Numerical analysis on the feasibility of a multi-layered dielectric sphere as a three-dimensional photonic crystal

The radiative decay rate of a dipole emitter inside the core of a multi-layered dielectric sphere is theoretically investigated. It is shown that, when the thickness of each layer coincides with a quarter wavelength, the multi-layered sphere has a great potential to work as a three-dimensional photonic crystal with a high quality factor and a small mode volume. From the analysis of the dipole position dependence of a radiative decay rate, we show that a smaller core radius, a quarter wavelength at the smallest, is more suitable for real applications. The investigation on the tolerance for thickness nonuniformity reveals that the thickness variation of 10% is tolerable.