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Physical Review A

Two-way transparency in the light-matter interaction: Optical precursors with electromagnetically induced transparency

Heejeong Jeong, Shengwang Du

Published Jan 8, 2009• 37 citations
Publisher

Abstract

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 $c$ 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.

DOI
10.1103/physreva.79.011802

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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.
We theoretically study the linear propagation of a stepwise pulse through a dilute dispersive medium when the frequency of the optical carrier coincides with the center of a natural or electromagnetically induced transparency window of the medium (slow-light systems). We obtain fully analytical expressions of the entirety of the step response and show that, for parameters representative of real experiments, Sommerfeld-Brillouin precursors, main field and second precursors (``postcursors'') can be distinctly observed, all with amplitudes comparable to that of the incident step. This behavior strongly contrasts with that of the systems generally considered up to now.
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.
Optical Sommerfeld-Brillouin precursors significantly ahead of a main field of comparable amplitude have been recently observed in an opaque medium with an electromagnetically induced transparency window [Wei et al., Phys. Rev. Lett. 103, 093602 (2009)]. We theoretically analyze in this article the somewhat similar results obtained when the transparency is induced by the propagating field itself and we establish an approximate analytic expression of the time delay of the main-field arrival, which fits fairly well the result obtained by numerically solving the Maxwell-Bloch equations.
This thesis investigates the result of modulation schemes in electromagnetically induced transparency (EIT) in rubidium vapor. Through the process of EIT, a control beam can be used to change the optical properties of a medium experienced by a probe field, generating a transparency window. The corresponding change in index of refraction results in slowed group velocity while the beam propagates through the medium. Modulation is used to transmit a message signal through a medium. In classical systems, this entails converting data into a radio frequency by adding a message to an electronic or optical carrier signal. The properties of EIT, light-slowing, and their impacts on a probe pulse with modulation will be confirmed through a detailed semi-classical analysis and by experimental observation.