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Physical Review A

Spontaneous-emission spectrum in an absorbing Fabry-Perot cavity

M. S. Tomaš, Zdravko Lenac

Published Sep 1, 1999• 24 citations
Publisher

Abstract

We discuss the frequency dependence of the spontaneous-emission rate (power) in a Fabry-Perot microcavity containing a Lorentz dielectric, with emphasis on modifications of the spectrum under the circumstances of the strong medium-cavity coupling. With the standard-cavity tuning, the total spontaneous-emission power spectrum consists of a multiwave version of the familiar low-frequency vacuum Rabi split peak and a broad structure on the high-frequency side coming from the enhanced spontaneous emission into the continuum of the obliquely propagating waves. This form of the spectrum derives from the properties of the (single-wave) radiation-intensity spectrum of the molecule. Depending on the observation direction, the radiation-intensity spectrum exhibits either a double-peak structure characteristic of the vacuum Rabi splitting, as observed in light transmisssion and reflection experiments, or a single-peak structure describing the enhanced spontaneous emission at the corresponding cavity resonant frequency.

DOI
10.1103/physreva.60.2431

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We discuss the frequency dependence of the spontaneous-emission rate (power) in a Fabry-Perot microcavity containing a Lorentz dielectric, with emphasis on modifications of the spectrum under the circumstances of the strong medium-cavity coupling. With the standard-cavity tuning, the total spontaneous-emission power spectrum consists of a multiwave version of the familiar low-frequency vacuum Rabi split peak and a broad structure on the high-frequency side coming from the enhanced spontaneous emission into the continuum of the obliquely propagating waves. This form of the spectrum derives from the properties of the (single-wave) radiation-intensity spectrum of the molecule. Depending on the observation direction, the radiation-intensity spectrum exhibits either a double-peak structure characteristic of the vacuum Rabi splitting, as observed in light transmisssion and reflection experiments, or a single-peak structure describing the enhanced spontaneous emission at the corresponding cavity resonant frequency.
The spectrum of spontaneously emitted photons from an atom interacting with a single cavity mode depends on the relative sizes of the mode coupling constant and the cavity loss rate. If the coupling constant is not too large, perturbation theory can he used to show that the atomic linewidth is either increased (enhanced spontaneous emission) or decreased (inhibited spontaneous emission) by the presence of the cavity. When the coupling constant is so large that perturbation theory cannot be used, the spontaneous- emission spectrum forms a doublet, with peaks located at the normal-mode frequencies for the coupled-dipole and cavity-mode oscillators (the so-called "vacuum" Rabi splitting).
Spontaneous emission in a one-dimensional Fabry-P\'erot-type optical cavity is analyzed quantum mechanically. Via a monolayer dielectric cavity model, expressions describing the atomic-location dependence of the emission intensities and the spectra observed on both sides of the cavity are obtained. The probability amplitude for the upper atomic state is analyzed and its time-evolution equation is given. The probability amplitude is shown to be proportional to ``the electric field amplitude for a single emission event'' introduced classically by Huang et al. [Appl. Phys. Lett. 61, 2961 (1992)]. An expression for the emission spectrum applicable to a general one-dimensional cavity structure is obtained.
We investigate the spontaneous emission (SE) spectrum of a qubit in a lossy resonant cavity. We use neither the rotating-wave approximation nor the Markov approximation. For the weak-coupling case, the SE spectrum of the qubit is a single peak, with its location depending on the spectral density of the qubit environment. Then, the asymmetry (of the location and heights of the two peaks) of the two SE peaks (which are related to the vacuum Rabi splitting) changes as the qubit–cavity coupling increases. Explicitly, for a qubit in a low-frequency intrinsic bath, the height asymmetry of the splitting peaks is enhanced as the qubit–cavity coupling strength increases. However, for a qubit in an Ohmic bath, the height asymmetry of the spectral peaks is inverted compared to the low-frequency bath case. With further increasing the qubit–cavity coupling to the ultra-strong regime, the height asymmetry of the left and right peaks is slightly inverted, which is consistent with the corresponding case of a low-frequency bath. This inversion of the asymmetry arises from the competition between the Ohmic bath and the cavity bath. Therefore, after considering the anti-rotating terms, our results explicitly show how the height asymmetry in the SE spectrum peaks depends on the qubit–cavity coupling and the type of intrinsic noise experienced by the qubit.
A complete set of cavity modes in planar dielectric microcavities is presented which naturally includes guided modes. We show that most of these orthonormal fields can be derived from a coherent superposition of plane waves incoming on the stack from the air and from the substrate. Spontaneous emission of a dipole located inside the microcavity is analyzed, in terms of cavity modes. Derivation of the radiation pattern in the air and in the substrate is presented. The power emitted into the guided modes is also determined. Finally, a numerical analysis of the radiative properties of an erbium atom located in a Fabry-P\'erot multilayer dielectric microcavity is investigated. We show that a large amount of light is emitted into the guided modes of the structure, in spite of the Fabry-P\'erot resonance, which increases the spontaneous emission rate in a normal direction. \textcopyright{} 1996 The American Physical Society.
We calculate the spontaneous-emission characteristics of a quantum-well exciton embedded in the center of a planar microcavity and compare them with the emission characteristics in a single-mode cavity with lateral confinement of the electromagnetic field. The results indicate that because the modal structure of a planar microcavity consists of a spectrally dense continuum, the exciton decays into the cavity continuum with a time constant close to the free-space spontaneous-emission lifetime, even under conditions in which its spectrum displays the vacuum Rabi splitting. This behavior contrasts with the case of cavities with lateral in-plane confinement of the field, in which the vacuum Rabi splitting is the signature of a dramatic modification of the spontaneous-emission lifetime. The technological implications of this difference are discussed.
We present a nonperturbative result for the spectrum of spontaneous photons emitted by an atom coupled on resonance to a standing-wave cavity mode. Motion of the atom through the standing-wave mode function is included in a classical way. We discuss the form of the spectrum as a function of the velocity of the atom in the limit of strong dipole coupling. For slow atoms the normal-mode doublet (``vacuum'' Rabi spectrum) survives with small changes. The motion of a fast atom through the standing wave averages the coupling constant to zero, and the spectrum reverts to a single peak. At intermediate velocities the spectrum has a complicated multipeaked structure that can be understood in terms of interfering probability amplitudes for different quantum-mechanical emission paths or as a frequency-modulation spectrum for radiating coupled oscillators.