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