Study On Stimulated Brillouin Scattering In Few-mode Fiber

Since the nonlinear Shannon limit of single-mode fiber,people try to find many ways to improve the communication capacity,one of them is Mode-division multiplexing（MDM）.However,the dispersion effect between multi-mode fiber modes is very serious,the advantages of few-mode fiber which is easier to control gradually come out.Stimulated Brillouin scattering（SBS）,as a nonlinear effect in optical fiber,has been applied in many fields,including fiber sensors,optical storage and fiber lasers.Besides,the phase shift characteristics of SBS effect can be used to compensate another nonlinear effect in the fiber,four-wave mixing（FWM）phase mismatch,to improve its efficiency.FWM can also be widely used in optical amplification,mode conversion and other research fields.Therefore,it is of great significance to study the amplitude-frequency and phase-frequency characteristics of SBS based on few-mode fiber.In this paper,the SBS effect is studied and simulated based on few-mode fiber,and the SBS phase shift response is used to compensate for the FWM’s phase mismatch.The specific work and results are as follows:（1）Based on the SBS dynamic characteristics in single-mode fiber and the theory of wave optics,the different mode’s coupled amplitude equations of pump wave and signal wave with time and space evolution are derived.And the Brillouin complex gain factor g_c is derived from the coupled amplitude equation of signal wave.The acousto-optic coupling coefficients which affect the coupling efficiency of different optical modes and acoustic modes are defined.Above all,we obtain the mathematical models of Brillouin gain spectrum（BGS）and Brillouin phase shift spectrum（BPS）.（2）BGS and BPS have different coupling efficiency for different pump-signal mode combinations.If the combination of LP₀₁-LP₀₁1 pump-signal mode pair is taken as the normalized reference,the BGS gain peak of the parallel-coupled LP_11a-LP_11a1a mode pair is about 89.7%of it;The BGS gain peak value of inter-mode coupling LP₀₁-LP₁₁1 mode pair is about 57.9%of it;The BGS gain peak value of vertically coupled LP_11a-LP_11b1b mode pair is about 29.8%of it.This is also true for the maximum phase shift.The above results show that in LP₀₁1 mode and LP₁₁1 mode,the intra-mode SBS process is more critical,and the inter-mode SBS effect of LP₁₁1 mode is mainly parallel coupling.In addition,through the calculation of the acousto-optic coupling coefficient of the acoustic mode under different pump-signal mode combinations,We found that the main fundamental modes and various low-order modes of the acoustic wave involved in the SBS effect.And the relatively higher order acoustic modes result in an increase in the total linewidth of the BGS.（3）We calculate the phase matching condition of three FWM processes theoretically,and point out that one of them is easy to be changed by the fluctuation of the external environment under the actual conditions,thus affecting the control of the FWM efficiency.Then,the phase mismatch factors of the other two FWM processes are compensated,and utilize the phase shift response of SBS process to FWM signal wave,so that the final phase mismatch of the inter-mode FWM process tends to zero.The results show that the absolute value of the maximum phase mismatch factor generated by the two FWM processes is the same,which is about 1.3×10⁵ km^-1-1.6×10⁵ km^-1.If SBS pump wave is injected in LP₀₁mode,the compensation of 1×10⁵ km^-11 can be generated at most;if SBS pump light is injected in LP₁₁1 mode,the compensation of 6×10⁴km^-1can be generated at most.