Numerical simulation of a laser resonator with an in-phase doughnut-like output beam

A numerical model of the toric concave mirror laser resonator is founded by using the eigenvector method. Numerical calculation shows that an in-phase doughnut-like beam mode with high beam quality can be obtained in this resonator, whose diffraction loss is the lowest, and whose intensity distribution covers the whole resonator mirror. Systematical simulations indicate that, different from the spherical stable resonator, the effects of Fresnel number of the resonator and curvature radius of the toric concave total reflector on output beam quality is not very obvious. Under the condition of curvature radius of 15 m, the M ² factor of the output beam of this resonator with a large range of Fresnel number from 6.2 to 12.6 is from 1.3 to 1.9. Furthermore, the diffraction loss is close to 1.0% or less than 1.0%. Under the condition of Fresnel number of 7.07, the M ² factor of the output beam of this resonator with curvature radius from 6 to 30 m is from 1.60 to 1.24, and the diffraction loss is close to 1.0% or less than 1.0%.