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Physical Review A

Resonant interaction of coupled polarization waves with a degenerate resonant two-photon transition

Alexander A. Zabolotskii

Published Dec 8, 2008• 2 citations
Publisher

Abstract

We study the propagation of linearly coupled polarization waves in a medium containing a two-level molecular dopant having a resonant degenerate two-photon transition. A Thirring-type model is derived for small amplitudes of waves and a solitary wave solution is obtained. For a case of three-wave interaction we derive an asymptotic approximate solution describing quasi-self-similar dynamics of light pulses. Solutions demonstrate that by using a dopant one is able to control the polarization of propagated light.

DOI
10.1103/physreva.78.063813

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We study the propagation of linearly coupled polarization waves in a medium containing a two-level molecular dopant having a resonant degenerate two-photon transition. A Thirring-type model is derived for small amplitudes of waves and a solitary wave solution is obtained. For a case of three-wave interaction we derive an asymptotic approximate solution describing quasi-self-similar dynamics of light pulses. Solutions demonstrate that by using a dopant one is able to control the polarization of propagated light.
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The evolution of an electromagnetic wave with slowly varying polarization, which interacts resonantly with the medium formed by degenerate two-level atoms, is studied using the wave function approach under the conditions of electromagnetically induced transparency. It is shown that the amplitude of the wave field propagates at the velocity of light in such a medium. The equation obtained for the polarization parameter has a solution in the form of a simple wave. The breaking length is determined. It is shown that the velocity of propagation of polarization waves may be much smaller than the velocity of light. The proposed approach is common for two-level systems with an arbitrary degeneracy. The case of a system with Zeeman degeneracy is analyzed in detail. The dependence of the velocity of propagation of the polarization structure on the amplitude and polarization is determined for an arbitrary level degeneracy. The evolution of the polarization structure in such a medium is discussed.
Coherent propagation of a circularly polarized pulse which is two-photon quasi-resonant with a medium of multi-level atoms is considered in the adiabatic following limit. The relevant pair of non-linear coupled partial differential equations are solved exactly for arbitrary pulse shapes. The development of the envelope and the phase of the pulse as it propagates through the medium is described analytically. Perturbation theoretical results are shown to apply only for small intensity or small distance of propagation or both. Qualitatively different results apply for higher intensities and longer distances of propagation. These include strong self-phase-modulation effects as well as reshaping of the pulse envelope.
We consider the two-photon propagation process under the two-fold approximation that (i) the excitation of the upper level of medium molecules remains small during the process, (ii) the intensity of one of the two participating electromagnetic waves is always small compared to that of the other wave. It is then shown that in the limit of the strong dynamical Stark effect the equations describing this process can be reduced to the classical Thirring model equations. This reduction permits one to develop a much simpler theory of wave interaction than was possible in the case of the original equations. As an example, the periodic solutions of two-photon propagation are considered and the Whitham modulational equations are obtained. The different forms of U - V pairs for the Thirring model are discussed in the appendix. Analogous theory can be developed for the stimulated Raman scattering process.
An analysis is made of the coherent interaction of a short pulse of polarised electromagnetic radiation with a medium in which the energy levels are degenerate in respect of the angular momentum projection. In the case of the j a = 1 → j b =0 transition it is found, without recourse to the approximation of slowly varying envelopes, that the system of the Maxwell–Bloch equations has an exact solution in the form of a steady-state solitary wave of duration equal to half the period of emission as a result of the investigated atomic transition. A new solution is obtained, in addition to a simple generalisation corresponding to a polarised video pulse. When the populations of the excited states with different projections of the angular momentum are different, the spherical components of the vector representing the electric field intensity do not behave proportionately: if one of them corresponds to a unipolar spike of the electric field, the other component is a variable-sign solitary wave.