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Multimode hollow microcavities in three-dimensional (3D) photonic crystals(PhCs) are designed for achieving enhanced coherent anti-Stokes Ramanscattering, which requires a cavity to have three high quality-factor (Q) modeswith equally spaced resonant frequencies. Cavities in 3D PhCs allows moreflexibility in design and tuning than their 2D slab counterparts, sinceradiation loss that degrades Q can be suppressed by the 3D photonic band gap.We first tune all the mode frequencies simultaneously by changing the materialand geometry of the cavity based on perturbation theory. Spectral spacingsbetween the multiple modes are adjusted according to the symmetry, volume andfield distribution of their mode profiles. The frequency and field distributionof the resonant modes are computed by solving Maxwell's equations in thefrequency domain.

Spectral tuning of multimode three-dimensional photonic crystal cavities for enhanced anti-Stokes Raman scattering