Spontaneous Emission in Nanophotonics

Abstract

In this thesis, we present semi-analytic theories of radiation noise in nanophotonic devices, which utilize new numerical software for solving light equations in nano-structures, combined with thermodynamic tools for including radiation noise. The first part of the thesis focuses on noise in lasers. Our formulation produces a formula for the width of the central spectral peaks (``the linewidth'') in single- and multimode lasers, as well as formulas for the sidepeaks, which arise due to relaxation oscillations. Our formulas contain almost all previously known effects and find new nonlinear and multimode corrections in complicated nanophotonic structures. We verify our theory with brute-force simulations of the semiclassical Maxwell--Bloch equations, augmented with random sources representing radiation noise. Moreover, we extend our theory of laser noise and include amplified spontaneous emission (ASE) near the lasing threshold. In the second part of the thesis, we discuss spontaneous emission at exceptional points (EPs)---exotic degeneracies in non-Hermitian systems. Our theory extends beyond spontaneous emission to any light--matter interaction described by the local density of states (e.g., absorption, thermal emission, and nonlinear frequency conversion). Whereas traditional spontaneous-emission theories imply infinite enhancement factors at EPs, we derive finite bounds on the enhancement, proving maximum enhancement of 4 in passive systems with second-order EPs and significantly larger enhancements (exceeding 400x) in gain-aided and higher-order EP systems. Finally, we demonstrate an application of our theory to higher-harmonic generation in nonlinear media with EPs.