Physical origin of the small modal volume of ultra-high-Q photonic double-heterostructure nanocavities

Abstract

We have recently demonstrated the fabrication of ultra-high-Q photonic double-heterostructure nanocavities with Q-factors of almost 1 million and ultra-small modal volumes with dimensions of optical wavelengths. Here, we describe the physical origin of the small modal volume by analysing the (imaginary) dispersion relations of the mode-gap of photonic crystal (PC) waveguides, where the mode-gap effect is the fundamental principle by which photons are confined in the nanocavities. By expanding the real dispersion relations of the propagation modes of different PC waveguides into their complex form, we obtain the (imaginary) dispersion relations of the mode-gap. It is shown that the ultra-small modal volume originates from the unusual dispersion relation of the propagation mode of the PC waveguide and that it can be engineered by the geometric parameters of the waveguide. This is demonstrated experimentally by the fabrication of photon tunnelling structures and measurement of their transmission characteristics. These results reported here will be very useful for the realization of high-Q cavities with ultra-small modal volumes and their application to nanophotonics.