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Physical Review A

Electromagnetically induced waveguiding in double- Λ systems

Hagay Shpaisman, A. D. Wilson‐Gordon, Harry Friedmann

Published Apr 12, 2005• 47 citations
Publisher

Abstract

Near the threshold for electromagnetically induced transparency (EIT) or coherent population trapping (CPT), two-photon-resonance-enhanced self-focusing of a $\ensuremath{\Lambda}$ system can be exploited to induce spatial confinement in a second, diffracting $\ensuremath{\Lambda}$ system. The diffracting $\ensuremath{\Lambda}$ system is characterized by parameters below the EIT or CPT threshold, and the two $\ensuremath{\Lambda}$ systems must be coupled to form a closed-loop double-$\ensuremath{\Lambda}$ system. The waveguiding effect is shown to be strongly phase dependent, indicating that it derives from the phase-dependent effective third-order susceptibility rather than the phase-independent effective first-order susceptibility, as is the case in previously studied systems. We also show that when the second $\ensuremath{\Lambda}$ system initially involves only a single laser beam, the loop is completed by the efficient generation of radiation at the four-wave-mixing frequency, within a propagation distance much shorter than the diffraction length. Both the applied and generated fields exhibit electromagnetically induced waveguiding.

DOI
10.1103/physreva.71.043812

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Near the threshold for electromagnetically induced transparency (EIT) or coherent population trapping (CPT), two-photon-resonance-enhanced self-focusing of a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ system can be exploited to induce spatial confinement in a second, diffracting \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ system. The diffracting \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ system is characterized by parameters below the EIT or CPT threshold, and the two \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ systems must be coupled to form a closed-loop double-\ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ system. The waveguiding effect is shown to be strongly phase dependent, indicating that it derives from the phase-dependent effective third-order susceptibility rather than the phase-independent effective first-order susceptibility, as is the case in previously studied systems. We also show that when the second \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ system initially involves only a single laser beam, the loop is completed by the efficient generation of radiation at the four-wave-mixing frequency, within a propagation distance much shorter than the diffraction length. Both the applied and generated fields exhibit electromagnetically induced waveguiding.
This study discusses electromagnetically induced waveguiding in double-/spl lambda/ systems. The waveguiding effect is shown to be strongly phase dependent, indicating that it derives from the phase-dependent effective third-order susceptibility rather than the phase-independent effective first-order susceptibility, as is the case in previously studied systems. This work also shows that when the second /spl Lambda/ system initially involves only a single laser beam, the loop is completed by the efficient generation of radiation at the four-wave mixing frequency, within a propagation distance much shorter than the diffraction length.
We theoretically investigate a double-Λ electromagnetically induced transparency (EIT) system. The property of the double-Λ medium with a closed-loop configuration depends on the relative phase of the applied laser fields. This phase-dependent mechanism differentiates the double-Λ medium from the conventional Kerr-based nonlinear medium, e.g., EIT-based nonlinear medium discussed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)], which depends only on the intensities of the applied laser fields. Steady-state analytical solutions for the phase-dependent system are obtained by solving the Maxwell-Bloch equations. In addition, we discuss efficient all-optical phase modulation and coherent light amplification based on the proposed double-Λ EIT scheme.
The effect of electromagnetically induced transparency in resonant four-wave-mixing schemes is investigated in an analysis that goes beyond perturbation theory in the coherent driving field. In addition we examine the case where the two-photon pump field is sufficiently strong to necessitate a nonperturbative treatment. This allows us to examine the cases where either one or both of the driving fields are strong. Phase matching is included in a plane-wave propagation treatment that matches the situation most likely to be encountered in actual experiments. The calculations are in part intended to model real experimental situations and thus incorporate driving and pump-field linewidths via the phase-diffusion model and Doppler broadening. With a strong pump-field laser, large enhancements in the efficiency of light generation occur at frequencies corresponding to the Autler-Townes satellites induced by the strong driving field. In this situation gain and high four-wave-mixing efficiency are simultaneously present, resulting in the production of a large intensity of coherent radiation. \textcopyright{} 1996 The American Physical Society.
An electromagnetically induced phase grating (EIG) controlled by coherent population trapping (CPT) in a four-level Y-type atomic system is studied. The CPT condition promotes significantly the dispersion of light into the first-order diffraction in constructing a phase modulation grating by transferring energy from zero-order to first-order diffraction. The diffraction efficiency of the phase grating is enhanced by up to 30% of the total probe intensity at the first-order diffraction. The present atomic scheme takes full advantage of the microwave-driven field for generating the EIG, which induces the quantum coherence and controls linear and nonlinear behaviors of the present system. Furthermore, it is noticed that the higher-order diffraction intensities are improved via a microwave-driven field and the phase and amplitude of the microwave field can improve the efficiency of the phase grating. These novel results could find potential applications in developing new photonic devices, such as all-optical switching at low light levels.
We study a double-Λ atomic scheme that interacts with four laser light beams so that a closed loop of radiation-induced transitions is formed. When specific relations for field phases, frequencies and amplitudes are satisfied, coherent superpositions (the so-called ‘dark states’) can be formed in a double-Λ, which leads to the well-known effect of electromagnetically induced transparency (EIT). If the interaction scheme in a double-Λ system is such that a closed loop is formed, the relative phase of the laser light fields becomes very important. We analyze here the effect of the lasers' relative phase on the EIT in double-Λ configuration of levels. The theoretical study of interactions of lasers with a double-Λ atomic scheme is commonly conducted by solving the optical Bloch equations (OBEs). We use here a perturbative method for solving OBEs, where the interaction of lasers with double-Λ is considered a perturbation. An advantage of the perturbative method is that it generally produces simpler solutions, and analytical expressions can be obtained. We present analytical expressions for the lower-order corrections of the EIT signal. Our results show that the EIT by the perturbative method can be approximated by the sum of products of complex Lorentzians. Through these expressions, we see in what way the relative phase affects the overall EIT profile.