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Journal of Shaanxi Normal University

Propagation of laser pulse in a three-level Λ-type medium

Li Yongfang

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

By choosing special temporal profiles of laser pulses,propagation equations which govern the propagation of them in a three-level Λ-type medium is simplified.Some explicit expressions of analytical solutions to the propagation equations are obtained.The physical mechanism of spatial and temporal evolution of the two laser pulses is analyzed analytically.It is shown that the shape of a laser pulse can be manipulated by group velocities or boundary conditions of the propagation equations.

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By choosing special temporal profiles of laser pulses,propagation equations which govern the propagation of them in a three-level Λ-type medium is simplified.Some explicit expressions of analytical solutions to the propagation equations are obtained.The physical mechanism of spatial and temporal evolution of the two laser pulses is analyzed analytically.It is shown that the shape of a laser pulse can be manipulated by group velocities or boundary conditions of the propagation equations.
The propagation of a weak-field pulse through a medium of three-level atoms is considered. Each atom has a $\ensuremath{\Lambda}$-type level scheme in which the two lower levels are stable. A strong control field drives one of the electronic transitions while the signal field drives the coupled transition under conditions where EIT (electromagnetically induced transparency) is usually operative. The input pulse is slowed and compressed as it enters the medium, adiabatically following the EIT solution. However, if the control field is changed suddenly when the pulse is in the medium, the signal field is transformed into two pulses, one of which propagates as a normal EIT pulse and the other with a different speed and an amplitude that oscillates in time. The temporal oscillations are transformed into both spatial and temporal oscillations as the pulse exits the medium. An analytic expression is derived for the pulse intensity which provides a good approximation to the exact result at all times. It is shown that the oscillating component of the exiting pulse can be spatially compressed in comparison with the input pulse.
The inverse scattering transform method is used in a study of the evolution of light pulses in an initially inverted three-level medium of the Λ type. An asymptotic solution describing the profile of the first spike is obtained for small-area priming pulses. It is shown that this asymptote is determined entirely by the initial populations of the lower levels and by the profile of the priming pulses. A special case of this problem is the propagation of two-component light in a laser amplifier using the degenerate J = 0–J = 1 transition.
We study the features of spatial and temporal evolution of two powerful short different-wavelength laser pulses interacting with optical dense three-level Lambda-type medium under condition of coherent population trapping for the general case of unequal transition oscillator strengths. The pulses are simultaneously sent into an atom. The durations of probe and coupling pulses T1,2T_{1,2}T1,2​ (T2>T1T_2>T_1T2​>T1​) are supposed to be shorter than all relaxation times in the medium. We present analytical and numerical solutions of the self-consistent set of coupled Schr\\"{o}dinger equations and reduced wave equations in adiabatic limit with taking into account the first non-adiabatic correction. The adiabaticity criterion with account of pulse propagation is studied. We find that propagation dynamics depends on the relationship between the transition oscillator strengths. It is shown that at the initial stage of propagation the envelopes of the pulses slightly change along the length of the medium. This distance can be large compared to one-photon resonant absorption length of the medium. Also it is possible a regime of complete reemitting of the probe pulse into the coupling one during propagation. A spatial evolution of the atomic Raman coherence is investigated in detail too.