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arXiv:1011.3871 · Physical Review A

Arrayed and checkerboard optical waveguides controlled by the electromagnetically induced transparency

Yongyao Li, Boris A. Malomed, Mingneng Feng, Jianying Zhou

Published Dec 10, 2010• 31 citations
arXivHTMLPDF

Abstract

We introduce two models of quasidiscrete optical systems: an array of waveguides doped by four-level $N$-type atoms, and a nonlinear checkerboard pattern, formed by doping with three-level atoms of the $\ensuremath{\Lambda}$-type. The dopant atoms are driven by external fields, to induce the effect of the electromagnetically induced transparency (EIT). These active systems offer advantages and additional degrees of freedom, in comparison with ordinary passive waveguiding systems. In the array of active waveguides, the driving field may adjust linear and nonlinear propagation regimes for a probe signal. The nonlinear checkerboard system supports the transmission of stable spatial solitons and their ``fuzzy'' counterparts, straight or oblique.

DOI
10.1103/physreva.82.063813

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We introduce two models of quasidiscrete optical systems: an array of waveguides doped by four-level NNN-type atoms, and a nonlinear checkerboard pattern, formed by doping with three-level atoms of the \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type. The dopant atoms are driven by external fields, to induce the effect of the electromagnetically induced transparency (EIT). These active systems offer advantages and additional degrees of freedom, in comparison with ordinary passive waveguiding systems. In the array of active waveguides, the driving field may adjust linear and nonlinear propagation regimes for a probe signal. The nonlinear checkerboard system supports the transmission of stable spatial solitons and their ``fuzzy'' counterparts, straight or oblique.
We introduce a model of resonant optical systems: a waveguide array doped periodically with resonant four-level N-type atoms. The dopant atoms are driven by external fields which induce the effect of the electromagnetically induced transparency (EIT). In this resonant waveguide arrays (RWA) system, the optical field propagates as quasi-discrete diffraction, breathing beam or stable spatial soliton when different initial amplitude and width of the probe are given. The critical values representing these transformations are obtained by the numerical simulations. In a further study of the oblique incidence, the soliton loses a portion of its energy while a kick (i.e., a transverse wave vector) is initially introduced. As the value of the kick becomes larger than a critical value, the soliton collapses.
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.
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.
We propose a scheme to realize the coherent control of optical soliton propagation and interaction in a three level Λ type electromagnetically induced transparency system with the control field being spatially modulated. We show that the spatial perturbation of the control field has no influence on the linear propagation properties and self-phase modulation of the probe field but can produce an equivalent external potential to affect the nonlinear propagation of the probe field. For single soliton propagation, we realize the transmission and trapping of optical solitons via external potential. For double soliton interaction, we realize the coherent control of attractive and repulsion interactions of two optical solitons and design an XNOR logical operation. Finally, for the triple soliton incident case, based on the coherent control of interaction between three solitons via external potential, we design a beam selector. The results obtained here are useful not only for the deep understanding of optical soliton interaction but also for applications in all optical quantum information processing.
We have studied nonlinear quantum optical effects in a doubly driven four-level atomic system in a homogeneously broadened regime. On application of two strong fields the system can be made to display double electromagnetically induced transparency (EIT) because of constructive quantum interference giving rise to nonlinear absorption at three-photon resonance condition. This fact may be used to obtain other phenomena like the effect of photon switching in a pulsed regime and large cross phase modulation (XPM) effect. We also show that the behaviour of spatial modulation of transparency of the weak probe beam in a three-level system interacted with a strong standing wave pump field can be dramatically changed in our four-level ladder type system. Here, strong coupling field acting on the uppermost transition is represented by a standing wave whereas strong pump and weak probe fields acting successively on the lower transitions are represented by travelling waves. The effect of double EIT on nonlinear light generation based on the four-wave-mixing (FWM) technique is also investigated. We have examined that the four wave mixing efficiency can be effectively controlled by varying the strength of the pump field.
Using density matrix eqution, the absorption and dispersion properties of a A-type four-level system driven by coherent fields are investigated. The result obtained by means of numerical method indicates that by adjusting the intensity of Rabi frequencies of the coherent field in the steady state, three, double or single electromagnetically induced transparency (EIT) can appear explicitly in this system. And the explanations of these phenomena are given by using the dressed states. In the three EIT, the location of transparent windows can be manipulated by controlling the detuning of the driving field. What's more, it is also found that the medium shows a large refractive index at each transparency window, and the group velocity of the probe laser can be enhanced.