Numerical study of the dependence of the excitation Brillouin scattering threshold on fluctuations in pump intensity
Preface: In the past few decades, stimulated Brillouin scattering (SBS) has attracted attention for its wide range of applications, such as phase distortion compensation for SBS phase conjugate mirrors, pulse compression, beam combination and finishing, Brillouin amplification, frequency combing, optical signal processing, etc.
SBS is a third-order nonlinear optical effect that is strictly dependent on Brillouin gain (i.e., G = gIL, where g is the gain coefficient of Brillouin medium, I is pump strength, and L is the length of Brillouin medium).
The Brillouin gain should exceed some certain values to generate SBS, this is the so-called SBS threshold, among the various parameters that affect the characteristics of SBS, the SBS threshold is very important, and many studies have been carried out on this parameter in recent years.
Stimulated Brillouin scattering (SBS) has been reported to be a major obstacle to power scaling in narrow linewidth laser systems, as it has almost one of the lowest thresholds in nonlinear effects.
In high-power single-frequency lasers, SBS suppression plays an important role, and there are several studies on SBS suppression in fiber laser amplifiers and laser plasma studies.
A very popular way to raise the SBS threshold is to extend the pump spectrum through phase modulation, however, when using phase modulation techniques, frequency modulation to amplitude modulation (FM to AM) effects occur at the top of the pulse waveform.
The FM to AM effect adds sinusoidal intensity modulation to the original smooth laser pulses, and thresholds may vary when these types of laser pulses are used as pumps for SBS studies.
Few studies involving the dependence between SBS thresholds and temporal intensity modulation of pump pulses have been found, which makes this field largely unexplored, and numerical studies have been made of the effect of temporal sinusoidal intensity modulation of pump pulses on SBS thresholds.
Based on the classical three-wave coupling equation describing the SBS process, the resulting SBS threshold can be calculated as a function of time intensity modulation index and modulation frequency.
The pump pulse is injected from one end of the Brillouin medium, the other local pump intensity along the longitudinal axis of the medium is zero, the Stokes light is not excited at the beginning, its amplitude is set to zero, and the sound wave ρ is a complex Gaussian random distribution function with a mean of zero.
Using the above proposed numerical model and main parameters, the SBS threshold with sinusoidal modulation pump pulse can be studied, and the distortion criterion and modulation frequency are considered to describe the time modulation of the pump pulse.
The waveforms of the pump and the corresponding Stokes light under different distortion criteria (and a fixed average pump intensity of 320 MW/cm²) clearly show that the intensity of the Stokes pulse varies with the α factor.
The higher the value of the α, the lower the intensity of the reflected Stokes light, which indicates that the time intensity modulation of the pump pulse somewhat suppresses the generation of SBS.
When the intensity modulation factor is below about 30%, the SBS threshold remains basically stable and hardly increases, and when the α factor is above 30%, the threshold value increases exponentially.
The pump pulse can be seen as a stack of five individual short pulses and a long substrate with a pulse width of 5 ns, each subpulse with a pulse width of about 1 ns and an associated SBS threshold above the 5 ns substrate.
The percentage of subpulses increases linearly with α, the total energy reflectivity decreases, the SBS threshold increases with increasing α, and the modulation frequency of the sinusoidal modulation pump pulse can be described by the number of modulation peaks with a fixed pulse width of 5 ns.
For a fixed pump average intensity (320 MW/cm²) and pulse width, waveforms of pump and Stokes light were calculated using 3, 5, 7, 9, and 11 modulation peaks.
As the number of modulation peaks increases, the duration of the Stokes pulse decreases, while the peak intensity of the Stokes pulse remains essentially unchanged, that is, the reflected energy decreases as the frequency of the pump pulse modulation increases, and the energy remains unchanged.
The higher the modulation frequency, the higher the SBS threshold, and when the number of modulation peaks is below 15, the SBS threshold increases with the number of modulation peaks, and remains stable when the number of modulation peaks is large.
The sinusoidal modulation pump pulse can be seen as a superposition of several sub-pulses, each of which excites the SBS independently, while the threshold is determined by the total reflectance.
As the number of modulation peaks increases, the pulse duration of each peak decreases, transient effects become significant, and the SBS threshold increases accordingly when the pump pulse width shortens to the phonon lifetime of Brillouin medium.
When the number of modulation peaks is greater than 15, the subpulse duration is less than three times the phonon lifetime, and its variation range is narrowed, resulting in a smooth change in the SBS threshold.
Sinusoidally modulated laser pulses caused by the FM to AM effect are common in high-power laser systems, and when such laser pulses are used as a pump source, the relationship between SBS thresholds and time modulation needs to be studied in detail.
Conclusion: According to the results of numerical calculation, it can be seen that the dependence between the excitation Brillouin scattering threshold and the pump intensity fluctuation is that when the distortion criterion is lower than 30%, the SBS threshold remains almost stable and the effect is minimal.
When the α factor is greater than 30%, the threshold value increases exponentially. , the SBS threshold increases with the shortening of the subpulse duration, but when the subpulse duration is less than three times the phonon lifetime, the SBS threshold tends to remain the same.
