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.
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, and the Fresnel number
F for an absorption length ${\ensuremath{\alpha}}^{\ensuremath{-}1}$. For both large
I0,0 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
I0,0>>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.
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.
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.
We report the first observations of the cw self-bending effect1 using an asymmetrical laser beam propagating in sodium vapor and discuss some concerns of practical and physical importance. The laser frequency was detuned below the D2 resonance until the maximum self-bending angle was observed. At ~200°C the nonlinear refractive index was found to be predominantly Kerrlike (Δn ≃ n 2 I) at experimental peak intensities up to ~220 W/cm2. This result is inconsistent with our numerical calculations of the saturation of the anomalous dispersion that includes power-broadened hole-burning of an inhomogeneously broadened two-level system,2 which predicts strong saturation of Δn. By analyzing either the self-deflection angle or the intensity at a single point in the far-field region as the input power was varied, we were able to determine that n2 ≃ − 10 − 7 cm2/W. Self-deflection angles as large as 5.9 mrad or eight times the diffraction angle were observed, which is more than enough for some useful applications such as resonatorless optical bistability, optical switching, and interconnecting, nonlinear optical coupling, and radiation protection, the latter of which we have demonstrated.
We describe a sensitive technique for observing small transverse modifications to intensity, phase, and polarization arising in nonlinear propagation of a laser beam through an atomic vapor. The technique, which in essence is an interferometric one, is based on the use of crossed polarizers that are nearly but not exactly pure circular. Illustrative results are presented for cw dye-laser radiation propagating through collisionally broadened atomic sodium that is near resonant to the D1 line. Well-defined ring patterns produced by nonlinear interactions are observed at both positive and negative laser detunings.