We propose a design concept for tailoring the local density of optical states (LDOS) in dielectric nanostructures, based on the phase distribution of the scattered optical fields induced by point-like emitters. First we demonstrate that the LDOS can be expressed in terms of a coherent summation of constructive and destructive contributions. By using an iterative approach, dielectric nanostructures can be designed to effectively remove the destructive terms. In this way, dielectric Mie resonators, featuring low LDOS for electric dipoles, can be reshaped to enable enhancements of 3 orders of magnitude. To demonstrate the generality of the method, we also design nanocavities that enhance the radiated power of a circular dipole, a quadrupole, and an arbitrary collection of coherent dipoles. Our concept provides a powerful tool for high-performance dielectric resonators and affords fundamental insights into light-matter coupling at the nanoscale.
Keywords: Purcell enhancement; dielectric nanoantennas; inverse design; local density of optical states; nanocavities.