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Forward and backward optical waves in metamaterials: nonlinear interaction

Andrei I. Maimistov, Ildar R. Gabitov, Elena V. Kazantseva

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

Considered is propagation of probe radiation through a medium with cubic optical nonlinearity perturbed by CW-or pulsed strong pump radiation with orthogonal polarization (1D-geometry).With respect to the probe radiation, the pump radiation induces in the medium inhomogeneities propagating with underor superluminal velocity.It is shown that in the case of superluminal propagation, reflected probe radiation has conjugated phase and Doppler-shifted frequency.

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Considered is propagation of probe radiation through a medium with cubic optical nonlinearity perturbed by CW-or pulsed strong pump radiation with orthogonal polarization (1D-geometry).With respect to the probe radiation, the pump radiation induces in the medium inhomogeneities propagating with underor superluminal velocity.It is shown that in the case of superluminal propagation, reflected probe radiation has conjugated phase and Doppler-shifted frequency.
The reflection of test radiation from a smooth inhomogeneity of medium characteristics propagating with a subluminal or superluminal velocity is analyzed. The equations describing the propagation of the forward- and counter-propagating waves in such an inhomogeneous medium are derived. Quasi-phase conjugation is demonstrated in the case of superluminal inhomogeneities. The Bragg resonance conditions are formulated and the conditions for increasing the reflection coefficient of radiation from an inhomogeneity are discussed.
The frequency conversion under the parametric Doppler effect, which occurs when weak probe radiation reflects off from a refractive index inhomogeneity induced in a nonlinear medium by intense pumping, has been analyzed. Under these conditions, the frequency dispersion of the medium is assumed to correspond to the single Lorentz oscillator model. It is shown that the presence of resonance and a spectral range forbidden for propagation may lead to a complex Doppler effect, where the incident radiation is single-frequency but the reflected radiation consists of two or three monochromatic waves, one of which has a phaseconjugated wavefront.
We study numerically the propagation of two-color light pulses through a metamaterial doped with active atoms such that the carrier frequencies of the pulses are in resonance with two atomic transitions in the Λ configuration and that one color propagates in the regime of positive refraction and the other in the regime of negative refraction. In such a metamaterial, one resonant color of light propagates with positive and the other with negative group velocity. We investigate nonlinear interaction of these forward- and backward-propagating waves and find self-trapped waves, counterpropagating radiation waves, and hot spots of medium excitation.
Contrary to popular belief, we demonstrate the feasibility of generating superluminal (and subluminal) probe (and signal) light via electromagnetically induced transparency in a medium comprising coupled double-ladder systems. This scheme can be realized in both homogeneously (radiative) as well as in inhomogeneously (Doppler) broadened atomic systems. Unlike more intricate earlier schemes, our scheme is based simply on steady-state propagation dynamics resulting from compensation of the inevitable absorption losses by large nonlinear gain generated through appropriate choice of the pump and coupling fields. We show how easily in this scheme the speed of weak probe (and signal) fields can be switched from subluminal to superluminal by simply varying the strengths of the coherent pump and coupling fields. Furthermore, it is shown that under these conditions both the signal and probe fields are intensity matched and both propagate with the same subluminal (or superluminal) group velocity without suffering loss or gain for long distance in the medium.
Abilities of the method of accumulation of coherent unstable response of a medium for amplification of the rotated component of the probe wave’s polarization in the atomic medium of three-level atoms are studied. Probe wave is examined in frames of the perturbation theory and its frequency is considered near to one photon resonance from the ground to the first excited level. The intense monochromatic pump field connects two excited energy levels and propagates through the medium without a change. The broadening of spectral lines caused by the relaxation processes and the Doppler broadening are included into the calculations. It is shown that by multiple consistent instantaneous change of input probe field’s phase from 0 to π and back, it is possible to obtain, in the tail part of the rotated component of the probe field, a separate narrowed light pulse along with the increase in intensity by more than an order of magnitude with respect to the input field.
A study is made of the excitation of inhomogeneous holographic gratings by ultrashort light pulses with an arbitrary amplitude and phase modulation in a cubic nonlinear medium. The relaxation and diffusion of a pulse-induced grating is considered. The problem of diffraction of probe radiation by an inhomogeneous grating is solved using an electrodynamic theory of perturbations and also using the coupled wave approximation. It is shown that a cubic nonlinear medium may be used to store and then to retrieve uniquely a complete complex coherence function of a pulse. A simple method is proposed for the determination of the area under an exciting pulse, which makes it possible to introduce integral parameters of such a pulse (including a generalized amplitude and duration) that can serve as satisfactory estimates of the corresponding real quantities.