  Polarization-resolved second-harmonic spectra are obtained from the resonant
modes of a two-dimensional planar photonic crystal microcavity patterned in a
free-standing InP slab. The photonic crystal microcavity is comprised of a
single missing-hole defect in a hexagonal photonic crystal host formed with
elliptically-shaped holes. The cavity supports two orthogonally-polarized
resonant modes split by 60 wavenumbers. Sum-frequency data are reported from
the nonlinear interaction of the two coherently excited modes, and the
polarization dependence is explained in terms of the nonlinear susceptibility
tensor of the host InP.
