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 Physics A Mathematical Nuclear and General

Frequency shifts in a single-mode laser

F Ahmad

Published Oct 11, 1974• 0 citations
Publisher

Abstract

The semi-classical laser equations are analysed outside the rotating-wave approximation and a new exact steady-state solution for stationary but inhomogeneously broadened atoms is obtained. Results applicable to any solid-state laser are derived and these are also relevant to a gas laser working near threshold or at very high intensities. The resonance frequency exhibits a Bloch-Siegert shift. New results in the theory of frequency pulling and pushing are obtained.

DOI
10.1088/0305-4470/7/15/019

Related papers

Theory of a Single-Mode Gas Laser

Howard Greenstein

A gas laser oscillating steadily in a single mode is described theoretically using the "generalized Bloch equations" as the point of departure. The nonlinear susceptibility is calculated without utilizing perturbation techniques, so that the theory retains validity for laser fields of arbitrary intensity. Expressions are presented for (1) the "gain profile" which exhibits the phenomenon of dual "hole burning," (2) the powertuning characteristics, including the conditions for the appearance of the central tuning dip, and (3) the frequency of oscillation, in which are displayed the effects of mode pulling and pushing. Emphasis is on a strongly inhomogeneous line and a high-$Q$ cavity, although some more general results are included as well. For excitations only slightly above threshold, a comparison is made with the Lamb single-mode theory, and in all cases agreement is found.

Physical Review•Nov 10, 1968•35 citations

Vibrational Bloch-Siegert effect in trapped ions

Ion Lizuain, Juan Gonzalo Muga, Jürgen Eschner

When trapped atoms are illuminated by weak lasers, off-resonant transitions cause shifts in the frequencies of the vibrational-sideband resonances. These frequency shifts may be understood in terms of Stark shifts of the individual levels or, as proposed here, as a vibrational Bloch-Siegert shift, an effect closely related to the usual (radio-frequency or optical) Bloch-Siegert shift and associated with rapidly oscillating terms when the rotating wave approximation is not made. Explicit analytic expressions are derived and compared to numerical results, and the similarities and differences between the usual and the vibrational Bloch-Siegert shifts are also spelled out.

arXiv:0801.1642•Physical Review A•May 19, 2008•9 citations

Discussion on two-photon laser oscillation process

Sun Son-gen

With the steady-state solution of the reduced optical Bloch equation, continuous two-photon lasing is analyzed. Formulas are derived for the steady-state gain, dispersion, and frequency pulling, and both homogeneous and inhomogeneous broadening are considered.

•Jan 1, 1987•1 citation

Semiclassical treatment of the optical maser

L. W. Davis

Using the semiclassical theory of radiation, the steady-state operation of the optical maser oscillator is studied in the case where a single "cavity" mode is excited. On introducing certain simplifying assumptions, a straightforward calculation leads to concise results for the frequency and amplitude of the field oscillations. These results are either well known or readily interpreted. For example, a frequency pulling effect is predicted which corresponds to the Bloch-Siegert shift, or alternatively is understandable as due to the Stark effect.

Proceedings of the IEEE•Jan 1, 1963•33 citations

Laser theory without the rotating wave approximation

Reeta Vyas, Surendra Singh

In laser theory and other branches of quantum electronics certain terms oscillating at twice the resonance frequency are dropped from the interaction Hamiltonian. The effect of these counterrotating terms on the operation of a single-mode laser is considered using the model of Scully and Lamb. It is found that these terms lead to a shift of the laser threshold and a broadening of the photon number distribution.

Annual Meeting Optical Society of America•Jan 1, 1985•0 citations

Phase and Frequency Dynamics in a Bidirectional Ring Laser

N. B. Abraham, Lois M. Hoffer, Gian Luca Lippi

Homogeneously broadened bidirectional ring lasers show alternation of the lasing direction induced dynamically by a long-lived population grating and slight detuning of the laser cavity from the atomic resonance1. We show that the mode switching is accompanied by abrupt jumps by pi in the total relative phase of the system2. Our analysis reveals that the carrier frequencies of the two modes are not equal even though the two unidirectional steady state solutions have the same frequency2. When one mode dominates and the other is suppressed, the dominant mode has the steady state frequency. However, a mode growing in strength has a frequency closer to the atomic resonance while a mode falling in strength has a frequency further from the atomic resonance. The dynamically induced mode-pulling and mode-pushing can be as much as 25 % of the steady state frequency detuning. The shifting frequencies of the modes indicate that the standing wave interference pattern rotates in the laser ring cavity, alternately moving clockwise and counterclockwise with nearly equal and constant speeds. The longitudinal spatial hole-burning pattern consequently also rotates in the ring tending to wash out the population grating and keeping it from developing an amplitude of much more than one percent of the spatially averaged population inversion.

Topical Meeting on Optical Bistability (OB)•Jan 1, 1988•0 citations
The semi-classical laser equations are analysed outside the rotating-wave approximation and a new exact steady-state solution for stationary but inhomogeneously broadened atoms is obtained. Results applicable to any solid-state laser are derived and these are also relevant to a gas laser working near threshold or at very high intensities. The resonance frequency exhibits a Bloch-Siegert shift. New results in the theory of frequency pulling and pushing are obtained.
A gas laser oscillating steadily in a single mode is described theoretically using the "generalized Bloch equations" as the point of departure. The nonlinear susceptibility is calculated without utilizing perturbation techniques, so that the theory retains validity for laser fields of arbitrary intensity. Expressions are presented for (1) the "gain profile" which exhibits the phenomenon of dual "hole burning," (2) the powertuning characteristics, including the conditions for the appearance of the central tuning dip, and (3) the frequency of oscillation, in which are displayed the effects of mode pulling and pushing. Emphasis is on a strongly inhomogeneous line and a high-QQQ cavity, although some more general results are included as well. For excitations only slightly above threshold, a comparison is made with the Lamb single-mode theory, and in all cases agreement is found.
When trapped atoms are illuminated by weak lasers, off-resonant transitions cause shifts in the frequencies of the vibrational-sideband resonances. These frequency shifts may be understood in terms of Stark shifts of the individual levels or, as proposed here, as a vibrational Bloch-Siegert shift, an effect closely related to the usual (radio-frequency or optical) Bloch-Siegert shift and associated with rapidly oscillating terms when the rotating wave approximation is not made. Explicit analytic expressions are derived and compared to numerical results, and the similarities and differences between the usual and the vibrational Bloch-Siegert shifts are also spelled out.
Using the semiclassical theory of radiation, the steady-state operation of the optical maser oscillator is studied in the case where a single "cavity" mode is excited. On introducing certain simplifying assumptions, a straightforward calculation leads to concise results for the frequency and amplitude of the field oscillations. These results are either well known or readily interpreted. For example, a frequency pulling effect is predicted which corresponds to the Bloch-Siegert shift, or alternatively is understandable as due to the Stark effect.
Homogeneously broadened bidirectional ring lasers show alternation of the lasing direction induced dynamically by a long-lived population grating and slight detuning of the laser cavity from the atomic resonance1. We show that the mode switching is accompanied by abrupt jumps by pi in the total relative phase of the system2. Our analysis reveals that the carrier frequencies of the two modes are not equal even though the two unidirectional steady state solutions have the same frequency2. When one mode dominates and the other is suppressed, the dominant mode has the steady state frequency. However, a mode growing in strength has a frequency closer to the atomic resonance while a mode falling in strength has a frequency further from the atomic resonance. The dynamically induced mode-pulling and mode-pushing can be as much as 25 % of the steady state frequency detuning. The shifting frequencies of the modes indicate that the standing wave interference pattern rotates in the laser ring cavity, alternately moving clockwise and counterclockwise with nearly equal and constant speeds. The longitudinal spatial hole-burning pattern consequently also rotates in the ring tending to wash out the population grating and keeping it from developing an amplitude of much more than one percent of the spatially averaged population inversion.