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.
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.
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.
The propagation of a weakly modulated light beam through a nonlinear material is treated. The optical field representing such a beam consists of a strong carrier-frequency component and two weak, symmetrically displaced sidebands that combine to form a field, which may be purely amplitude modulated (AM), frequency modulated (FM), or some combination of these two modulation forms. It is shown that, for any optical nonlinearity, two modulation forms exist that have the property that the form of modulation is invariant under propagation of the beam. If a modulation form other than one of these natural modes is injected into the nonlinear medium, the modulation form will change as the beam propagates, asymptotically approaching the natural mode that experiences the lower attenuation. Explicit expressions for these natural modes are presented for the case in which the nonlinear medium can be modeled as a collection of two-level atoms. For the special case of an on-resonance pump beam, the natural modes correspond to pure amplitude modulation and pure frequency modulation. This formalism provides a general description of saturation spectroscopy for both AM and FM fields. Formulas are derived for the rate at which a pure FM beam is converted to an AM beam owing to its interaction with a two-level atomic medium. We also consider the variation that is due to propagation of the depth of modulation of an AM wave interacting resonantly with two-level atoms. The formalism predicts the existence of spectral features whose shape depends sensitively on the internal relaxation processes of the material. Experimental spectra are presented for ruby, alexandrite, and fluorescein in glass and are interpreted.
The coupled Maxwell-Schrodinger equations are used to describe propagation of a pulse in a nonlinear absorbing medium. The absorber is assumed to be comprised of a homogeneously broadened system of two-level atoms that are exactly resonant with the field. Numerical calculations have been performed for incident pulses of hyperbolic-secant shape and of duration that is long compared to the atomic phase-memory time. Selected values of input intensity are considered. For intensities below a certain level the calculations nearly agree with rate-equation predictions, but as the incident intensity is increased we find that optical nutation comes into play. The nutation effect leads to pulse breakup as the packet penetrates into the medium. An analytical calculation, for the case of an applied optical field of step-function form, has been performed in order to provide additional insight about the intensity threshold for nutation.
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.