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Physical Review A

Diffractive effects in pulse propagation through a resonant medium

Sudhakar Prasad, Roy J. Glauber

Published Mar 1, 1985• 5 citations
Publisher

Abstract

The propagation of a weak optical pulse through a resonant two-level atomic medium is discussed in the paraxial approximation. Transverse propagation effects within that approximation are treated exactly by development of the method of Fresnel transforms. In particular, for a temporally short pulse with an amplitude of arbitrary transverse spatial dependence it is shown that longitudinal propagation is not affected by diffractive spreading. Thus diffraction does not attenuate the characteristic ringing of one-dimensional pulse propagation in resonant media.

DOI
10.1103/physreva.31.1575

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The propagation of a weak optical pulse through a resonant two-level atomic medium is discussed in the paraxial approximation. Transverse propagation effects within that approximation are treated exactly by development of the method of Fresnel transforms. In particular, for a temporally short pulse with an amplitude of arbitrary transverse spatial dependence it is shown that longitudinal propagation is not affected by diffractive spreading. Thus diffraction does not attenuate the characteristic ringing of one-dimensional pulse propagation in resonant media.
We theoretically predict a novel phenomenon of the diffraction-free propagation of the paraxial optical beam in the isotropic or cubic linear medium with spatial dispersion.Under the weak spatial dispersion condition,the paraxial wave equation is derived,in which there is the diffraction term with the coefficient Γ that depends on the compensation between the classic diffraction and spatial dispersion.Near the exction dipole absorption line,we can have Γ=0,then the beam propagates diffraction-freely,and its shape keeps unchangeable.Discussed are also the physical mechanism and the possible experimental candidates of crystals for the phenomenon.
In this book, we focus on the stochastic nature of pulses to achieve a more realistic description of ultra-short optical pulses affected by noise. In order to simulate ultra-short pulses, various stochastic pulse models were applied. The effects of pulse amplitude and phase fluctuations on its propagation in various linear and non-linear media were studied based on optical coherence theory. The response of the medium atoms to the applied stochastic pulses was investigated for the particular resonant case in which the pulse frequency nearly coincides with the atom resonance frequency. Analytical and numerical propagation methods were applied to explore evolutions of ultra-short stochastic pulses in the vicinity of optical resonance.
This thesis deals with the study of propagation effects experienced by weak light pulses as they propagate in atomic media driven by strong pulses. We explore both the ultra-short and long pulse regime and investigate the phenomena that arise at these different time scales. In the short pulse regime, a strongly driven two level atomic system presents transient light shifts, and non-adiabatic transitions occur between these adiabatic levels. We have studied a method to probe these light shifts in real time by propagating a weak probe through the medium. The light shifts enrich the spectrum of the probe and the probe gets shaped as a result. In this way a strongly driven two-level system can act as an active pulse shaper, and can introduce oscillations in the temporal profile of an ultra-short pulse at a time scale shorter than the pulse duration. We also show that by driving the system with two time delayed non-resonant strong fields, the non-adiabatic effects can be rendered phase dependent. This gives very sensitive phase control of the excited state population and can be used to formulate new techniques in interferometry. In the long pulse regime we present a new method of slowing light that can be realized in a double two-level system interacting with two orthogonally polarized light pulses that propagate along different axis. Spatio-temporal dependence of the total polarization induces a grating in the ground Zeeman coherence. The stronger of the two fields (the control field) is diffracted from this grating into the direction of the weak probe field compensating for the absorption of this latter field. A transparency window is thus created in the absorption spectrum of the probe leading to the slowing down of light. The transparency window exhibits characteristics similar to the one obtained by EIT (electromagnetic induced transparency) method. However, the important difference between our method and the traditional EIT method, is that ours doesn't rely on realizing dark state in the system. This may open the possibility of slowing down light in more complex atomic media. Moreover, when the linear absorptive response of the medium is cancelled in this manner, the nonlinear response becomes more important. In the situation where fields propagate in the same direction and have same frequency, two regimes have been investigated. For small optical depths, the effective susceptibility behaves as chi_lin exp[2 i phi] (with phi the phase difference between two fields). This renders phase control of the medium response, and the medium can be changed from an absorber to an amplifier, with normal or anomalous dispersion, by adjusting the relative phase phi.  In the regime of large optical thickness, phase saturation takes place and the effective susceptibility turns into chi_lin*, changing an absorber into an amplifier without effecting the dispersive response (chi_lin is linear susceptibility).
The propagation of ultrashort x-ray pulses through a resonant attenuating two-level atom medium is investigated on the basis of the temporal point-source (the Green-function) formalism. A general case of the small-area pulse (SAP) approximation of a traveling coherent wave is considered. The patterns of the SAP envelope E(t,z) and energy U(z) evolution within the medium are calculated in the cases of incident Lorentzian and exponential pulses and their dependence on the temporal bandwidth ${\mathrm{\ensuremath{\tau}}}_{\mathrm{band}}$ in comparison with the total dissipative relaxation time (lifetime) T2{\mathrm{T}}_{2}T2​ . It is shown that if ${\mathrm{\ensuremath{\tau}}}_{\mathrm{band}}$ is the same order or smaller than T2{\mathrm{T}}_{2}T2​ , the reshaping (oscillations) of the pulse envelope and/or low energy-loss effects occur in accord with the general conclusions pointed out by Crisp [Phys. Rev. A 1, 1604 (1970)] in the case of the SAP for coherent light traveling through a resonant medium. The experimental conditions for the observation of penetration effects of the SAP of x rays are discussed. Based on the theoretical study, it is found that an ultrashort x-ray pulse emitted by an ultrashort laser-produced plasma propagates through thin resonant medium foils with low energy loss.
The effect of transverse perturbations on the propagation of electromagnetic π pulses in an amplifying two-level medium is studied. The cases of quasi-monochromatic and extremely short pulses are considered. The equations describing the behavior of the transverse size of the pulse during its propagation in the medium are derived. It is shown that, if the ratios of the diffraction length to the length of dispersion spreading are smaller than certain critical values, self-focusing regimes are realized for both types of pulses. Otherwise, at a finite distance, blowup of defocusing occurs, after which the amplified pulse propagates as if it is a one-dimensional pulse, with the velocity equal to the velocity of light in vacuum. Similarities and distinctions in the dynamics of propagation of extremely short and quasi-monochromatic pulses are indicated.