Photonic crystals of one- or two-dimensional periodicity can be used to ach
ieve three-dimensional photon confinement in dielectric waveguides with mod
al volumes of the order of a cubic half-wavelength. Since photonic crystals
of low-dimensional periodicity do not have full three-dimensional bandgaps
, the microcavities undergo increasing radiation losses with decreasing mod
al volumes. High-Q resonant modes can be generated by reducing the strength
of the photon confinement. Increasingly, larger modal volumes lead to lowe
r radiation losses and more efficient coupling to waveguide modes outside t
he cavity.