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Journal of Experimental and Theoretical Physics

Role of nonlinear refraction in the generation of terahertz field pulses by light fields

Alexander A. Zabolotskii

Published Jul 1, 2013• 2 citations
Publisher

Abstract

The generation of microwave (terahertz) pulses without any envelope in a four-level quasi-resonant medium is considered. Two intense quasi-monochromatic laser fields lead to a partial upper-level population. Microwave field pulses cause the transition between these levels. For appropriately chosen scales, the evolution of the fields is shown to be described by the pseudo-spin evolution equations in a microwave field with the inclusion of nonlinear refraction caused by an adiabatic upper-level population. The evolution of terahertz field pulses is described outside the scope of the slow-envelope approximation. When a number of standard approximations are taken into account, this system of equations is shown to be equivalent to an integrable version of the generalized reduced Maxwell-Bloch equations or to the generalized three-wave mixing equations. The soliton solution found by the inverse scattering transform method is used as an example to show that nonlinear refraction leads to a strong compression of the microwave (terahertz) field soliton.

DOI
10.1134/s1063776113080104

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The generation of microwave (terahertz) pulses without any envelope in a four-level quasi-resonant medium is considered. Two intense quasi-monochromatic laser fields lead to a partial upper-level population. Microwave field pulses cause the transition between these levels. For appropriately chosen scales, the evolution of the fields is shown to be described by the pseudo-spin evolution equations in a microwave field with the inclusion of nonlinear refraction caused by an adiabatic upper-level population. The evolution of terahertz field pulses is described outside the scope of the slow-envelope approximation. When a number of standard approximations are taken into account, this system of equations is shown to be equivalent to an integrable version of the generalized reduced Maxwell-Bloch equations or to the generalized three-wave mixing equations. The soliton solution found by the inverse scattering transform method is used as an example to show that nonlinear refraction leads to a strong compression of the microwave (terahertz) field soliton.
A theory of quasi-resonance for the model of atoms with an arbitrary number of levels is developed by the method of unitary transformation without recourse to Bloch’s equations. Corrections to the results known from the theory of adiabatic following, which refine these results and take into account dispersion of the nonlinear response of the resonant system, are obtained. The condition for quasi-resonance with a single atomic transition is shown to impose stringent limitations on the form of the nonlinear evolution equation for the electric field envelope of the pulse with dispersion of the nonlinear response taken into account, which prohibit the reduction of the equation indicated to familiar, fully integrable systems.
The nonlinear dynamics of a vector two-component optical pulse propagating in quasi-resonance conditions in a medium of nonsymmetric quantum objects is investigated for Stark splitting of quantum energy levels by an external electric field. We consider the case when the ordinary component of the optical pulse induces σ transitions, while the extraordinary component induces the π transition and shifts the frequencies of the allowed transitions due to the dynamic Stark effect. It is found that under Zakharov-Benney resonance conditions, the propagation of the optical pulse is accompanied by generation of an electromagnetic pulse in the terahertz band and is described by the vector generalization of the nonlinear Yajima-Oikawa system. It is shown that this system (as well as its formal generalization with an arbitrary number of optical components) is integrable by the inverse scattering transformation method. The corresponding Darboux transformations are found for obtaining multisoliton solutions. The influence of transverse effects on the propagation of vector solitons is investigated. The conditions under which transverse dynamics leads to self-focusing (defocusing) of solitons are determined.
A planar homogeneous waveguide array with two-level systems has been considered. The evolution of an electromagnetic field is described by the Maxwell-Bloch equations taking into account the action of the fields of neighboring waveguides beyond the slow-envelope approximation. It has been shown that the model in the continuous approximation is reduced to an integrable system of equations, including the case of a nonzero static dipole moment. The model can be used to analyze the nonlinear mechanism of the compression of pulses and the conditions of overcoming of the diffraction limit.
Self-induced transparency is analyzed for optical pulses interacting with a two-level system by solving an integrable system of evolution equations without using the slowly varying envelope approximation. A suitable modification of the inverse scattering method is developed to find soliton solutions. The characteristics of linearly and circularly polarized optical solitons (including those created in a laser) are compared. To assess the scope of the two-level model, the effects due to additional levels are analyzed in the adiabatic approximation. It is shown that these effects violate the integrability of the model and lead to loss of self-induced transparency for pulses with duration comparable to oscillation period. However, self-induced transparency is recovered in the quasi-monochromatic limit. Applications of the results are discussed.
We develop a general method allowing one to construct the consistent theory of light pulse propagation through an atomic medium in arbitrary nonlinear regime with respect to the field strength, taking into account the light polarization, temporal (frequency), and spatial dispersions. The method is based on the reduced Maxwell equation, atomic density matrix formalism, and adiabatic approximation. In order to demonstrate the efficiency of our method we investigate in detail the case of propagation of the pulses under conditions of coherent population trapping in a medium of two-level atoms with degenerate energy levels. Equations describing the evolution of various field parameters are derived. It is shown that pulses of ellipticity and spatial orientation of polarization ellipse propagate with slowing. Analytical expressions for the slowing factor are obtained. Previously unknown effects of the stimulated phase modulation and the generation of a phase pilot pulse by the variation of spatial orientation of the polarization ellipse are predicted.