Gradient-index dark hole based on conformal mapping with etendue conservation.

Abstract

An omnidirectional light collector consisting of an axisymmetric spatially gradient refractive index medium can almost perfectly absorb light rays, regardless of where they come from. Based on the conformal mapping with complex gradient-index medium, the omnidirectional light collector, which is here called a dark hole, is able to be designed with an exponential function. The dark hole, however, has a reflective boundary where the Fresnel reflection occurs, which might lessen the absorption efficiency. To design a dark hole with consideration of the Fresnel reflection loss, a method to estimate its absorptance is necessary. Therefore, a formula to calculate the absorptance of the dark hole is derived based on the Lagrangian optics with the etendue conservation. Absorptances calculated using the formula agree well with those calculated using the Mie scattering theory in refractive index small-difference limit, which validates the formula. Absorptance of a dark hole with a silicon core and another dark hole with a complex gradient-index intermediate medium are calculated using the formula to be more than 98.8%. A micro-size dark hole is also shown to efficiently collect light rays with an absorptance of more than 95% using FDTD (finite-difference time-domain) simulation.