Uniform Asymptotics Applied to Ultrawideband Pulse Propagation

Cartwright, Natalie A.; Oughstun, Kurt E.

doi:10.1137/050635833

Cited by 38 publications

(43 citation statements)

References 20 publications

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“…They concluded that for a sufficiently fast input pulse, a transient forerunner, now known as Sommerfeld-Brillouin (SB) precursor, travels with the velocity of light in vacuum, followed by the main pulse traveling at group velocity. Optical precursors have been studied extensively both theoretically [4][5][6][7][8][9] and experimentally [10][11][12][13][14]. Precursor behaviors have been reported in γ rays [15], microwaves [16], sound [17,18], optical waves [10][11][12], and single-photon correlations [13,14].…”

Section: Introductionmentioning

confidence: 99%

Optical coherent transients in cold atoms: From free-induction decay to optical precursors

et al. 2010

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We report theoretical and experimental studies of the propagation of a square-modulated laser pulse through a laser-cooled atomic ensemble of two-level absorbers, as well as through a three-level system with electromagnetically induced transparency. We find that the transmission characteristics over a wide range of optical depth can be fully accounted for as optical coherent transients excited by the wide spectral content of the square-modulated optical pulse. We show that both time-domain atom-field coupled equations and frequency-domain linear dispersion theory give precisely the same description of the optical transients at a weak power limit. At low optical depth with moderate absorption, resonant excitation dominates and free-induction decay (FID) contributes mostly to the transient field. At high optical depth when absorption and propagation effects become significant, lossless optical precursors start to dominate the transient response. By varying the optical depth from 0 to 45, we observe that optical transients evolve gradually from FID to optical precursors. We thus show that FID and optical precursors, which have been considered as two different optical transients for many decades, can be unified within a single theoretical frame and they are the manifestations of the same physical process in two different regimes.

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Section: Introductionmentioning

confidence: 99%

Optical coherent transients in cold atoms: From free-induction decay to optical precursors

et al. 2010

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“…This front, in the form of a transient wave now known as the Sommerfeld-Brillouin precursor, is then followed by the main pulse traveling at its group velocity. This conclusion, while qualitatively correct, was found to be quantitatively incorrect, particularly on greatly underestimating the amplitude and duration of the precursors [3]. With the intriguing possibility that precursors might be useful as optical probes of biological tissues or in underwater communication [4,5], there has been renewed interest in this problem.…”

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confidence: 99%

Optical Precursors with Electromagnetically Induced Transparency in Cold Atoms

et al. 2009

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We report the observation of Sommerfeld-Brillouin optical precursors generated from a long squaremodulated laser pulse propagating through a cold atomic ensemble with electromagnetically induced transparency. The optical depth ( 0 L) of the medium can be varied from 0 up to 50. We demonstrated that the step-on rising and step-off falling edges propagate with the speed of light in vacuum without a slow light effect. At high 0 L, the precursor is separated from the delayed main pulse at the rising edge, while at the falling edge, we observe damped oscillatory structures resulting from the interference between the precursor and main field.

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“…We present it here to illustrate the intermediate case with (c 0 /l c )/ω c = O(1). We remark moreover that this model has common features with the Lorentz dielectric model of the classical situation analyzed for precursors in homogeneous dispersive media [7]. The phase function in (33) is now…”

Section: Appendix a Mixing And Exponentially Decorrelating Mediamentioning

confidence: 99%

“…Following [7] we consider in this paper a source function of the form of a step function modulated sine wave…”

Section: Fractional Precursorsmentioning

confidence: 99%

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Fractional precursors in random media

Garnier¹,

Sølna²

2010

Waves in Random and Complex Media

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When a broadband pulse penetrates into a dissipative and dispersive medium, phase dispersion and frequency-dependent attenuation alter the pulse in a way that results in the appearance of a precursor field with an algebraic decay. We derive here the existence of precursors in nondispersive, non-dissipative, but randomly heterogeneous and multiscale media. The shape of the precursor and its fractional power law decay with propagation distance depend on the random medium class. Three principal scattering precursor classes can be identified : (i) In exponentially decorrelating random media, and more generally in mixing random media, the precursor has a Gaussian shape and a peak amplitude that decays as the square root of the inverse of the propagation distance. (ii) In short-range correlation media, with rough multiscale medium fluctuations, the precursor has a skewed shape with a tail that exhibits an anomalous power law decay in time and a peak amplitude that exhibits an anomalous power law decay with propagation distance, both of which depend on the Hurst exponent that characterizes the roughness of the medium. (iii) In long-range correlation media with long-range memory, the situation mimics that of class (ii), but with modified power laws.

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Uniform Asymptotics Applied to Ultrawideband Pulse Propagation

Cited by 38 publications

References 20 publications

Optical coherent transients in cold atoms: From free-induction decay to optical precursors

Optical coherent transients in cold atoms: From free-induction decay to optical precursors

Optical Precursors with Electromagnetically Induced Transparency in Cold Atoms

Fractional precursors in random media

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