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Physical Review A

Spontaneous emission and photon dynamics in dielectric microcavities

David P. Fussell, Marc M. Dignam, Michael J. Steel, C. Martijn de Sterke, R. C. McPhedran

Published Oct 5, 2006• 16 citations
Publisher

Abstract

We consider spontaneous emission in dielectric microcavities with multiple resonances that may overlap in both position and frequency. By projecting the Green tensor onto a set of quasimodes associated with the resonances, we derive the reduced spontaneous emission rate. To demonstrate the accuracy and computational efficiency of our approach, we model spontaneous emission in a two-dimensional photonic crystal with two coupled defects. Employing a quantum mechanical interpretation, we show that the spontaneous emission involves both direct decay into the individual quasimodes and photon transfer between the quasimodes. The quantum path interference between these different emission channels can cause the spontaneous emission rate to differ dramatically from the rate obtained by the summation over resonant line shapes. We also show how our approach can be used to determine the emission into particular quasimodes of multiple-resonance microcavities.

DOI
10.1103/physreva.74.043806

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We consider spontaneous emission in dielectric microcavities with multiple resonances that may overlap in both position and frequency. By projecting the Green tensor onto a set of quasimodes associated with the resonances, we derive the reduced spontaneous emission rate. To demonstrate the accuracy and computational efficiency of our approach, we model spontaneous emission in a two-dimensional photonic crystal with two coupled defects. Employing a quantum mechanical interpretation, we show that the spontaneous emission involves both direct decay into the individual quasimodes and photon transfer between the quasimodes. The quantum path interference between these different emission channels can cause the spontaneous emission rate to differ dramatically from the rate obtained by the summation over resonant line shapes. We also show how our approach can be used to determine the emission into particular quasimodes of multiple-resonance microcavities.
We examine theoretically the spontaneous emission rate in optical microstructures with cavity resonances that overlap in both position and frequency. Using projection techniques, we show that the spontaneous emission in such structures can be accurately described by the direct emission and quantum path interference of emission into a few discrete resonant modes, even though the exact infinite-dimensional problem involves a coupling to the continuum of radiation states. Moreover, we obtain an efficient numerical time-domain method for determining the spontaneous emission rate that incorporates these effects, including the suppression of spontaneous emission into some modes.
Starting from a quantum Maxwell equation for the vector potential operator, we study the spontaneous emission properties of a two-level atom interacting with the electromagnetic field in a lossless and inhomogeneous dielectric structure and express the spontaneous emission rate, the external quantum efficiency, and the spontaneous emission factor in terms of the classical Green function of the dielectric structure. Comparing these results with the corresponding classical results, we show that the above quantities can be calculated from the radiation field of a classical dipole. Based on this correspondence, a numerical algorithm is developed to calculate the modification of spontaneous emission in microcavities. The line shape of the emission spectrum of the light source and the decay of the cavity resonant modes are automatically taken into account in this algorithm. The approximate expressions for the spontaneous emission rate and the spontaneous emission factor are discussed.
A detailed account of the calculation on the spontaneous emission rate in a very short optical cavity with plane-parallel dielectric mirrors is given. A cavity model consisting of a pair of plane dielectric slabs is used. Guided modes as well as outgoing modes are considered. The emission rate from a two-level atom is calculated under quantum-mechanical perturbation approximation. The enhancement factor for the rate is found to be of the order of unity except for extremely short cavities. The concept of quasimodes in a very short cavity and their effective area are discussed in relation to the enhancement factor. The coupling ratios into various quasimodes are derived.
We consider the process of spontaneous emission of a two-level atom embedded into a periodic layered dielectric structure. When the resonant atomic frequency lies within the photon-density-of-states gap, of width \ensuremath{\Gamma}, the atom emits light during a time interval t\ensuremath{\Gamma}\ensuremath{\ll}1 until the spontaneous emission becomes fully inhibited. We discuss the enhancing of spontaneous emission by tuning the atomic resonance with a one-mode microcavity. In the \ensuremath{\lambda}/4-shifted distributed feedback microcavities which possess the \ensuremath{\delta}-function-like density of states, in the middle of the gap, the process of spontaneous emission has damped Rabi oscillation behavior; the damping depends on the width of the gap and the height of its walls. A profile of the density-of-states gap can be determined from the experimental data on the temporal behavior of the atomic spontaneous decay.
Impressive progress has been achieved in controlling the spontaneous emission rate for emitters in Nanophotonic structures, such as microcavities, photonic crystals and nano-antennas. In all cases, however, the modification of the emission is stationary in time. Thus, the emission rate is time-independent and the distribution of photon emission times are stochastic and follow an exponential distribution in the weak coupling regime. In this paper, by using fast all-optical switching of a microcavity, the cavity resonance is tuned within tens of picosesonds. This drastically changes the local optical density of states at the emission frequency within the emission lifetime of the emitters. This paper theoretically studied an ensemble of two-level sources with a time dependent decay rate and have derived the excited state population and emitted intensity as a function of time for continuous wave and pulsed excitation. Deterministic bursts of dramatically enhanced or inhibited emission intensity within short intervals. Thereby, we control the photon distribution to show behavior that strongly deviates from single exponential decay. This can be used to protect quantum information systems against decoherence and to realize non-Markovian dynamics in cavity quantum electrodynamics.