Phase-Matched Second-Harmonic Generation in Biaxial Crystals

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Abstract
The allowed directions for phase‐matched second‐harmonic generation in acentric biaxial crystals are obtained by considering the intersections of the index surfaces at the fundamental and harmonic frequencies; the topology of these intersections is determined by the principal refractive indices. There are thirteen distinguishable cases for optically well‐behaved biaxial crystals and the phase‐matching directions for them are shown as loci on the stereographic projection. Phase‐matching that is insensitive to small changes in the direction of propagation is possible when some principal refractive indices are equal; the mismatch of the wave vectors is given for deviations from the phase‐matching direction in such cases. The disposition of the principal axes of the optical indicatrix and the symmetry of the point groups C2v, D2, Cs, C2, and C1 are examined to find those situations which have a nonzero element in the second‐order polarizability tensor that will give second‐harmonic generation. Phase‐matched second‐harmonic generation experiments in the biaxial crystals dipotassium tartrate, lithium sulfate and ammonium oxalate demonstrate some of the possible phase‐matching situations.