Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Modern Optics

Modified spontaneous emission in cylindrical microcavities: Waveguiding and distributed Bragg reflecting structures

M. A. Rippin, P. L. Knight

Published Apr 1, 1996• 30 citations
Publisher

Abstract

We study the density of modes, and associated spontaneous emission properties, of cylindrical cavities exhibiting waveguiding. A model of a microstructure composed of a metallized cylinder with multiple internal dielectric layers (distributed Bragg reflectors) has been used to describe the Helmholtz modes and their quantization. A two-level excited atom is placed within the structure and interacts in the dipole approximation with the quantized vacuum modes. To describe this we have derived expressions for the density of modes which an interacting atom sees, and which determine the subsequent time evolution of the excited-state probability of the atom. This simple model allows the investigation of the two major influences on the density of modes, the waveguiding nature of a cylinder and the frequency selectivity of the distributed Bragg reflecting mirrors and shows that the interplay between these two factors can have significant design consequences for the smallest of practical structures. We determine the so-called “β factors” characterizing the coupling efficiency and threshold properties of the structure and show that values close to unity are expected. We also show that reversible spontaneous emission, or vacuum Rabi splitting, is expected, for some practically realizable structures.

DOI
10.1080/09500349608232784

Related papers

Spontaneous decay rate and Casimir–Polder interaction of a two-level atom in a Bragg-reflector cylindrical structure

Nguyen Dung Chinh, Tran Minh Hien

Abstract Spontaneous decay rate and Casimir–Polder interaction of an excited two-level atom enclosed in a distributed-Bragg-reflector cylindrical waveguide are studied. Conditions for resonances to exist are established by comparing the distributed-Bragg-reflector-waveguide results with those of a perfectly reflecting hollow waveguide, and taking advantage of the simplicity of the Green tensor of the latter. The Casimir–Polder potential is obtained and found to exhibit a potential well along the cylinder axis. The results remain valid when realistic frequency-dependent permittivities of Si and SiO 2 are used.

Journal of Physics B Atomic Molecular and Optical Physics•May 21, 2019•5 citations

Cavity-modified spontaneous emission: From Rabi oscillations to exponential decay

H. Gie\Sen, Jill D. Berger, Georg Mohs +2 more

We revisit the problem of spontaneous emission by a two-level system in a cavity, concentrating in particular on those aspects associated with the finite propagation time of light between the atom and the cavity boundaries. We find that spontaneous emission always occurs first at the free space rate and there is then an abrupt change in these dynamics when light reflected by the cavity mirrors returns to the atom, leading to interference effects that result either in an enhancement or a reduction of this rate or in a periodic exchange of excitation between the atom and the cavity field. From this point of view, reversible spontaneous emission in terms of single-mode ``vacuum Rabi oscillations'' can be interpreted as resulting from the interference between the multimode partial waves reflected at the cavity mirrors and the instantaneously radiated light. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Apr 1, 1996•49 citations

Quantum analysis and the classical analysis of spontaneous emission in a microcavity

Yong Xu, Reginald K. Lee, Amnon Yariv

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.

Physical Review A•Feb 14, 2000•118 citations

Cavity quantum electrodynamics

Prasanta Kumar Basu, Bratati Mukhopadhyay, Rikmantra Basu

Abstract Inhibition and enhancement of spontaneous emission rate, first proposed by Purcell, is discussed in terms of altered density-of-modes in various types of solid-state cavities and the Purcell factor is derived for two-level atomic system. The conditions for observing Purcell factor and experimental findings in micropillars embedded with Quantum Dots (QD)s are discussed. The strong interaction between photons and matter in the form of QD excitons, dispersion relations for ground and excited states separated by Rabi splitting are discussed. Experimental photoluminescence spectra showing anticrossing of exciton lines and cavity lines by temperature and other tuning methods are used to illustrate the strong light-matter interaction. The Jayness–Cummins model based on second quantization is presented to point out Rabi oscillation, Purcell effect, and other novel features. Microcavity structures for observing cavity quantum electrodynamics effects are mentioned. Microcavity lasers predicting thresholdless operation for unity spontaneous emission coupling factors are discussed.

•Apr 5, 2022•0 citations

Dynamics of the spontaneous emission of an atom into the photon-density-of-states gap: Solvable quantum-electrodynamical model

Rashit F. Nabiev, Po-Chiang Yeh, J. J. Sánchez-Mondragón

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.

Physical Review A•Apr 1, 1993•55 citations

Spontaneous Emission in a Cylindrical Waveguide

Silvia Casulleras

In this work we study the spontaneous emission of a two-level atom placed inside a hollow cylindrical waveguide of infinite length and with perfectly electric conducting walls. The atom, whose electric dipole moment is assumed to be oriented along the symmetry axis of the waveguide, couples to a photonic band structure with a non-linear dispersion relation. We address two different regimes of coupling between the atom and the photonic band structure. In particular, we refer to the regime where the internal frequency of the a.tom is close to a band edge as the strong coupling regime and to the regime where the internal frequency is far from a band edge as the weak coupling regime. In the weak coupling regime, we find that the a.tom decays exponentially with a modified decayed rate due to the presence of the waveguide, and that the line-shape of the emitted photons within every band takes the form of a Lorentzian. In the strong coupling regime, we find a non-exponential decay of the atom, which is due to non-Markovian dynamics of the system. Moreover, the population of the atom presents oscillations in time and it converges to a non-zero positive value, indicating that the a.tom never fully decays. In this regime the spectrum of the emitted photons becomes more involved.

•Jan 1, 2018•0 citations
We study the density of modes, and associated spontaneous emission properties, of cylindrical cavities exhibiting waveguiding. A model of a microstructure composed of a metallized cylinder with multiple internal dielectric layers (distributed Bragg reflectors) has been used to describe the Helmholtz modes and their quantization. A two-level excited atom is placed within the structure and interacts in the dipole approximation with the quantized vacuum modes. To describe this we have derived expressions for the density of modes which an interacting atom sees, and which determine the subsequent time evolution of the excited-state probability of the atom. This simple model allows the investigation of the two major influences on the density of modes, the waveguiding nature of a cylinder and the frequency selectivity of the distributed Bragg reflecting mirrors and shows that the interplay between these two factors can have significant design consequences for the smallest of practical structures. We determine the so-called “β factors” characterizing the coupling efficiency and threshold properties of the structure and show that values close to unity are expected. We also show that reversible spontaneous emission, or vacuum Rabi splitting, is expected, for some practically realizable structures.
Abstract Spontaneous decay rate and Casimir–Polder interaction of an excited two-level atom enclosed in a distributed-Bragg-reflector cylindrical waveguide are studied. Conditions for resonances to exist are established by comparing the distributed-Bragg-reflector-waveguide results with those of a perfectly reflecting hollow waveguide, and taking advantage of the simplicity of the Green tensor of the latter. The Casimir–Polder potential is obtained and found to exhibit a potential well along the cylinder axis. The results remain valid when realistic frequency-dependent permittivities of Si and SiO 2 are used.
We revisit the problem of spontaneous emission by a two-level system in a cavity, concentrating in particular on those aspects associated with the finite propagation time of light between the atom and the cavity boundaries. We find that spontaneous emission always occurs first at the free space rate and there is then an abrupt change in these dynamics when light reflected by the cavity mirrors returns to the atom, leading to interference effects that result either in an enhancement or a reduction of this rate or in a periodic exchange of excitation between the atom and the cavity field. From this point of view, reversible spontaneous emission in terms of single-mode ``vacuum Rabi oscillations'' can be interpreted as resulting from the interference between the multimode partial waves reflected at the cavity mirrors and the instantaneously radiated light. \textcopyright{} 1996 The American Physical Society.
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.
Abstract Inhibition and enhancement of spontaneous emission rate, first proposed by Purcell, is discussed in terms of altered density-of-modes in various types of solid-state cavities and the Purcell factor is derived for two-level atomic system. The conditions for observing Purcell factor and experimental findings in micropillars embedded with Quantum Dots (QD)s are discussed. The strong interaction between photons and matter in the form of QD excitons, dispersion relations for ground and excited states separated by Rabi splitting are discussed. Experimental photoluminescence spectra showing anticrossing of exciton lines and cavity lines by temperature and other tuning methods are used to illustrate the strong light-matter interaction. The Jayness–Cummins model based on second quantization is presented to point out Rabi oscillation, Purcell effect, and other novel features. Microcavity structures for observing cavity quantum electrodynamics effects are mentioned. Microcavity lasers predicting thresholdless operation for unity spontaneous emission coupling factors are discussed.
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.
In this work we study the spontaneous emission of a two-level atom placed inside a hollow cylindrical waveguide of infinite length and with perfectly electric conducting walls. The atom, whose electric dipole moment is assumed to be oriented along the symmetry axis of the waveguide, couples to a photonic band structure with a non-linear dispersion relation. We address two different regimes of coupling between the atom and the photonic band structure. In particular, we refer to the regime where the internal frequency of the a.tom is close to a band edge as the strong coupling regime and to the regime where the internal frequency is far from a band edge as the weak coupling regime. In the weak coupling regime, we find that the a.tom decays exponentially with a modified decayed rate due to the presence of the waveguide, and that the line-shape of the emitted photons within every band takes the form of a Lorentzian. In the strong coupling regime, we find a non-exponential decay of the atom, which is due to non-Markovian dynamics of the system. Moreover, the population of the atom presents oscillations in time and it converges to a non-zero positive value, indicating that the a.tom never fully decays. In this regime the spectrum of the emitted photons becomes more involved.