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Physical Review A

Propagation of two-dimensional pulses in electromagnetically induced transparency media

Per Arve, Peter Jänes, Lars Thylen

Published Jun 14, 2004• 41 citations
Publisher

Abstract

The propagation in two dimensions of ``optical'' pulses in electromagnetically induced transparency media is analyzed. Results are presented for coupled Maxwell-Bloch equations with slowly varying envelope approximation, for both adiabatic and nonadiabatic situations. The possibility of changing the direction of the pulse by a switch of control beam direction is investigated in detail.

DOI
10.1103/physreva.69.063809

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Journal of Experimental and Theoretical Physics•Jun 1, 2004•3 citations
The propagation in two dimensions of ``optical'' pulses in electromagnetically induced transparency media is analyzed. Results are presented for coupled Maxwell-Bloch equations with slowly varying envelope approximation, for both adiabatic and nonadiabatic situations. The possibility of changing the direction of the pulse by a switch of control beam direction is investigated in detail.
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.
The influence of a phase-modulated control field on the phenomenon of electromagnetically induced transparency (EIT) is investigated theoretically. We show that the phase modulation changes the dispersive properties of the medium considerably since it results in temporal oscillations of the transparency window in frequency space. This is in marked contrast to the standard EIT setup, where the transparency window is fixed and determined by the two-photon resonance condition. In particular, we find that the phase modulation enables the propagation of probe pulses with disjoint frequency spectra at different times and allows the shifting of the central frequency of a probe pulse almost without distortion of its shape. We employ the time-dependent susceptibility of the medium to explain and analyze our results and demonstrate that this concept yields qualitative as well as quantitative agreement with the numerical integration of Maxwell-Bloch equations. Our theoretical model can be applied to other media with time-dependent susceptibilities.
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.