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arXiv:nlin/0611011

Stimulated Raman Transfer of SIT Solitons

B. D. Clader, Joseph H. Eberly

Published Nov 6, 2006• 0 citations
arXivHTMLPDF

Abstract

We treat theoretically the two-pulse plane-wave propagation problem associated with the stimulated Raman process. A strong pump pulse and a weak probe pulse interact self-consistently during mutual propagation through a medium in the three-level lambda configuration. We treat the pulse interaction fully coherently, but take initially incoherent mixed ground states to describe the medium. We present analytic pulse envelope solutions to the nonlinear evolution equations, and then test them numerically. We show that the entire process can be interpreted consistently as a three-regime evolution, in which the first and last regimes display behavior quantitatively the same as self-induced transparency. They are connected through a Raman transfer process in the intermediate regime.

DOI
10.48550/arxiv.nlin/0611011

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We treat theoretically the two-pulse plane-wave propagation problem associated with the stimulated Raman process. A strong pump pulse and a weak probe pulse interact self-consistently during mutual propagation through a medium in the three-level lambda configuration. We treat the pulse interaction fully coherently, but take initially incoherent mixed ground states to describe the medium. We present analytic pulse envelope solutions to the nonlinear evolution equations, and then test them numerically. We show that the entire process can be interpreted consistently as a three-regime evolution, in which the first and last regimes display behavior quantitatively the same as self-induced transparency. They are connected through a Raman transfer process in the intermediate regime.
We examine fully coherent two-pulse propagation in a $\ensuremath{\Lambda}$-type medium, under two-photon resonance conditions and including inhomogeneous broadening. We examine the effects of both short pulse preparation and medium preparation. We contrast the cases in which the two pulses have or have not matched envelopes, and media with and without ground state coherence. We find that an extended interpretation of the area theorem for single-pulse self-induced transparency is able to unify two-pulse propagation scenarios, including some aspects of electromagnetically induced transparency and stimulated Raman scattering. We present numerical solutions of both three-level and adiabatically reduced two-level density matrix equations and Maxwell's equations, and show that many features of the solutions are quickly interpreted with the aid of analytical solutions that we also provide for restricted cases of pulse shapes and preparation of the medium. In the limit of large one-photon detuning, we show that the adiabatic two-level equations commonly used to study stimulated Raman scattering are not reliable for pulse areas in the $2\ensuremath{\pi}$ range, which allows puzzling features of previous numerical work to be understood.
The spatial and temporal dynamics of two short pulses propagating in an optically dense medium of resonant three-level Λ-atoms is investigated numerically and analytically. The maximum coherence for the Raman transition due to coherent population trapping. It is shown that, at the initial stage of propagation, the waveforms of such pulses only slightly change along the length of the medium, which may considerably exceed the length of linear absorption for a single weak pulse. As the length of the absorbing medium increases, the energy of the probe (first) pulse is completely transferred into the second (control) pulse.
The coherent propagation of two optical short pulses through a resonant medium consisting of two three-level atoms in the configuration is investigated. A self-consisting analytical solution without steady state or adiabatic approximations is presented. The electric field in the model studied consists of two co-propagating plane waves, each of which is in near resonance with a transition in the absorber. The density matrix of two three level atoms is studied. Also, the reduced density matrices are stated. The present approach for the semiclassical treatment of resonant coherent interactions in three-level atoms represents a generalization of the Maxwell- Bloch equations for a two-level system. The Maxwell-Bloch equations reduced to the non-linear pendulum equation. The solution shows that the two pulses can propagate simultaneously without loss under some conditions about the pulses and the medium. The propagation of the two pulses through the medium without any constrains approves the self -induced transparency (SIT) phenomenon.
The standard self-induced transparency (SIT) phenomenon represents the lossless propagation of a long multicycle stable soliton in an absorbing two-level resonant medium, if the soliton's envelope area equals $2\ensuremath{\pi}$ ($2\ensuremath{\pi}$ pulse). In this case, the leading half of the $2\ensuremath{\pi}$ pulse excites the medium, while the trailing half completely brings the medium back to the ground state. In this work, we theoretically demonstrate an analogous phenomenon for subcycle pulses propagating in an arbitrary multilevel resonant medium. The duration of the obtained solitary pulses must be smaller than the periods of resonant transitions in the medium. The obtained subcycle solitary solutions first turn an initially unexcited multi-level resonant medium to excited levels and then fully return it back to the ground state.
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.
Using a numerical approach we report on the cloning dynamics of simultaneous self-induced transparency (SIT) and nonlinear Schrödinger (NLS) solitons in a doped nonlinear dispersive medium. This technique involves a three-level atomic system interacting resonantly with two optical fields within a Lambda scheme. As a result, a pulse in the signal frequency is transformed into a replica of the pulse in the pump frequency. The atomic population evolution shows that the basic mechanism behind the cloning process is the coherent population trapping effect. Furthermore, it is shown that the signal clone presents characteristics of both the SIT soliton and NLS soliton.