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Technical Physics Letters

Effect of non-Markovian relaxation on self-induced transparency soliton

Guram T. Adamashvili

Published Sep 1, 2011• 0 citations
Publisher

Abstract

The influence of non-Markovian transverse relaxation on a nonlinear optical wave that is formed under the conditions of self-induced transparency is considered. Using a perturbation theory based on the inverse scattering method and memory function formalism, explicit analytical expressions are obtained for the parameters of this soliton (2π-pulse). It is established that allowance for the memory effects leads to qualitatively new results in comparison to the McCall-Hahn and other theories.

DOI
10.1134/s1063785011090021

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The influence of non-Markovian transverse relaxation on a nonlinear optical wave that is formed under the conditions of self-induced transparency is considered. Using a perturbation theory based on the inverse scattering method and memory function formalism, explicit analytical expressions are obtained for the parameters of this soliton (2π-pulse). It is established that allowance for the memory effects leads to qualitatively new results in comparison to the McCall-Hahn and other theories.
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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 review is given of the current status of the self-induced transparency effect. The McCall–Hahn theory (2π pulses) is considered and its generalization to the case of phase modulation of radiation pulses, degeneracy of transitions, and two-photon resonance is discussed. The relationship with the theory of nonlinear waves, obeying the Korteweg–de Vries equation, is pointed out. The possibility of similar coherent effects in direct interband transitions in semiconductors is discussed. A summary is given of the experimental results demonstrating a strong fall in the absorption and a considerable slowing down of light pulses, typical of the self-induced transparency. Possible physical applications of the effect, based on these properties, are discussed.
A more accurate description of the 2 pi pulse of self-induced transparency is obtained. This is an exact solution of an approximate form of the Maxwell-Bloch equations in which only backscattering is neglected; the equations are valid at densities less than about 10 18 atoms cm -3 . At such densities the 2 pi sech pulse of McCall and Hahn (1967, 1969) remains a good approximate well into the picosecond range. The more accurate solution is chirped by a factor proportional to the square of the ratio of the spectral width of the pulse to its carrier wave frequency. The stability of this pulse solution and other N soliton solutions of the approximate Maxwell-Bloch equations is demonstrated.
A systematic perturbation expansion with respect to the small parameter ${(\ensuremath{\Delta}\ensuremath{\tau}\ensuremath{\omega})}^{\ensuremath{-}1}$, $\ensuremath{\Delta}\ensuremath{\tau}$ being the duration of the pulse and $\ensuremath{\omega}$ the optical frequency, is introduced. This method is applied to the problem of self-induced transparency for sharp-line absorbers at exact resonance. Corrections to the McCall and Hahn solution are obtained which describe the propagation of the form-preserving pulse with modulated frequency and slightly changed shape, group velocity, and wave vector. Earlier results by Marth, Holmes, and Eberly on phase modulation and wave-vector shift are confirmed.