Random wavenumber and nonlinear parametric effect of speckle field

Abstract

Speckle field is a relatively common phenomenon. But the speckle has special application value in nonlinear optical domain because it can be used to suppress different nonlinear processes that are caused by high power laser. To enhance the suppression capability, it is necessary to reveal the basic mechanism of the speckle parameter nonlinear optical interaction process. In this work, the coupling wave equation under the wave number mismatch condition is used to analyze the parameter process of speckles field. The solving process of the coupling wave equation is introduced in detail. And the wave number or phase matching condition is fully discussed. Furthermore, the threshold of the nonlinear gain is analyzed when the wave number does not fully meet the matching condition. To describe the solution of the coupling wave equation more clearly, the undetermined coefficient of the exact analytical solution is discussed. Since the boundary field will affect the confirmation of the undetermined coefficient, the characteristic of boundary field should be analyzed first. The nonlinear process of the speckle field is a three-wave interaction process. The different boundary conditions will affect the three-wave interaction process. And it is found that if the complex amplitudes of the three waves at the boundary are not zero, the undetermined coefficient will be changed with the phrase parameters of the three waves. To achieve the maximum value, the boundary waves must meet the phase matching condition. The wave number of the speckle filed is not an invariant, because of its random distribution characteristic. Therefore, during the analysis of the three-wave interaction process, the segment handling method is used to ensure the effective solving of the first order coupling wave equation. On the other hand, the randomly fluctuation of the wave number destroys the phase matching condition of the boundary. It is just through the basic mechanism that the speckle field can be used to suppress the nonlinear gain of high-power optical field. Both the theoretical analyses and the numerical calculation results show that the speckle field has good suppression effect for some typical nonlinear parameter process, such as stimulated Brillouin scattering.