Effect of linewidth on intensity noise induced by stimulated Brillouin scattering in single-mode fibers

Jiejun Zhao; Jiejun Zhao; Fei Yang; Fang Wei; Xi Zhang; Xi Zhang; Zhidan Ding; Zhidan Ding; Rui Wu; Rui Wu; Haiwen Cai; Haiwen Cai

doi:10.1364/OE.393239

1. Introduction

When light travels in a fiber, light scattering caused by material inhomogeneity adds a lot of noise to the transmission signals. These noises will greatly affect the performance of low-noise RF-photonic applications such as time-frequency transfer over optical fibers [1], optoelectronic oscillators [2–5], radio-over-fiber [6–8], φ-OTDR [9] and precision Doppler radar remoting [10]. Therefore, it is very important to conduct research on the characteristics, sources and control methods of the noises.

There have been numerous published works reporting that the fiber scattering mechanism is the source of the induced noise in fiber communication [11,12]. Researchers used the backscatter spectrum and transmitted noise spectrum with an offset frequency from 10 Hz to 1 MHz to elucidate the relationship between noise and input power [13]. Results indicated that in a 6-km long fiber, Rayleigh scattering and stimulated Brillouin scattering (SBS) dominate the scattering-induced noise with an input power below and above 11 dBm, respectively. Double Brillouin scattering also causes noise at input powers above 13 dBm. When a laser with wide-linewidth is used, the intensity noise power caused by Rayleigh scattering increases linearly with optical power and fiber length in the offset frequency range of 10 Hz to 1 MHz [14,15]. However, when a narrow-linewidth laser is used, a different phenomenon occurs [16]. The scattering-induced noise power scales super-linearly with fiber lengths up to 10 km in the offset frequency range of 500 Hz to 10 kHz, and linearly in the frequency range of 10 Hz to 100 Hz. In [17], noises induced through the double Rayleigh scattering (DRS) of a high-coherence-length laser in long fibers was reported to be the dominant noise in an offset frequency range above 10 Hz, which is a cumulative effect of DRS. The coherence length decreases as the laser frequency noise increases. Moreover, the scattering noise does not accumulate when the coherence length is significantly smaller than the fiber length. Therefore, the effect of DRS-induced intensity noise can be reduced by increasing the 1/f noise of the laser. It was reported that in a 25-km long dispersion-shifted fiber, Brillouin scattering could produce noise in a wide offset frequency range of 0 Hz to 1 GHz [18]. Another researches reported that the bandwidth of SBS-induced transmission intensity noise in a 25-km long fiber is in the order of 10 kHz. Even when the input power is significantly lower than the SBS threshold, scattering-induced intensity noises are still stronger than flicker noise. If the pump power is sufficiently strong, there are low-frequency holes and high-frequency jitter ripples in the scattering-induced noise spectrum. Furthermore, the researchers simultaneously proved that transmission intensity noise at low frequency is caused by stochastic Brillouin scattering-induced pump light depletion [19].

The effect of laser linewidth on the intensity noise induced by Rayleigh scattering has been confirmed [16], however, to our knowledge, no study has yet described the effect of laser linewidth on Brillouin scattering-induced intensity noise. In this study, we present our results emanating from research on this specific topic. For the first time, we have observed in the experiments that SBS-induced intensity noises in laser transmission in single-mode fibers is affected by laser linewidth. The backscatter spectrum shows that Brillouin scattering dominates the scattering-induced noise with an input power above 11 dBm. In addition, a narrower laser linewidth results in a lower relative intensity noise (RIN) when the transmission distance is short. For a longer distance, a narrower laser linewidth will result in a smaller RIN at high frequency but a larger RIN at low frequency. The Brillouin linewidth parameter is introduced into the SBS three-wave coupling equation to simulate the transmission process. Excellent agreement between theory and experiment is obtained in this study. It is theoretically confirmed that the intensity noise evolution in the transmission process occurs primarily owing to the SBS. Furthermore, we confirm that with an increase in fiber length, RIN is suppressed in the low-frequency region.

2. Experimental setup and results

The experimental setup is shown in Fig. 1. We measured the intensity noise and spectrum characteristics of three single-frequency laser sources with varying linewidths. The first is a distributed feedback semiconductor diode laser, whose linewidth is about 500 kHz, marked as “DFB-LD”; the second is a Fabry-Perot external cavity semiconductor laser with a linewidth of 20 kHz, marked as “FP-ECL”; the third is a planar waveguide external cavity semiconductor laser, with an intrinsic linewidth of about 5 kHz, marked as “PWG-ECL”. An Erbium-doped fiber amplifier (EDFA) with a variable optical attenuator (VOA) were used to adjust the output power. This was done as the power used in the experiment required real-time adjustment and exceeded the power capabilities of the individual lasers. We used a high-precision optical spectrum analyzer (OSA) (APEX AP2041B) to measure the optical domain reflection spectrum of the fiber and a RIN measurement setup (blue dotted frame in Fig. 1) to measure the intensity noise of the forward transmission. The OSA measurement bandwidth is greater than 300 nm with 1550 nm center wavelength and 5 MHz (0.04 nm) frequency resolution. A circulator was used to guide the scattered light into the OSA. The operating principle of the RIN measurement setup is as follows: the optical signal transmitted through the fiber link was adjusted to a fixed output power of 1.2 dBm. Then the direct current (DC) of the photodetector (PD) output passed through a bias circuit and was measured with a digital multimeter. After the PD, a low noise amplifier (LNA) is used to increase the sensitivity of our measurement system. The LNA is alternating current (AC)-coupled with 20 Hz frequency. The AC-coupled filters out the DC from the light beam effectively, which allows us to measure the noise frequency level as close to the center carrier as possible. Finally, the power spectrum density (PSD) of the low noise amplifier (LNA) output is calculated, and the RIN-PSD relative to the normalization of the DC can be obtained.

Fig. 1. Experimental setup for reflection spectrum and transmission relative intensity noise (RIN) power spectrum density (PSD) of an optical fiber link.

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First, we measured the reflected output spectrum of DFB-LD with different pump powers, as shown in Figs. 2(a) and 2(b). The inset results indicate that the scattered spectrum primarily contains Rayleigh-scattered light and positive first-order Stokes light with center frequencies of 193.587334 THz and 193.598115 THz, respectively. The frequency interval of the scattered spectrum is the standard Brillouin frequency shift of 10.8 GHz. The results indicate that SBS dominates scattering-induced noise with an input power above 11 dBm (Fig. 2(c)), which is approximately 15–30 dB higher than that in Rayleigh scattering. Rayleigh scattering mainly dominates the intensity noise in an offset frequency range below 10 kHz [13]. In this work, our experiment mainly focused on the transmission intensity noise in an offset frequency range from 10 kHz to 40 MHz. Owing to the above two reasons, the RIN in this frequency range is functioned by the SBS, which is also theoretically proven through the simulation of SBS three-wave coupling equation.

Fig. 2. (a) Schematic of the positive level stimulated Brillouin backscattering spectrum of DFB-LD for several input powers levels. (b) Rayleigh backscattering spectrum of DFB-LD for several input powers levels. (c) Scattering power as a function of input power. (d) Positive level stimulated Brillouin scattering (SBS) spectrum using DFB-LD, ECL-FP and ECL-PWG.

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Figure 2(d) shows the backscattering spectrum of three different lasers. The pump power in each scenario is 16 dBm subsequent to a 5-km fiber transmission. The linewidth of Brillouin-gain spectrum produced by DFB-LD is wider than that of ECL-FP and ECL-PWG, whereas the linewidth of ECL-FP is slightly larger than that of ECL-PWG. However, the OSA cannot distinguish the exact value of the linewidth of Brillouin-gain spectrum. This study primarily focuses on the changing trend.

Second, we measured the RIN-PSD characteristics of three single-frequency laser sources, with different linewidths, at three different transmission fiber lengths as well as the RIN characteristics of the lasers, as shown in Fig. 3. The RIN-PSD results of the lasers show that the laser linewidth affects the intensity noise subsequent to transmission through fiber. The linewidths of the lasers have distinct performance consequences for the various fiber lengths.

Fig. 3. RIN spectrum for DFB-LD, FP-ECL, and PWG-ECL, with linewidths of 500, 20, and 5 kHz, respectively. Results are measured for the laser itself and three different fiber lengths.

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For a 5-km fiber, a narrower laser linewidth lead to a smaller RIN. For example, at a 10-kHz offset frequency, the RIN of DFB-LD is 6 dB higher than that of ECL-FP and 12 dB higher compared to ECL-PWG. At a 1-MHz offset frequency, these values change to 3 dB and 20 dB, respectively. When a 10-km fiber is used, the RIN can be reduced by reducing the laser linewidth in the offset frequency range above approximately 1 MHz, while there is practically no difference in the frequency range of 60 kHz to 500 kHz. For a 20-km fiber, in the frequency range below approximately 1 MHz, DFB-LD suppresses noise compared to the noise of ECL-FP and ECL-PWG. For instance, at 100 kHz, the RIN of DFB-LD is 5 and 9 dB lower than that of ECL-FP and ECL-PWG, respectively. In the range of approximately 10–40 MHz, the noise deteriorates as the laser linewidth increases.

From these phenomena, we observed that different lasers induced different RIN. The primary differences between these lasers were the linewidths and RIN of the lasers themselves. However, the scattering noise discussed in this article is higher than the RIN of the laser itself, which can be seen in Fig. 3. For DFB-LD, the RIN level of the laser is 35 dB @ 10 kHz, 25 dB @ 100 kHz, and 16 dB @ 1 MHz smaller than the RIN subsequent to 5 km fiber transmission. For ECL-FP, the RIN after 5 km fiber transmission is 35 dB @ 10 kHz, 25 dB @ 100 kHz, and 16 dB @ 1 MHz higher than the RIN of the laser itself. For ECL-PWG, the value is 35 dB @ 10 kHz, 34 dB @ 100 kHz, and 8 dB @ 1 MHz. For the offset frequency region greater than 1 MHz, the RIN subsequent to 5 km fiber transmission degrades by about 5 dB-10 dB compared to the RIN of the laser itself. Therefore, the effect of RIN of the laser itself is small and can be ignored. The critical factor is the effect of laser linewidth on RIN at different lengths. The reasons for these phenomena will be proved in detail from a theoretical perspective.

Intensity noise exhibits a low-frequency saturation suppression phenomenon. The noise power decays, as opposed to accumulating, when the length of the fiber increases to a specific level. Figure 4 shows the fiber length dependence on the intensity noise spectrum of the transmission signal, using DFB-LD. Seven different fiber lengths, from 2 to 20 km, are shown in Fig. 4(a). Experimental results reveal that there is a peak value of the fiber length, where RIN exhibits a saturation effect (15 km). Furthermore, from Fig. 4(b), as the fiber length increases to 20 km, suppression occurs at the frequency range from 10 kHz to 1 MHz. As the length increases, when the transmission length is less than the saturation length, will start accumulating. If the transmission length increases further, the noise will no longer accumulate, however, it will start attenuating.

Fig. 4. (a) RIN using DFB-LD for several lengths. (b) RIN vs. fiber length for different offset frequencies.

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To exclude the possibility that the laser input power has a saturation suppression effect, we investigated the transmitted laser RIN-PSD for several input powers levels. Figure 5(a) shows a plot of RIN from a 5-km single-mode fiber using DFB-LD with input power ranging from 10 dBm to 17 dBm. According to previous research, when the input power level exceeds 11 dBm and the offset frequency exceeds 10 kHz, Brillouin scattering dominates the RIN spectrum, which deviates from the RIN of the laser itself. We find that for offset frequencies beyond 10 kHz, the transmission noise increases with increasing optical power. When the laser output power increases to 16 dBm, the noise has a saturation effect, with no suppression effect, as shown in Fig. 5(b). The entire curve conforms to the characteristics of the sigmoid logical function, and the curve-fit R-square coefficient is greater than 99.6%.

Fig. 5. (a) RIN using DFB-LD for several pump power; (b) RIN vs. pump power for different offset frequencies.

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Figure 6 shows the change in RIN using the lasers at different offset frequencies with input power of 10 to 17 dBm. Measurements were recorded at three different offset frequencies: 10 kHz, 1 MHz, and 40 MHz. The results show that RIN linearly varies from 10 to 12 dBm, increases exponentially from 12 to 16 dBm, and saturates above 16 dBm. At the 1-MHz offset frequency, the RIN difference of the three lasers is greater than 10 kHz. At an offset frequency of 40 MHz, as the power increases, the RIN difference between the three lasers increases. In summary, RIN will have a saturation effect as the input power increases, however, this would be without a suppression effect. The influence of the input power on lasers with different linewidths in the fiber is different.

Fig. 6. RIN vs. pump power using three lasers with different offset frequencies (a) 10 kHz; (b) 1 MHz; (c) 40 MHz.

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3. Simulations and discussion

The transmitted light field was simulated based on the SBS three-wave coupling equation. The intensity noise spectrum subsequent to transmission was calculated based on the transmitted light field. The relevant equations are given below [19,20]:

(1)$$\begin{array}{l} \frac{{\partial {E_L}(z,t)}}{{\partial z}}{ + }\frac{n}{c}\frac{{\partial {E_L}(z,t)}}{{\partial t}} ={-} \frac{\alpha }{2}{E_L}(z,t) + i\kappa {E_S}(z,t)\rho (z,t)\\ \frac{{\partial {E_S}(z,t)}}{{\partial z}} - \frac{n}{c}\frac{{\partial {E_S}(z,t)}}{{\partial t}} = \frac{\alpha }{2}{E_S}(z,t) - i\kappa {E_L}(z,t){\rho ^ \ast }(z,t)\\ \frac{{\partial \rho (z,t)}}{{\partial t}} + \frac{\Gamma }{2}\rho (z,t) = i\Lambda {E_L}(z,t)E_S^ \ast (z,t) + f(z,t), \end{array}$$

where $E_{L}(z,L)$ and $E_{S}(z,L)$ are the pump light and Stokes light field, respectively. $f(z,t)$ is the Langevin Gaussian white noise source used to describe the thermal fluctuation characteristics in the fiber with an average value of 0 and variance of $\textrm{Q} = (2k_{B}\,{T}\rho _{0}\Gamma )/({v_{A}}^{2}A_{eff})$; κ and Λ are the Brillouin coupling coefficients for photons and phonons, respectively. $\Lambda = \gamma \Omega /(2cZ{v_{A}}^{2})$ and $\kappa = ng_{0}\Gamma /(2Z\Lambda)$, where Z is impedance in vacuum; and Γ is the Brillouin linewidth parameter, whose relationship with the linewidth of Brillouin-gain spectrum is $\Delta \nu_{B} \propto \Gamma /2\pi$. The Brillouin frequency shift is related to the effective mode coefficient, $n_{p}$, phonon velocity, ${v_{A}}$, and pump wavelength, $\lambda_{p}$, with $\nu_{B} = 2n_{p}v{A}/\lambda{p}$ [21]. From this expression, it can be deduced that the linewidth of the Brillouin-gain spectrum is proportional to the pump laser linewidth:

(2)$$\Delta {\nu _B} \propto - {{{2}{n_p}{v_A}\Delta {\lambda _p}} \mathord{\left/ {\vphantom {{{2}{n_p}{v_A}\Delta {\lambda_p}} {\lambda_p^2}}} \right.} {\lambda _p^2}} \propto {{{2}{n_p}{v_A}\Delta {\nu _p}} \mathord{\left/ {\vphantom {{{2}{n_p}{v_A}\Delta {\nu_p}} c}} \right.} c}.$$

Γ is not only related to phonon lifetime, T_B, but also the pump laser linewidth, $\Delta \nu_{p}$, such that,

(3)$$\Gamma = f({{T_B},\Delta {v_p}} ).$$

Therefore, the pump laser linewidth $\Delta \nu_{p}$ would affect the coupling coefficients in SBS process through the Γ. In the three-wave coupling equations, the change in the pump laser linewidth $\Delta \nu_{p}$ can also be expressed by varying Γ. Furthermore, Table 1 gives the meanings and values of other physical parameters in the equations.

Table 1. Descriptions of the parameters used in this study

View Table

The finite difference time domain (FDTD) method is used to solve Eqs. (1)–(3), and by obtaining a pump laser light field, ${E_{L}(z,L)}$, the RIN-PSD is calculated from:

(4)$${S_{RIN}} = {{\frac{2}{{R\tau }}{{\left|{\int\limits_0^\tau {\nu (t)\exp ( - 2\pi ift)\textrm{d}t} } \right|}^2}} \mathord{\left/ {\vphantom {{\frac{2}{{R\tau }}{{\left|{\int\limits_0^\tau {\nu (t)\exp ( - 2\pi ift)\textrm{d}t} } \right|}^2}} {{S_0}}}} \right.} {{S_0}}},$$

where $\nu (t) = \eta {A_{eff}}R{{{\varepsilon _0}cn{{|{E(z = L,t)} |}^2}} \mathord{\left/ {\vphantom {{{\varepsilon_0}cn{{|{E(z = L,t)} |}^2}} 2}} \right.} 2}$, $\varepsilon_{0}$ is the permittivity in vacuum, L is the length of the fiber, and $S_{0}$ is the average light intensity noise.

According to the physical process derived above, the intensity noises affected by the linewidth of Brillouin-gain spectrum, fiber length and input power were simulated. Figure 7(a) shows the simulation results of three different linewidths of Brillouin-gain spectrum for various transmission lengths. It is shown that for a 5-km long fiber, in the offset frequency range from 500 Hz to 100 MHz, as the Brillouin linewidth increases, so does the RIN. For a 10-km long fiber, there is a tendency for it to saturate and be less affected by the Brillouin linewidth below 1 MHz. However, for an offset frequency range above 1 MHz, the larger Brillouin linewidth leads to high levels of RIN. In a 25-km long fiber, the larger Brillouin linewidth leads to smaller RIN below 1 MHz and larger RIN above 1 MHz. There is excellent agreement between the theoretical and experimental RIN-PSD results. The variation of RIN with input power agrees with the experimental results. With the increase of power, the noise has a saturation, with no suppression, as shown in Fig. 5 and Fig. 7(d).

Fig. 7. Simulation results based on an SBS three-wave coupling equation. (a) RIN for several Brillouin linewidths; (b) RIN for several input powers. (c) RIN for several fiber lengths; (d) Evolution of RIN with fiber length. Insets are RIN vs. pump power with different offset frequencies.

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It can be seen that the trend in the low-frequency range is distinctive under different transmission lengths; therefore, we simulated the fiber length dependence of the RIN-PSD of the transmitted light using a 30-MHz linewidth of Brillouin-gain spectrum, as shown in Fig. 7(b). Moreover, a fiber length extreme point exists. The longer the fiber length, the greater the RIN at a fiber length shorter than the extreme point. Nevertheless, when the fiber length surpasses this peak, the RIN decreases with an increasing fiber length. Figure 7(c) shows the variation of RIN with the fiber length at different offset frequencies. As the fiber length increases, the RIN initially increases linearly, subsequent to which it reaches saturation, and finally the suppression effect is observed. The noise is the highest at an offset frequency of 10 kHz. Moreover, as the offset frequency increases, the noise lowers which is consistent with the Lorentz curve characteristics [17].

The primary dissimilarity between theoretical observations and our experiment is the ripples in the offset frequency range of 1–10 MHz, which may be caused by multiple interferences of Brillouin scattering. Double Brillouin scattering can also cause Fresnel fringes in the transmitted spectrum, whose frequency interval corresponds to the fiber length. To explain this phenomenon, a more comprehensive theoretical model is required. For example, in addition to the pump laser linewidth, when the RIN of the laser itself is large to some degree, it may also have an effect on the intensity noise, this content will be discussed in future research.

The SBS-induced RIN is caused by the depletion of the pump wave and the stochastic Brillouin wave in the laser transmission process through the fiber. And the depletion of the pump wave increases with the increase of the input laser power, which also leads to the RIN increases non-linearly [19]. This conclusion is different from the RIN of the laser which has a decreasing trend with output power. It is because that the RIN of the laser mainly comes from the interference of spontaneous emission to the stimulated emission. A greater output power lead to a larger proportion of stimulated emission as well as a smaller degree of interference from spontaneous emission, and then a smaller corresponding RIN.

4. Conclusion

In this work, we performed an experiment to measure the RIN of three different linewidth lasers subsequent to fiber transmission. It was observed that RIN changes in scale with the laser linewidth and transmission length. The reflection spectrum confirmed that the SBS gain is approximately 15−30 dB larger than the Rayleigh gain with large input power. Thus, SBS dominates the scattering-induced noise in our experiments. SBS three-wave coupling equation was used to simulate the relationship between the linewidth of Brillouin-gain spectrum and the pump laser linewidth. Light fields with different linewidths and fiber lengths were obtained followed by the calculation of transmission RIN. By varying the linewidth of Brillouin-gain spectrum, the simulation results show excellent agreement with the experimental results related to the change in laser linewidths. Narrower laser linewidths led to lower RIN when the transmission distance was short. For longer distances, the narrower laser linewidth would result in smaller RIN at high frequencies, with larger RIN at low frequencies. This work confirms the connection between the SBS gain spectrum linewidth and its induced noise in terms of the pump laser linewidth, which helps in further understanding the noise characteristics of optical fiber information transmission and perception systems and development of effective methods to optimize noise control and improve system performance.

However, it is necessary to further study the physical mechanism and obtain comprehensive experimental data, quantify and clarify the correlation, and promote the comprehensive understanding and utilization of the control of non-linear scattering-induced noise.

Funding

National Natural Science Foundation of China (61535014, 61775225, 61875214); Chinese Academy of Sciences (XDB43000000).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

References

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Symbol	Meaning	Value	Symbol	Meaning	Value
n	refractive index	1.45	$g_{0}$	Brillouin gain	1.12×10-11 m/W
c	velocity of light in vacuum	299792458 m/s	$A_{e f f}$	effective area of the fiber	80 µm2
α	fiber absorption coefficient	0.25 dB/km	γ	electrostrictive constant	0.902
$ρ_{0}$	average density	2210 kg/m3	Ω	acoustic frequency	10.86 GHz
R	load resistance	50 Ω	η	PD response rate	0.9 I/W
$v_{A}$	velocity of sound in fiber	5960 m/s	$k_{B}$	Boltzmann constant	1.38×10-23J/K

Effect of linewidth on intensity noise induced by stimulated Brillouin scattering in single-mode fibers

Abstract

1. Introduction

2. Experimental setup and results

3. Simulations and discussion

4. Conclusion

Funding

Disclosures

References

Cited By

Figures (7)

Tables (1)

Equations (4)

Optics Express