Aspherical telescopes for laser amplifiers in the theory of optical inverse problems

An approach is developed to provide a framework in which the task of searching for and selecting the configuration of a two-mirror telescope is formulated as an optical inverse problem: the telescope configuration is found from a given amplitude and/or phase distribution of the field in the plane of the output mirror aperture. Integral equations are obtained for determination of the shape of the telescope mirrors. The solutions of this inverse problem are studied in the geometric optics approximation. A numerical investigation is made of the output radiation power and of the axial radiation intensity in the far-field zone as a function of the configuration of a telescope amplifier and of the input beam characteristics. The use of an aspherical telescope makes it possible to increase, compared with the spherical configuration, the output radiation power and the axial power density of the focused beam by optimisation of the number of trips the radiation makes inside the telescope and of the amplitude distribution of the output radiation.