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Journal of Experimental and Theoretical Physics

Periodic waves in the theory of self-induced transparency

A. M. Kamchatnov, Maxim Valentinovich Pavlov

Published Jan 1, 1995• 6 citations
OpenAlex

Abstract

A general singly periodic solution of the Maxwell-Bloch equations describing self-induced transparency in a medium composed of two-level atoms has been obtained. The solution is represented in effective form and depends on all four parameters of the problem (the Riemann invariants). The Whitham equations are derived, which give the evolution of the Riemann invariants for modulated periodic solutions. O 1995 American Institute of Physics.

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Journal of Experimental and Theoretical Physics Letters•May 1, 2010•1 citation
A general singly periodic solution of the Maxwell-Bloch equations describing self-induced transparency in a medium composed of two-level atoms has been obtained. The solution is represented in effective form and depends on all four parameters of the problem (the Riemann invariants). The Whitham equations are derived, which give the evolution of the Riemann invariants for modulated periodic solutions. O 1995 American Institute of Physics.
The phenomenon that describes the effect of a coherent medium response to an incident electric field, to which the medium is totally transparent and which undergoes lossless propagation, is known as self-induced transparency (SIT). SIT was first discovered by McCall and Hahn (1969) in the case of nondegenerate two-level atoms. Special solutions for the two-level system were found by Lamb (1971), while the initial value problem for the propagation of a pulse through a resonant two-level optical medium was solved by Inverse Scattering Transform (IST) in [1, 2]. It is possible to formulate the SIT equations in the framework of the IST also in the case of a three-level system, as in [3]. While the associated scattering problem is the same as for the coupled nonlinear Schrödinger equation, the time evolution depends on asymptotic values of the material polarizability envelopes and is highly non-trivial. This talk will address the solution of the initial value problem for the SIT equations for three level systems, for generic preparation of the medium, and
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.
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.
The evolution of the electromagnetic field in a two-level medium occurring in a matrix with finite response time has been studied. An integrable variant of the Maxwell-Bloch equations with allowance for nonlinear dispersion is derived and solved using the inverse scattering problem. It is shown that the nonlinear dispersion caused by the finite response time of the matrix yields a new possibility of controlling soliton parameters. A particular case of the constructed model can be used to describe field pulses in the parameter domain that occurs between the regions of applicability of the quasi-monochromatic approximation and the approximation of unidirectional propagation of pulses with durations on the order of the oscillation period.
A theory of optical two-component pulse of self-induced transparency in a dispersive medium has been developed. Using the generalized version of the perturbative expansion method, the system of material equations for an ensemble of two-level atoms and the wave equation in a dispersive medium are reduced to coupled nonlinear Schrödinger equations. A solution in the form of a phase-modulated two-component 0π0\pi 0π pulse is obtained. The pulse components oscillate at the sum and difference frequencies in the vicinity of the carrier-wave frequency. Explicit analytical expressions for the parameters and formation conditions of a nonlinear wave, which depend on the dispersive properties of the medium, are presented. Known results are obtained for a particular case.
The formation and evolution of a localized plasmon-polariton soliton in a metallic cylinder surrounded by a layer of two-level atoms with a frequency close to the plasmon resonance have been investigated. The dynamics of the transverse plasmons in a extended medium is described in the hydrodynamic approximation. It has been shown that the evolution equation can be reduced to Maxwell-Bloch-like equations, which describe self-induced transparency in optics. The effect of losses and nonlinearities caused by the self-action of the electron cloud on the evolution of soliton structures has been studied numerically.