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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Optical transparency effects in the modes of long-short-wave-length resonance

Sergey Vladimirovich Sazonov, N. V. Ustinov

Published Apr 20, 2004• 2 citations
Publisher

Abstract

The distinctive features of the propagation of the two-component electromagnetic pulses in an anisotropic media are studied in the frameworks of the system of equations of the resonance of long and short waves. It is shown that an interaction of the light with the quantum systems, which have a constant dipole momentum nonequal to zero, occurs not only in the usual mode of the self-induced transparency, but also in two new modes. In the first one (supertransparency), the pulse propagation causes the significant change of the population density of quantum levels, while its group velocity remains close to linear one. In the second mode (extraordinary transparency), the group velocity of the pulse changes significantly, but the population of the levels is practically invariable. It is also noted that the largest change of the population takes place, if the carrier frequency of the solitons is less than the resonant frequency, at that the detuning value depends on the duration of the pulses.

DOI
10.1117/12.561001

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 5, 1999•0 citations
The distinctive features of the propagation of the two-component electromagnetic pulses in an anisotropic media are studied in the frameworks of the system of equations of the resonance of long and short waves. It is shown that an interaction of the light with the quantum systems, which have a constant dipole momentum nonequal to zero, occurs not only in the usual mode of the self-induced transparency, but also in two new modes. In the first one (supertransparency), the pulse propagation causes the significant change of the population density of quantum levels, while its group velocity remains close to linear one. In the second mode (extraordinary transparency), the group velocity of the pulse changes significantly, but the population of the levels is practically invariable. It is also noted that the largest change of the population takes place, if the carrier frequency of the solitons is less than the resonant frequency, at that the detuning value depends on the duration of the pulses.
The propagation of a two-component laser pulse in an optically uniaxial medium is investigated under the conditions of the Zakharov-Benney resonance (viz., resonance of long and short waves). The short-wave ordinary component of the pulse, which is in resonance with the atomic subsystem, effectively generates a video pulse of the extraordinary wave (long-wave component). The latter dynamically detunes the ordinary pulse from the resonance and causes its phase modulation due to nonzero diagonal matrix elements of the dipole moment. An approximate operator approach is proposed for solving constitutive equations for the density matrix, which is equivalent to the asymptotic WKB method and makes it possible to reduce the analysis to solving a system of nonlinear wave equations for both components of the pulse. The possibility an extraordinary wave video pulse being generated with the help of a quasimonochromatic ordinary pulse with a longer wave-length. It is shown that, when the ordinary component dominates, the self-induced transparency mode is realized; in the opposite limit, the effect known as extraordinary transparency takes place. Solitary pulses corresponding to the latter case experience a decrease in the velocity of propagation, which is similar to that observed for self-induced transparency and practically do not change the population of quantum levels. Physical situations reducing the initial system of constituent and wave equations to familiar integrable models are analyzed.
Nonlinear two-component electromagnetic pulse propagation through a resonant axially symmetric anisotropic medium having a permanent dipole moment is analyzed under conditions of strong coupling between the ordinary (short-wavelength) and extraordinary (long-wavelength) pulse components. It is shown that a pulse can propagate through the medium in regimes different from self-induced transparency if its ordinary component is detuned off resonance. In particular, a pulse propagating in the regime of self-induced super-transparency substantially changes quantum-level populations, but its group velocity remains almost equal to the linear velocity. If a pulse propagates in the extraordinary transparency regime and the carrier-frequency detuning from resonance is small, then its group velocity is substantially lower, while the level populations remain virtually invariant. Regimes of propagation through weakly excited media under quasi-resonance conditions are also identified.
The modes of nonlinear propagation of the two-component electromagnetic pulses through optically uniaxial media containing resonant particles are studied. The features of their manifestation in the "dense" media and in the media with expressed positive and negative birefringences are discussed. It is shown that exponentially and rationally decreasing solutions of the system of material and wave equations allow us also to describe the propagation of the pulses of the self-induced transparency in isotropic media in the case, when the direct electric dipole-dipole interaction between the resonant particles is taken into account.
Propagation of a pulse of self-induced transparency in a resonance medium is discussed for the case when it is necessary to take into account the direct electric dipole-dipole interaction between atoms. An equation for the envelope of a wave packet—the sine-Gordon equation—is obtained for the case of durations short compared to ω 0 −1 (ω0 is the transition frequency). The dependence of the velocity and the amplitude of the soliton on the magnitude of the dipole-dipole interaction of atoms is examined in the adiabatic approximation.
We study the effects of dispersion in carrier waves on the properties of soliton self--induced transparency (SIT) in two level media. We found substantial impact of dispersion effects on typical SIT soliton features. For example, the degree of SIT pulse velocity slowing down (acceleration) is determined by the ratio of the incoming pulse frequency over atomic transition frequency - x=ω/ω0x=ω/ω_0x=ω/ω0​. Specifically, an immediate pulse stopping is predicted for absorbing media when pulse duration time exceeds some critical value. In the sharp line limit stopping may emerge only for frequency ratio above unity, while for the inhomogeneously broadened systems it appears irrespective of the value of xxx. Analysis performed on the basis of Mcall\& Hahn \textit{Area theorem} implies that pulse stopping is achieved when Ber's absorption coefficient approaches infinity, that is, pulse energy is fully absorbed in the medium. In the case of amplifying media super-luminal motion is predicted as in the case of resonance. However, there is a lowest value in the frequency ratio below which the pulse velocity tends to the sub-luminal region. These new features of the SIT phenomenon open novel ways on how it may be exploited for the control of electromagnetic wave radiation in two-level media. This may be achieved by varying frequency ratio.
Quantum coherence and interference in atomic systems can lead to interesting optical phenomena such as nonabsorbing resonances, lasing without inversion, generating an ultrahigh index of refraction without absorption, propagation of light pulses without losses. In the last-named is given the title transparency. Up to now it is known some types of transparency in multi-level resonant media. One of them is electromagnetically induced transparency (EIT). The phenomenon of EIT in the propagation of laser radiation through an absorbing medium has been recently investigated and explained in terms of quantum coherence and interference for multi-level atomic system. For instance in the (Lambda) -system, if the atomic medium is prepared in a quantum superposition of states, matched pulses, i.e., a pair of optical pulses whose amplitude and phase have a well defined relation, propagate without absorption. The mechanism of coherent population trapping is responsible for EIT in a (Lambda) -system. There is another, well known mechanism for creating transparency in a two-state atom: self-induced transparency, or SIT. Here, a single pulse whose area (the integral of its Rabi frequency over time) is 2(pi) is applied to the medium. Such a pulse causes the atoms to cycle smoothly from the ground to the excited state and then back again. In principle, such a pulse can propagate over long distances. SIT can be generalized to multi-level systems and multiple quasi-monochromatic fields. Generalization of SIT in a (Lambda) -system was obtained in reference 2. In this report we present a new type of transparency (combined transparency). This type describes propagation of laser pulse through a (Lambda) -type medium where the initial atomic state is prepared in the form of spatially varying coherent superposition of low-energetic states (initial coherency gradient). The common envelope behaves as usual 2(pi) hyperbolic secant pulse, but the ratio between the components of frequencies transitions 1> yields 3> and 2> yields 3> changes due to coherent Raman scattering so (phi) equals atan(E1/E2) equals (pi) /2-Gz, where z is the coordinate, G is the constant determined by both the incident pulse parameters and the initial coherence between the atomic states. Our solution demonstrates a direct connection of EIT in adiabatic regime to the SIT effects. This type of a transparency is given the title screw-type transparency, because for the given form of incident pulse (pitch of screw) medium is transparent, if medium's the initial coherence gradient is correspondingly prepared (thread on a engine nut). Besides a transparency, this phenomenon contains a transformation of the incident pulse frequency during the process of the propagation. This property of the phenomena can be result in a complete conversion of the frequency.