General theory of spontaneous emission near exceptional points

• DOI: 10.1364/oe.25.012325
• Publication Date: 2017-05-17T16:21:32Z
• Authors: Adi Pick; Bo Zhen; Owen D. Miller; Chia W. Hsu; Felipe Hernandez; Alejandro W. Rodr...; Marin Soljačić; Steven G. Johnson
• Keywords: 0103 physical sciences; FOS: Physical sciences; 01 natural sciences; 7. Clean energy; Physics - Optics; Optics (physics.optics)

15 pages, 7 figures<br/>We present a general theory of 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 $400\times$) in gain-aided and higher-order EP systems. In contrast to non-degenerate resonances, EPs are associated with non-Lorentzian emission curves, leading to enhancements that scale polynomially with the resonance quality factor.<br/>