Efficient analytic model to optimum design laser resonator and optical coupling system of diode-end-pumped solid-state lasers: influence of gain medium length and pump beam M2 factor.

A comprehensive analytical model for optimization longitudinal pumping of ideal four-level lasers is presented for accurate analysis by removing limiting assumptions on active length and pump-beam radius in the gain medium. By taking into account the circular-symmetric Gaussian pump beam including the M2 factor, an analytical formula for the root mean square of the pump beam in the active medium is developed to relate properties of the gain medium and pump beam to the requirement on efficient optimum design. Under the condition of minimum root mean square of pump-beam radius inside the active medium, the key parameters of the optimum optical coupling system have been analytically derived. Using these parameters, optimum mode size and maximum output efficiency are derived as a function of the gain medium length, absorption coefficient, pump-beam M2 factor, and input power. Dependence of the obtained parameters on the gain medium length, absorption coefficient, pump-beam M2 factor, and input power has been investigated. The results of this theory are found to be more comprehensive than the previous theoretical investigations. The present model provides a straightforward procedure to design the optimum laser resonator and the coupling optics for maximizing the output.