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Journal of Optics

Optical precursors with finite rise and fall time

J. F. Chen, M. M. T. Loy, George K. Wong, Shengwang Du

Published Sep 24, 2010• 9 citations
Publisher

Abstract

We report results of both theoretical and experimental studies of optical precursors generated from a square-modulated probe laser pulse having a finite rise and fall time and propagating through a cold atomic ensemble, under the conditions of either a two-level Lorentz absorber system or a three-level system with electromagnetically induced transparency (EIT). Because of the finiteness of the rise (and fall) time, the precursor signal is observed to decrease with increasing optical depth (α 0 L ). We find that the precursor can experience little absorption even at high optical depth if the rise (and fall) time is sufficiently short. At an optical depth of α 0 L = 42, the normalized precursor peak intensity is observed to increase from 9% to 27% when the rise (and fall) time is shortened from 7 to 3 ns. Meanwhile, we reaffirm that there is no violation of Einstein's causality principle in light propagation through both slow and fast light media. In the EIT system with high optical depth, the main field propagates with a subluminal group velocity and it is separated from the precursor. In the two-level system, the effect of negative group velocity in the anomalous dispersion regime is observed, but we detect no advancement in the rising edge of the precursors. In both cases, the leading edges of the precursors show no detectable delay to that through vacuum.

DOI
10.1088/2040-8978/12/10/104010

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We report results of both theoretical and experimental studies of optical precursors generated from a square-modulated probe laser pulse having a finite rise and fall time and propagating through a cold atomic ensemble, under the conditions of either a two-level Lorentz absorber system or a three-level system with electromagnetically induced transparency (EIT). Because of the finiteness of the rise (and fall) time, the precursor signal is observed to decrease with increasing optical depth (α 0 L ). We find that the precursor can experience little absorption even at high optical depth if the rise (and fall) time is sufficiently short. At an optical depth of α 0 L = 42, the normalized precursor peak intensity is observed to increase from 9% to 27% when the rise (and fall) time is shortened from 7 to 3 ns. Meanwhile, we reaffirm that there is no violation of Einstein's causality principle in light propagation through both slow and fast light media. In the EIT system with high optical depth, the main field propagates with a subluminal group velocity and it is separated from the precursor. In the two-level system, the effect of negative group velocity in the anomalous dispersion regime is observed, but we detect no advancement in the rising edge of the precursors. In both cases, the leading edges of the precursors show no detectable delay to that through vacuum.
We report the observation of Sommerfeld-Brillouin optical precursors generated from a long square-modulated laser pulse propagating through a cold atomic ensemble with electromagnetically induced transparency. The optical depth (alpha(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 alpha(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.
Optical precursors were first studied by Sommerfield and Brillouin in 1914 to resolve the apparent contradictions between fast light propagation and the theory of relativity. They showed theoretically that the front edge of a step-modulated pulse does not interact with the medium and always travels at c because the dispersive material has a finite response time to the optical pulse. The past experimental studies of precursors in classical pulse propagation were always focused on an opaque medium with single or multiple Lorentz absorption lines. In these cases, the precursor signal cannot be separated from the main pulse or otherwise the main field is absorbed. However, the electromagnetically induced transparency (EIT) technique was successfully used to separate precursors from the main pulse due to the slow-light effect in cold atoms. The EIT refers to the absorption suppression or elimination of a probe field through atomic coherence in a certain medium dressed by a strong coupling field. In this paper, a four-level double-lambda atomic system with two upper states coupled to the excited state is explored to separate optical precursors from a square-modulated laser pulse with the effect of spontaneously generated coherence (SGC). The SGC effect occurs in the process of spontaneous emission, in which the atom decays from closely placed upper levels to a single ground level. The quantum interference between the decay channels takes place, which leads to decay induced transparency, thus enhancing the Kerr nonlinearity and amplification without inversion. With the assistance of spontaneously generated coherence, an EIT window appears with steep normal dispersion when the trigger field is far from resonance. Then we can obtain the optical precursors which are separated from the main pulse due to the slow-light effects in the EIT window. In the absence of SGC, the main pulse is absorbed by an opaque medium with Lorentz absorptive lines, so the slow-light effect could not take place. In addition, we obtain the stacked optical precursors with the input probe field amplitude or phase modulated by designing a series of square pulses. For the amplitude modulation case, the peak power reaches about 4.5 times that of the input pulse. With the phase modulation we obtain a transient pulse with a peak power of 14 times that of the input, as a result of constructive interference between the stacked precursors and main field. We expect these findings to be instructive in devising optical devices for optical communication, detection and medical imaging among other applications.
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.
We theoretically study classical step-modulated pulse propagation in an optically thick medium with electromagnetically induced transparency (EIT) using a fast Fourier transform and a proposed hybrid-asymptotic analysis. The 100% transmitted leading edge traveling at ccc consists of Sommerfeld-Brillouin precursors. The main signal, falling inside of the narrow EIT window, experiences a steep dispersion and slow group velocity. We suggest active control of the precursors and main signal separately by adjusting the parameters of the medium and incident pulse.