© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

IEEE Journal of Quantum Electronics

On the spontaneous lifetime change in an ideal planar microcavity-transition from a mode continuum to quantized modes

Gunnar G. Bjork

Published Jan 1, 1994• 74 citations

Abstract

The spontaneous emission lifetime of an atom is known to be influenced by its environment. In general, the lifetime will be different if the atom is suspended in free space than if it is placed inside a cavity. A simple cavity geometry in which to explore this effect is the planar cavity. In a paper by Brorson, Yokoyama, and Ippen, the authors derived the minimum lifetime in a planar cavity to be one-third of the free space (no cavity) lifetime, and the appropriate mirror spacing was found to be one-half wavelength. In a paper by Yamamoto, Machida, and Bjork, it was concluded that the lifetime for a half-wavelength-long cavity was only two-thirds of the free space lifetime. In this paper, the discrepancy between these results is clarified and it is shown that the shortest lifetime is indeed one-third of the free space lifetime; but to achieve this, the cavity has to be slightly longer than one-half wavelength. This will influence the emission mode pattern in a way that, in general, is undesirable for a surface emitting laser. It is also shown that a strictly half-wavelength-long cavity has a lifetime of two-thirds of the free space lifetime. The model employed has the attractive feature that if allows a smooth transition from a fully open system with the atom interacting with a mode continuum, to the fully closed system with quantized photon modes.>

DOI: 10.1109/3.328610

Related papers

Spontaneous emission in planar semiconductor microcavities displaying vacuum Rabi splitting

Izo I. Abram, J. L. Oudar

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.

Physical Review A•May 1, 1995•25 citations

Spontaneous Emission in Dielectric Planar Microcavities

Gunnar G. Bjork, Y. Yamamoto

In this chapter, the author calculates the modification of the spontaneous emission pattems and the corresponding rate change using classical physics. To derive the spontaneous emission pattems or rates the readers must average the emission rate at each frequency over this distribution function. It is important to understand that this assumption is only valid if the emission line is homogeneously broadened (albeit not necessarily at its natural linewidth limit due to the radiative decay). One more thing needs to be pointed out before the readers move on to a more exact calculation of the spontaneous emission pattern and the emission rate of a dielectric cavity. In the ideal mirror the reflection takes place at a well-defined plane. Integration of the emission over all solid angles and all wavelengths gives us information about the total spontaneous emission rate, or, equivalently, about the spontaneous emission lifetime of an emitter in a dielectric cavity.

CRC Press eBooks•Jul 9, 2020•4 citations

Calculation of lifetime dependence of Er3+ on cavity length in dielectric half-wave and full-wave microcavities

C.C. Lin, D. G. Deppe

Angular spontaneous emission rates and lifetimes of Er3+ in Si/SiO2 microcavities are calculated for cavity lengths close to full and half-wavelengths. For a half-wavelength cavity, the calculations show that the spontaneous lifetime is sensitive to the variation of cavity length, and agrees very well with the experimental data measured by Vredenberg, Hunt, Schubert, Jacobson, Poate, and Zydzik [Phys. Rev. Lett. 71, 517 (1993)]. This variation comes from a coupling rate change into the cavity normal. For a full wavelength cavity, the lifetime is less sensitive to cavity length due to strong coupling of spontaneous emission to a fundamental waveguide mode.

Journal of Applied Physics•May 1, 1994•6 citations

Microcavity Lasers and QED

Gunnar G. Bjork

This chapter gives an overview of the field as it stands at the time of writing in mid 1995. It shows how the picture radically changes when there is more than one atom in the cavity. The simplest light-atom interaction one can think of is the coupling between a single atom and a single mode of the electromagnetic field. This system provides considerable insight into the fundamental physics of the light-atom coupling but the reader is warned that the more general many mode-many atom interactions are much richer in their dynamics. An atom in free space couples not only to one, but to a continuum of modes. The mathematics of the Weisskopf-Wigner theory of spontaneous emission tends to obscure the relatively simple physics of the emission process. An alternative, shorter way of calculating the single atom spontaneous emission rate is to use Fermi’s Golden rule, which is a prescription for calculating general transition rates to first order in perturbation theory.

CRC Press eBooks•Dec 23, 2020•0 citations

Theory of transient spontaneous emission by an atom in a planar microcavity

Ottavia Jedrkiewicz, R. Loudon

We study the transient regime of spontaneous emission by an atom excited in a planar high-Q microcavity. The variation of the spatial distribution of the radiation outside the cavity is determined as a function of the increasing number of internal reflections for transition dipole moments parallel and perpendicular to the mirrors and for mirror separations equal to $\ensuremath{\lambda}/2$ and $\ensuremath{\lambda}/4.$ Particular attention is given to the parallel dipole in the $\ensuremath{\lambda}/2$ cavity, where the number of reflections is closely proportional to the elapsed time. It is shown that the transient regime extends over times of the order of the cavity decay time, in contrast to the effectively one-dimensional cavities previously studied, where the steady state is achieved after the cavity round-trip time. The field distribution inside the cavity tends to a steady-state form whose dimension parallel to the mirrors is of the order of the transverse coherence length. Despite this transverse localization of the field excitation, it is shown that the conditions for the achievement of strong atom-field coupling and the observation of Rabi oscillations cannot be met in the planar microcavity.

Physical Review A•Dec 1, 1999•10 citations

Cavity quantum electrodynamics

Partha Ghose

Introduction Ever since 1916/17 when Einstein argued [45] [46] that spontaneous emission must occur if matter and radiation are to achieve thermal equilibrium, physicists have believed that spontaneous emission is an inherent quantum mechanical property of atoms and that excited atoms inevitably radiate. This view, however, overlooks the fact that spontaneous emission is a consequence of the coupling of quantized energy states of atoms with the quantized radiation field, and is a manifestation of quantum noise or of emission ‘stimulated’ by ‘vacuum fluctuations’. An infinity of vacuum states is available to the photon radiated by an excited atom placed in free space, leading to the effective irreversibility of such emissions. If these vacuum states are modified, as for example by placing an excited atom between closely spaced mirrors or in a small cavity (essentially the Casimir effect), spontaneous emission can be greatly inhibited or enhanced or even made reversible. Recent advances in atomic and optical techniques have made it possible to control and manipulate spontaneous emission. A whole new branch of quantum optics called ‘cavity QED’ has developed since 1987 utilizing these dramatic changes in spontaneous emission rates in cavities to construct new kinds of microscopic masers or micromasers that operate with a single atom and a few photons or with photons emitted in pairs in a two-photon transition.

Cambridge University Press eBooks•Apr 29, 1999•0 citations

The spontaneous emission lifetime of an atom is known to be influenced by its environment. In general, the lifetime will be different if the atom is suspended in free space than if it is placed inside a cavity. A simple cavity geometry in which to explore this effect is the planar cavity. In a paper by Brorson, Yokoyama, and Ippen, the authors derived the minimum lifetime in a planar cavity to be one-third of the free space (no cavity) lifetime, and the appropriate mirror spacing was found to be one-half wavelength. In a paper by Yamamoto, Machida, and Bjork, it was concluded that the lifetime for a half-wavelength-long cavity was only two-thirds of the free space lifetime. In this paper, the discrepancy between these results is clarified and it is shown that the shortest lifetime is indeed one-third of the free space lifetime; but to achieve this, the cavity has to be slightly longer than one-half wavelength. This will influence the emission mode pattern in a way that, in general, is undesirable for a surface emitting laser. It is also shown that a strictly half-wavelength-long cavity has a lifetime of two-thirds of the free space lifetime. The model employed has the attractive feature that if allows a smooth transition from a fully open system with the atom interacting with a mode continuum, to the fully closed system with quantized photon modes.>

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.

In this chapter, the author calculates the modification of the spontaneous emission pattems and the corresponding rate change using classical physics. To derive the spontaneous emission pattems or rates the readers must average the emission rate at each frequency over this distribution function. It is important to understand that this assumption is only valid if the emission line is homogeneously broadened (albeit not necessarily at its natural linewidth limit due to the radiative decay). One more thing needs to be pointed out before the readers move on to a more exact calculation of the spontaneous emission pattern and the emission rate of a dielectric cavity. In the ideal mirror the reflection takes place at a well-defined plane. Integration of the emission over all solid angles and all wavelengths gives us information about the total spontaneous emission rate, or, equivalently, about the spontaneous emission lifetime of an emitter in a dielectric cavity.

Angular spontaneous emission rates and lifetimes of Er3+ in Si/SiO2 microcavities are calculated for cavity lengths close to full and half-wavelengths. For a half-wavelength cavity, the calculations show that the spontaneous lifetime is sensitive to the variation of cavity length, and agrees very well with the experimental data measured by Vredenberg, Hunt, Schubert, Jacobson, Poate, and Zydzik [Phys. Rev. Lett. 71, 517 (1993)]. This variation comes from a coupling rate change into the cavity normal. For a full wavelength cavity, the lifetime is less sensitive to cavity length due to strong coupling of spontaneous emission to a fundamental waveguide mode.

This chapter gives an overview of the field as it stands at the time of writing in mid 1995. It shows how the picture radically changes when there is more than one atom in the cavity. The simplest light-atom interaction one can think of is the coupling between a single atom and a single mode of the electromagnetic field. This system provides considerable insight into the fundamental physics of the light-atom coupling but the reader is warned that the more general many mode-many atom interactions are much richer in their dynamics. An atom in free space couples not only to one, but to a continuum of modes. The mathematics of the Weisskopf-Wigner theory of spontaneous emission tends to obscure the relatively simple physics of the emission process. An alternative, shorter way of calculating the single atom spontaneous emission rate is to use Fermi’s Golden rule, which is a prescription for calculating general transition rates to first order in perturbation theory.

We study the transient regime of spontaneous emission by an atom excited in a planar high-Q microcavity. The variation of the spatial distribution of the radiation outside the cavity is determined as a function of the increasing number of internal reflections for transition dipole moments parallel and perpendicular to the mirrors and for mirror separations equal to $\ensuremath{\lambda}/2$ and $\ensuremath{\lambda}/4.$ Particular attention is given to the parallel dipole in the $\ensuremath{\lambda}/2$ cavity, where the number of reflections is closely proportional to the elapsed time. It is shown that the transient regime extends over times of the order of the cavity decay time, in contrast to the effectively one-dimensional cavities previously studied, where the steady state is achieved after the cavity round-trip time. The field distribution inside the cavity tends to a steady-state form whose dimension parallel to the mirrors is of the order of the transverse coherence length. Despite this transverse localization of the field excitation, it is shown that the conditions for the achievement of strong atom-field coupling and the observation of Rabi oscillations cannot be met in the planar microcavity.

Introduction Ever since 1916/17 when Einstein argued [45] [46] that spontaneous emission must occur if matter and radiation are to achieve thermal equilibrium, physicists have believed that spontaneous emission is an inherent quantum mechanical property of atoms and that excited atoms inevitably radiate. This view, however, overlooks the fact that spontaneous emission is a consequence of the coupling of quantized energy states of atoms with the quantized radiation field, and is a manifestation of quantum noise or of emission ‘stimulated’ by ‘vacuum fluctuations’. An infinity of vacuum states is available to the photon radiated by an excited atom placed in free space, leading to the effective irreversibility of such emissions. If these vacuum states are modified, as for example by placing an excited atom between closely spaced mirrors or in a small cavity (essentially the Casimir effect), spontaneous emission can be greatly inhibited or enhanced or even made reversible. Recent advances in atomic and optical techniques have made it possible to control and manipulate spontaneous emission. A whole new branch of quantum optics called ‘cavity QED’ has developed since 1987 utilizing these dramatic changes in spontaneous emission rates in cavities to construct new kinds of microscopic masers or micromasers that operate with a single atom and a few photons or with photons emitted in pairs in a two-photon transition.