Abstract
A numerical model for amplification of ultrashort pulses with high repetition rates in fiber amplifiers is presented. The pulse propagation is modeled by jointly solving the steady-state rate equations and the generalized nonlinear Schrödinger equation, which allows accurate treatment of nonlinear and dispersive effects whilst considering arbitrary spatial and spectral gain dependencies. Comparison of data acquired by using the developed model and experimental results prove to be in good agreement.
Highlights
A numerical model for amplification of ultrashort pulses with high repetition rates in fiber amplifiers is presented
A conceptually simple method was developed for solving the rate equations (RE) and the generalized nonlinear Schrödinger equation (GNLSE) together in a fiber amplifiers (FA) in the case of a high repetition rate source and a continuous wave (CW) pump
As the model is based on RK4 schemes when solving both the GNLSE and the RE, it has a global accuracy proportional to the fourth order of the step-size
Summary
Where e is the electron charge, n0 the refractive index of the host, m is the electron mass, 0 is the free space permittivity, fij is the oscillator strength, λij is the transition line center, gi′j is the lineshape, ωsig is the angular frequency of the incident light, Ni,j are the population densities and gi,j are the degeneracy factors. Using the relation between oscillator strength, absorption cross-sections and the Einstein coefficients[34], equation (11) can be re-expressed as nij (n02 + 2)2 18ωij c σa,ij (12). This equation is to be summed over all transitions in order to get the net contribution. The resulting refractive index and the one for fused silica is used to solve the standard eigenvalue equation for a step-index fiber[31] to determine the propagation constant of the fundamental mode, for all the wavelengths in the considered spectral window at different levels of inversion.
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