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

Physical Review A

Mirror transmission and laser phase diffusion in the quantum regime

Sudhakar Prasad, Bartram S. Abbott

Published Oct 1, 1988• 8 citations
Publisher

Abstract

We consider how the finite transmission of the output mirror of a laser operating well above threshold affects laser phase diffusion in the quantum regime. In our traveling-wave analysis, the cavity loses field energy discretely only once every round trip. For a low-Q cavity, the linewidth that arises from phase diffusion can differ significantly from the Schawlow-Townes result derived using traditional theories based on a distributed-loss picture.

DOI
10.1103/physreva.38.3551

Related papers

Nonuniform phase diffusion in a laser

Martin P. van Exter, W. A. Hamel, J. P. Woerdman

The simple intuitive picture of phase diffusion in a traveling wave is introduced to calculate the fundamental (Schawlow-Townes) limit to the laser linewidth. Contrary to the usual phase-diffusion model, our variety is not limited to the regime of low outcoupling; it predicts an enhancement of the linewidth for large outcoupling. It is demonstrated that the results of the traveling-wave phase-diffusion model are identical to those of the theory of nonorthogonal eigenmodes. Finally, the effects of saturation on the linewidth are estimated.

Physical Review A•Jun 1, 1991•25 citations

Theory of a homogeneously broadened laser with arbitrary mirror outcoupling: Intrinsic linewidth and phase diffusion

Sudhakar Prasad

We present a theory of the homogeneously broadened laser that is based on the simple boundary conditions that govern the connection of intracavity traveling fields and the leaking vacuum field at the cavity mirrors. The approach is uniformly valid for arbitrary output-mirror transmissions. We compute the intrinsic linewidth of the laser both below and above threshold and for arbitrary mirror outcoupling. In the limit of complete output-mirror transmission, for which any semblance of the cavity to a lasing cavity is completely untenable and the laser is severely below threshold, we show that the laser linewidth reduces to the natural linewidth of spontaneous emission by atoms in free space. Above threshold, in contrast with most previously obtained results, the fundamental linewidth exhibits a power-independent contribution that arises from gain saturation that is spatially nonuniform.

Physical Review A•Aug 1, 1992•24 citations

Theory for the linewidth of a bad-cavity laser

Martin P. van Exter, S. J. M. Kuppens, J. P. Woerdman

We derive the quantum-limited linewidth of a bad-cavity laser, where the cavity-loss rate can be comparable to or larger than the gain bandwidth. We allow for incomplete inversion and arbitrary mirror losses and show how the position-dependent gain, refractive index, and populations co-determine the laser linewidth. The result obtained factorizes in parts that have straightforward physical interpretations. In the bad-cavity regime the laser linewidth is shown to be reduced as compared to the Schawlow-Townes expression as a result of anomalous dispersion associated with the optical gain. Saturation is shown to lead to a power-independent contribution to the laser linewidth; the magnitude of this contribution depends critically on the assumed pumping and decay rates.

Physical Review A•Jan 1, 1995•46 citations

Quantum theory of a one-dimensional laser with output coupling. II. Phase noise above threshold

Kikuo Ujihara

Phase noise of a one-dimensional laser with output coupling that is oscillating well above threshold is analyzed on the basis of a multimode formulation of the field. The phase diffusion, both in time and space, is calculated for the output beam taking into account the lowest-order moments of the thermal and the quantum noise forces. Thermal noise is introduced automatically without assuming any absorbing atoms or heatbaths, and is interpreted as the amplified, ambient thermal radiation that penetrates the laser cavity. Quantum noise is treated by the quantum Langevin method. The resulting linewidth formula differs from that of a conventional theory by factors that are determined by the degree of output coupling and by the nonuniform distribution of the saturated gain in the cavity.

Physical Review A•Jun 1, 1984•13 citations

Effect of laser intensity fluctuations on laser linewidth

Ning Lu

We study the linewidth of a one-photon laser through the approach of the two-time correlation function. Our numerical calculations cover the regions of below, near, and above threshold. Well below threshold, the laser linewidth decreases linearly with increasing linear gain. Near and above threshold, in comparison with the approximate linewidth given by the phase-diffusion coefficient at the mean photon number (which is inversely proportional to the laser intensity---the Schawlow-Townes formula), we find that the laser intensity fluctuations increase the laser linewidth and that the Schawlow-Townes formula is valid only when the mean photon number is large and the photon-number variance is much smaller than the square of the mean photon number. Near threshold, the laser linewidth can be twice as large as that given by the phase-diffusion coefficient at the mean photon number (i.e., twice as large as that given by the Schawlow-Townes formula).

Physical Review A•May 1, 1993•7 citations

Squeezing of spontaneous emission in a laser

Julio R. Gea-Banacloche

It is predicted that a laser's phase-diffusion rate (its Schawlow-Townes linewidth) may be reduced by as much as one-half when the laser is coupled out to ``squeezed vacuum'' as opposed to ordinary vacuum. The effect is important because it is directly related to spontaneous emission in a squeezed vacuum. It shows that a part of spontaneous emission is due to amplified zero-point noise and that, therefore, in a squeezed field the random phases of the spontaneously emitted photons are no longer uniformly distributed.

Physical Review Letters•Aug 3, 1987•68 citations
We consider how the finite transmission of the output mirror of a laser operating well above threshold affects laser phase diffusion in the quantum regime. In our traveling-wave analysis, the cavity loses field energy discretely only once every round trip. For a low-Q cavity, the linewidth that arises from phase diffusion can differ significantly from the Schawlow-Townes result derived using traditional theories based on a distributed-loss picture.
The simple intuitive picture of phase diffusion in a traveling wave is introduced to calculate the fundamental (Schawlow-Townes) limit to the laser linewidth. Contrary to the usual phase-diffusion model, our variety is not limited to the regime of low outcoupling; it predicts an enhancement of the linewidth for large outcoupling. It is demonstrated that the results of the traveling-wave phase-diffusion model are identical to those of the theory of nonorthogonal eigenmodes. Finally, the effects of saturation on the linewidth are estimated.
We present a theory of the homogeneously broadened laser that is based on the simple boundary conditions that govern the connection of intracavity traveling fields and the leaking vacuum field at the cavity mirrors. The approach is uniformly valid for arbitrary output-mirror transmissions. We compute the intrinsic linewidth of the laser both below and above threshold and for arbitrary mirror outcoupling. In the limit of complete output-mirror transmission, for which any semblance of the cavity to a lasing cavity is completely untenable and the laser is severely below threshold, we show that the laser linewidth reduces to the natural linewidth of spontaneous emission by atoms in free space. Above threshold, in contrast with most previously obtained results, the fundamental linewidth exhibits a power-independent contribution that arises from gain saturation that is spatially nonuniform.
We derive the quantum-limited linewidth of a bad-cavity laser, where the cavity-loss rate can be comparable to or larger than the gain bandwidth. We allow for incomplete inversion and arbitrary mirror losses and show how the position-dependent gain, refractive index, and populations co-determine the laser linewidth. The result obtained factorizes in parts that have straightforward physical interpretations. In the bad-cavity regime the laser linewidth is shown to be reduced as compared to the Schawlow-Townes expression as a result of anomalous dispersion associated with the optical gain. Saturation is shown to lead to a power-independent contribution to the laser linewidth; the magnitude of this contribution depends critically on the assumed pumping and decay rates.
Phase noise of a one-dimensional laser with output coupling that is oscillating well above threshold is analyzed on the basis of a multimode formulation of the field. The phase diffusion, both in time and space, is calculated for the output beam taking into account the lowest-order moments of the thermal and the quantum noise forces. Thermal noise is introduced automatically without assuming any absorbing atoms or heatbaths, and is interpreted as the amplified, ambient thermal radiation that penetrates the laser cavity. Quantum noise is treated by the quantum Langevin method. The resulting linewidth formula differs from that of a conventional theory by factors that are determined by the degree of output coupling and by the nonuniform distribution of the saturated gain in the cavity.
We study the linewidth of a one-photon laser through the approach of the two-time correlation function. Our numerical calculations cover the regions of below, near, and above threshold. Well below threshold, the laser linewidth decreases linearly with increasing linear gain. Near and above threshold, in comparison with the approximate linewidth given by the phase-diffusion coefficient at the mean photon number (which is inversely proportional to the laser intensity---the Schawlow-Townes formula), we find that the laser intensity fluctuations increase the laser linewidth and that the Schawlow-Townes formula is valid only when the mean photon number is large and the photon-number variance is much smaller than the square of the mean photon number. Near threshold, the laser linewidth can be twice as large as that given by the phase-diffusion coefficient at the mean photon number (i.e., twice as large as that given by the Schawlow-Townes formula).
It is predicted that a laser's phase-diffusion rate (its Schawlow-Townes linewidth) may be reduced by as much as one-half when the laser is coupled out to ``squeezed vacuum'' as opposed to ordinary vacuum. The effect is important because it is directly related to spontaneous emission in a squeezed vacuum. It shows that a part of spontaneous emission is due to amplified zero-point noise and that, therefore, in a squeezed field the random phases of the spontaneously emitted photons are no longer uniformly distributed.