Direct measurement and analytical description of the mode alignment in inversely tapered silicon nano-resonators

Inversely tapered silicon photonic resonators on silicon substrates were shown to host multiple high-Q whispering gallery modes and constitute versatile building blocks for CMOS compatible solid state lighting, optical sensing and modulator devices. So far, numerical analyses by the finite difference time domain method have been used to predict the height distribution of whispering gallery modes in such resonators. In this study, we provide an experimental evidence of this mode distribution along the resonator height by selectively exciting whispering gallery modes using cathodoluminescence spectroscopy. Further we derive analytical functions that permit to relate the height distribution of modes with a defined polarization, symmetry and effective refractive index to the geometrical shape of the inversely tapered resonators.