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

Soviet Journal of Quantum Electronics

On-resonance self-focusing of coherent optical pulses in absorbers

F. P. Mattar

Published Dec 31, 1977• 0 citations
Publisher

Abstract

Analytic and numerical solutions of the Maxwell–Bloch equations, including transverse and timedependent phase variations, predict on-resonance self-focusing (SF) and elucidate its formation due to the combined effect of diffraction and inertial response of the medium. This new SF can be characterized by a simple parameter in terms of the beam and medium parameters. Recently, two independent experiments on SF in Na and Ne demonstrated convincingly this new SF effect for spatially nonuniform self-induced transparency pulses propagating in thick resonant absorbers.

DOI
10.1070/qe1977v007n12abeh008259

Related papers

Coherent On-Resonance Self-Focusing of Optical Pulses in Absorbers

H. M. Gibbs, Bouwe Bolger, F. P. Mattar +3 more

Self-focusing of spatially nonuniform coherent pulses has been seen in the center of Na and Ne transitions. Self-focusing and temporal reshaping were studied as a function of laser detuning in Na. The dependence of on-resonance self-focusing upon input pulse area was observed in Ne. Numerical solutions of the Maxwell-Bloch equations including transverse variations predict coherent self-focusing and yield a single parameter for estimating its importance for a given beam diameter and sample absorption.

Physical Review Letters•Dec 27, 1976•50 citations

Spatial distortions of laser pulses in coherent on-resonance propagation: Large-scale self-focusing

Jacques de Lamare, Michel Comte, Ph.J. Kupecek

When cylindrical symmetry is assumed, a numerical study of coherent on-resonance self-focusing of laser pulses in atomic media reveals a well-defined dependence on the interaction's parameters for the focusing distance and the maximal on-axis energy density reached at the focus. We interpreted this focusing to be the result of a diaphragm effect at the edge of the pulse. This can be readily explained by considering the transverse dependence of local self-induced transparency phenomena first described by McCall and Hahn [Phys. Rev. Lett. 18, 908 (1967); Phys. Rev. 183, 457 (1969)]. From this interpretation and the well-known Maxwell-Bloch equations, we derived a theoretical quantitative model for coherent on-resonance large-scale self-focusing, that is to say, focusing of the beam as a whole. Our main results include the above-mentioned exact parametric dependence for the focusing distance, as well as predictions about the ratios of on-axis energy densities and pulse transverse sizes between the input and focus planes. All of these predictions appear to corroborate the results of an experiment on a ${\mathrm{Tm}}^{169}$ vapor.

Physical Review A•Oct 1, 1994•11 citations

Optical Solitons in Media with Resonant and Non-resonant Self-focusing Nonlinearities

Evgeny V. Doktorov, R. A. Vlasov

Special features of generating a self-induced transparency in a medium with both resonant and non-resonant (Kerr-type) nonlinearities are considered. Soliton solutions of the Maxwell-Bloch equations are found, taking into account the diffraction divergence of the light beam. It is shown that solitons emerge in such a medium under conditions of two-dimensional optical beam scanning along the medium surface, and have non-coinciding propagating directions of the amplitude and phase fronts. As a necessary condition for the existence of solitons, there is a definite relationship between the scanning velocity and the parameters of the medium and radiation.

Optica Acta International Journal of Optics•Feb 1, 1983•72 citations

Optical solitons in dense resonant media

Anatoly A. Afanas'ev, R. A. Vlasov, A. G. Cherstvyi

Exact single-soliton solutions of the modified system of Maxwell-Bloch equations, in which the dipole-dipole interactions of the atoms of a dense resonant medium are taken into account, are obtained. Two propagation regimes are analyzed: “coherent,” where the pulse duration is much shorter than both relaxation times ( T p ≪ T 1 , T 2 ), and “incoherent,” where the pulse duration falls between the relaxation times ( T 2 ≪ T p ≪ T 1 ). It is predicted, for the first time, that soliton propagation of an ultrashort pulse is possible in a dense resonant absorbing medium in an incoherent interaction regime. The differences between the amplitude and phase characteristics of the solitons considered and the corresponding characteristics of the solitons for McCall-Hahn self-induced transparency are noted.

Journal of Experimental and Theoretical Physics•Mar 1, 2000•9 citations

Self-focused light propagation in a fully saturable medium: Theory

Marla L. Dowell, B. D. Paul, Alan C. Gallagher +1 more

A comprehensive model of intense laser light propagation in a fully saturable medium is presented. This model employs the Maxwell-Bloch equations for a two-level atomic system. Light propagating through a medium creates intensity-dependent index of refraction gradients that reduce to a Kerr nonlinearity only for a weak field. When the laser detuning is positive, self-induced index gradients cause the beam to self-focus. Stationary filaments occur when self-focusing exactly balances diffraction. There exists a unique set of two-dimensional fundamental (and higher mode) solutions for which the filament transverse profile (not Gaussian in general) depends on the following quantities: density of saturable absorbers, laser detuning from resonance, laser power, and natural linewidth. (In contrast the Kerr solution does not have a unique filament diameter.) Emphasis will be placed on propagation of Gaussian incident beams; deviations from the stationary solution in either shape or power generally give rise to oscillating spatial patterns, including donutlike profiles, or beam breakup.

Physical Review A•Oct 1, 1995•23 citations

Transverse effects associated with the propagation of coherent optical pulses in resonant media

F. P. Mattar, Maurice C. Newstein

Analytical and numerical methods are used to study the transverse reshaping that occurs when ultrashort optical pulses propagate through media resonant to the pulse-carrier frequency. The field is described by the scalar quasi-optic equation, and the material system by the full Bloch equations describing a distribution of homogeneously broadened two-level molecules. Transverse derivatives in the field equation provide the coupling leading to the development of radially dependent frequency variations and phase curvature. We have studied the origin and evolution of transverse energy flow and investigated the conditions under which this leads to significant coherent self-focusing. The physical mechanisms responsible for the onset and development of the focusing phenomenon are discussed and related to other types of self-confinement of optical pulses.

IEEE Journal of Quantum Electronics•Jul 1, 1977•26 citations
Analytic and numerical solutions of the Maxwell–Bloch equations, including transverse and timedependent phase variations, predict on-resonance self-focusing (SF) and elucidate its formation due to the combined effect of diffraction and inertial response of the medium. This new SF can be characterized by a simple parameter in terms of the beam and medium parameters. Recently, two independent experiments on SF in Na and Ne demonstrated convincingly this new SF effect for spatially nonuniform self-induced transparency pulses propagating in thick resonant absorbers.
Self-focusing of spatially nonuniform coherent pulses has been seen in the center of Na and Ne transitions. Self-focusing and temporal reshaping were studied as a function of laser detuning in Na. The dependence of on-resonance self-focusing upon input pulse area was observed in Ne. Numerical solutions of the Maxwell-Bloch equations including transverse variations predict coherent self-focusing and yield a single parameter for estimating its importance for a given beam diameter and sample absorption.
When cylindrical symmetry is assumed, a numerical study of coherent on-resonance self-focusing of laser pulses in atomic media reveals a well-defined dependence on the interaction's parameters for the focusing distance and the maximal on-axis energy density reached at the focus. We interpreted this focusing to be the result of a diaphragm effect at the edge of the pulse. This can be readily explained by considering the transverse dependence of local self-induced transparency phenomena first described by McCall and Hahn [Phys. Rev. Lett. 18, 908 (1967); Phys. Rev. 183, 457 (1969)]. From this interpretation and the well-known Maxwell-Bloch equations, we derived a theoretical quantitative model for coherent on-resonance large-scale self-focusing, that is to say, focusing of the beam as a whole. Our main results include the above-mentioned exact parametric dependence for the focusing distance, as well as predictions about the ratios of on-axis energy densities and pulse transverse sizes between the input and focus planes. All of these predictions appear to corroborate the results of an experiment on a Tm169{\mathrm{Tm}}^{169}Tm169 vapor.
Special features of generating a self-induced transparency in a medium with both resonant and non-resonant (Kerr-type) nonlinearities are considered. Soliton solutions of the Maxwell-Bloch equations are found, taking into account the diffraction divergence of the light beam. It is shown that solitons emerge in such a medium under conditions of two-dimensional optical beam scanning along the medium surface, and have non-coinciding propagating directions of the amplitude and phase fronts. As a necessary condition for the existence of solitons, there is a definite relationship between the scanning velocity and the parameters of the medium and radiation.
Exact single-soliton solutions of the modified system of Maxwell-Bloch equations, in which the dipole-dipole interactions of the atoms of a dense resonant medium are taken into account, are obtained. Two propagation regimes are analyzed: “coherent,” where the pulse duration is much shorter than both relaxation times ( T p ≪ T 1 , T 2 ), and “incoherent,” where the pulse duration falls between the relaxation times ( T 2 ≪ T p ≪ T 1 ). It is predicted, for the first time, that soliton propagation of an ultrashort pulse is possible in a dense resonant absorbing medium in an incoherent interaction regime. The differences between the amplitude and phase characteristics of the solitons considered and the corresponding characteristics of the solitons for McCall-Hahn self-induced transparency are noted.
A comprehensive model of intense laser light propagation in a fully saturable medium is presented. This model employs the Maxwell-Bloch equations for a two-level atomic system. Light propagating through a medium creates intensity-dependent index of refraction gradients that reduce to a Kerr nonlinearity only for a weak field. When the laser detuning is positive, self-induced index gradients cause the beam to self-focus. Stationary filaments occur when self-focusing exactly balances diffraction. There exists a unique set of two-dimensional fundamental (and higher mode) solutions for which the filament transverse profile (not Gaussian in general) depends on the following quantities: density of saturable absorbers, laser detuning from resonance, laser power, and natural linewidth. (In contrast the Kerr solution does not have a unique filament diameter.) Emphasis will be placed on propagation of Gaussian incident beams; deviations from the stationary solution in either shape or power generally give rise to oscillating spatial patterns, including donutlike profiles, or beam breakup.
Analytical and numerical methods are used to study the transverse reshaping that occurs when ultrashort optical pulses propagate through media resonant to the pulse-carrier frequency. The field is described by the scalar quasi-optic equation, and the material system by the full Bloch equations describing a distribution of homogeneously broadened two-level molecules. Transverse derivatives in the field equation provide the coupling leading to the development of radially dependent frequency variations and phase curvature. We have studied the origin and evolution of transverse energy flow and investigated the conditions under which this leads to significant coherent self-focusing. The physical mechanisms responsible for the onset and development of the focusing phenomenon are discussed and related to other types of self-confinement of optical pulses.