PARAXIAL WAVE THEORY OF 2ND-HARMONIC AND 3RD-HARMONIC GENERATION IN UNIAXIAL CRYSTALS .1. NARROW-BAND PUMP FIELDS

We present a paraxial wave formulation of three-wave mixing in a negative uniaxial crystal, including effects of diffraction and transverse walkoff. The theory, though general, is applied specifically to second harmonic generation in KDP with Nd:glass laser radiation, followed by the mixing of the second harmonic with the fundamental in a second KDP crystal to produce third ; harmonic radiation near 0.35 mu m. For applications of interest, which can involve third harmonic conversion efficiencies approaching 90%, walkoff is potentially much more deleterious to conversion than diffraction. However, walkoff is negligible when the angular spectrum of the pump field does not have substantial contributions from spatial frequencies greater than or similar to (aL)(-1), where L is the crystal length and a depends upon the derivative of each extraordinary refractive index with respect to the angle between the optic axis and the direction of wave propagation. A similar result, scaling as L(-1/2) rather than L(-1), holds for diffraction. We consider the case of monochromatic fields in order to isolate the effects of diffraction and transverse walkoff from effects of finite pulse durations and spectral bandwidth, which are addressed in a forthcoming paper. We find that, for inertial confinement fusion applications, neither diffraction nor walkoff should significantly limit the conversion of narrowband 1.05 mu m radiation to 0.35 mu m if the crystals are of high optical quality, and if the input wavefront does not have significant spatial frequency components larger than (aL)(-1). Small phase variations across the input pump wavefront have a negligible effect on conversion efficiencies at low pump intensities, but can significantly reduce third harmonic conversion efficiencies at higher drives.