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

Effects of transverse profile of probe and driving fields on the gain in a Raman-driven four-level system

Hanzhuang Zhang, Jin-Yue Gao

Published Sep 1, 1997• 3 citations
Publisher

Abstract

In this paper the effects of the transverse profile of the probe and driving fields on the gain in a Raman-driven four-level system are discussed. The results show that when transverse effects are included, the probe gain spectrum has a different structure compared with that in the plane-wave approximation, the optimum focal position of a focus lens for the maximum gain is not at the center of the sample cell, and the gain is very sensitive to the changes of focal position when the waist of the driving field is small.

DOI
10.1103/physreva.56.2225

Related papers

TRANSVERSE DIFFRACTION EFFECTS OF LIGHT FIELDS ON THE GAIN WITHOUT POPULATION INVERSION

Hanzhuang Zhang, Gao Jin-Yue, 吉林大学物理系

We discussed transverse diffraction effects of probe and driving fields on the gain in the model of Raman driven four level atomic system. The calculated results showed that the spectrum of the probe field has different structure compared with that in plane wave approximation due to the transverse diffraction effects of light fields, and the optimum focal position of a focus lens for the maximum gain is in the vicinity of a sample cell.

Acta Physica Sinica•Jan 1, 1997•0 citations

Comparative study of focusing with scalar and vector beams in an active Raman gain system

Partha Das, Tarak Nath Dey

We investigate the focusing characteristics of scalar and vector beams within an atomic medium. An active-Raman-gain configuration is employed to achieve significant Kerr nonlinearity in a four-state atomic system. The probe beams can attain focusing within the medium through careful selection of input beam intensities and the spatial profile of the control field. We analytically derive the linear and third-order nonlinear susceptibilities for both scalar and vector probe beams. Our observations indicate that, in addition to the energy transfer from the control beam to the probe beam, the giant cross-Kerr nonlinearity facilitates the focusing of the scalar probe beam into a significantly smaller spot size. Conversely, the vector probe beams exhibit gain-induced narrowing. Furthermore, we evaluate the state of polarization for the vector beam at the minimum beam waist, observing a polarization rotation and a change in ellipticity during propagation. Through the mechanism of focusing, we achieve a reduced spot size for the probe beam, which may have substantial implications for resolution enhancement in microscopy applications.

arXiv:2506.05093•Physical Review A•Aug 28, 2025•1 citation

Transverse profile effects on lasing without population inversion

Franco Prati, J. Mompart, R. Corbalán

We analyse the effects of a Gaussian transverse profile for the driving and laser fields on lasing without population inversion, in four different three-level schemes. We show that the lasing domains can be considerably reduced with respect to the plane-wave case in the V and in the cascade configuration driven in the upper transition, while in the and in the cascade configuration driven in the lower transition such domains are always larger in the Gaussian case.

Journal of Optics B Quantum and Semiclassical Optics•Jan 1, 1999•2 citations

Transverse Effect of Field in an Open V-type Inversionless Lasing System

Fan Xi

The transverse effect of the fields was studied by densitymatrix equations of motion in an open Vtype system and Hurwitz criteria.The result shows that comparing with the case in the plane wave approximation,the transverse profile of the field leads to an obvious variation of the fashion that the system obtains inversionless lasing through instability of nonlasing solution,and makes the system more easy to obtain inversionless lasing through instability of pitchfork bifurcation;the value of the ratio of the active medium transverse section to the beam waist has a determinant effect on size of the instability region in which inversionless lasing arises,and the Raman inversion region increases with increasing of value of the ratio;the effects of unsaturated gain,loss of laser cavity,the ratio of atomic injection rates and atomic exit rate varying on the instability region in which inversionless lasing arises are much different from that in the plane wave approximation case.

Journal of Optoelectronics·laser•Jan 1, 2003•0 citations

Effect of finite bandwidths of probe and driving fields on refractive index and gain in a Raman-driven four-level system

Hanzhuang Zhang, Jin-Yue Gao

Zeitschrift für Physik D Atoms Molecules and Clusters•Mar 1, 1996•3 citations

Phase control of probe response in a Doppler-broadened N -type four-level system

Xijun Fan, Zhongbo Liu, Ying Liang +2 more

In this paper, we investigate theoretically the effect of the relative phase ($\ensuremath{\phi}$) between the probe and driving fields on gain (absorption) and dispersion of the probe field in a Doppler-broadened $N$-type four-level system with spontaneously generated coherence from different respects. It is shown that gain (absorption) and dispersion are very sensitive to variations in the relative phase, and changing the Doppler width also has an obvious effect on the phase-dependent gain (absorption) and dispersion. When the probe and driving fields have the same propagation directions (copropagating), for the same Doppler width, the dispersion curve with $\ensuremath{\phi}=\ensuremath{\alpha}$ is the same as the gain (absorption) curve with $\ensuremath{\phi}=\ensuremath{\alpha}+\ensuremath{\pi}/2$; however, when the probe and driving fields have opposite propagation directions (counterpropagating), the dispersion curve and gain (absorption) curve are different and the difference becomes more considerable with an increase in Doppler width. In the co- and counterpropagating cases, gain (absorption) and dispersion always vary periodically with varying $\ensuremath{\phi}$, and the period is 2\ensuremath{\pi}. By adjusting the value of $\ensuremath{\phi}$, the largest gain (absorption) and dispersion can be obtained, and a large index of refraction without absorption can be realized. Generally speaking, gain decreases with an increase in Doppler width, but by adjusting value of $\ensuremath{\phi}$, at some special values of Doppler width, a larger gain than that without Doppler broadening can be obtained. Our study also shows that gain in the copropagating case is much larger than that in the counterpropagating case.

Physical Review A•Apr 6, 2011•16 citations
In this paper the effects of the transverse profile of the probe and driving fields on the gain in a Raman-driven four-level system are discussed. The results show that when transverse effects are included, the probe gain spectrum has a different structure compared with that in the plane-wave approximation, the optimum focal position of a focus lens for the maximum gain is not at the center of the sample cell, and the gain is very sensitive to the changes of focal position when the waist of the driving field is small.
We investigate the focusing characteristics of scalar and vector beams within an atomic medium. An active-Raman-gain configuration is employed to achieve significant Kerr nonlinearity in a four-state atomic system. The probe beams can attain focusing within the medium through careful selection of input beam intensities and the spatial profile of the control field. We analytically derive the linear and third-order nonlinear susceptibilities for both scalar and vector probe beams. Our observations indicate that, in addition to the energy transfer from the control beam to the probe beam, the giant cross-Kerr nonlinearity facilitates the focusing of the scalar probe beam into a significantly smaller spot size. Conversely, the vector probe beams exhibit gain-induced narrowing. Furthermore, we evaluate the state of polarization for the vector beam at the minimum beam waist, observing a polarization rotation and a change in ellipticity during propagation. Through the mechanism of focusing, we achieve a reduced spot size for the probe beam, which may have substantial implications for resolution enhancement in microscopy applications.
The transverse effect of the fields was studied by densitymatrix equations of motion in an open Vtype system and Hurwitz criteria.The result shows that comparing with the case in the plane wave approximation,the transverse profile of the field leads to an obvious variation of the fashion that the system obtains inversionless lasing through instability of nonlasing solution,and makes the system more easy to obtain inversionless lasing through instability of pitchfork bifurcation;the value of the ratio of the active medium transverse section to the beam waist has a determinant effect on size of the instability region in which inversionless lasing arises,and the Raman inversion region increases with increasing of value of the ratio;the effects of unsaturated gain,loss of laser cavity,the ratio of atomic injection rates and atomic exit rate varying on the instability region in which inversionless lasing arises are much different from that in the plane wave approximation case.
In this paper, we investigate theoretically the effect of the relative phase ($\ensuremath{\phi}$) between the probe and driving fields on gain (absorption) and dispersion of the probe field in a Doppler-broadened NNN-type four-level system with spontaneously generated coherence from different respects. It is shown that gain (absorption) and dispersion are very sensitive to variations in the relative phase, and changing the Doppler width also has an obvious effect on the phase-dependent gain (absorption) and dispersion. When the probe and driving fields have the same propagation directions (copropagating), for the same Doppler width, the dispersion curve with $\ensuremath{\phi}=\ensuremath{\alpha}$ is the same as the gain (absorption) curve with $\ensuremath{\phi}=\ensuremath{\alpha}+\ensuremath{\pi}/2$; however, when the probe and driving fields have opposite propagation directions (counterpropagating), the dispersion curve and gain (absorption) curve are different and the difference becomes more considerable with an increase in Doppler width. In the co- and counterpropagating cases, gain (absorption) and dispersion always vary periodically with varying $\ensuremath{\phi}$, and the period is 2\ensuremath{\pi}. By adjusting the value of $\ensuremath{\phi}$, the largest gain (absorption) and dispersion can be obtained, and a large index of refraction without absorption can be realized. Generally speaking, gain decreases with an increase in Doppler width, but by adjusting value of $\ensuremath{\phi}$, at some special values of Doppler width, a larger gain than that without Doppler broadening can be obtained. Our study also shows that gain in the copropagating case is much larger than that in the counterpropagating case.