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Physical Review A

Self-focusing and spatial ringing of intense cw light propagating through a strong absorbing medium

Martine Le Berre, Elisabeth Ressayre, Andree A. Tallet

Published Mar 1, 1982• 38 citations
Publisher

Abstract

This paper deals with the strongly nonlinear regime of the atom and field interaction which arises for both high cw input intensities and large absorption. The intensity of the light inside the medium is then highly nonlinear with respect to the incident one, the order of magnitude of the nonlinearity being approximately $\ensuremath{\alpha}1$, for a cell of length $l$ and an absorption length ${\ensuremath{\alpha}}^{\ensuremath{-}1}$. The transverse effects related to such a regime are analytically treated. They are shown to induce self-focusing, blooming, and also spatial ringing. These features strongly depend on the distance of the screen from the cell, on the detuning between the incident wavelength and that of the atomic transition, and on the input intensity. For self-focusing, analytical expressions of the focal point, of the waist, and of the maximum intensity are given. This model for transverse effects in strong nonlinear propagation of pulses would contribute to explain recent anomalous observations.

DOI
10.1103/physreva.25.1604

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Resonant self-focusing of a cw intense light beam

Martine Le Berre, Elisabeth Ressayre, Andree A. Tallet

A single pass of an intense cw light beam through a strongly absorbing medium can be characterized by two parameters, the input on-axis intensity normalized to the saturation value ${I}_{0,0}$, and the Fresnel number $F$ for an absorption length ${\ensuremath{\alpha}}^{\ensuremath{-}1}$. For both large ${I}_{0,0}$ and $F$, propagation can be divided in two parts: At the very beginning, the transverse profile of the beam experiences an encoding. For a beam tuned exactly on resonance, encoding reduces to a stripping of the profile from the wings to the center, progressively, as the light beam goes further into the cell. For $F>>1$ and ${I}_{0,0}>>1$, and both of the same order of magnitude, this stripping can be modeled by a circular aperture placed at the end of the encoding region. Afterwards, the beam is assumed to propagate in free space, its profile exhibits Fresnel interferences and on-axis enhancement. Using a perturbative treatment, the width and the location of the aperture are analytically estimated, and the model is successfully compared with numerical predictions of on-resonance self-focusing. For ${I}_{0,0}\ensuremath{\lesssim}F$, the stripping and free-space propagation cannot be separated because near-axis stripping coexists with large diffraction effects on the wings. This case, the best for observing cw on-resonance enhancement, would gain in a more sophisticated model, taking into account diffraction by successive apertures.

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Observation of Self-Focusing via Saturable Absorption in Atomic Na

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There has been recent interest in the phenomenon of on-axis enhancement of an intense cw laser beam in a strongly absorbing, nonrefractive, nonlinear medium.1,2 The purpose of this paper is to present experimental observations of this cw on-resonant enhancement (CORE) and the associated Fresnel fringe structure and narrowing (self-focusing) of the spatial profile. We use the collisionally broadened D1 line of atomic sodium. We also illustrate the relatively close agreement of predictions1 based on a simple model of homogeneously broadened two-state absorbers.

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

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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.

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Observation of continuous-wave on-resonance enhancement (A)

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Recently, Boshier and Sandle1 predicted an unexpected and interesting phenomenon of the propagation of intense cw light through a strongly absorptive two-level medium: an enhancement of the on-axis intensity occurs with the laser frequency tuned to exact resonance with the atomic transition. Previously, cw self-focusing was thought to occur only on the high-frequency side of the resonance where nonlinear dispersion gives rise to an effective positive lens that focuses the entire beam,2,3 And indeed this cw on-resonance enhancement (CORE) arises from a different mechanism: the nonlinear absorption strips away the outer portions of the beam while diffraction of the light in the outer edge of the remaining core directs some of the beam toward the axis, resulting in near-field Fresnel fringes and CORE.

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NONLINEAR OPTICAL TRANSVERSE EFFECTS: CW ON-RESONANCE ENHANCEMENT, CW OFF-RESONANCE INTERFERENCE RINGS, CROSSTALK, INTRACAVITY PHASE SWITCHING, SELF-DEFOCUSING IN GALLIUM-ARSENIDE BISTABLE ETALON, SELF-FOCUSING AND SELF-DEFOCUSING OPTICAL BISTABILITY, AND INSTABILITIES (SODIUM VAPOR, WAVE PROPAGATION, OPTICAL CHAOS).

Kuochou Tai

Nonlinear optical transverse effects, which arise from the interaction of a Gaussian beam with a nonlinear medium, are discussed. They are cw on-resonance enhancement (CORE), cw off-resonance rings, crosstalk, intracavity phase switching, self-defocusing of a bistable etalon, and thin-sample-encoding (TSE) self-lensing (i.e., self-focusing or self-defocusing) bistability and instabilities. CORE is the enhancement of the on-axis intensity of an on-resonance laser beam in a two-level medium. We report the first observation of CORE using sodium vapor. Cw off-resonance rings, resulting from a pure phase encoding or from simultaneous phase and amplitude encodings, are observed using sodium vapor. These rings have been observed many time before, but we have made the first careful comparison with numerical calculations. Parallel operation and external switching are two crucial themes for the application of bistable optical devices (BODs). For parallel operation, crosstalk between nearby BODs on the same etalon due to diffraction coupling may need to be avoided. Minimum separations needed to ensure independent operation are computed. For external switching, intracavity phase switching using a plane-wave input can switch on (or off) a BOD using an external pulse. The validity of this concept for a Gaussian input is numerically simulated. Self-defocusing effects, resulting in some interesting effects in the transverse bistable loops, are observed using a GaAs-GaAlAs bistable etalon. The results are confirmed by numerical simulations. TSE self-lensing bistability is observed using a short sodium cell and a single mirror. TSE self-lensing bistability results from an enhancement in the feedback via self-lensing of the beam. The lack of an optical resonator and the use of a thin medium make TSE setup a good candidate to study the Ikeda instability. We report the first observation of the Ikeda instability in this all-optical passive system using a cw input. Numerical simulations show a rich bifurcation sequence not yet fully studied experimentally.

•Jan 1, 1984•0 citations

Transverse effect of superradiation due to nonlinear effect in Rb atomic medium

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We report on the investigation on the transverse effect of superradiation (SR) in Rb atomic medium by analyzing and comparing the diffraction patterns in the far-field under the circumstances that Gaussian and Bessel beam are taken as the excitation respectively. It is found that Gaussian SR shows a ring-pattern and its beam profile is closely dependent on the incident power and position of the sample cell. The experimental results are in good agreement with the simulations using semi-classical theory of SR together with spatial self-phase modulation (SPM), indicating that the transverse effect of SR is mainly attributed to its propagation in the nonlinear medium. By contrast, the beam profile of Bessel SR is hardly influenced by the input power thanks to its non-diffraction property. The comparison further confirms that the transverse effect of the SR is the result of the nonlinear effect for SR. This work provides useful information in understanding the physics behind the transverse effect of SR, which would be of significance in the applications of SR, such as enhancement on the beam quality and efficiency of the SR sources.

Optics Express•Oct 28, 2019•0 citations
This paper deals with the strongly nonlinear regime of the atom and field interaction which arises for both high cw input intensities and large absorption. The intensity of the light inside the medium is then highly nonlinear with respect to the incident one, the order of magnitude of the nonlinearity being approximately \ensuremathα1\ensuremath{\alpha}1\ensuremathα1, for a cell of length lll and an absorption length \ensuremathα\ensuremath−1{\ensuremath{\alpha}}^{\ensuremath{-}1}\ensuremathα\ensuremath−1. The transverse effects related to such a regime are analytically treated. They are shown to induce self-focusing, blooming, and also spatial ringing. These features strongly depend on the distance of the screen from the cell, on the detuning between the incident wavelength and that of the atomic transition, and on the input intensity. For self-focusing, analytical expressions of the focal point, of the waist, and of the maximum intensity are given. This model for transverse effects in strong nonlinear propagation of pulses would contribute to explain recent anomalous observations.
A single pass of an intense cw light beam through a strongly absorbing medium can be characterized by two parameters, the input on-axis intensity normalized to the saturation value I0,0{I}_{0,0}I0,0​, and the Fresnel number FFF for an absorption length ${\ensuremath{\alpha}}^{\ensuremath{-}1}$. For both large I0,0{I}_{0,0}I0,0​ and FFF, propagation can be divided in two parts: At the very beginning, the transverse profile of the beam experiences an encoding. For a beam tuned exactly on resonance, encoding reduces to a stripping of the profile from the wings to the center, progressively, as the light beam goes further into the cell. For F>>1F>>1F>>1 and I0,0>>1{I}_{0,0}>>1I0,0​>>1, and both of the same order of magnitude, this stripping can be modeled by a circular aperture placed at the end of the encoding region. Afterwards, the beam is assumed to propagate in free space, its profile exhibits Fresnel interferences and on-axis enhancement. Using a perturbative treatment, the width and the location of the aperture are analytically estimated, and the model is successfully compared with numerical predictions of on-resonance self-focusing. For ${I}_{0,0}\ensuremath{\lesssim}F$, the stripping and free-space propagation cannot be separated because near-axis stripping coexists with large diffraction effects on the wings. This case, the best for observing cw on-resonance enhancement, would gain in a more sophisticated model, taking into account diffraction by successive apertures.
There has been recent interest in the phenomenon of on-axis enhancement of an intense cw laser beam in a strongly absorbing, nonrefractive, nonlinear medium.1,2 The purpose of this paper is to present experimental observations of this cw on-resonant enhancement (CORE) and the associated Fresnel fringe structure and narrowing (self-focusing) of the spatial profile. We use the collisionally broadened D1 line of atomic sodium. We also illustrate the relatively close agreement of predictions1 based on a simple model of homogeneously broadened two-state absorbers.
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.
Recently, Boshier and Sandle1 predicted an unexpected and interesting phenomenon of the propagation of intense cw light through a strongly absorptive two-level medium: an enhancement of the on-axis intensity occurs with the laser frequency tuned to exact resonance with the atomic transition. Previously, cw self-focusing was thought to occur only on the high-frequency side of the resonance where nonlinear dispersion gives rise to an effective positive lens that focuses the entire beam,2,3 And indeed this cw on-resonance enhancement (CORE) arises from a different mechanism: the nonlinear absorption strips away the outer portions of the beam while diffraction of the light in the outer edge of the remaining core directs some of the beam toward the axis, resulting in near-field Fresnel fringes and CORE.
Nonlinear optical transverse effects, which arise from the interaction of a Gaussian beam with a nonlinear medium, are discussed. They are cw on-resonance enhancement (CORE), cw off-resonance rings, crosstalk, intracavity phase switching, self-defocusing of a bistable etalon, and thin-sample-encoding (TSE) self-lensing (i.e., self-focusing or self-defocusing) bistability and instabilities. CORE is the enhancement of the on-axis intensity of an on-resonance laser beam in a two-level medium. We report the first observation of CORE using sodium vapor. Cw off-resonance rings, resulting from a pure phase encoding or from simultaneous phase and amplitude encodings, are observed using sodium vapor. These rings have been observed many time before, but we have made the first careful comparison with numerical calculations. Parallel operation and external switching are two crucial themes for the application of bistable optical devices (BODs). For parallel operation, crosstalk between nearby BODs on the same etalon due to diffraction coupling may need to be avoided. Minimum separations needed to ensure independent operation are computed. For external switching, intracavity phase switching using a plane-wave input can switch on (or off) a BOD using an external pulse. The validity of this concept for a Gaussian input is numerically simulated. Self-defocusing effects, resulting in some interesting effects in the transverse bistable loops, are observed using a GaAs-GaAlAs bistable etalon. The results are confirmed by numerical simulations. TSE self-lensing bistability is observed using a short sodium cell and a single mirror. TSE self-lensing bistability results from an enhancement in the feedback via self-lensing of the beam. The lack of an optical resonator and the use of a thin medium make TSE setup a good candidate to study the Ikeda instability. We report the first observation of the Ikeda instability in this all-optical passive system using a cw input. Numerical simulations show a rich bifurcation sequence not yet fully studied experimentally.
We report on the investigation on the transverse effect of superradiation (SR) in Rb atomic medium by analyzing and comparing the diffraction patterns in the far-field under the circumstances that Gaussian and Bessel beam are taken as the excitation respectively. It is found that Gaussian SR shows a ring-pattern and its beam profile is closely dependent on the incident power and position of the sample cell. The experimental results are in good agreement with the simulations using semi-classical theory of SR together with spatial self-phase modulation (SPM), indicating that the transverse effect of SR is mainly attributed to its propagation in the nonlinear medium. By contrast, the beam profile of Bessel SR is hardly influenced by the input power thanks to its non-diffraction property. The comparison further confirms that the transverse effect of the SR is the result of the nonlinear effect for SR. This work provides useful information in understanding the physics behind the transverse effect of SR, which would be of significance in the applications of SR, such as enhancement on the beam quality and efficiency of the SR sources.