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Bulletin of the Russian Academy of Sciences Physics

Dynamics of electromagnetic field in two-level doped systems

Mikhail B. Belonenko, A. S. Sasov

Published Jan 1, 2007• 0 citations
Publisher

Abstract

The dynamics of solitons of self-inducted transparency is theoretically and numerically investigated in the case when atoms described in the two-level approximation fit into a medium with ferroelectric properties. The interaction between electromagnetic pulses in the medium and two-level dopant atoms is considered.
DOI
10.3103/s1062873807010339

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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 study the propagation dynamics of a single pair of probe and coupling laser pulses in a three-level cascade atomic medium by numerical solving the Maxwell-Bloch equations for atoms and fields. Influences of the pulse durations, intensity and pulse area of the coupling laser on the probe laser propagation are investigated. We found the conditions that the undistorted probe pulse in such i.e., the effect is established. Under conditions, the ground state population is trapped in a dark state. Full Text: PDF References A. Imamoglu, S.E. Harris, Lasers without inversion: interference of dressed lifetime-broadened states, Opt. Lett. 14 (1989) 1344. CrossRef K.J. Boller, A. Imamoglu, S.E. Harris, Observation of electromagnetically induced transparency, Phys. Rev. Lett. 66 (1991) 2593. CrossRef A.S. Zibrov, M.D. Lukin, D.E. Nikonov, L. Hollberg, M.O. Scully, V.L. Velichansky, and H.G. Robinson, Experimental Demonstration of Laser Oscillation without Population Inversion via Quantum Interference in Rb, Phys. Rev. Lett. 75 (1995) 1499. CrossRef L.V. Hau, S. E. Harris, Z. Dutton, C.H. Bejroozi, speed reduction to 17 metres per second in an ultracold atomic gas, Nature, 397 (1999) 594. CrossRef L.V. Doai, D.X. Khoa, and N.H. Bang, EIT enhanced self-Kerr nonlinearity in the three-level lambda system under Doppler broadening, Phys. Scr. 90 (2015)045502. CrossRef D.X. Khoa, L.V. Doai, D.H. Son, and N.H. Bang, Enhancement of self-Kerr nonlinearity via electromagnetically induced transparency in a five-level cascade system: an analytical approach, J. Opt. Soc. Am. B, 31, N6 (2014), pp. 1330. CrossRef F.T. Hioe and R. Grobe, Matched Optical Solitary Waves for Three- and Five-Level Systems, Phys. Rev. Lett. 73, (1994) 2559. CrossRef S.E. Harris and Z.F. Luo, Preparation energy for electromagnetically induced transparency, Phys. Rev. A. 52 (1995) R928. CrossRef V. G. Arkhipkin, I.V. Timofeev, Adiabatic propagation of short pulses under conditions of electromagnetically induced transparency, Quantum Electronics, 30 (2000) 180. CrossRef M. Kiffner, T. N. Dey, Dynamical control of pulse propagation in electromagnetically induced transparency, Phys. Rev. A. 79 (2009) 023829. CrossRef R. Yu, J. Li, P. Huang, A. Zheng, X. Yang, Dynamic control of light propagation and optical switching through an RF-driven cascade-type atomic medium, Phys. Lett. A. 373 (2009) 2992. CrossRef E. Paspalakis,N. J. Kylstra and P. L. Knight, Propagation and nonlinear generation dynamics in a coherently prepared four-level system, Phys. Rev. A 65 (2002) 053808. CrossRef E. Ignesti, R. Buffa, L. Fini, E. Sali, M. V. Tognetti, S. Cavalieri, Controlling the propagation of broadband light pulses by Induced Transparency, Opt. Commun, 285 (2012) 1185. CrossRef P. R. Bermanand C. H. Raymond Ooi, Pulse propagation in a medium of ?-type atoms, Phys. Rev. A 86 (2012), 053812. CrossRef G. Buica, T. Nakajima, Propagation of two short laser pulse trains in a ?-type three-level medium under conditions of electromagnetically induced transparency, Opt. Commun. 332 (2014) 59. CrossRef L. V. Doai, P. V. Trong, D. X. Khoa, and Ng. H. Bang, Electromagnetically induced transparency in five-level cascade scheme of 85Rb atoms: An analytical approach, Optik, 125 (2014) 3666?3669. CrossRef J.H. Eberly, Transmission of dressed fields in three-level media, Quantum Semiclass. Opt. 7 (1995) 373. CrossRef M.D. Crisp, Propagation of Small-Area Pulses of Coherent Light through a Resonant Medium, Phys. Rev. A 1 (1970) 1604. CrossRef
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 consider self-induced transparency (SIT) in a two-level atomic system in the presence of an additional control laser field. We find that the dynamics of the SIT process are profoundly modified by the control field, in a manner reminiscent of the modification of other nonlinear optical interactions through the process of electromagnetically induced transparency. The presence of the control field allows SIT to occur under a much broader range of conditions and leads to dramatically reduced values of the group velocity of the SIT soliton.
The formation and evolution of a localized plasmon-polariton soliton in a metallic cylinder surrounded by a layer of two-level atoms with a frequency close to the plasmon resonance have been investigated. The dynamics of the transverse plasmons in a extended medium is described in the hydrodynamic approximation. It has been shown that the evolution equation can be reduced to Maxwell-Bloch-like equations, which describe self-induced transparency in optics. The effect of losses and nonlinearities caused by the self-action of the electron cloud on the evolution of soliton structures has been studied numerically.
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.