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Journal of Physics B Atomic and Molecular Physics

Two-photon self-induced transparency in a resonant medium. II. Transient pulse behaviour

N Tan-no, Kenichi Yokoto, Humio Inaba

Published Feb 21, 1975• 10 citations
Publisher

Abstract

For pt.I see ibid., vol.8, no.3, 339 (1975). The transient behaviour of two short optical pulses in two-photon coherent propagation is obtained by calculating numerically the coherent propagation equations which couple the two electromagnetic pulses and the atomic system in self-consistent fashion. The coherent interaction of the two different frequency pulses gives rise to lossless propagation in the absorptive medium. This description is characterized by a two-photon area theorem. Novel coherent propagation effects of peak amplification and multiple pulse breakup are found. These effects are ascribed to two-photon self-induced transparency analogous to that of a one-photon transition in a two-level system. A difference of input intensity between the two different frequency pulses yields curious modulation effects involving sharp peak amplification and marked pulse breakup for the low-intensity input. In contrast, the high-intensity input pulse displays a smooth variation with distance and time. Low-loss pulse transmission above threshold, and pulse advance and delay are found for the present case in contrast to that for one-photon self-induced transparency.

DOI
10.1088/0022-3700/8/3/005

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Optical pulse probing of coherency gradient in Λ-medium

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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.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 5, 1999•0 citations
For pt.I see ibid., vol.8, no.3, 339 (1975). The transient behaviour of two short optical pulses in two-photon coherent propagation is obtained by calculating numerically the coherent propagation equations which couple the two electromagnetic pulses and the atomic system in self-consistent fashion. The coherent interaction of the two different frequency pulses gives rise to lossless propagation in the absorptive medium. This description is characterized by a two-photon area theorem. Novel coherent propagation effects of peak amplification and multiple pulse breakup are found. These effects are ascribed to two-photon self-induced transparency analogous to that of a one-photon transition in a two-level system. A difference of input intensity between the two different frequency pulses yields curious modulation effects involving sharp peak amplification and marked pulse breakup for the low-intensity input. In contrast, the high-intensity input pulse displays a smooth variation with distance and time. Low-loss pulse transmission above threshold, and pulse advance and delay are found for the present case in contrast to that for one-photon self-induced transparency.
The authors develop a theoretical analysis which describes coherent nonlinear resonant effects where two optical pulses of different frequencies undergo two-photon self-induced transparency (two-photon SIT) in an inhomogeneously broadened three-level system. The field (Maxwell) and atomic (Schrodinger; density matrix representation) equations are coupled in a self-consistent manner by virtue of the resultant macroscopic polarizations at the two frequencies. This treatment is accomplished under circumstances where atomic coherence plays a predominant role. The resulting equations yield a new two-photon area theorem which gives first the intensity dependent, two-photon absorption law analogous to Beer's law for the one-photon transition. Secondly, a 2 pi Lorentzian pulse solution is derived which propagates without loss at the modified pulse velocity.
In this paper we develop a theoretical analysis which describes a coherent transient effect of two entering pulses---one laser and one Stokes---in a Raman-active medium. The field (Maxwell) and atomic (Schr\"odinger, density-matrix representation) equations are coupled in a self-consistent manner in time and space by virtue of the resultant second-order nonlinear macroscopic polarizations at the two frequencies. This treatment is accomplished under the circumstances where atomic coherence plays a predominant role. The equations derived here may be referred to as "Raman Bloch-Maxwell equations." The resultant equations yield a new aspect of transient stimulated Raman scattering and thus coherent Raman propagation. The transient-pulse behavior may be understood as self-induced modulation of coherent amplification and absorption. The self-induced modulation for the step-function input pulse is described by a combination of Jacobian elliptic functions depending on the input intensity. Computer calculations of transient-pulse evolution reveal interesting pulse breakup phenomena with peak amplification, energy transmission, pulse advance or delay, and pulse-narrowing effects.
The propagation of two pulses in a three-level absorber is treated by using Maxwell's equations and an effective "two-photon Bloch equations" which are analogous to the one-photon Bloch equations, except for two-photon coupling and frequency shifts. I derive relaxation-dependent shifts in the equilibrium $2n\ensuremath{\pi}$ Lorentzian pulses. Part of these shifts depends on weighted time integrals of harmonics of the area and hence remove the propagation degeneracy of pulses having equal areas but different shapes. Absorption of small-area pulses is studied as a function of absorption length, input energies, and relaxation, and it is found that a local enhancement in the transmission occurs as a function of the absorption length.
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.