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AIP conference proceedings

On-resonance diffraction-induced phase in two-fields three-level coherent propagation

Jiří Teichmann, F. P. Mattar

Published Jan 1, 1988• 0 citations
Publisher

Abstract

Coherent pulse propagation began with McCall’s & Hahn’s discovery of self‐Induced‐Transparency (SIT)[1] theoretically and experimentally. Even for collimated beams of finite extent a diffraction‐induced phase develops. Using a perturbational treatment[2–5] the time‐ and radially‐dependent phase φ, its wavefront curvature ∂φ/∂ρ, and the associated transverse energy flux current JT=A 2∂φ/∂ρ are calculated. The energy is redistributed across the beams. The evolving pulse departs from the uniform‐plane‐wave (UPW) counterparts. The onset of the radial reshaping and dynamic self‐action is demonstrated.

DOI
10.1063/1.37524

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Physical Review A•Oct 1, 1994•11 citations
Coherent pulse propagation began with McCall’s & Hahn’s discovery of self‐Induced‐Transparency (SIT)[1] theoretically and experimentally. Even for collimated beams of finite extent a diffraction‐induced phase develops. Using a perturbational treatment[2–5] the time‐ and radially‐dependent phase φ, its wavefront curvature ∂φ/∂ρ, and the associated transverse energy flux current JT=A 2∂φ/∂ρ are calculated. The energy is redistributed across the beams. The evolving pulse departs from the uniform‐plane‐wave (UPW) counterparts. The onset of the radial reshaping and dynamic self‐action is demonstrated.
The goal of this communication is to show that different transmission characteristics are obtained for each pulse shape when diffraction is accounted for even if the time‐integrated areas are equal. For weakly overlapped two‐field propagation it was argued that each pulse evolution obeys its own area theorem. In our case the pulses are strongly overlapped and they mutually influence each other. We have worked out the transverse variation beyond the physical situation where a specific self‐similar Gaussian mode can be assumed. Detailed temporal and frequency reshaping of coherent pulses with finite beam extent in a three‐level absorber is reported.
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.
The coherent frequency conversion between on‐resonance pump and probe beams is examined in the physical situation where the nonlinear gain balances the diffraction for the probe transition. The semiclassical paraxial‐Maxwell‐Bloch formalism is adopted as introduced in propagational studies in two‐level Self‐Induced‐Transparency (SIT)[1]. The probe builds up from an input deterministic seed. The asymptotic stabilization of the probe area is reported in conjunction with pump depletion and diffraction rigorously accounted for. Without diffraction the soliton does not appear. The Laplacian term (which describes transverse coupling) is included.
This paper is devoted to understanding the temporal synchronization of the two-color superfluorescence output powers. Following McCall and Feld et al., the monochromatic superfluorescence can be described in terms of a semi-classical propagational model that shares the same equations as Self-Induced Transparency (SIT). Thus it became important to understand double SIT that was discovered by McCall and Hahn (MH) to correctly interpret co-propagating beams with coherent exchange of energy and nonlinear phase evolution. A further motivation would be to elucidate pump and Stokes synchronization as well as pump depletion effect on Stokes buildup in Raman forward amplifier. In this work, we describe how the diffraction affects the longitudinal and transverse reshaping associated affects the simultaneous resonant propagation of two different-wavelength optical pulses in a three-level medium. The pulse lengths are shorter than any of the relaxation times, thus, the interaction is coherent. The material response has an inertial characteristic, which precludes its description with two instantaneous susceptibilities, and requires instead the density matrix formulism. A semi-classical formulism, as introduced by Konopnicki and Eberly (KE), is adopted in which two paraxial Maxwell field equations are closely intertwined in the generalized three-level Bloch equations.
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.