Controlling spontaneous emission in inertial and dissipative nematic liquid crystals: the role of critical phenomena

We develop a rigorous, field-theoretical approach to the study of spontaneous emission in inertial and dissipative nematic liquid crystals, disclosing an alternative application of the massive Stueckelberg gauge theory to describe critical phenomena in these systems. This approach allows one not only to unveil the role of phase transitions in the spontaneous emission in liquid crystals but also to make quantitative predictions for quantum emission in realistic nematics of current scientific and technological interest in the field of metamaterials. Specifically, we predict that one can switch on and off quantum emission in liquid crystals by varying the temperature in the vicinities of the crystalline-to-nematic phase transition, for both the inertial and dissipative cases. We also predict from first principles the value of the critical exponent that characterizes such a transition, which we show not only to be independent of the inertial or dissipative dynamics, but also to be in good agreement with experiments. We determine the orientation of the dipole moment of the emitter relative to the nematic director that inhibits spontaneous emission, paving the way to achieve directionality of the emitted radiation, a result that could be applied in tuneable photonic devices such as metasurfaces and tuneable light sources.