Phase-Matched Second-Harmonic Generation in Biaxial Crystals

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.

Optical, vibrational, thermal, electrical, damage, and phase-matching properties of lithium thioindate

“…The phase-matching loci for collinear SHG can be categorized using the classification of Hobden [62]. Our calculations based on the relatively simple transcendental equations derived by Yao et al [63], predict that no phasematched SHG is possible below 1617 nm.…”

General analysis of type I second-harmonic generation with elliptical Gaussian beams

“…With biaxial crystals 26,27 there are rather too many configurations to describe here, but one can derive a value for the walk-off angle by using…”

Femtosecond nonlinear frequency conversion based on BiB3O6

“…4 and 5. The points where possible loci of directions change their topological pattern correspond to the fundamental wavelengths for which the transitions between the different Hobden classes take place [107], see Table 4.…”