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AIP conference proceedings

Double self-induced-transparency (SIT) in three-level absorbers

F. P. Mattar, J. A. Delettrez, Jiří Teichmann, J. P. Babuel-Peyrissac

Published Jan 1, 1988• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.37407

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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.
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.
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.
The propagation of two pulses in a three-level absorber is treated by using Maxwell's equations and an effective "two-photon Bloch equations" which are analogous to the one-photon Bloch equations, except for two-photon coupling and frequency shifts. I derive relaxation-dependent shifts in the equilibrium $2n\ensuremath{\pi}$ Lorentzian pulses. Part of these shifts depends on weighted time integrals of harmonics of the area and hence remove the propagation degeneracy of pulses having equal areas but different shapes. Absorption of small-area pulses is studied as a function of absorption length, input energies, and relaxation, and it is found that a local enhancement in the transmission occurs as a function of the absorption length.
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.
The propagation of two ultrashort radiation pulses interacting via an intermediate level is analyzed by numerical integration of a system of equations describing coherent interaction between radiation and a three-level medium. It is shown that the propagation of the pulses depends strongly on their areas on entry to the medium and on the relationship between the dipole moments of transitions between neighboring levels. Substantial temporal narrowing was established for fairly high-power pulses (4π and 6π pulses) and this may be utilized to control their durations. Investigations are also made of the influence of relaxation processes, delay of pulses relative to one another on entry to the medium, and nonresonant dispersion during pulse propagation under the specified conditions.
Self-induced transparency (SIT) is a kind of coherent transient phenomena in two-level atomic system. The optical pulse with an area that is an integer multiple of 2π, which causes SIT in an absorber, is stable and a kind of soliton. Thus SIT is expected to be useful in pulse compression and pulse shaping. In this paper, we discuss some problems in experiments of SIT and surveys the experimental results of SIT. It is also described the recent experimental results of coherent nonlinear pulse propagation in BiI3 crystal using tunable sub-picosecond pulses.