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Quantum Electronics

Induced transparency under transient Raman scattering conditions

Evald E. Fradkin, V V Kozlov, Maxim Voronov

Published Sep 30, 1999• 0 citations
Publisher

Abstract

An exact semiclassical solution to the problem of the simultaneous propagation of weak and strong pulses interacting with adjacent transitions of a three-level V-scheme was found. The homogeneous and inhomogeneous broadening of the absorption lines of a gaseous medium was examined. It was shown that the computational formulas are suitable for any profile and area under the strong pulse, although numerical calculations were performed for a 2π pulse. The results were compared with those obtained by integration of the system of equations for the density matrix (carried out in the τ 3 ≪ τ 1 approximation, where τ 3 and τ 1 are the durations of the weak and strong pulses, respectively) and also with a theoretical estimate. A qualitative explanation of the phenomenon mentioned above was proposed.

DOI
10.1070/qe1999v029n09abeh001575

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An exact semiclassical solution to the problem of the simultaneous propagation of weak and strong pulses interacting with adjacent transitions of a three-level V-scheme was found. The homogeneous and inhomogeneous broadening of the absorption lines of a gaseous medium was examined. It was shown that the computational formulas are suitable for any profile and area under the strong pulse, although numerical calculations were performed for a 2π pulse. The results were compared with those obtained by integration of the system of equations for the density matrix (carried out in the τ 3 ≪ τ 1 approximation, where τ 3 and τ 1 are the durations of the weak and strong pulses, respectively) and also with a theoretical estimate. A qualitative explanation of the phenomenon mentioned above was proposed.
In the limit of pulse durations that are shorter than the characteristic times of atomic decays, the dynamics of the propagation of a probe light pulse under the action of a driving pulse in the form of a self-induced transparency soliton applied to the adjacent transition of the V -scheme is considered. For a three-level absorber, it is shown that, in the absence of two-photon inhomogeneous broadening, the effect of soliton-induced transparency (SOIT) for the probe field takes place, which consists of the probe pulse undergoing forced localization by the driving pulse and propagates further without a change in the energy or shape. This type of transparency has no threshold with respect to both the energy and the area and is observed for arbitrarily weak pulses. The SOIT effect disappears in the presence of a two-photon inhomogeneous broad-ening. The effect of Raman amplification in a three-level amplifier with the Raman population inversion is considered. It is demonstrated that, under the action of the two-photon inhomogeneous broadening, the effect of Raman amplification becomes a threshold effect. The broader the two-photon inhomogeneous contour, the larger the Raman inversion required to initiate generation.
The coherent propagation of two optical short pulses through a resonant medium consisting of two three-level atoms in the configuration is investigated. A self-consisting analytical solution without steady state or adiabatic approximations is presented. The electric field in the model studied consists of two co-propagating plane waves, each of which is in near resonance with a transition in the absorber. The density matrix of two three level atoms is studied. Also, the reduced density matrices are stated. The present approach for the semiclassical treatment of resonant coherent interactions in three-level atoms represents a generalization of the Maxwell- Bloch equations for a two-level system. The Maxwell-Bloch equations reduced to the non-linear pendulum equation. The solution shows that the two pulses can propagate simultaneously without loss under some conditions about the pulses and the medium. The propagation of the two pulses through the medium without any constrains approves the self -induced transparency (SIT) phenomenon.
Strong and short coherent pulses of electromagnetic radiation propagate through extended absorbing media with anomalously low absorption, they are delayed and reshaped. This article presents experimental results and calculations for propagation of 10.6-\ensuremath{\mu} wavelength pulses through gaseous SF6{\mathrm{F}}_{6}F6​. The degeneracy of overlapping levels of SF6{\mathrm{F}}_{6}F6​ in that spectral region is important, and enables us to use a simple model to describe observed phenomena. We assume a continuous distribution of dipole moments. Results are particularly interesting in two regimes of excitation. One corresponds to very strong excitation and \ensuremath{\sim}20 absorption lengths in the medium: Pulses sharpen at their leading edge, while their front part gets absorbed. The other pertains to much lower excitation and only 2 absorption lengths: Reradiation can be distinguished and long delays result which qualitatively resemble the behavior of a two-level system in self-induced transparency. Fairly conclusive agreement is obtained between a previous theoretical treatment of a homogeneously broadened multilevel medium and experiment. The agreement is substantiated by computer calculations. In three Appendixes we present the observation of focusing effects, the theory of an experiment related to transient nutation, and some remarks on photon-echo polarization experiments in optically thick media.
The propagation of two ultrashort radiation pulses interacting via an intermediate level is analyzed by numerical integration of a system of equations describing coherent interaction between radiation and a three-level medium. It is shown that the propagation of the pulses depends strongly on their areas on entry to the medium and on the relationship between the dipole moments of transitions between neighboring levels. Substantial temporal narrowing was established for fairly high-power pulses (4π and 6π pulses) and this may be utilized to control their durations. Investigations are also made of the influence of relaxation processes, delay of pulses relative to one another on entry to the medium, and nonresonant dispersion during pulse propagation under the specified conditions.
The coherent V -configuration interaction between an optically dense resonantly-absorbing three-level medium (neon) and two ultrashort superradiance pulses with converging wave fronts is investigated experimentally and theoretically. Both separate and combined propagation of pulses with wavelengths λ 1 =614.3 nm (strong field, θ 1 ⩾ π ) and λ 3 =594.5 nm (weak field, θ 3 ≈/20) are studied. For propagation of a separate strong-field pulse, supertransparency of the absorbing medium was observed, which is associated with the generation of a soliton-like pulse at the difference frequency (Δ ν ≈1700 MHz) and the dispersion-diffraction stabilization effect. Under these conditions a weak-field pulse is completely absorbed. Combined propagation of the pulses leads to novel effects. A below-threshold pulse (weak field) was observed to pass through the absorber while interacting coherently with a strong-field pulse at a neighboring transition. It is shown theoretically that absorption of the weak pulse is reduced for two reasons: first, as a result of incoherent transparency of the resonance transition caused by emptying of the lower level by the field of the strong pulse, and second, as a result of coherent transfer of polarization between the upper levels via the two-photon processes. When the conditions for combined propagation are met, the latter mechanism ensures inversionless amplification of a weak pulse over a wide band of frequencies. In this case, the gain can even exceed the linear absorption coefficient in absolute value. A difference in propagation velocities of the weak and strong pulses was recorded experimentally, along with a shift in the carrier frequency of the weak field towards the red (≈600 MHz). A mechanism for transfer of phase modulation from a strong pulse to a weak pulse via the common lower level is discussed theoretically.
The effect of soliton-induced transparency (SOIT) that arises for a weak pulse that interacts with one of allowed transitions of inhomogeneously broadened three-level atoms with the V configuration of the levels under the action of a self-induced transparency soliton that simultaneously interacts with the adjacent transition is studied theoretically. The effect is explained by phasing of the ensemble of dipoles oscillating with different frequencies in the soliton field. The weak pulse is locked by the soliton, so that both pulses propagate with the same velocity independently of the ratio of the propagation constants. If the latter are equal, the weak pulse loses no energy; when they are different, the rate of energy loss is considerably slower than it follows from Beer’s law.