Statistical Model of a Laser Beam with Random Phase Distortions of the Field Inside an Unstable Resonator

The dependence of the correlation function of output laser radiation on statistical characteristics of spatially distributed random phase distortions in an unstable resonator has been theoretically studied. The intra-resonator field is considered in the geometric optics approximation. The applicability conditions of the optical-geometrical approach are formulated. The main condition is as follows: within the boundaries of a separate, arbitrarily isolated wavefront inhomogeneity, the amplitude of wavefront distortions should be much smaller than the regular distortion introduced into the field due to the reflection from nominally spherical resonator mirrors. The power distribution for a focused resonance laser beam as a function of the resonator characteristics and field phase distortions is studied. In the Fresnel approximation, it is shown that a focused beam can be represented by the sum of diffraction-limited and scattered components. The power of the components is determined by the phase distortion dispersion. The divergence of the scattered component depends on the dispersion of wavefront tilt angles and the dispersion of the field phase distortions. The specific features of the optimization model of an optical laser transmitter with an unstable resonator have been investigated. Under typical conditions, for an annular output beam, the intensity of the focused radiation is maximum when the laser output power is lower than the maximum value by a factor of 1.2 to 1.9.