Graded index photonic hole: Analytical and rigorous full wave solution

Abstract

We present a rigorous full wave approach to the omnidirectional photonic hole (PH), an optical system inspired by celestial phenomena and characterized by a radially graded refractive index $n(r)\ensuremath{\sim}1/{r}^{\ensuremath{\alpha}/2}$. It is analytically demonstrated that light capture is effective for $\ensuremath{\alpha}\ensuremath{\ge}{\ensuremath{\alpha}}_{c}=2$. Our analyses are corroborated by precise numerical simulations of steady-state and time-evolution behaviors. The simulations indicate that the optical energy entering the PH system can be kept in captivity for a time duration ${t}_{d}$ scaling as ${t}_{d}\ensuremath{\sim}1/({\ensuremath{\alpha}}_{c}\ensuremath{-}\ensuremath{\alpha})$ when $\ensuremath{\alpha}$ approaches ${\ensuremath{\alpha}}_{c}$. A crucial difference in the time evolution of fields is shown between the cases with $\ensuremath{\alpha}$ close to and equal to ${\ensuremath{\alpha}}_{c}$.