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What is fiber optic Brillouin scattering

Brillouin scattering is an effect caused by the χ (3) nonlinearity of the medium, especially the nonlinear part associated with phonons. Incident photons can be converted into lower energy scattered photons (usually propagating in the backward direction) and phonons. The coupling of the optical field and the phonon occurs through electrostriction. The phonon field can emerge spontaneously even at low optical power and then reflect heat generated. For higher optical foci, a stimulation effect may occur in which the light field significantly increases the number of phonons. Above some threshold power of the beam in the medium, stimulated Brillouin scattering can reflect most of the power of the incident beam. This process involves a strong nonlinear optical gain of the backward reflected wave: the initially weakly back-propagating wave can be strongly amplified at an appropriate optical frequency. Here, the two back-propagating waves produce a traveling refractive index grating; the higher the reflected power, the stronger the refractive index grating and the higher the effective reflectivity.

The frequency of the reflected beam is slightly lower than the frequency of the incident beam; the frequency difference ν 乙 corresponds to the frequency of the emitted phonon. The so-called Brillouin frequency shift is set by the phase matching requirement. For pure reverse Brillouin scattering, the Brillouin shift can be calculated from the refractive index n, the speed of sound v a and the vacuum wavelength λ

(For Brillouin scattering in fibers, the effective refractive index must be used.)

In optical fibers, Brillouin scattering essentially occurs only in the reverse direction. However, the forward Brillouin scattering may also be weak due to acoustic waveguides.

The Brillouin frequency shift depends on the material composition and to some extent on the temperature and pressure of the medium. This dependence is used for fiber optic sensors.

Another important application of excited Brillouin scattering is optical phase conjugation. For example, there exist phase-conjugated mirrors for high-power Q-switched lasers, which make it possible to compensate for thermal aberrations occurring in the forward and backward directions in the laser crystal.

Brillouin scattering in optical fibers

Stimulated Brillouin scattering (SBS) is often encountered when narrowband optical signals (e.g., from single-frequency lasers) are amplified in fiber amplifiers or propagated only through passive fibers. Although the material nonlinearity of, e.g., silica is not actually very high, the typically smaller effective mode area and longer propagation length strongly contribute to the nonlinear effect.

Figure 1 shows what happens when a monochromatic light wave is injected into a 10 m long fiber. The counter-propagating Brillouin-shifted wave starts with a quantum rise with a very low optical power, but grows rapidly. Nevertheless, it is still much less than 1 W of input power.

Figure 1: Pump power (propagation from left to right, red curve) and obtained Brillouin signal power (right to left, orange curve) in a 10 m long fiber. The pump input power is 1 W.

For a slightly increased pump power of 1.8 W, the Brillouin gain (in dB) almost doubles and the Brillouin wave becomes stronger.

Figure 2: Same as Figure 1, but with 1.8 W pump power.

 

In order to increase the pump power further, the power of the Brillouin wave will become comparable to the pump power. In this case, a large amount of pump depletion occurs. For high SBS gains, this does not lead to a stable situation but to chaotic fluctuations in the power.

If the fiber is several kilometers long, the milliwatt power is sufficient to cause significant Brillouin scattering. However, propagation losses must then be considered, which are substantial for such fiber lengths. It affects both the pump wave and the Brillouin wave.

For quartz fibers, the Brillouin frequency shift is about 10-20 GHz and the intrinsic bandwidth of the Brillouin gain is typically 50-100 MHz, depending on the strong acoustic absorption (short phonon lifetime of about 10) NS). However, the Brillouin gain spectrum may be “smeared” due to various effects, such as lateral variations of the acoustic phase velocity [14, 19] or longitudinal temperature variations. As a result, the peak gain may be significantly reduced, leading to a higher SBS threshold.

The fiber Brillouin threshold for narrowband continuous-wave light typically corresponds to a Brillouin gain on the order of 90 dB. (With additional laser gain in an active fiber, the threshold may be even lower.) For a series of ultrashort pulses, the SBS threshold is determined not by the peak power, but by the power spectral density, as described in the Spotlight article.

SBS introduces the most stringent power limits for amplification and passive propagation of narrowband optical signals in optical fibers. To increase the Brillouin threshold, one can increase the bandwidth of the light beyond the Brillouin gain bandwidth, reduce the fiber length, connect fibers with slightly different Brillouin displacements, or (in high-power active fiber optic devices) use varying temperatures longitudinally [21]. Attempts have also been made to reduce the overlap of guided light and acoustic waves, or to introduce significant propagation loss of acoustic waves. SBS issues such as doping concentration, effective mode area and pump propagation direction can be reduced to some extent by basic amplifier design modifications.

On the other hand, Brillouin gain can be used to operate Brillouin fiber lasers . Such devices are usually made as fiber ring lasers. They may have relatively low pumping thresholds and very small linewidths due to low resonator losses.

The temperature dependence of the Brillouin shift can be used for temperature and pressure sensing.

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