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 Applied Physics

Size-Dependent Spontaneous Energy Loss in Lasers due to Self-Stimulated Emission

Tom Waite

Published Jun 1, 1964• 14 citations
Publisher

Abstract

Laser amplifiers when pumped to a significant degree of population inversion undergo decay via (1) natural spontaneous emission of radiation from individual excited atoms, and (2) a size-dependent decay due to self-amplification of the spontaneously emitted radiation which passes through a large fraction of the amplifier length before escaping. This latter effect has a definite size threshold near which the decay rate changes several orders of magnitude. The decay rate is roughly independent of size except near the threshold.

DOI
10.1063/1.1713719

Related papers

Lasing in Random Media

Hui W. Cao

A photon, unlike an electron, can stimulate an excited atom to emit a second photon into the same electromagnetic mode. This stimulated emission process is the foundation for light amplification and oscillation (i.e., self-generation). Initially, the term LASER referred to Light Amplification by Stimulated Emission of Radiation. Nowadays laser often means Light Oscillation by Stimulated Emission, which should literally be called "€œLOSER"€ instead of "€œLASER." To distinguish the above two devices, the former is called a laser amplifier, the latter a laser oscillator (Siegman 1986). Laser oscillation occurs when the photon generation rate exceeds the photon loss rate in a system. If gain saturation were absent, the photon number in a laser oscillator would diverge in time. In other words, the rate equation for the photon number would acquire an unstable solution above the oscillation threshold. In reality, gain saturation reduces the photon generation rate to the photon loss rate so that the number of photons in the oscillator remains at a finite value.

SPIE eBooks•Mar 16, 2010•3 citations

STIMULATED EMISSION AND DIPOLE OSCILLATORS

Murray, Iii Sargent

The phenomena which are principally responsible for the interaction of radiation with matter in everyday life are absorption and spontaneous emis­ sion. Light falling on matter is absorbed, leaving atoms in excited states which spontaneously emit radiation with a spread of frequency inversely proportional to the decay time. The situation is modified when the atomic decay times are sufficiently long and the radiation sufficiently intense, for then radiation may fall on excited atoms, resulting in stimulated emission rather than absorption. We saw in Chap. 2 that this third process was required to obtain the Planck blackbody radiation law in Einstein’s derivation. It is stimulated emission which enables an atomic medium to amplify incident radiation, and therefore is an essential ingredient in light amplifiers and oscillators. In fact, the word LASER is an acronym for Light Amplification by Stimulated Emission of Radiation.

CRC Press eBooks•Mar 5, 2018•1 citation

Lasers without inversion: one-photon stimulated emission in a three-level atom

Constantine Mavroyannis

I consider light amplification arising from the competition between absorption and stimulated emission of an excitation, which is induced by a laser field at low intensities interacting with a three-level atom. The lifetime of the induced excitation is 105–106 times longer than those of spontaneously emitted excitations. Conditions are established under which the stimulated emission prevails over the induced absorption, and the net negative intensity is 102–103 times greater than those of spontaneously emitted excitations, indicating that significant amplification occurs near the frequency of the laser field. PACS numbers: 32.80-t, 42.50.-p, 42.50H2

Journal of the Optical Society of America B•Dec 1, 1993•3 citations

Emission of Radiation from a System of Many Excited Atoms

V. Ernst, P. Stehle

The Weisskopf-Wigner theory of the natural linewidth of a single isolated atom is extended to a system of $N(\ensuremath{\gg}1)$ identical nonoverlapping atoms which are all in the same excited state at time $t=0$. The positions ${\mathrm{X}}_{1}\ensuremath{\cdots}{\mathrm{X}}_{N}$ of the atoms are assumed to fill a volume $\mathcal{U}$ of given shape and size with macroscopically constant density. Emission of radiation from this system takes place only in the form of one narrow, but nonzero-width, bundle of nearly equal photons, which contains all the emitted radiation. If the density of atoms within $\mathcal{U}$ exceeds a certain threshold, the rate of emission of photons has the form of a typical spike. All effects depend sensitively on the shape and size of $\mathcal{U}$ and on the density of atoms within $\mathcal{U}$, and cannot be explained in conventional terms of spontaneous or stimulated emission of radiation.

Physical Review•Dec 25, 1968•183 citations

Lasers without inversion: Two-photon stimulated emission in a three-level atom

Constantine Mavroyannis

Although the two-photon spontaneous emission is electric dipole forbidden, there is a two-photon stimulated emission whose lifetime is much longer in comparison to those of excitations spontaneously emitted by the excited states of the atom. Conditions are established under which the two-photon stimulated emission prevails, indicating that significant amplification is likely to occur near the two-photon frequency.

Physical Review A•Dec 1, 1992•14 citations

A fresh look at continuous-wave lasers: How they really work!

Markus Pollnau

This lecture describes the operation principle of a continuous-wave (cw) laser. In order to keep the photon rate equation and its solution simple, usually the spontaneous-emission rate is neglected with the argument that it is so much smaller than the stimulated-emission rate. The direct consequence is that in a cw laser the gain would equal the losses. Yet, additional implications are that the light emitted by such a laser would be a pure sine wave with an infinite coherence length, its linewidth would become a delta function, its Q-factor would assume an infinite value, the coherent photon number would build up and coherence would manifest itself inside the resonator only when pumping above the laser threshold, and the threshold inversion would depend only on the total resonator losses. None of these implications holds true for any laser that mankind has ever created. Starting from vacuum fluctuations, we consider spontaneous emission directly in the photon rate equation, thereby a priori avoiding all these inconsistencies. It is then straight-forward to see that in a cw laser the gain is smaller than the losses, a cw laser does not only have a finite linewidth that can be derived in a very simple manner, but also a finite Q-factor, as well as two laser thresholds which are both different from the commonly assumed “threshold inversion‿. This work was performed in collaboration with Dr. Marc Eichhorn from the French-German Research Institute of St. Louis, France.

•Oct 1, 2013•0 citations
Laser amplifiers when pumped to a significant degree of population inversion undergo decay via (1) natural spontaneous emission of radiation from individual excited atoms, and (2) a size-dependent decay due to self-amplification of the spontaneously emitted radiation which passes through a large fraction of the amplifier length before escaping. This latter effect has a definite size threshold near which the decay rate changes several orders of magnitude. The decay rate is roughly independent of size except near the threshold.
A photon, unlike an electron, can stimulate an excited atom to emit a second photon into the same electromagnetic mode. This stimulated emission process is the foundation for light amplification and oscillation (i.e., self-generation). Initially, the term LASER referred to Light Amplification by Stimulated Emission of Radiation. Nowadays laser often means Light Oscillation by Stimulated Emission, which should literally be called "€œLOSER"€ instead of "€œLASER." To distinguish the above two devices, the former is called a laser amplifier, the latter a laser oscillator (Siegman 1986). Laser oscillation occurs when the photon generation rate exceeds the photon loss rate in a system. If gain saturation were absent, the photon number in a laser oscillator would diverge in time. In other words, the rate equation for the photon number would acquire an unstable solution above the oscillation threshold. In reality, gain saturation reduces the photon generation rate to the photon loss rate so that the number of photons in the oscillator remains at a finite value.
The phenomena which are principally responsible for the interaction of radiation with matter in everyday life are absorption and spontaneous emis­ sion. Light falling on matter is absorbed, leaving atoms in excited states which spontaneously emit radiation with a spread of frequency inversely proportional to the decay time. The situation is modified when the atomic decay times are sufficiently long and the radiation sufficiently intense, for then radiation may fall on excited atoms, resulting in stimulated emission rather than absorption. We saw in Chap. 2 that this third process was required to obtain the Planck blackbody radiation law in Einstein’s derivation. It is stimulated emission which enables an atomic medium to amplify incident radiation, and therefore is an essential ingredient in light amplifiers and oscillators. In fact, the word LASER is an acronym for Light Amplification by Stimulated Emission of Radiation.
I consider light amplification arising from the competition between absorption and stimulated emission of an excitation, which is induced by a laser field at low intensities interacting with a three-level atom. The lifetime of the induced excitation is 105–106 times longer than those of spontaneously emitted excitations. Conditions are established under which the stimulated emission prevails over the induced absorption, and the net negative intensity is 102–103 times greater than those of spontaneously emitted excitations, indicating that significant amplification occurs near the frequency of the laser field. PACS numbers: 32.80-t, 42.50.-p, 42.50H2
The Weisskopf-Wigner theory of the natural linewidth of a single isolated atom is extended to a system of $N(\ensuremath{\gg}1)$ identical nonoverlapping atoms which are all in the same excited state at time t=0t=0t=0. The positions ${\mathrm{X}}_{1}\ensuremath{\cdots}{\mathrm{X}}_{N}$ of the atoms are assumed to fill a volume U\mathcal{U}U of given shape and size with macroscopically constant density. Emission of radiation from this system takes place only in the form of one narrow, but nonzero-width, bundle of nearly equal photons, which contains all the emitted radiation. If the density of atoms within U\mathcal{U}U exceeds a certain threshold, the rate of emission of photons has the form of a typical spike. All effects depend sensitively on the shape and size of U\mathcal{U}U and on the density of atoms within U\mathcal{U}U, and cannot be explained in conventional terms of spontaneous or stimulated emission of radiation.
This lecture describes the operation principle of a continuous-wave (cw) laser. In order to keep the photon rate equation and its solution simple, usually the spontaneous-emission rate is neglected with the argument that it is so much smaller than the stimulated-emission rate. The direct consequence is that in a cw laser the gain would equal the losses. Yet, additional implications are that the light emitted by such a laser would be a pure sine wave with an infinite coherence length, its linewidth would become a delta function, its Q-factor would assume an infinite value, the coherent photon number would build up and coherence would manifest itself inside the resonator only when pumping above the laser threshold, and the threshold inversion would depend only on the total resonator losses. None of these implications holds true for any laser that mankind has ever created. Starting from vacuum fluctuations, we consider spontaneous emission directly in the photon rate equation, thereby a priori avoiding all these inconsistencies. It is then straight-forward to see that in a cw laser the gain is smaller than the losses, a cw laser does not only have a finite linewidth that can be derived in a very simple manner, but also a finite Q-factor, as well as two laser thresholds which are both different from the commonly assumed “threshold inversion‿. This work was performed in collaboration with Dr. Marc Eichhorn from the French-German Research Institute of St. Louis, France.