Electromagnetic cavity with arbitrary Q and small modal volume without a complete photonic bandgap

We show how an electromagnetic cavity with arbitrarily high Q and small (bounded) modal volume can be formed in two or three dimensions with a proper choice of dielectric constants. Unlike in previous work, neither a complete photonic bandgap nor a trade-off in mode localization for Q is required. Rather, scattering and radiation are prohibited by a perfect mode match of the TE-polarized modes in each subsection of a Bragg resonator. Q values in excess of 10(5) are demonstrated through finite-difference time-domain simulations of two- and three-dimensional structures with modal areas or volumes of the order of the wavelength squared or cubed.