on reflection impairments in remotely seeded WDM-PON have focused mainly on SBS Stokes and Rayleigh backscattering (RB), which was identified as the dominant detrimental effect, while SBS was controlled by setting the seed power bellow the SBS threshold [6, 21, 22]. Additionally, in future, such systems may rely on pulse shaping (e.g. Nyquist) paired with narrow channel spacing and high data rates towards increased spectral efficiency [23]. To the best of our knowledge, the impact of SBS anti-Stokes on remodulated US seed in such scenario is yet to be reported.
Fig. 1 Remote carrier-seeded scenario in bidirectional wavelength - reuse DWDM PON and spectral distribution of its distributed reflection contributors to the system impairment.
This paper follows two complementary objectives. Firstly, we experimentally validate the extended SBS model for the first time, and secondly, demonstrate the relevance of the anti-Stokes contribution in scenario of remotely seeded, single feeder bidirectional (ultra)-dense WDM PON. We define the conditions in which SBS requires extensive consideration of the interaction of both Stokes and anti-Stokes waves with the US seed wave, numerically and experimentally. We stress that in such conditions, anti-Stokes may considerably affect the remote seed launch power optimization for full compliance with standardized reflection tolerance. Hence, we assess the remote seed power budget penalty induced by anti-Stokes contribution towards maintaining the standardized ORL requirement.
2. Extended SBS model
Two conceptually different variants of SBS modeling are distinguished. One deals with the initiation of the SBS by externally applied laser source, and it is usually referred to as the SBS amplifier [9]. The other approach involves the theoretical treatment proposed both by Boyd et al. [24] and Zel’dovich et al. [25] and models the noise initiated SBS, commonly referred to as the SBS generator.
In the analysis of the optical power coupling within the externally seeded SBS parametric process, the standard model for the SBS amplifier given in [9] accounts for the interaction between the pump and the frequency upshifted Stokes wave. However, the standard model may be expanded by including the terms for frequency upshifted contribution, referred to as the anti-Stokes, occurring due to backscattering from the ongoing acoustic wave [9]. Assuming inverse geometry for the ongoing acoustic wave responsible for the frequency conversion to the anti-Stokes frequency [9], the steady-state solutions for acoustic wave equations considering beat terms that yield the wave number and the frequency of the acoustic wave at hand (i.e. energy and momentum conservation), are given as [2, 9]:
where ρs and ρa denote the amplitudes of the retiring and the ongoing sound waves, qs and qa being their corresponding wave numbers. γe is the electrostrictive constant, ε0 is the fiber dielectric constant, while Ap, As and Aa represent the pump, the Stokes and the anti-Stokes field amplitudes, respectively. ΓB is the Brillouin linewidth, full width at half maximum (FWHM), and ΩB is the angular Brillouin central frequency. SBS gain factor (gs,a stands for the Stokes and the anti-Stokes, respectively) is then given as [9, 26]:where g0 is the line-center SBS gain factor, n is the refractive index at given frequency, c is the speed of light, v is the sound velocity, ρ0 is the mean acoustic density of the fiber, and ω is the angular frequency. We hereby distinguish between the Stokes and anti-Stokes line-center gain factors g0s and g0a towards experimentally assessing their respective efficiencies. Gain factor depends on the frequency detuning ∆Ω/2π = (ΩB – Ω)/2π from Stokes and anti-Stokes frequencies in accordance with the Eq. (3). The maximum value for the gain factor is thus found for zero detuning ∆Ω, at line-center Stokes and anti-Stokes frequencies which are down- and up-shifted from the pump frequency ν0 = ω/2π by the Brillouin shift ∆νB.We further derive the equations for optical power by considering only nonlinear polarization contributions that act as phase matched source terms in the wave equation [9, 26]. Thus, assuming the monochromatic pump and the backward direction of the SBS waves within the longitudinal spatial coordinate z, the following set of equations describes the optical power transfer when considering the anti-Stokes contribution, hereby referred to as the extended model:
where Pp, Ps and Pa stand for the pump, the Stokes and the anti-Stokes optical powers respectively. Aeff and α are the fiber effective area and attenuation coefficient, respectively.In the absence of the anti-Stokes terms, introduced by the Eq. (6) and the second term on the right-hand side of the Eq. (4), the set is reduced to the commonly used set of coupled equations accounting for the interaction between the pump and the Stokes wave [9]. Therefore, the model predicts anti-Stokes contribution to the power transfer from the pump to the Stokes frequency. It should be noted that the model does not predict the gain and loss peaks occurring away from the main SBS frequency shift, attributed to the non-uniform fiber composition. However, these contributions are well explored in [27].
Since the pump and probe waves are coherently coupled through the SBS process, the effect is also polarization dependent [28]. The set of Eqs. (4-6) is still generalized, since polarization may be accounted for by applying a polarization multiplication factor to the SBS gain g [28]. However, we hereby focus on the case of matched polarization for maximum SBS gain in both simulation and experiment, as to assess the worst case system scenario that does not rely on polarization control for SBS suppression.
The set of coupled differential equations was solved by using variable order Runge-Kutta method suitable for stiff problems, along with a double-shooting algorithm to constrain the fiber simulation outputs to the initial conditions applied in the experiment, within 0.01 dB of error margin. The experimental data are then used to extract the SBS parameters of the fibers under consideration.
3. Experimental validation and fiber parameter extraction
3.1 Experimental setup
Various measurement techniques have been used for the characterization of SBS gain spectra [29–32]. For the purpose of SBS parameter extraction we hereby perform a detailed characterization of the SBS gain and loss spectra by implementing the single-laser pump and probe technique [32]. The technique consists of launching a CW pump at a fixed frequency ν0, with a counter propagating wave generated by a Mach Zehnder modulator (MZM), driven with a sinusoid of a variable frequency νP, such that ∆Ω/2π = ∆νB - νP = ∆ν represents the probe frequency detuning from the Brillouin frequency, as shown in Fig. 2. The sidebands of the modulated wave act as probes, experiencing gain and loss through interaction with the pump within the SBS parametric process.
Measurements were conducted using the setup shown in Fig. 3. The CW pump light (ν0 = 1548.115 nm) was generated by using a spectrally narrow tunable laser source (TLS) with a linewidth of 5 MHz (FWHM). The pump light was partially coupled into an 8.8 km long fiber under test, while the remaining part of the pump light was intensity modulated using an external MZM driven by a sinusoid excitation [32]. Thus, MZM output signal contained no carrier, but modulation sidebands acting as probes that were thereafter amplified by using Er-doped fiber amplifier (EDFA). MZM biasing optimization enables individual control over the optical powers of the probes as described in [32], which allowed increasing the power considered for the anti-Stokes probe up to 10 dBm. The MZM modulation frequency was adjusted to position the sideband probes near Stokes and anti-Stokes frequencies, ν0 - ∆νB and ν0 + ∆νB, and swept across their gain/loss spectra with the resolution of 1 MHz, performing detailed characterization by using optical spectrum analyzer (OSA). The pump input power was varied by using variable optical attenuator (VOA) to investigate its impact on the SBS gain/loss spectra. Polarization controllers (PC) were adjusted to ensure the maximum efficiency of the SBS process [28]. By using an isolator (ISO), with over 45 dB of isolation, the backscattered light was blocked from re-entering the EDFA/TLS. Two different fiber types are considered for the parameter extraction: dispersion shifted fiber (DSF) and standard single mode fiber (SMF). The fiber attenuation coefficient, α, measured for the DSF and SMF was 0.23 dB/km and 0.28 dB/km, respectively.
3.2 Parameter extraction
In this section, SBS parameters required for the extended model were extracted for both fiber types, and thereafter validated using SBS threshold metric. Simulations of the SBS Stokes gain and anti-Stokes loss spectra based on the set of Eqs. (4-6) were carried out and compared to the experimentally obtained data, by using the root mean-square error (RMSE) based objective function as a best-fit criterion towards extracting the SBS parameters:
where Fj is the RMSE between calculated and measured values, cj(i) and mj(i), respectively, and N is the number of measurement points. Four fitness functions were considered simultaneously for each fiber type: maximum and minimum pump launch power for Stokes and anti-Stokes spectra, thus totaling eight functions (j = 1, 2...8).The procedure was complete once a fair agreement between the experimental and the numerical results was achieved. The results for gain and loss experienced by the external probes at Stokes and anti-Stokes frequencies, respectively, are shown in Fig. 4 for four different pump launch powers in DSF. Expectedly, the Stokes gain and anti-Stokes loss intensify as pump power is increased. Deviation from the experimental results is observed in the proximity of the adjacent SBS peaks that correspond to the secondary acoustic modes within the fiber, which are not of interest in this work but may be included by SBS gain considerations presented in [27]. Fiber effective area adopted in the simulation, Aeff, was 55 μm2 for DSF and 80 μm2 for SMF. For spectral analysis presented in Fig. 4, both Stokes and anti-Stokes probes were kept at −20 dBm of optical power. The extracted fiber parameters are shown in Table 1. FWHM linewidths of 32.5 MHz and 29.5 MHz, as well as SBS frequency shifts of 10.55 GHz and 11.15 GHz were obtained for DSF and SMF, respectively. Furthermore, extracted values of line-center gain factor were 0.7·10−11 m/W for DSF, and 0.6·10−11 m/W for SMF. It is of note that all parameters related to Stokes and anti-Stokes spectra were distinguished through independent variables in the parameter extraction procedure. Nevertheless, the parameter extraction based on the best-fit criteria with the experimental data resulted in equal line-center gain factors for Stokes and anti-Stokes, supporting the assumption that the Stokes and the anti-Stokes processes occur with same parametric efficiency when considering polarization matched case. To the best of our knowledge, this work provides first experimental proof of the latter, which thus far had been indirectly assumed in works such as [2].
Fig. 4 Experimental validation of the extended SBS model for the (a) Stokes and (b) anti-Stokes spectra in DSF, considering different pump launch powers PP (0).
Table 1. Extracted SBS fiber parameters.
Experimental SBS gain/loss peak values (g = g0) at Stokes/anti-Stokes frequencies for different pump powers are summarized in Fig. 5 (markers), indicating a good agreement with the simulated data (lines) for the extracted parameters outlined in Table 1.
Fig. 5 Experimental validation of the extended SBS model for the peak Stokes gain and anti-Stokes loss versus pump launch power PP (0).
The validity of the model and the extracted parameters was also verified for the calculation of SBS threshold, a typically considered metric for quantization of the SBS impact in a system scenario, against values obtained both experimentally and using semi-analytical approach. We hereby adopt the general definition of SBS threshold as the pump launch power yielding the backscattered Stokes power equal to that of the transmitted pump [5,33]. Following that assumption, SBS threshold is evaluated numerically using the Eqs. (4-6), assuming −40 dBm of Stokes and anti-Stokes probe powers (such that the anti-Stokes contribution is negligible), and experimentally obtained using the setup presented in Fig. 3. The result is further validated by using the approach based on the semi-analytical equation presented in [5]. It is of note that the fully analytical approximation for the SBS threshold, derived by using Smith's formula [5], is not considered here as it ought to be used strictly for considerations of long fiber spans. The results presented in Table 2 indicate that the extracted fiber parameters yield a fair agreement between the experimental and numerical SBS threshold values for both fiber types. As evidenced by Fig. 5 and measured SBS threshold (Pth) results presented in Table 2, for the pump power close to or beyond the threshold, the SBS gain/loss exceeds 30 dB in both fibers, and so its effect in bidirectional remotely seeded PON scenario ought to be carefully addressed.
Table 2. Measured and simulated SBS threshold, Pth.
4. Anti-Stokes contribution to the SBS gain
Due to the two-fold nature of the SBS power transfer, occurring from the anti-Stokes frequency to that of the pump and further on to the Stokes frequency, the anti-Stokes contribution to the Stokes gain is not a priori negligible. Thus, the anti-Stokes probe power range leading to a considerable contribution to the Stokes gain is explored next, for various input powers of the pump and the Stokes probe. The experimental results are used for validation of the extended model, in reference to the standard modeling towards defining its accuracy range.
4.1 Experimental validation
Anti-Stokes contribution to the Stokes gain was experimentally characterized for a range of near-end pump input power, and far-end Stokes/anti-Stokes probe powers. We first considered the anti-Stokes probe power range between −20 dBm and 10 dBm while keeping the Stokes probe power constant at −20 dBm. Based on the experimental data, numerical solution relying on the extended SBS model is compared to that of the standard model discarding the anti-Stokes contribution. The results presented in Fig. 6 indicate a fair agreement with the experimental data when anti-Stokes is accounted for through extended SBS model (full lines), indicating the power range in which the standard model (dotted lines) is no longer accurate in its SBS gain prediction. In effect, for the pump powers well below the SBS threshold and the anti-Stokes seeded by 10 dBm probe, its contribution to SBS gain exceeds 5.5 dB. Conversely, due to the effect of saturation, at pump powers close to SBS threshold the contribution of the anti-Stokes seeded by 10 dBm probe is below 1.5 dB. Namely, as the ratio between the pump launch power Pp (0) and anti-Stokes probe power Pa (L) is decreased, the contribution to the SBS gain becomes more relevant. As identified in this particular case of 8.8 km long DSF, if the average power that coincides with the anti-Stokes frequency spectrum at the far-end of the fiber is below −5 dBm, the Stokes gain is no longer considerably affected and is well predicted by the standard modeling for all considered values of pump launch power. Relevant input power limits leading to a considerable anti-Stokes contribution are next generalized in terms of fiber parameters.
Fig. 6 Experimental validation (markers) of the extended SBS model (full lines) using the standard SBS model as a reference (dashed lines) [9], for the anti-Stokes probe input power contribution to the SBS Stokes output power considering several pump powers in an 8.8 km long DSF.
SBS power transfer characterization is generalized by considering the fraction of the input pump power that is backscattered on the Stokes frequency γ, for given Stokes and anti-Stokes probe to pump input power ratios, denoted as a and b, respectively [9]:
where generalized effect of fiber properties and pump launch power is introduced through the gain factor G [9]. Figure 7(a) shows γ for several values of a calculated using Eqs. (4-6) (lines) as well as the approach based on the transcendental equation (markers) [9]. For the sake of comparison against the transcendental equation [9], we here consider the case of lossless fiber propagation (α = 0). As a is decreased, SBS process gains efficiency and γ increases for a fixed value of G. As shown in Fig. 7(a), for the Stokes probe powers comparable to that of the pump, complete power transfer (γ = 1) occurs for the values of exponential gain G below 10. On the other hand, Fig. 7(b) shows SBS power transfer characteristics when accounting for the anti-Stokes contribution to the SBS gain, considering a = 30 dB. Evidently, as b is decreased below 10 dB, the effect of anti-Stokes is no longer negligible.Fig. 7 Simulated SBS Stokes power transfer γ versus exponential gain factor G (a) w/o anti-Stokes contribution and for several values of a, comparing the extended SBS model (Eqs. (4-6) with the transcendental equation from [9]; (b) for fixed value of a = 30 dB considering several values of b.
To validate the former, we measured γ using the setup presented in Fig. 3, considering DSF (α = 0.23 dB/km) for its lower SBS threshold, over a range of G imposed by the practical limitations of the experimental equipment available. The results presented in Fig. 8, for the case of a = 30 dB and b in the range between 15 dB and −5 dB, showcase a fair match between the experimental and numerical data obtained by using the Eqs. (4-6) and previously extracted fiber parameters presented in Table 1. The results show that input powers at the anti-Stokes frequency for which b ≤ 10 dB lead to significant increase of backscattered pump power fraction γ. Thus, depending on the required reflection tolerance of a system at hand, maximum exponential gain factor G may be derived and considered for an acceptable tradeoff between the fiber parameters and pump launch power, towards mitigating the SBS induced reflection penalty.
Fig. 8 Experimental and simulated SBS Stokes power transfer γ as a function of exponential gain G for a fixed value of a = 30 dB, considering several values of b.
4.2 The effect on reflection tolerance and remote seed power budget
In remotely seeded PON scenario presented in Fig. 1, the remote US signal seed acts as the CW SBS pump. In scenarios implying the US signal bandwidth higher than typical SBS shift ∆νB, such as NGEPON [34], the spectral content of the US signal generated at the ONU and coinciding with the SBS spectra acts as the probe for the Stokes and anti-Stokes, as depicted in Fig. 2. The US signal spectral shape will thus affect the Stokes and anti-Stokes initial conditions in the fiber far-end, relative to the Eq. (8). Thereupon, this section directly relates the pump-to-Stokes and -anti-Stokes ratios launch power ratios, a and b respectively, to the system reflection tolerance in the aforementioned scenario. Figure 9 shows maximum exponential gain factor G, tolerated for backscattering of γ = 10% (a-b), 1% (c-d) and 0.1% (e-f) of the US seed launch power acting as the SBS pump, considering L∙α of 4 dB (a, c, e) and 6 dB (b, d, f). Clearly, the Stokes and the anti-Stokes probe launch powers will affect the exponential gain G tolerated for the same fraction of the US seed backscattering. In this regard, the anti-Stokes launch power becomes a relevant factor for the pump-to-anti-Stokes launch power ratio b ≤ 10 dB. Furthermore, as the reflection tolerance is decreased from 10% to 0.1%, exponential gain optimization becomes considerably more rigorous, and for a fixed SBS line-center gain factor g0 ought to be managed by means of a reduced fiber span and/or increased fiber attenuation coefficient α. Unfortunately, both these mitigation strategies would lead to a reduced power budget and network splitting ratio. In effect, for a and b below 5 dB, considering a standard 20 km Corning SMF-28 (α = 0.2 dB/km), exponential gain factor G ought to be limited to 1.6 to avoid Stokes reflection over 0.1% of the US seed launch power. Conversely, for increased fiber attenuation coefficient of 0.3 dB/km, G tolerated for the same reflection tolerance is doubled, allowing increased g0, fiber span and/or US seed launch power. Thus, in a scenario of comparable launch powers of bidirectional SBS crosstalk contributors, an optimal value of G factor ought to be considered as to avoid significant crosstalk related to the power transfer to the Stokes frequency. It is of note that as the considered reflection tolerance is decreased by decreasing γ, anti-Stokes contribution (parameter b) starts to dominate the maximum gain limitation Gmax.
Fig. 9 Maximum exponential gain factor G tolerated for several values of γ, considering parameters in Table 1, different fiber attenuation coefficients and a range of pump-to-Stokes and -anti-Stokes launch power ratios, a and b.
From Fig. 9, required US seed launch power may be related to fiber parameters that allow target reflection tolerance. Namely, considering the scenario in Fig. 1, if a downstream (DS) signal is launched from the OLT with power PDS into a fiber with given parameters, maximum remote US seed launch power can be calculated for a targeted ORL, by using a set of simple relations. First, reflectivity is related to the required ORL by:
where Gmax is the corresponding value of maximum gain extracted from Fig. 9 for given values of a and b, depending on the US signal spectral shape and power. Next, maximum remote US seed power is readily calculated by:Conversely, for a fixed value of G parameter, a limit on fiber launch powers of counter-propagating US spectral content that coincides with the Stokes and the anti-Stokes frequencies for a given ORL can be assessed, and applied to the US signal pulse shaping or data rate optimization for SBS mitigation. In effect, let us consider the modulation of the US seed for an US signal with bandwidth, modulation format and/or pulse shaping that yields high power spectral occupation coinciding with the remote seed SBS spectra (e.g. Nyquist), such that a = b = 5 dB. If we further consider typical values of 0 dBm for the DS signal launch power at 1550 nm [13], g0 = 1∙10−11 m/W of a standard 20 km Corning SMF-28 (α = 0.2 dB/km), from Eqs. (9-10) and data presented in Fig. 9(e), the calculated maximum US seed launch power is −2 dBm for 32 dB of ORL [13].We next calculated the impact of anti-Stokes contribution to the remote seed launch power limit for various SBS thresholds by considering a range of anti-Stokes seed launch powers at the fiber far-end. As mentioned, the criteria used for maximum backscattering power tolerated by the counter-propagating DS signal is ORL = 32 dB, established by the NGPON2 standard [13]. DS signal launch power considered here is 0 dBm, while the SBS threshold is evaluated by using the semi-analytical approach [5], as discussed in section 3.2. The results, presented in Fig. 10, indicate that remote seed power budget penalty increases with decreased SBS threshold due to higher power transfer efficiency. In effect, in order to keep remote seed budget penalty within 0.5 dB while maintaining 32 dB of ORL for 0 dBm DS lauch power, SBS threshold as high as 17 dBm would allow tolerance to anti-Stokes seed power of up to 2 dBm. In contrast, SBS threshold as low as 5 dBm would impose a limit of −11 dBm of anti-Stokes seed power. These requirements may be even more stringent considering additional backscattering contributors, such as RB and local reflections.
Fig. 10 Remote seed power budget penalty versus anti-Stokes lauch power for 0 dBm of DS signal launch power and 32 dB of ORL, considering various SBS thresholds.
In effect, un-optimized US signal spectral content coinciding with the anti-Stokes spectrum leads to important seed power budget limitations in remotely seeded PONs. Having in mind considerations made on standardized ORL requirement, a basic rule of thumb may be formulated: given transmission over standard 20 km SMF and typical launch powers in PON, in case that the average power coinciding with the anti-Stokes frequency exceeds −10 dBm its contribution to the average backscattered power ought to be considered. Notably, it is conclusive that anti-Stokes contribution is likely to have implications on the stochastic nature of the SBS as well, through relevant system parameters such as noise figure (NF). These considerations are, however, outside the scope of this work.
Finally, it is of note that the impact of anti-Stokes on SBS Stokes gain may have considerable implications and should also be carefully considered under other relevant scenarios relying on external seeding, such as narrowband Brillouin fiber lasers and/or Brillouin fiber amplifiers, where high power operation is often implied [1, 35].
5. Conclusions
In this paper we assess the anti-Stokes contribution to the SBS Stokes gain and its system implications in carrier-seeded wavelength reuse PON operating at per-channel data rates exceeding SBS frequency shift. Extended SBS model, considering both Stokes and anti-Stokes contributions, has been experimentally validated for a wide range of remote seed and SBS probe launch powers, defining the range of operating conditions in which it enhances the performance of widely used standard modeling.
Taking into account the anti-Stokes contribution to the pump-Stokes power coupling, relevant contribution to the SBS gain is found even for pump powers below SBS threshold and pump-to-anti-Stokes seed power ratios below 10 dB. The latter imposes a penalty on the US seed power budget towards maintaining the standardized ORL requirement, to a degree that is strongly dependent on fiber parameters. Considering typical launch powers in PON and a wide range of SBS thresholds, we found that this penalty may be minimized provided that the average US power coinciding with the anti-Stokes spectrum is kept below −10 dBm. Thus, in scenarios relying on chirped operation and/or pulse shaping techniques, the optimization of US signal power spectral density is suggested in order to avoid the remote seed power budget penalty resulting from the anti-Stokes contribution to the SBS gain.
Acknowledgments
This work is supported by the European Structural Investment Funds (ESIF), through the Operational Competitiveness and Internationalization Programme (COMPETE 2020) under FutPON project [Nr. 003145 (POCI-01-0247-FEDER-003145)], as well as Fundação para a Ciência e Tecnologia within the scope of UID/EEA/50008/2013.
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