Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap

We describe and demonstrate a new mechanism for low radiation losses in structures lacking a complete band gap, and show how resonant cavities with ${\text{Q>10}}^3$ can be achieved without sacrificing strong localization in 3d. This involves a forced cancellation in the lowest-order term(s) of the multipole far-field radiation expansion. We focus on the system of photonic-crystal slabs, one- to two-dimensionally periodic dielectric structures of finite height with vertical index guiding. Simulations and analytical results in 2d and 3d are presented.