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 negat ive 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 KD P crystal to produce third ; harmonic radiation near 0.35 mu m. For ap plications of interest, which can involve third harmonic conversion ef ficiencies approaching 90%, walkoff is potentially much more deleterio us to conversion than diffraction. However, walkoff is negligible when the angular spectrum of the pump field does not have substantial cont ributions from spatial frequencies greater than or similar to (aL)(-1) , where L is the crystal length and a depends upon the derivative of e ach extraordinary refractive index with respect to the angle between t he optic axis and the direction of wave propagation. A similar result, scaling as L(-1/2) rather than L(-1), holds for diffraction. We consi der the case of monochromatic fields in order to isolate the effects o f diffraction and transverse walkoff from effects of finite pulse dura tions and spectral bandwidth, which are addressed in a forthcoming pap er. We find that, for inertial confinement fusion applications, neithe r 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 hi gh optical quality, and if the input wavefront does not have significa nt spatial frequency components larger than (aL)(-1). Small phase vari ations across the input pump wavefront have a negligible effect on con version efficiencies at low pump intensities, but can significantly re duce third harmonic conversion efficiencies at higher drives.