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Optica Acta International Journal of Optics

Optical Solitons in Media with Resonant and Non-resonant Self-focusing Nonlinearities

Evgeny V. Doktorov, R. A. Vlasov

Published Feb 1, 1983• 72 citations
Publisher

Abstract

Special features of generating a self-induced transparency in a medium with both resonant and non-resonant (Kerr-type) nonlinearities are considered. Soliton solutions of the Maxwell-Bloch equations are found, taking into account the diffraction divergence of the light beam. It is shown that solitons emerge in such a medium under conditions of two-dimensional optical beam scanning along the medium surface, and have non-coinciding propagating directions of the amplitude and phase fronts. As a necessary condition for the existence of solitons, there is a definite relationship between the scanning velocity and the parameters of the medium and radiation.

DOI
10.1080/713821151

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Special features of generating a self-induced transparency in a medium with both resonant and non-resonant (Kerr-type) nonlinearities are considered. Soliton solutions of the Maxwell-Bloch equations are found, taking into account the diffraction divergence of the light beam. It is shown that solitons emerge in such a medium under conditions of two-dimensional optical beam scanning along the medium surface, and have non-coinciding propagating directions of the amplitude and phase fronts. As a necessary condition for the existence of solitons, there is a definite relationship between the scanning velocity and the parameters of the medium and radiation.
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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.
Analytic and numerical solutions of the Maxwell–Bloch equations, including transverse and timedependent phase variations, predict on-resonance self-focusing (SF) and elucidate its formation due to the combined effect of diffraction and inertial response of the medium. This new SF can be characterized by a simple parameter in terms of the beam and medium parameters. Recently, two independent experiments on SF in Na and Ne demonstrated convincingly this new SF effect for spatially nonuniform self-induced transparency pulses propagating in thick resonant absorbers.
We have found a steady-state solution for a pulse propagating in imhogeneously broadened resonant two-level atoms embedded in a dispersive and nonlinear Kerr lossless host medium. The pulse is of an unchirped hyperbolic-secant form with a linear spatial phase delay. There are several salient features in this solution which are different from the results obtained previously. First, for the given parameters of the medium and carrier frequency, the group velocity, the amplitude, and the pulse width are uniquely determined. Second, the group velocity is independent of the density of the resonant atoms. Third, the solution exists in the positive dispersion region, which is different from solitons in fibers.
This paper presents the analytic solutions of self-induced transparency with transverse variations in resonant media by a self-consistent power series approximation method. We solve the Maxwell-Bloch equations by retaining all integral terms from the inhomogeneous broadening and the second-derivative terms with respect to distance and time. The lowest-order approximation is presented in detail. We discuss the characteristics of the distortionless pulses that propagate in an inhomogeneously broadening medium. It is shown that the group velocity and peak power of the self-induced transparency solitons could be represented in terms of the pulse width, the angle between phase velocity and group velocity, and the basic material parameters of the resonant medium. The chirping of the soliton is also discussed.
One-dimensional pulse propagations in the electromagnetically induced media are studied. The Maxwell–Bloch equations for a three-level medium are simplified with the approximations of slowly varying amplitudes, negligible irreversible relaxations and exact resonances. An analysis is made for the case where the integrable condition is satisfied; the oscillation strengths for the two transitions are equall. Through the Bäcklund transformation, one-soliton solutions including the so-called simulton are derived.