Mid-infrared absorption, emission, and non-linear response in extreme sub-wavelength films

We present an analytical formalism to predict the minimal thickness of a film, with an intrinsic absorption resonance, required to perfectly absorb all incident light. We show that on resonance, perfect absorption can be achieved at thicknesses well below one-thousandth of a free-space wavelength. The developed analytical formalism is validated numerically using rigorous coupled wave analysis and finite element techniques, and experimentally using thin-film superlattices of tin-doped indium oxide nanocrystals with collective plasmon resonances mimicking the absorption resonances considered in our analytical model. We further consider perfectly absorbing structures consisting of thin, non-resonant, but high loss, films, and show that perfect absorption can often only be achieved at film thicknesses well below what can be fabricated experimentally. We overcome this limitation by introducing the concept of thin-film dilution, and show, analytically, numerically, and experimentally, that these diluted films can accurately mimic the theoretical optical properties of nanometer, or even sub-atomic, thickness films. This work provides a path towards the rational design of ultra-thin absorbers for bolometric or non-linear optical applications.