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Acta Physica Sinica

The propagation properties of broadband pulse

Li Qin, Guo Hong

Published Jan 1, 2011• 4 citations
Publisher

Abstract

The propagation of broadband pulse in a medium with electromagnetically induced transparency (EIT) was studied. The results show that if the carrier frequency of pulse is exactly tuned to the center of the transparency window, and the pulse spectrum is broader than transparency window, the pulse is temporally broadened and the delay effect is significant. If the carrier frequency of pulse the is exactly tuned to the region of absorption, and the pulse spectrum is wide with respect to the width of absorption line, the pulse begins to distort after a certain distance and is split into two parts at last. The peak value depends not only on the frequency and intensity of the coupling field, but also on the length of the sample. Under appropriate conditions, strong and time domain narrowed pulse can be obtained in the output light.

DOI
10.7498/aps.60.054204

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arXiv:1406.0245•Physical Review A•Jan 19, 2016•18 citations
The propagation of broadband pulse in a medium with electromagnetically induced transparency (EIT) was studied. The results show that if the carrier frequency of pulse is exactly tuned to the center of the transparency window, and the pulse spectrum is broader than transparency window, the pulse is temporally broadened and the delay effect is significant. If the carrier frequency of pulse the is exactly tuned to the region of absorption, and the pulse spectrum is wide with respect to the width of absorption line, the pulse begins to distort after a certain distance and is split into two parts at last. The peak value depends not only on the frequency and intensity of the coupling field, but also on the length of the sample. Under appropriate conditions, strong and time domain narrowed pulse can be obtained in the output light.
A simple analytical solution for the propagation of a weak Gaussian pulse in a dense absorptive medium with electromagnetically induced transparency is found. This solution is applied to the analysis of three regimes: (1) and (2) the pulse spectrum is narrower than the transparency window [which is narrow (1) or wide (2) with respect to the width of the absorption line] and (3) the pulse spectrum is broader than the transparency window. It is shown that the pulse maintains its area in all three regimes and maintains its Gaussian shape but narrows in spectrum in regime 1. In regime 2, the pulse begins to distort after a certain distance. In regime 3, the pulse is split into two parts. One part is an adiabatic part with a spectrum defined by the effective width of the transparency window for a thick medium and the other is an oscillating nonadiabatic part of short duration. The adiabatic part propagates slowly and the nonadiabatic part propagates with a velocity close to the speed of light. Thus in regime 3, the medium acts as a time-frequency filter, separating the narrow and wide spectrum components of the pulse in time at the output of the absorber.
This report shows that the electromagnetically-induced transparency (EIT) window can be used as a time-to-frequency filter for the probe pulse whose spectrum is much broader than the width of the EIT window. This study demonstrates that the narrow spectral region of the pulse, coincident with the EIT window, develops in a long Gaussian pulse with slow group velocity. An analytical theory is developed describing the propagation of a small amplitude pulse through an optically dense absorptive medium with a narrow EIT window.
The influence of a phase-modulated control field on the phenomenon of electromagnetically induced transparency (EIT) is investigated theoretically. We show that the phase modulation changes the dispersive properties of the medium considerably since it results in temporal oscillations of the transparency window in frequency space. This is in marked contrast to the standard EIT setup, where the transparency window is fixed and determined by the two-photon resonance condition. In particular, we find that the phase modulation enables the propagation of probe pulses with disjoint frequency spectra at different times and allows the shifting of the central frequency of a probe pulse almost without distortion of its shape. We employ the time-dependent susceptibility of the medium to explain and analyze our results and demonstrate that this concept yields qualitative as well as quantitative agreement with the numerical integration of Maxwell-Bloch equations. Our theoretical model can be applied to other media with time-dependent susceptibilities.
The absorption and dispersion properties of an N-type four-level system with Doppler(broadening) effect were investigated.In this system we considered two coherent fields and a probe field.When the second coherent field is absent,this system is a single three-level configuration,and the absorption line is just one clear electromagnetically induced transparency(EIT) window.While the second coherent field exists,there are two EIT windows which become wide and deep with the(coherent) intensity increasing.The position width and absorbance of the transparency windows can be manipulated by adjusting the detuning of the driving field.In addition,we also found that the medium shows a large refractive index at each transparency window,and the group velocity of the probe laser can be reduced.
Electromagnetically induced transparency (EIT) has been proposed as a way to greatly enhance cross-phase modulation, with the possibility of leading to few-photon-level optical nonlinearities [Schmidt and Imamoglu, Opt. Lett. 21, 1936 (1996)]. This enhancement grows as the transparency window width, ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{EIT}}$, is narrowed. Decreasing ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{EIT}}$, however, has been shown to increase the response time of the nonlinear medium. This suggests that, for a given pulse duration, the nonlinearity would diminish once the window width became narrower than this pulse bandwidth. We show that this is not the case: the peak phase shift saturates but does not decrease. We show that in the regimes of most practical interest---narrow EIT windows perturbed by short signal pulses---the enhancement offered by EIT is not only in the magnitude of the nonlinear phase shift but also in its increased duration. That is, for the case of signal pulses much shorter (temporally) than the inverse EIT bandwidth, the narrow window serves to prolong the effect of the passing signal pulse, leading to an integrated phase shift that grows linearly with $1/{\mathrm{\ensuremath{\Delta}}}_{\mathrm{EIT}}$; this continued growth of the integrated phase shift improves the detectability of the phase shift, in principle, without bound. For many purposes, it is this detectability which is of more interest than the absolute magnitude of the peak phase shift. We present analytical expressions based on a linear time-invariant model that accounts for the temporal behavior of the cross-phase modulation for several parameter ranges of interest. We conclude that in order to optimize the detectability of the EIT-based cross-phase shift, one should use the narrowest possible EIT window and a signal pulse that is as broadband as the excited-state linewidth and detuned by half a linewidth.