Improving performance prediction of diode end-pumped solid-state Nd:YAG rod amplifiers by incorporating pump mode evolution

Master Oscillator Power Amplifier (MOPA) systems find extensive use in laser development to increase the optical power of laser emissions from a Master Oscillator (MO). Commonly used are the cylindrical rod MOPAs that are optically excited using a multimode fiber-coupled (FC) diode laser emission in an end-pumped configuration. Current analytical 3D models that incorporate thermal effects, gain saturation, and iterative Fourier beam propagation methods, collectively, rely on static approximations of the evolution of the FC pump beam profile over the longitudinal volume of the amplifier crystal. Furthermore, in general, the spectral behavior of the FC diode emission is assumed to be static, and the thermal wavelength shift is not accounted for in the simulation. In this work, we demonstrate a novel approach for accurate modeling of the multimode FC pump beam emission as a complex field using a phase-only Gaussian to flat-top (FT) diffractive optical element, thus allowing for the inclusion of the pump beam into the iterative propagation method. Additionally, we present a method for precise calibration of the model using simple experimental measurements of the diode emission spectrum. The theoretical model is experimentally validated using an end-pumped Nd:YAG crystal rod to perform single-pass amplification of a Gaussian beam, showing excellent agreement with predicted output powers over the calibrated range of pump powers. Furthermore, we provide experimental data that exhibits a strong correlation between the Gaussian to FT phase-only transformation and the multimode FC diode evolution in free-space propagation.