Synthesis of laser resonator configurations as an inverse problem in optics

The problem of seeking and selecting the configuration for a laser resonator is approached from a new direction: as an inverse problem in optics. Specifically, the configuration (the complex reflection coefficients of the resonator mirrors) is found from a given amplitude distribution and/or phase distribution of the field in the plane of the output aperture. Closed integral equations are constructed for determining the complex reflection coefficients. Exact analytic solutions are derived for certain cases. The problem of developing an algorithm for deforming the mirrors of a resonator in order to control the power of the laser radiation is formulated and solved as an inverse problem of synthesizing the geometric configuration of a resonator from a given phase distribution of the output radiation. The results of a numerical study of the output power of controlled resonators and of the axial intensity of the radiation in the far zone are reported. In selecting one- or two-mirror layout for controlling the configuration of a resonator, one should be guided primarily by the comparative complexity of developing the deformable mirrors and control systems.