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Journal of the Optical Society of America B

Goos–Hänchen shift of the reflected beam in a standing-wave coupled electromagnetically induced transparency system

Xiaojun Zhang, Hai-Hua Wang, Chun-Liang Wang, Yan Xu, Zhipeng Liang, Cunbo Fan, Chengze Liu, Jin-Yue Gao

Published Oct 8, 2015• 13 citations
Publisher

Abstract

The Goos–Hänchen shift of the reflected beam in a standing-wave coupled electromagnetically induced transparency medium is investigated. We adopt the three-level Λ system as a model of Rb87 atomic media. Under the influence of two counterpropagating coupling fields, the incident beam is converted into a reflected one, with the Goos–Hänchen shift. We briefly discuss the rules for obtaining efficient reflection in such an atomic system, and carefully investigate the Goos–Hänchen shift and its dependence on the beam width of the incident field. Both the cases with and without Doppler broadening are considered. In order to provide a clearer physical picture on the large shift that could be realized, the concept of penetration depth is used to analyze the shift phenomenologically.

DOI
10.1364/josab.32.002281

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The Goos–Hänchen shift of the reflected beam in a standing-wave coupled electromagnetically induced transparency medium is investigated. We adopt the three-level Λ system as a model of Rb87 atomic media. Under the influence of two counterpropagating coupling fields, the incident beam is converted into a reflected one, with the Goos–Hänchen shift. We briefly discuss the rules for obtaining efficient reflection in such an atomic system, and carefully investigate the Goos–Hänchen shift and its dependence on the beam width of the incident field. Both the cases with and without Doppler broadening are considered. In order to provide a clearer physical picture on the large shift that could be realized, the concept of penetration depth is used to analyze the shift phenomenologically.
The Goos-H\"anchen shift of the system composed by two cavity walls and an intracavity atomic sample is presented. The atomic sample is treated as a four-level double-$\ensuremath{\Lambda}$ system, driven by the two counterpropagating coupling fields. The probe field experiences the discontinuous refractive index variation and is reflected. Moreover, under the phase-matching condition, the four-wave mixing effect based on electromagnetically induced transparency can cause effective reflection. The Goos-H\"anchen shifts appear in both situations and are carefully investigated in this article. We refer to the first one with the incident and reflected light having identical wavelength as the linear Goos-H\"anchen shift, and the second one with the reflection wavelength determined by the phase-matching condition as the nonlinear Goos-H\"anchen shift. The differences between the two kinds of shifts, such as the incident angle range, conditions for the shift peaks, and controllability, are discussed.
This paper hints at the Goos-Hänchen shift properties of a cavity containing an ensemble of atoms using a four-level atomic system involving a Rydberg state. By means of the stationary phase theory and density matrix formalism in quantum optics, we study theoretically the Goos-Hänchen shifts in both reflected and transmitted light beams. It is realized that as a result of the interaction between Rydberg and excited states in such a four-level atom-light coupling scheme the maximum positive and negative Goos-Hänchen shifts can be obtained in reflected and transmitted light beams owning to the effect of the Rydberg electromagnetically induced transparency (EIT) or Rydberg electromagnetically induced absorption. In particular, when the switching field is absent and the Rydberg EIT is dominant in the medium, a giant Goos-Hänchen shift can be achieved for both reflected and transmitted light beams.
The behavior of the Goos-Hanchen (GH) shifts in the reflected and transmitted light beam which is incident on a cavity containing an intracavity medium of three-level or four-level atoms with electromagnetically induced transparency (EIT) is discussed. We report a coherent control of the GH shift in a fixed configuration or device via superluminal and subluminal wave propagation. For superluminal wave propagation, we observe negative GH shifts in the reflected part of the incident light whereas the shifts are positive in the transmitted light beam. This corresponds to the negative group index of the cavity in the former case and positive group index of the cavity in the latter. For subluminal wave propagation, the behavior of the GH shifts in the reflected light changes and positive shifts appear
We study the Goos-Hänchen shift (GHS) of a reflected light beam from a cavity containing a double-[Formula: see text] atomic medium that is bounded by two glass slabs. Applying both coherent and incoherent fields to the atomic medium leads to positive and negative controllability of GHS. For some specific values of the parameters of the system, the amplitude of the GHS becomes large, namely, in the order of [Formula: see text] times the wavelength of the incident light beam. These large shifts are found at more than one angle of incidence with a wide range of parameters of the atomic medium.
The behavior of the Goos-H\"anchen (GH) shifts in the reflected and transmitted light beam which is incident on a cavity containing an intracavity medium of three-level or four-level atoms with electromagnetically induced transparency (EIT) is discussed. We report a coherent control of the GH shift in a fixed configuration or device via superluminal and subluminal wave propagation. For superluminal wave propagation, we observe negative GH shifts in the reflected part of the incident light whereas the shifts are positive in the transmitted light beam. This corresponds to the negative group index of the cavity in the former case and positive group index of the cavity in the latter. For subluminal wave propagation, the behavior of the GH shifts in the reflected light changes and positive shifts appear; however, the GH shifts in the transmitted light remains positive. The corresponding group index of the cavity is positive in both cases.
The influence of spontaneous generated coherence (SGC) on the Goos–Hänchen (GH) shift in the reflected light is presented. A weak probe light is incident on a cavity containing three-level gaseous atomic medium consist of 85Rb atoms. The atom–field interaction follows electromagnetically induced transparency configuration, and the SGC modifies the dispersion and absorption properties of a system [Y. Niu and S. Gong, Phys. Rev. A 73, 053811 (2006)]. The SGC enhances the Kerr nonlinearity which leads to giant negative and positive GH shifts in the reflected light. Further, the control of negative and positive GH shifts is achieved via manipulation of probe field detuning.