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Optics Letters

Nonlinear propagation of ultraslow pulses in media with electromagnetically induced transparency

Jing Cheng, Shensheng Han, YiJing Yan

Published Oct 1, 2005• 6 citations
Publisher

Abstract

The nonlinear behavior of a probe pulse propagating in a medium with electromagnetically induced transparency is studied both numerically and analytically. A new type of nonlinear wave equation is proposed in which the noninstantaneous response of nonlinear polarization is treated properly. The resulting nonlinear behavior of the propagating probe pulse is shown to be fundamentally different from that predicted by the simple nonlinear Schrödinger-like wave equation that considers only instantaneous Kerr nonlinearity.

DOI
10.1364/ol.30.002638

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The nonlinear behavior of a probe pulse propagating in a medium with electromagnetically induced transparency is studied both numerically and analytically. A new type of nonlinear wave equation is proposed in which the noninstantaneous response of nonlinear polarization is treated properly. The resulting nonlinear behavior of the propagating probe pulse is shown to be fundamentally different from that predicted by the simple nonlinear Schrödinger-like wave equation that considers only instantaneous Kerr nonlinearity.
We study the ultraslow optical solitons in a resonant three-level atomic system via electromagnetically induced transparency under a density-matrix (DM) approach. The results of linear and nonlinear optical properties are compared with those obtained by using an amplitude variable (AV) approach. It is found that the results for both approaches are the same in the linear regime if the corresponding relations between the population-coherence decay rates in the DM approach and the energy-level decay rates in the AV approach are appropriately imposed. However, in the nonlinear regime there is a small difference for the self-phase modulation coefficient of the nonlinear Schrödinger equation that governs the time evolution of probe pulse envelope. All analytical predicts are checked by numerical simulations.
We develop a fully quantum treatment of electromagnetically induced transparency (EIT) in a vapor of three-level ΛΛΛ-type atoms. Both the probe and coupling lasers with arbitrary intensities are quantized, and treated on the same footing. In addition to reproducing known results on ultraslow pulse propagation at the lowest order in the ratio of their Rabi frequencies, our treatment uncovers that the atomic medium with EIT exhibits giant Kerr as well as higher order non-linearities. Enhancement of many orders of magnitude is predicted for higher-order refractive-index coefficients.
We present a simple model for the nonlinear optical response of atomic gases for pulses with center wavelengths in the transparency region and peak fields for which ionization is not prevalent. By comparing with simulations based on the Schrödinger equation for a hydrogen atom we demonstrate that the model accurately captures the dispersion of the nonlinear polarization as well as noninstantaneous effects for a variety of photon energies and also a two-color pulse. Our approach should be of utility in simulating near- and mid-infrared pulse propagation in dielectric media for which extreme nonlinear effects can arise.
We study electromagnetically induced transparency (EIT) and nonlinear pulse propagation in a resonant atomic gas confined in a microwaveguide. We find that the quantum-interference effect in this system can be greatly enhanced due to the reduction of the mode volume of the optical field. In particular, compared with atomic gases in free space, the EIT transparency window in the present confined system can be much wider and deeper, the group velocity of the probe field can be much slower, and the Kerr nonlinearity of the system can be much stronger. We show that a more efficient production of ultraslow optical solitons in the present system may be achieved with much slower propagating velocity and lower generation power. Features of EIT and pulse propagation in the present system are very promising for practical applications in optical information processing and transmission.
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.
By solving the self-consistent system of Maxwell and density-matrix equations in the case where the time of relaxations to the ground state is much shorter than the pulse duration we derive an analytical solution for the probe pulse propagation. We obtain an excellent consistency of our analytical solution with direct numerical integration. We investigate the asymptotic behavior of analytical solution and show that under certain conditions it passes to the well-known dark-state polariton propagation regime. We analyzed the dynamics of propagation and, in particular, explain the fact that in the well-known experiments only fractions of pulses were stored.