Propagation offset characteristics of annular laser beams from confocal unstable resonators through the natural atmosphere

Based on the laser field from a positive confocal unstable resonator (ab initio), the propagation characteristics of the beam through atmosphere are investigated by means of fast Fourier transform (FFT), and it is assumed that the refractive index and absorption of atmosphere are only decided by the air molecules. Considering the thermal effects of the laser beam and wind velocity of air, we evaluate the beam offsets, beam spreading, and beam qualities of the laser field transmitting from the resonator through the natural atmosphere. Meanwhile, the far-field intensity distributions of the laser beam with various intensities in the atmosphere are obtained. It is shown that the far-field diffraction patterns are deformed due to absorption of air and wind velocity. β parameter and Strehl ratio, which are usually used for high-power lasers, are introduced to estimate the beam quality characteristics. With increasing the intensity of the beam, the far-field diagram patterns are outspreaded, the peak intensities reduced, the peak centers shifted, and the beam quality characteristics greatly degraded.