Classical Purcell factors and spontaneous emission decay rates in a linear gain medium

Abstract

Recently the photonic golden rule, which predicts that the spontaneous emission rate of an atom depends on the projected local density of states (LDOS), was shown to fail in an optical medium with a linear gain amplifier. We present a classical light-matter theory to fix this widely used spontaneous emission rate, fully recovering the quantum mechanical rate reported in Franke et al., Phys. Rev. Lett. 127, 013602 (2021). The corrected classical Purcell factor, for media containing linear amplifiers, is obtained in two different forms, both of which can easily be calculated in any standard classical Maxwell solver. We also derive explicit analytical results in terms of quasinormal modes, which are useful for studying practical cavity structures in an efficient way, including the presence of local field effects for finite-size dipole emitters embedded inside lossy or gain materials (using a real cavity model). Finally, we derive a full classical correspondence from the viewpoint of quantized quasinormal modes in the bad cavity limit. Example numerical calculations are shown for coupled loss-gain microdisk resonators, showing excellent agreement between few mode expansions and full numerical dipole simulations.

18 pages, 6 figures

References in corpus (10)

• Strong Off-Resonant Enhancement of Spontaneous Emission in Metal-Dielectric-Metal Plasmon Waveguide Structures
• Local-field correction to the spontaneous decay rate of atoms embedded in bodies of finite size
• Quantized quasinormal mode description of non-linear cavity QED effects from coupled resonators with a Fano-like resonance
• Unveiling the Enhancement of Spontaneous Emission at Exceptional Points
• Design of an efficient single photon source from a metallic nanorod dimer: a quasinormal mode finite-difference time-domain approach
• Quantized quasinormal mode theory of coupled lossy and amplifying resonators
• Fluctuation-dissipation theorem and fundamental photon commutation relations in lossy nanostructures using quasinormal modes
• Connecting classical and quantum mode theories for coupled lossy cavity resonators using quasinormal modes
• Quasi-normal mode approach to the local-field problem in quantum optics
• Impact of mode regularization for quasinormal mode perturbation theories

Cited by in corpus (6)

• Inverse-designed dispersive time-varying nanostructures
• Broadband Dipole Absorption in Dispersive Photonic Time Crystals
• What is the spectral density of the reservoir for a lossy quantized cavity?
• Spontaneous emission decay and excitation in photonic time crystals
• Gain-compensated metal cavity modes and a million-fold improvement of Purcell factors
• Gain-modified emission dynamics between two quantum emitters in a plasmonic gain cavity system