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IEEE Journal of Quantum Electronics

Coherent absorption in a homogeneously broadened medium

Lee E. Estes, D. Eteson, Lorenzo M. Narducci

Published Sep 1, 1970• 8 citations
Publisher

Abstract

An investigation of the propagation properties of a short pulse in a resonant absorber with a homogeneously broadened transition is presented with two main questions in mind: 1) the influence of the input pulse area on the transitory regime and on the steady-state propagation; 2) the effects of atomic coherence on the pulse shaping and the time delay of the leading edge of the pulse. The transitory regime of a propagating pulse is investigated and the stability of some asymptotic wave form confirmed. As expected, the transversal relaxation mechanism affects critically the major features of the coherent interaction. A detailed analysis of this problem is also presented.

DOI
10.1109/jqe.1970.1076528

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It is shown that the absorbtion of a weak field in a thick resonant absorber is a reversible process even in the case of the homogeneous broadening of the absorption line. As an example, the propagation of a long rectangular pulse with sharp edges in an optically dense resonant medium is studied theoretically in the linear response approximation. Transient nutation (TN), free induction decay (FID), and transients, induced by the phase switch of the incident pulse, are considered. It is shown that in exact resonance the amplitude of FID increases with the length of the medium. FID arises due to the scattered radiation field (dipoles ringing). In a thick medium the scattered field is almost of the same amplitude but opposite in phase with the incident radiation field. Both fields interfere destructively to produce what is seen as radiation damping at the output of the medium. The scattered field needs time to develop. Therefore, the leading edge of the pulse is not absorbed, demonstrating temporal transparency followed by TN. Phase shift (180${}^{\ensuremath{\circ}}$) of the pulse brings the incident pulse in phase with the scattered radiation. Constructive interference of the pulse with the scattered radiation field produces a short pulse with an amplitude that is two times larger than the amplitude of the incident pulse. If the input pulse is detuned from resonance, for a particular detuning and optical thickness of the medium the amplitude of the transient pulse, induced by the phase shift, is nearly three times larger than the amplitude of the incident pulse. This is explained by the interference of the scattered field, the phase-shifted input field, and the slowly propagating part of the pulse, developed before the phase shift.

Physical Review A•Feb 21, 2012•13 citations
An investigation of the propagation properties of a short pulse in a resonant absorber with a homogeneously broadened transition is presented with two main questions in mind: 1) the influence of the input pulse area on the transitory regime and on the steady-state propagation; 2) the effects of atomic coherence on the pulse shaping and the time delay of the leading edge of the pulse. The transitory regime of a propagating pulse is investigated and the stability of some asymptotic wave form confirmed. As expected, the transversal relaxation mechanism affects critically the major features of the coherent interaction. A detailed analysis of this problem is also presented.
The optical density of a resonant medium significantly affects the output signal in time resolved nonlinear optical interactions. The resonant interaction with a medium reshapes any propagating short pulse, and the mutual interaction of several such pulses, as in four-wave mixing, must be treated self-consistently. We present a theoretical framework for the proper handling of the propagation of all pulses, input as well as generated, in the small area limit. For optically thick resonant absorbers, negative time delay signals are observed, and the apparent decay rate of the induced polarization is faster than the rate observed for thin samples. We experimentally measure degenerate four-wave mixing in an atomic medium as an example, and demonstrate the quality of the theoretical model by the excellent fit to measured signals over several orders of magnitude. The improved understanding enables us to provide a simple, but surprisingly accurate, estimate for the apparent decay rate in homogeneously broadened optically thick media: If the absorption is given by \ensuremath{\alpha}, the propagation length is L, and the transverse relaxation time is T2{\mathit{T}}_{2}T2​, the apparent decay rate 2/Ta{\mathit{T}}_{\mathit{a}}Ta​ of a time resolved four-wave mixing signal is given by 2/Ta{\mathit{T}}_{\mathit{a}}Ta​=(2/T2{\mathit{T}}_{2}T2​)(1+\ensuremath{\alpha}L/2).
The initial value problem for the propagation of a pulse through a resonant two-level optical medium is solved by the inverse scattering method. In general, an incident pulse decomposes not only into a special class of pulses to which the medium is transparent but also yields radiation which is absorbed by the medium. In this respect ``this problem'' has properties markedly different from other dispersive and reversible wave phenomena some of which are tractable by the inverse scattering method. Indeed, it is remarkable that in the present case the method still applies. In particular, we show that, while there are an infinite number of local conservation laws, the integrated densities, and in particular the energy, are only conserved for a very special class of initial conditions. The theoretical results obtained are in close agreement with all the qualitative features observed in the experiments on coherent pulse propagation. Finally, we also show that causality is preserved. Two new and novel features are introduced and briefly discussed. First, we show that if the homogeneous broadening effect is a function of position in the medium, the pulses may speed up and slow down accordingly, without losing their permanent identities. Second, we have found a new kind of solution mode corresponding to a proper eigenvalue of the scattering problem which is not a bound state.
The observation of self-induced transparency on the magnetic dipole 2P1/2 F = 3 5 2P3/2 F′ = 4, j MF = 0 transition of atomic iodine has been extended to cover pulse areas up to 4 ~. Laser pulses of various areas have been shown to be reshaped considerably by the coherent field-matter interaction. Pulses have been found to narrow by two-thirds for a 3 ~ -pulse. The lower limit of the homogeneous relaxation time T′2 of atomic iodine vapour is determined from pulse broadening and transmission measurements.
We present a numerical study of the nonsteady state pulse propagation in a resonant inhomogeneously broadened absorber embedded in a dielectric medium with a Kerr-type nonlinearity. We abandon the a priori assumption for the existence of steady state solutions and examine the problem from a more physical point of view, i.e., we study the way in which the pulse actually propagates in the resonant Kerr medium and whether it eventually evolves toward a steady state. We find that the individual atomic dipoles are dephased and that their evolution depends on detunings. We believe that this is the reason for small energy losses which deny the attainment of a truly steady state pulse.
It is shown that the absorbtion of a weak field in a thick resonant absorber is a reversible process even in the case of the homogeneous broadening of the absorption line. As an example, the propagation of a long rectangular pulse with sharp edges in an optically dense resonant medium is studied theoretically in the linear response approximation. Transient nutation (TN), free induction decay (FID), and transients, induced by the phase switch of the incident pulse, are considered. It is shown that in exact resonance the amplitude of FID increases with the length of the medium. FID arises due to the scattered radiation field (dipoles ringing). In a thick medium the scattered field is almost of the same amplitude but opposite in phase with the incident radiation field. Both fields interfere destructively to produce what is seen as radiation damping at the output of the medium. The scattered field needs time to develop. Therefore, the leading edge of the pulse is not absorbed, demonstrating temporal transparency followed by TN. Phase shift (180${}^{\ensuremath{\circ}}$) of the pulse brings the incident pulse in phase with the scattered radiation. Constructive interference of the pulse with the scattered radiation field produces a short pulse with an amplitude that is two times larger than the amplitude of the incident pulse. If the input pulse is detuned from resonance, for a particular detuning and optical thickness of the medium the amplitude of the transient pulse, induced by the phase shift, is nearly three times larger than the amplitude of the incident pulse. This is explained by the interference of the scattered field, the phase-shifted input field, and the slowly propagating part of the pulse, developed before the phase shift.