Theory of thermal self-action in second-harmonic generation in nonlinear crystals

An analysis is made of the influence of radial thermal gradients, which appear in a nonlinear crystal because of the absorption of incident pump radiation, on the process of second-harmonic generation. A complete solution of the steady-state heat conduction equation is obtained for an infinitely long but radially bounded cylinder illuminated with a Gaussian fundamental-frequency beam. The distortions of the temporal and spatial distributions are discussed and the dependences of the conversion coefficient on the length of a crystal, average power, and mismatch along the beam axis are considered. It is shown that, in particular, in some cases the harmonic emerging from a nonlinear crystal can have an annular structure. It is shown that radial thermal gradients in lithium metaniobate crystals can be partly compensated by the induced birefringence.