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We present experimental and theoretical investigation of intensity noise features in SBS for experimental configuration utilized injection locking of two semiconductor lasers for Stokes signal generation. Significant decreasing of the intensity noise of the Stokes signal with the frequency equal to the Brillouin resonance is observed and analytically explained.
©2006 Optical Society of America
1. Introduction
As well known the stimulated Brillouin scattering (SBS) induces a limit in a fiber optical transmission system mainly by restriction of the maximum launched optical power and increasing of the relative intensity noise (RIN) of the transmitted signal [1].
On the other hand, Brillouin-based optical fiber sensors have attracted a great deal of interest due to their potential use for monitoring temperature and strain distribution within large structures in civil engineering. In number of configuration the Brillouin interaction is performed in the stimulated regime [2–4], thus requiring the need for two counter-propagating waves, a powerful pump wave and a weak seed Stokes wave. When particular phase matching conditions are met, an acoustic wave is generated that converts power from the pump to the Stokes signal. This leads to a local amplification of the Stokes signal, which yields a variation of the detected parameters at the fiber end. It is clear that the accuracy of such sensors is also limited by the Stokes intensity noise.
The source of the broadband intensity noise of the transmitted Stokes has been attributed to a variety of sources: beating of the pump light with the anti-Stokes wave [5], filtering of the noise from thermally generated acoustic phonons [6, 7], and a non-linear phase shift at the optical carrier frequency due to asymmetry of the Brillouin gain spectrum [8]. In Ref. [9] it was shown that amplification by a Brillouin amplifier can improve the SNR of an SBS-degraded signal by more than 6 dB. The improvement depends on both the magnitude of the gain and-more critically - the detuning of the gain peak from the optical carrier frequency.
The paper presents experimental and theoretical investigations of Stokes intensity noise features in SBS for an experimental configuration utilized injection locking of two semiconductor lasers for Stokes signal generation. Injection locking of two DFB semiconductor lasers opens new possibilities for generating signals for Brillouin setup. Number of configurations may be designed for generation of various signals, such as pure AM, pure FM, frequency-shifted or frequency sweeping optical wave forms [10]. Here we employ the injection locking of two semiconductor lasers to generate intensity stable and, simultaneously, frequency tunable CW-radiation that potentially could be used as the Stokes seed signal.
In this work, we demonstrate theoretically and experimentally that the primary source of the relatively low frequency (1–700 MHz) intensity noise is mainly due to beat between spontaneously scattered Stokes and amplified Stokes seed signals. The characterization of the intensity noise for a frequency domain ranging up to 700 MHz has been performed with an experimental setup reproducing the Brillouin Optical Time Domain Analysis (BOTDA) configuration. The intensity noise power has been measured as a function on the pump and Stokes powers for a wide range of parameters and simultaneously as a dependence on the Stokes frequency detuning from the Brillouin peak frequency.
2. Experimental setup
Figure 1 shows the experimental setup for the amplified Stokes intensity noise measurement. A single mode optical fiber SMF-28 with the length of 4 km is used as a test Brillouin media to provide interaction between the pump wave and the Stokes seed signal. A master DFB tuneable laser operating at 1549.5 nm generates CW radiation with a linewidth of ~150 KHz. A 3-dB coupler splits the radiation onto two beams. After amplification in the Er-doped amplifier (EDFA-1), the first beam is used as the pump wave. The second beam passes through an acousto-optical modulator operating around ~10.87 GHz, amplified in the second Er-doped fiber amplifier (EDFA-2) and causes injection locking of a slave DFB laser. The injected power forces the slave laser to generate CW-radiation with a stable 0.3-mW power at the frequency Stokes-shifted with respect to the frequency of the pump wave. The radiation of the slave DFB laser is used as a Stokes seed signal for Brillouin interaction in the test fiber. At working bias current, the slave laser RIN was equal to -130 dB/Hz that is actually below the noise limit of our measurement system. Both lasers employed in the experimental configuration have built-in optical isolators but even a small portion of radiation, which passes through the slave’s isolator, has efficiently locked it [10]. Additional isolators and circulators prevent back influence of the slave laser on the master one. The experimentally measured locking range was about 700–800 MHz for injected power estimated as -35 dBm. Locking regime can be permanently verified by monitoring the interference pattern between two lasers. The fringe visibility was about 0.97-1 for approximately equal interfering beams intensity.
The Stokes radiation at the fiber end is detected by a 500-MHz digital oscilloscope equipped with a ~1GHz-photodiode and analyzed by a 25-GHz radio-frequency spectrum analyzer. A variable attenuator (VA) sets the pump power introduced to the test fiber up to 2Pth, where Pth is the SBS threshold power estimated equal to 9.4 dBm.
Fig. 1. Experimental setup. EDFA- Er-doped fiber amplifier, VA-variable attenuator, OI-optical isolator, PC-polarisation controller, OSA- optical spectrum analyzer, MG – microwave generator, PD-photodiode.
3. Results and discussion
Experimentally the intensity noise power has been measured as a root-mean-square (RMS) of the ac coupled Stokes power detected by the photodiode PD-1 in frequency range from 10 Hz to 110 MHz. Figure 2 presents the RMS power versus the Stokes frequency shift induced by the acousto-optical modulator. An amplified dc Stokes component via detuning frequency for different pump power is shown in Fig. 3. The maximum amplified SBS seed signal was equal to 8.7 mW for the maximal pump power of 17.2 mW. Significant (more than two times) pump depletion was recorded under this condition for zero detuning frequency.
When the modulation frequency coincides with the SBS shift ~10.87 GHz (the Stokes detuning frequency is zero) the intensity noise is suppressed to the level determined mainly by the noise of the seeding source. Indeed, this level is found to be independent of the pump power (see Fig. 4). In contrast, with the Stokes frequency detuning more than ~50 MHz, the intensity noise power does not depend on the detuning frequency, but exhibits exponential dependence on the pump power that is typical for SBS initiated from the spontaneous noise. In view of the above, we can conclude that SBS initiated from the spontaneous noise makes a major contribution to the intensity power in the case of the large frequency detuning. Another interesting feature that the intensity noise power exhibits a remarkable maximum near a detuning frequency of ~15–20 MHz. This corresponds approximately to the linewidth of the Brillouin amplification in optical fibers at 1550 nm [7].
Fig. 2. RMS of ac-coupled Stokes component, experimental (solid with symbols) and calculated (solid) values for different pump power: blue - 8.4dBm (0.8Pth), red -10.4 dBm (1.27 Pth), ◌ - 11.4dBm (1.6Pth), black - 12.4dBm (2.0 Pth).
Fig. 3. Amplified dc-coupled Stokes component for different pump power: ▽-8.4dBm (0.8Pth), Δ -10.4 dBm (1.27Pth), ◌ - 11.4dBm (1.6Pth), □ - 12.4dBm (2.0 Pth).
In order to explain the observed intensity noise features, the mutual interaction between pump wave, the seed signal, and Brillouin noise in the optical fiber should be taken into account. Let us consider these three waves interacting in the fiber. Monochromatic pump at frequency ν1 with power equal to P1(z), monochromatic seed Stokes signal P2(z), at frequency ν2, varying around Brillouin frequency νs = ν1-ΔνSBS, where ΔνSBS≈10.87 GHz is SBS shift, and noise Stokes component PN(Z,Ṽ) with Gaussian shape alignment on Brillouin central frequency νS = ν1-ΔνSBS.
The simulations are based on the assumption that the noise Stokes component in contrast to the Stokes seed signal cannot lead to the pump depletion. Under this assumption the interaction between seed Stokes and pump can be described by a steady state system:
where,
where g -is SBS amplification, Aeff - is effective mode area, ν = ν2-νS - detuning frequency, α- is losses, and T2- is the hypersound relaxation time.
Amplification for ṽ - noise component by non-depleted pump P1(z, ν) is described by:
Therefore, the noise component can be found as:
where
is spontaneous Brillouin noise, and
Using boundary conditions for P1(0, ν), P2(L, ν), and PN(L, ν̃) we can find the Stokes component P2(0, ν) and noise spectrum PN(0, ν, ν̃) at the fiber input.
Now, the RMS of the photodiode current I(t) can be found as:
The results of RMS calculations are presented in Fig. 2. A fitting parameter for the plotting the theoretical results was the same as experimentally measured Stokes noise level in absence of the pump. As we can see, the calculated RMS demonstrates qualitatively the same behaviour as experimentally measured one. However, the quantitative difference was observed for the maximum and minimum values of RMS near a 15 -20 MHz and zero detuning frequency, correspondingly. This discrepancy can be attributed to the simplicity of the theoretical model that did not take into account the non-monochromatic nature of the pump and Stokes, their polarization uncertainty inside the fiber, and influence of an additional noise generated in Er-doped amplifiers. However, the next theoretical consideration probably required significantly modified model for the explanation of this discrepancy.
Qualitatively, the intensity noise behavior can be explained in the following way. The pump provides amplification for the Stokes seed wave and noise Stokes component in the fiber, but with different amplification coefficients that also depend on the frequency detuning. The beating between the Stokes seed wave and the Brillouin noise which was detected at the fiber end makes a major contribution to the intensity noise power registered in the experiment. Therefore the intensity noise power should be proportional to the product of the Stokes signal amplification coefficient and noise amplification one. When the Stokes frequency is far from the Brillouin resonance (>50 MHz) the amplification of the seed signal is obviously minimal and the second amplification coefficient should be maximal because all pump power is available for amplification of the Brillouin noise. Under this condition the intensity noise power does not depend on the detuning frequency and the beat spectrum between seed Stokes and noise Stokes does not change it’s envelope with detuning frequency increasing (see Fig. 5).
Fig. 5. Stokes intensity noise spectrum, pump equal to 1.6 Pth, detuning frequencies equal to 160 and 200 MHz.
With the detuning frequency near zero, the amplification of seeding signal is maximal and the amplification of the Brillouin noise is minimal because the effective power conversion to the seeding signal depletes the pump power level, which is available for amplification of the Brillouin noise. Therefore, the maximum of the intensity noise power should be related to a specific balance between the seed Stokes signal and the Brillouin noise that can be found by detuning the seed laser frequency within the Brillouin amplification line. Indeed, Fig. 6 presents Stokes intensity noise spectrum for different values of the detuning frequencies. The noise envelope moves synchronously with detuning increasing and reaches the maximum between 15–20 MHz.
Fig. 6. Stokes intensity noise spectrum. Pump equal to 1.6 Pth. Detuning frequencies equal to 0, 10, 20, 30 and 40 MHz.
4. Conclusion
We have shown that the Stokes intensity noise demonstrates complex behaviour versus detuning between central Brillouin gain frequency and seed Stokes frequency. With a large detuning, more than ~50MHz, the intensity noise does not depend on the detuning frequency. Amplified spontaneous noise is found to make a major contribution to the intensity noise power in this case. In the opposite limit, with the Stokes frequency just near the Brillouin peak, the role of SBS noise becomes negligible and the intensity noise power drastically reduces to the level determined by the noise of the seeding source. But what is surprising is that a detuning of the Stokes frequency by ~15–20 MHz from the Brillouin peak causes a significant enhancement of the intensity noise power with respect to the noise levels observed in both limit cases, i.e. at low and high detuning frequencies. We believe that this feature is attributed to a specific balance between the Stokes seed signal and the Stokes spontaneous noise that can be achieved in BOTDA configuration when the detuning frequency becomes approximately equal to the width of the SBS gain.
These results have important consequences for distributed temperature and strain sensors, which utilized stimulated Brillouin scattering with Stokes seed signals and Brillouin amplifier systems with noticeable pump depletion.
Acknowledgments
We gratefully acknowledge financial support through grant P45919-Y from the Consejo Nacional de Ciencia y Tecnología, México, Telkom SA, Ltd, Marconi Communications South Africa (Pty) Ltd, and THRIP. The work of A.Fotiadi was supported by Interuniversity Attraction Pole program (IAP V 18) of the Belgian Science Policy.
References and links
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