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Physical Review A

Modal analysis of spontaneous emission in a planar microcavity

Hervé Rigneault, Serge Monneret

Published Sep 1, 1996• 91 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.54.2356

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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.
A complete set of cavity modes in planar dielectric multilayer structures is presented which naturally includes the guided modes. We show that most of these orthonormal fields can be derived from a coherent superposition of plane waves incident on the stack from the air and from the substrate. Using this set of cavity modes, we present a quantization scheme in idealized lossless stratified dielectric structures. This enables us to discuss the vacuum quantum fluctuations of the fields within the multilayer stack. The spontaneous emission of photons by a two-level atom located at any position inside the stratified planar structure is derived using the quantum approach and standard perturbation theory. The spontaneous emission rate as well as the radiation pattern in the air, in the substrate and in the guided mode are presented. Finally, a numerical analysis of the radiative properties of an erbium atom located in an asymmetrical Fabry - Perot multilayer structure is investigated. We show that a large part of the emitted power is directed in one half-space although a significant amount of light remains trapped in the guided modes of the structure.
Spontaneous emission of erbium atoms implanted in various planar multidielectric stacks is investigated. Computational and experimental analyses are performed so as to assess the amount of light leaking into the radiative and the guided modes of the structures. The key point is the demonstration of the dominant emission into the guided modes, even though the atoms are implanted in the spacer of a resonant microcavity structure. The result is of practical interest since it challenges the conventional idea about the electromagnetic confinement, which is likely to be reached within planar microcavities.
A three-dimensional quantum nonperturbative theory of spontaneous emission in a planar microcavity is developed on the basis of a complete set of orthogonal standing-wave mode functions. Earlier results on the spontaneous decay rate and far-field emission pattern which have been obtained in a perturbative fashion are shown to be contained in our theory. Time evolution of the initially excited atomic state is considered and comparison with perturbative results is given. It is found that though the Fabry-Perot cavity is of an open type, vacuum-field Rabi oscillations are still possible. Conditions that are favorable for this strong coupling regime are discussed. The near-field spontaneous-emission pattern and the transition from the near field to the far field are investigated. For moderate mirror reflectivities, the spread in the near-field emission pattern is found to be in good agreement with the effective mode radius concept. When the mirror reflectivity increases, however, one has a strong coupling regime and together with it, multiple reabsorptions and reemissions of the photon may occur, leading to a better localization of the photon around the atomic position. These considerations may be useful in designing microlasers of the planar type.
We study the spontaneous-emission of a single atom located between two parallel infinite plates where one of the plates is partially reflective and the plate separation is of the order of the wavelength of the atomic transition. We pay particular attention to the nature of the field modes in such a finite finesse cavity, including the full three-dimensional nature of the field. We then compute the decay rate of an excited atom placed inside such a cavity. The angular distributions of the spontaneous-emission and of the cavity field vacuum fluctuation variances are investigated. Finally, we examine the output field from an atom inside a finite finesse microcavity. We show that the radiation transmitted outside such microcavity forms a nondiffracting Bessel beam. \textcopyright{} 1996 The American Physical Society.
A general analysis of spontaneous emission in the vicinity of a symmetric slab dielectric waveguide is presented using explicit energy-normalized functions for the complete set of bound and radiating TE and TM modes. Expressions for the spontaneous emission rates are derived for each mode type, and calculated results are presented illustrating the emission behavior as a function of the position of the radiating atom, for various slab waveguides. The model is used to analyze the spontaneous emission coupling efficiency to guided modes in planar erbium-doped amplifier structures. Spontaneous emission factors for the TE and TM modes are calculated for the cases of erbium doping of the core and of the cladding.>