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

Annual Meeting Optical Society of America

Photon number distributions for an inhomogeneously broadened laser with an absorber

Mansour Mortazavi, Surendra Singh

Published Jan 1, 1987• 0 citations
Publisher

Abstract

An equation of motion for the density matrix of the field of an inhomogeneously broadened single-mode laser containing a saturable absorber is derived. Using the photon number representation this equation is solved in the steady state. High-intensity photon number distributions are obtained for the on-resonance operation of the laser. Off-resonance operation is also considered. Curves are presented to illustrate the behavior, and the results are compared with earlier investigations.

DOI
10.1364/oam.1987.md3

Related papers

Inhomogeneously broadened laser with a saturable absorber

Mansour Mortazavi, Surendra Singh

A quantum theory for a laser with inhomogeneously broadened active and absorber atoms is presented. Photon-number distributions are derived for both on- and off-resonance operation of the laser, and the results are compared with the results of earlier investigations.

Physical Review A•Jan 1, 1987•5 citations

Off-resonance operation of inhomogeneously broadened two-photon lasers

S. G. Sun, D. L. Lin, Xiao-shen Li

We generalize Lamb's quantum theory of lasers to treat the off-resonance operation of two-transition lasers in inhomogeneously broadened media. The master equation is derived from the density-matrix equation of motion in the Doppler limit. We first find the stationary-state solution from which we then obtain such operation characteristics as the threshold condition, the mean photon number, and the half-width of photon distribution. Compared with the one-transition laser, it is found that in the two-transition laser it is much easier to start oscillation and to obtain higher gain. Furthermore, we find that the two-transition laser is less sensitive to the detuning effect and its deviation from the coherent state is smaller than that of the one-transition laser. The remarkably different hole-burning phenomenon is also discussed.

Physical Review A•Sep 1, 1988•1 citation

Theory of the degenerate two-photon laser

A. W. Boone, S. Swain

We derive the equation of motion for the field density matrix of the degenerate two-photon laser under conditions of two-photon resonance starting from the full microscopic Hamiltonian. Our results are compared with the corresponding quantities obtained from the standard effective Hamiltonian. As we have shown for the nondegenerate case, the full diagonal density-matrix equations tend to the effective Hamiltonian density-matrix equations in an appropriate limit, but the equations of motion for the off-diagonal elements do not coincide. The equations obtained using a more accurate form of the effective Hamiltonian, in which Stark shifts are included, do agree. In this paper we concentrate on the photon-number distribution and the nature of the phase transition that takes place in the neighborhood of the two-photon lasing transition threshold. We determine the steady-state mean photon numbers and consider the stability of the solutions. A solution is found where the mean photon number is zero, but this is found to be a stable solution only for sufficiently weak pumping, whereas in the standard effective Hamiltonian approach it is always stable. As the pumping strength is increased, a range of detunings is reached in which there are two stable solutions. The amplitude of the zero-photon peak diminishes very rapidly as the pumping strength increases. Finally, for sufficiently large detunings, a single, stable, steady-state solution is obtained. The nature of the phase transition is illustrated by presenting plots of the photon-number distribution against detuning and pumping rate. The photon-number fluctuations about the mean are also discussed.

Physical Review A•Jan 1, 1990•37 citations

Theory of a Laser with an Inhomogeneously Broadened Saturable Absorber*

Rajarshi Roy, Surendra Singh

Many quantum optical systems exhibit first-order phase transition analogy.1 Fluctuations of the optical field in such systems are due to spontaneous emission noise. The nature of these fluctuations for various systems has been discussed using various approaches. Fully quantum mechanical and Langevin equation treatments have been given for the dye laser2,3 and the laser with a saturable absorber (LSA) with homogeneously broadened media.2,4 For inhomogeneously broadened media, such treatments are either valid for low intensities or do not fully take into account the effect of quantum noise.5 In this contribution we present a fully quantum mechanical treatment for the LSA with an inhomogeneously broadened absorber using the Foch state representation of the density matrix.2,6

International Meeting on Instabilities and Dynamics of Lasers and Nonlinear Optical Systems•Jan 1, 1985•0 citations

Nonresonant operation of two-transition lasers in an inhomogeneously broadened medium

D. L. Lin, S. G. Sun

The master equation for the nonresonant operation of inhomogeneously broadened two‐transition laser is derived from the density matrix equation of motion. Operation characteristics are calculated from the steady state solution of the master equation and are compared with those of a one‐transition laser. It is shown that the two‐transition laser operation has a number of advantages.

AIP conference proceedings•Jan 1, 1988•0 citations

Quantum statistical theory of the ring laser

Surendra Singh

A unified quantum treatment is presented for bidirectional two-mode ring lasers using the approach of Haken and co-workers. Equations of motion for the reduced density matrix of the field have been derived and used to study the fluctuation properties of the radiation field in different kinds of active media. The steady-state photon number distribution for an inhomogeneously broadened gas ring laser is derived. It is shown that for equal losses the relative fluctuations and normalized cross correlation of the photon numbers approach values $\frac{1}{3}$ and $\ensuremath{-}\frac{1}{3}$, respectively, for large excitations. For unequal losses the laser may emit typical single-mode laser radiation in the direction of the favored mode and typical equilibrium blackbody radiation in the direction of the weaker mode. Our results generally agree with the predictions of earlier treatments when the losses are equal. However, for unequal losses we predict different behavior for large excitations. Effects of detuning, spatial, and temporal variation of atomic inversion on the fluctuation properties have been investigated in the coherent-state diagonal representation of the density matrix, and steady-state intensity distributions have been derived for various kinds of active atoms. It is shown that for inhomogeneously broadened solid-state ring lasers spatial inhomogeneities may couple the modes strongly and the statistical properties of such lasers, characterized by a double-peaked intensity distribution and large relative-intensity fluctuations, may be similar to those of a homogeneously broadened ring laser. Curves are presented to illustrate the behavior.

Physical Review A•Feb 1, 1981•14 citations
An equation of motion for the density matrix of the field of an inhomogeneously broadened single-mode laser containing a saturable absorber is derived. Using the photon number representation this equation is solved in the steady state. High-intensity photon number distributions are obtained for the on-resonance operation of the laser. Off-resonance operation is also considered. Curves are presented to illustrate the behavior, and the results are compared with earlier investigations.
We generalize Lamb's quantum theory of lasers to treat the off-resonance operation of two-transition lasers in inhomogeneously broadened media. The master equation is derived from the density-matrix equation of motion in the Doppler limit. We first find the stationary-state solution from which we then obtain such operation characteristics as the threshold condition, the mean photon number, and the half-width of photon distribution. Compared with the one-transition laser, it is found that in the two-transition laser it is much easier to start oscillation and to obtain higher gain. Furthermore, we find that the two-transition laser is less sensitive to the detuning effect and its deviation from the coherent state is smaller than that of the one-transition laser. The remarkably different hole-burning phenomenon is also discussed.
We derive the equation of motion for the field density matrix of the degenerate two-photon laser under conditions of two-photon resonance starting from the full microscopic Hamiltonian. Our results are compared with the corresponding quantities obtained from the standard effective Hamiltonian. As we have shown for the nondegenerate case, the full diagonal density-matrix equations tend to the effective Hamiltonian density-matrix equations in an appropriate limit, but the equations of motion for the off-diagonal elements do not coincide. The equations obtained using a more accurate form of the effective Hamiltonian, in which Stark shifts are included, do agree. In this paper we concentrate on the photon-number distribution and the nature of the phase transition that takes place in the neighborhood of the two-photon lasing transition threshold. We determine the steady-state mean photon numbers and consider the stability of the solutions. A solution is found where the mean photon number is zero, but this is found to be a stable solution only for sufficiently weak pumping, whereas in the standard effective Hamiltonian approach it is always stable. As the pumping strength is increased, a range of detunings is reached in which there are two stable solutions. The amplitude of the zero-photon peak diminishes very rapidly as the pumping strength increases. Finally, for sufficiently large detunings, a single, stable, steady-state solution is obtained. The nature of the phase transition is illustrated by presenting plots of the photon-number distribution against detuning and pumping rate. The photon-number fluctuations about the mean are also discussed.
Many quantum optical systems exhibit first-order phase transition analogy.1 Fluctuations of the optical field in such systems are due to spontaneous emission noise. The nature of these fluctuations for various systems has been discussed using various approaches. Fully quantum mechanical and Langevin equation treatments have been given for the dye laser2,3 and the laser with a saturable absorber (LSA) with homogeneously broadened media.2,4 For inhomogeneously broadened media, such treatments are either valid for low intensities or do not fully take into account the effect of quantum noise.5 In this contribution we present a fully quantum mechanical treatment for the LSA with an inhomogeneously broadened absorber using the Foch state representation of the density matrix.2,6
A unified quantum treatment is presented for bidirectional two-mode ring lasers using the approach of Haken and co-workers. Equations of motion for the reduced density matrix of the field have been derived and used to study the fluctuation properties of the radiation field in different kinds of active media. The steady-state photon number distribution for an inhomogeneously broadened gas ring laser is derived. It is shown that for equal losses the relative fluctuations and normalized cross correlation of the photon numbers approach values 13\frac{1}{3}31​ and $\ensuremath{-}\frac{1}{3}$, respectively, for large excitations. For unequal losses the laser may emit typical single-mode laser radiation in the direction of the favored mode and typical equilibrium blackbody radiation in the direction of the weaker mode. Our results generally agree with the predictions of earlier treatments when the losses are equal. However, for unequal losses we predict different behavior for large excitations. Effects of detuning, spatial, and temporal variation of atomic inversion on the fluctuation properties have been investigated in the coherent-state diagonal representation of the density matrix, and steady-state intensity distributions have been derived for various kinds of active atoms. It is shown that for inhomogeneously broadened solid-state ring lasers spatial inhomogeneities may couple the modes strongly and the statistical properties of such lasers, characterized by a double-peaked intensity distribution and large relative-intensity fluctuations, may be similar to those of a homogeneously broadened ring laser. Curves are presented to illustrate the behavior.