Maximum permissible pulse duration in second-harmonic generation in a KDR crystal

When the second harmonic is generated from a high-power short laser pulse, the temperature within the laser beam channel in the nonlinear crystal increases. This is undesirable because it disturbs the phase-matching conditions. An expression is obtained for the maximum power density in the laser beam channel which can be used without serious deterioration of the efficiency of the nonlinear crystal. The same effect sets a limit to the pulse duration (for a fixed pulse power). It is shown that the power density in the beam channel must not exceed a certain generalized parameter, defined in terms of the optical and elastic properties of the nonlinear crystal. A quantitative estimate obtained for a KDP crystal gives 10 J/cm³ for this parameter.