Characteristic Pulse Generation In Cavity Enhancement

In recent years,the development of compact free electron lasers has begun to sprout.At present,experimental schemes have been proposed and proved to be theoretically feasible.In this type of scheme,in order to reduce the volume of the free electron laser,a steady-state microbunching(SSMB)is added to the scheme.At present,as far as we know,in SSMB systems,nanosecond laser pulse field with megawatt-level average power is required.To our knowledge,such power level is difficult and expensive to achieve with direct generation methods.On the other hand,in the past few decades,continuous wave and ultrashort pulse optical cavity power enhancement have achieved 7.5 k W and 670 k W of average power in the cavity,respectively.However,for nanosecond pulse,cavity enhancement in a narrow linewidth cavity has not been achieved.In order to obtain a megawatt-level average power nanosecond laser pulse,it is necessary to conduct in-depth research on nanosecond pulse cavity enhancement.When studying nanosecond pulse cavity enhancement,it is necessary to consider the linewidth of the cavity,the bandwidth of the beam and impedance matching.This article will use the multi-beam interference model and use mathematical software to perform cavity enhancement calculation.Then this paper concludes that traditional nanosecond pulse cannot be enhanced in a narrow linewidth cavity.On this basis,this paper proposes a nanosecond pulse with a comb-like structure in the frequency domain.In this paper,a numerical analysis of the enhancement process of this kind of pulse in a traveling wave narrow linewidth cavity is carried out.At the same time,this paper also performs square wave shaping on the pulse,and analyzes the enhancement of the square pulse in the cavity in the same conditions.This article also proposes some schemes for generating such pulse.When studying the enhanced cavity,this article also considers that a peculiar pulse,rouge wave,whice can be generated in the cavity by means of mode locking.Rouge wave has been proved to be closely related to the formation of nonlinear breathers and solitons caused by modulation instability.Within the framework of the one-dimensional nonlinear Schrodinger equation(NLSE),the Peregrine soliton described by a class of nonlinear Akhmediev breathers is considered to be the prototype of the rougr wave.Therefore,in order to have a deeper understanding of the formation of rouge solutions,this paper also studies the relationship between NLSE and rouge wave,and proposes a method for solving NLSE.This paper derives NLSE,uses the function series expansion method to solve the two-dimensional NLSE,and gives a series of soliton solutions in the approximate analytical series expansion form.Based on these soliton solutions,this paper uses mathematical software to analyze the convergence of the series solution`s coefficients and obtain a series of numerical solutions of different forms,and verify the correctness of the method in a one-dimensional situation.