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International Laser Science Conference

Coherent pump dynamics, depletion, and transverse effects on the superfluorescence/Stokes/probe (SF, St, Prb) beam buildup and its asymptotic evolution of a stabilized on-axis swept-gain Raman forward amplifiers/spectroscopy studies

F. P. Mattar, P. R. Berman

Published Jan 1, 1986• 0 citations
Publisher

Abstract

A computer movie illustrating a rigorous multimode calculation of SF, St, Prb buildup in Raman studies is presented. This coherent copropagational study based on Maxwell-Bloch formalism1 includes phase and transverse variations, nonlinear asymmetric dispersion, pump spatial depletion, and time-dependent variations in population inversion density. Theλ scheme is selected so that the active transitions are optically thick for both the pump (α p l > 5) and the SF (α sf l > 35) pulses. This choice of Beer lengths, i.e., of oscillator strengths, insures that the two pulses never cease to overlap and optimizes the SF initially small signal growth. The pump interacts like a self-induced transparency while the SF, St, Prb evolves as a small-area in a two-level emitter which can be described as a nonlinear pendulum in the pane wave. For a given ratio of Beer lengths, distinct Fresnel numbers, atomic density numbers, small signal SF, St, Prb time-integrated energy stabilization or self-focusing may arise, as observed experimentally. For a sufficiently larger propagation distance, an asymptotic evolution of a quasisolitary nonhyperbolic-secant pulse of constant area is reported.

DOI
10.1364/ils.1986.thc6

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Nov 7, 1983•1 citation
A computer movie illustrating a rigorous multimode calculation of SF, St, Prb buildup in Raman studies is presented. This coherent copropagational study based on Maxwell-Bloch formalism1 includes phase and transverse variations, nonlinear asymmetric dispersion, pump spatial depletion, and time-dependent variations in population inversion density. Theλ scheme is selected so that the active transitions are optically thick for both the pump (α p l > 5) and the SF (α sf l > 35) pulses. This choice of Beer lengths, i.e., of oscillator strengths, insures that the two pulses never cease to overlap and optimizes the SF initially small signal growth. The pump interacts like a self-induced transparency while the SF, St, Prb evolves as a small-area in a two-level emitter which can be described as a nonlinear pendulum in the pane wave. For a given ratio of Beer lengths, distinct Fresnel numbers, atomic density numbers, small signal SF, St, Prb time-integrated energy stabilization or self-focusing may arise, as observed experimentally. For a sufficiently larger propagation distance, an asymptotic evolution of a quasisolitary nonhyperbolic-secant pulse of constant area is reported.
Analytic and numerical calculations for the propagational dependence of Rabi-Split resulting from a strong resonant pump and a coupled weak off-resonance probe are presented for a Lambda three-level atomic configuration. A semi-classical Maxwell-Bloch formulism was adopted for both the perturbational (using stationary phase and steepest descent asymptotic techniques) and the rigorous computational treatments. This calculation can be considered as a Double Self-Induced Transparency SIT' where the strong pump (multiple of 2n on-axis area) experiences coherent pulse break up, coherent self-focusing 2-4 and depletion as the weak probe (multiple of 0.02n area) cooperatively builds up. Different transition gain ratios (i.e., oscillator strength: p2w) are considered to insure that the weak probe does not get (a) delayed with respect to the pump or (b) get out of synchronization, and cease to overlap. The probe detuning can be as large as the input on-axis pump Rabi frequency. The interplay of nonlinear Raman gain action, dispersion and diffraction give rise concommitantly to a number of effects previously studied independently such as self-phase modulation, wave front encoding, transverse ring formation, self-focusing, quasi-trapping (when pump detuning is also allowed), and asymptotic three-level solitary waves.
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.
Delay statistics of amplified quantum initiation of SF are reported as manifestly important in both the pump/SF partial and total overlap regimes for τp/τR < 1 (pump pulse length to cooperative radiation time ratio) as a function of the Fresnel number F for a given atomic density N. The Mattar et al. formulation1 is adopted with phase, transverse variations, and copropagation in conjunction with the Bowden and Sung2 initiation through Langevin forces of bivariate normally distributed amplitudes and uniformly random phase in both pump and SF transitions lp and lsf. Unusual temporal distortion is exhibited in the SF pulse for some trajectories when lp is present, F is large, and τp is shortened. However, when diffraction strengthens, i.e., decreases, the communication between adjacent shells improves and significantly reduces the statistics uncertainty associated with the delay difference σ (τdp – τdsf)/[τdp + τdsf], and the less likely the phase wave is to be exhibited. The SF is not shielded from any fluctuations in the pump pulse.
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.
Experimental studies of spatial and temporal coherence of SRS in hydrogen [1] have pointed out the need of a quantum theory in the nonlinear regime. Previous studies have dealt either with diffraction in a linearized regime [2] or with a nonlinear light‐matter description in the uniform‐plane‐wave regime [3]. Both diffraction and nonlinear effects are examined herein. The Stokes pulse builds up from quantum initiation as does the superfluorescence SF emission [4]. The interplay of diffraction coupling, transverse variations of the atomic density and quantum fluctuations on the Stokes buildup was simulated using a self‐consistant numerical algorithm [5] previously developed for finite beam effects in Self‐Induced‐Transparency [6,7].
Recent work is reviewed where dynamic diffraction coupling is examined in Superfluorescence SF with use of a one-way semiclassical model in which diffraction and transverse density variations are rigorously included. The Cs data are correctly simulated for the first time in conjunction with both an average tipping angle and quantum fluctuation (either longitudinal or transverse) at the initiating stage. This comprehensive review also encompasses rigorously the effects of pump dynamics on the SF evolution. The terminology is unified. Specification of certain pump beam initial conditions at a given frequency results in specific SF characteristics at another frequency as recently observed in CH3F and Ba. Pump dynamics are studied in both the average value of the tipping angle and quantum fluctuation at the initiation stage.