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arXiv:1002.3779 · Physical Review A

All-optical steering of light via spatial Bloch oscillations in a gas of three-level atoms

Chao Hang, V. V. Konotop

Published May 25, 2010• 20 citations
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Abstract

A standing-wave control field applied to a three-level atomic medium in a planar hollow-core photonic crystal waveguide creates periodic variations of linear and nonlinear refractive indexes of the medium. This property can be used for efficient steering of light. In this work, we study, both analytically and numerically, the dynamics of probe optical beams in such structures. By properly designing the spatial dependence of the nonlinearity, it is possible to induce long-living Bloch oscillations of spatial gap solitons, thus providing desirable change in the direction of the beam propagation without inducing appreciable diffraction. Due to the significant enhancement of the nonlinearity, such self-focusing of the probe beam can be reached at extremely weak light intensities.

DOI
10.1103/physreva.81.053849

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A standing-wave control field applied to a three-level atomic medium in a planar hollow-core photonic crystal waveguide creates periodic variations of linear and nonlinear refractive indexes of the medium. This property can be used for efficient steering of light. In this work, we study, both analytically and numerically, the dynamics of probe optical beams in such structures. By properly designing the spatial dependence of the nonlinearity, it is possible to induce long-living Bloch oscillations of spatial gap solitons, thus providing desirable change in the direction of the beam propagation without inducing appreciable diffraction. Due to the significant enhancement of the nonlinearity, such self-focusing of the probe beam can be reached at extremely weak light intensities.
The dynamics of matter waves in linear and nonlinear optical lattices subject to a spatially uniform linear force is studied both analytically and numerically. It is shown that by properly designing the spatial dependence of the scattering length it is possible to induce long-living Bloch oscillations of gap-soliton matter waves in optical lattices. This occurs when the effective nonlinearity and the effective mass of the soliton have opposite signs for all values of the crystal momentum in the Brillouin zone. The results apply to all systems modeled by the periodic nonlinear Schrödinger equation, including propagation of light in photonic and photorefractive crystals with tilted band structures.
We consider propagation of a weakly nonlinear probe light beam in a resonant three-level atomic system where an optical lattice is induced by a standing-wave control field and conditions for electromagnetically induced transparency are created. We employ a unified theory to solve the respective nonlinear system of equations in various regimes and investigate formation of spatial optical solitons and instabilities, both analytically and numerically. We show that the effect of the lattice is twofold. On the one hand it allows one to reduce the probe beam intensity necessary for observation of nonlinear effects until the level of one-photon energy, and on the other hand the lattice allows for implementation of different dynamical regimes either by simple manipulation of its parameters or by varying one- and two-photon detunings or by changing the geometry of the incident probe beam.
We study the interaction of the medium composed of three-level atoms in A configuration interacting with two laser fields: weak probe field and strong control field. The probe field enters the medium under a certain angle, and it is initially in the form of the spatial soliton, while the control field is periodically modulated. The system of optical Bloch equations is analytically solved in the stationary regime by the perturbation method in order to obtain linear and third-order nonlinear susceptibility of the medium with respect to the probe field. After a straightforward algebraic procedure, using the approximation of the slow-varying field envelope, the nonlinear Schrödinger equation for the probe field is obtained. It is numerically solved by applying the spectral Fourier split-step method. It is found that, for properly chosen values of the probe and control field detunings and control Rabi frequency, the probe field behaves as a solitary wave whose direction does not depend on the incident angle. Moreover, the regime consisting of Bloch-like oscillations can be identified. The simulation is performed by choosing the corresponding levels of Mg atoms.
We show that a weak probe light beam can form spatial solitons in an electromagnetically induced transparency (EIT) medium composed of four-level atoms and a coupling light field. We find that the coupling light beam can induce a highly controllable nonlinear waveguide and exert very strong effects on the dynamical behavior of the solitons. Hence, in the EIT medium, it is not only possible to produce spatial solitons at very low light intensities but also simultaneously control these solitons by using the coupling-light-induced nonlinear waveguide.
Raman effect in gases can generate an extremely long-living wave of coherence that can lead to the establishment of an almost perfect temporal periodic variation of the medium refractive index. We show theoretically and numerically that the equations, regulate the pulse propagation in hollow-core photonic crystal fibers filled by Raman-active gas, are exactly identical to a classical problem in quantum condensed matter physics - but with the role of space and time reversed - namely an electron in a periodic potential subject to a constant electric field. We are therefore able to infer the existence of Wannier-Stark ladders, Bloch oscillations, and Zener tunneling, phenomena that are normally associated with condensed matter physics, using purely optical means.
We propose a scheme for guiding light by the modulated electromagnetically induced transparency (EIT) in a three-level atomic system. By using a periodically modulated control field, the linear and nonlinear susceptibilities are changed cyclically for the probe field, which results in the deflection of propagation direction of the probe beam. Propagation direction/path and output position of the probe soliton in the modulated EIT medium can be controlled precisely via adjusting the modulation period of the control field. By changing its initial amplitude, the probe beam can also be guided to a desired output position in the atomic system, driven by a periodic control field. These properties offer a novel way of soliton control, based on the modulated EIT effect.