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Journal of the Optical Society of America B

Continuous-wave off-resonance rings and continuous-wave on-resonance enhancement

Martine Le Berre, Elisabeth Ressayre, Andree A. Tallet, Kuochou Tai, H. M. Gibbs, Michael C. Rushford, Nasser N. Peyghambarian

Published Aug 1, 1984• 25 citations
Publisher

Abstract

Continuous-wave (cw) off-resonance rings and cw on-resonance enhancement (CORE) are observed as a result of an optical beam propagating through sodium vapor. They are interpreted in terms of diffraction-free encoding (DFE) followed by free-space propagation. They are discussed with respect to the three regimes of DFE, namely, pure phase encoding, on-resonance pure amplitude encoding leading to stripping, and the intermediate case involving both phase and amplitude encodings. First there are far-field interference rings displaying pure phase encoding. They are observed on both sides of resonance, as expected by theory. Second, there is CORE, which is a Fresnel diffraction manifestation resulting from the stripping of the beam profile by the nonlinear medium, and in the far field, the corresponding Fraunhofer patterns. CORE is observed in an inhomogeneously broadened system, and the role of Doppler broadening is theoretically studied. Finally, there are off-resonance rings involving both phase and amplitude encodings. They are numerically simulated and discussed with respect to DFE predictions.

DOI
10.1364/josab.1.000591

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Continuous-wave (cw) off-resonance rings and cw on-resonance enhancement (CORE) are observed as a result of an optical beam propagating through sodium vapor. They are interpreted in terms of diffraction-free encoding (DFE) followed by free-space propagation. They are discussed with respect to the three regimes of DFE, namely, pure phase encoding, on-resonance pure amplitude encoding leading to stripping, and the intermediate case involving both phase and amplitude encodings. First there are far-field interference rings displaying pure phase encoding. They are observed on both sides of resonance, as expected by theory. Second, there is CORE, which is a Fresnel diffraction manifestation resulting from the stripping of the beam profile by the nonlinear medium, and in the far field, the corresponding Fraunhofer patterns. CORE is observed in an inhomogeneously broadened system, and the role of Doppler broadening is theoretically studied. Finally, there are off-resonance rings involving both phase and amplitude encodings. They are numerically simulated and discussed with respect to DFE predictions.
Nonlinear beam propagation in absorbing media was originally examined by numerical simulations of the propagation of an electric field interacting with homogeneously broadened two-level atoms.1,2 Two significant predictions of the theory were cw on-resonance enhancement (CORE) and Fresnel ring encoding on the propagating beam. CORE has been observed in sodium vapor experiments3 where the center intensity of a beam traveling through an absorbing media increased by 69%. Fresnel ring encoding of an Ar-ion laser beam propagating through a sample of pink ruby has also been demonstrated.4 We further the work by discussing the experimental study of the effect of an absorbing birefringent media on a propagating laser beam.
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.
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.
Two spectral regions of gain exist for a weak probe beam propagating through a medium of two-level-atoms pumped by a strong near-resonance field. Experimentally a cw ring-dye laser is used to explore this gain at the Na D₂ resonance in a vapor. Plane-wave calculations of probe-gain spectra which include the Doppler broadening inherent in a vapor agree well with experimental spectra obtained with a Fabry-Perot interferometer. Such two-beam-coupling gain might have applications as optical pre- or power amplifiers. The gain is also the primary step in four-wave-mixing. Mixing of the pump and sideband which experiences gain produces the medium polarization from which the fourth-wave arises. For phase-matched propagation the fourth-wave, which is at a frequency that experiences little or negative probe-gain (i.e., absorption), grows at nearly the same rate as the primary sideband. Together the two sidebands extract far more than twice as much energy from the pump than does the primary sideband acting alone. Experimentally four-wave-mixing which arises from noise at the gain-sideband-frequency is sometimes accompanied by conical emission at the fourth-wave sideband. Since this sideband is also seen on axis the explanation cannot be simply phase-matching. Simulations which include the full transverse nature of the experiment are currently running on a CRAY supercomputer. These simulations indicate that the radial variation of the medium index of refraction is responsible for conical emission.
We present a simple, analytically tractable, generalized aperture model for treating the stripping of a laser beam in a medium with saturable absorption. The model departs from previous treatments in allowing a soft transition from transparency to opacity, which yields a physically realistic diffraction-free amplitude encoding for the laser beam and thereby reduces unphysical fringes in subsequent beam evolution. The model is applied to the problem of cw exactly resonant self-focusing in a vapor of two-state atoms. It is confirmed that for strong beam saturation and absorption that is not too strong, beam propagation can be well modeled as a single stripping–diffraction sequence. A simple interpretation of the on-axis enhancement features is given.