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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Polarization properties of self-induced transparency under Raman resonance

Ashat M. Basharov

Published Nov 15, 2001• 0 citations
Publisher

Abstract

Self-induced transparency under two-photon and Raman resonances is studied theoretically in the cases of small angular momentum of resonant transition and essentially different intensity of resonant waves. The last corresponds to the condition of experiment of Grabtchikov et al [Phys.Rev.Lett.81,5808 (1998)]. The problem with account to wave polarization was reduced to generalized Maxwell-Bloch equations which are exactly integrable by the inverse scattering transform method.

DOI
10.1117/12.447970

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Self-induced transparency under two-photon and Raman resonances is studied theoretically in the cases of small angular momentum of resonant transition and essentially different intensity of resonant waves. The last corresponds to the condition of experiment of Grabtchikov et al [Phys.Rev.Lett.81,5808 (1998)]. The problem with account to wave polarization was reduced to generalized Maxwell-Bloch equations which are exactly integrable by the inverse scattering transform method.
A study is made of steady-state ultrashort electromagnetic radiation pulses of two different wavelengths propagating at the same velocity in a three-level medium under exact resonance conditions. It is shown that such pulses (simultons) correspond to the soliton solutions of the corresponding generalized reduced Maxwell–Bloch equations which thus represent a new example of a system of evolution equations that can be solved exactly by the inverse scattering method. A full characterization of a simulton requires the knowledge of its duration and phase and also of a two-dimensional vector (called the internal polarization vector) with the components equal to the relative amplitudes of the pulses forming a simulton. Collision of two different simultons generally changes their polarizations. An expression is obtained for the angle of rotation of the polarization vectors as a function of the simulton amplitudes and their initial polarizations.
A theory based on the method of the inverse scattering problem is presented describing propagation of an ultrashort light pulse under the condition that resonant interaction with atoms of the medium is initially switched on by an additional Stark pulse. A Hamiltonian form of the Maxwell-Bloch equation is found without redefining the spatiotemporal variables. The method of the inverse scattering problem is based on a special spectral problem. Equations of the Gel’fand-Levitan-Marchenko type and a soliton solution are obtained.
Abstract The effect of self-induced transparency is investigated for a three-level system with a V -scheme of the allowed transitions in the case where one of the transitions is resonant while another one is quasiresonant. The generalized system of the wave and material equations for the resonant transition, taking into account the presence of a quasiresonant transition, is derived. This system is integrable, and its soliton solutions are investigated. It is shown that quasiresonant transition has an influence on the profile of the optical soliton and leads to its phase modulation. The conditions under which the propagation of the soliton is followed by the full inversion of the populations of quantum levels of the resonant transition are established.
The authors develop a theoretical analysis which describes coherent nonlinear resonant effects where two optical pulses of different frequencies undergo two-photon self-induced transparency (two-photon SIT) in an inhomogeneously broadened three-level system. The field (Maxwell) and atomic (Schrodinger; density matrix representation) equations are coupled in a self-consistent manner by virtue of the resultant macroscopic polarizations at the two frequencies. This treatment is accomplished under circumstances where atomic coherence plays a predominant role. The resulting equations yield a new two-photon area theorem which gives first the intensity dependent, two-photon absorption law analogous to Beer's law for the one-photon transition. Secondly, a 2 pi Lorentzian pulse solution is derived which propagates without loss at the modified pulse velocity.
A theory of dispersive soliton of the self-induced transparency in a medium consisting of atoms or semiconductor quantum dots of two types is considered. A two-component medium is modeled by a set of two-level atoms of two types embedded into a conductive host material. These types of atoms correspond to passive atoms (attenuator atoms) and active atoms (amplifier atoms) with inverse population of the energetic levels. The complete solution is given of the Maxwell--Bloch equations for ensembles of two-type atoms with different parameters and different initial conditions by inverse scattering transform. The solutions of the Maxwell--Bloch equations for many-component atomic systems by inverse scattering transform are also discussed. The influence of the difference between dipole moments of atoms, the longitudinal and transverse relaxation times, pumping, and conductivity on the soliton is taken into account by means of perturbation theory. The memory effects are described in terms of generalized non-Markovian optical Bloch equations. The condition of a balance between the energy supplied and lost is obtained.