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Physical Review A

Gain-assisted control of the Goos-Hänchen shift

Ziauddin Ziauddin, Sajid Qamar

Published Nov 23, 2011• 68 citations
Publisher

Abstract

A gain-assisted model is considered to study the Goos-H$\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\text{a}}$nchen (GH) shift behavior in the reflected and transmitted light. In this model, a probe light is incident on a cavity containing three-level dilute gaseous atomic medium. The atom-field interaction follows two-photon Raman transitions, and the dielectric susceptibility of the medium exhibits dispersion and gain properties [L. J. Wang, A. Kuzmich, and A. Dogariu, Nature (London) 406, 227 (2000)]. Under appropriate conditions, two gain peaks are observed with anomalous dispersion between the peaks, whereas normal dispersion can be observed at and around the gain maxima. The manipulation of the detuning associated with the probe light field which interacts with the intracavity medium during its propagation through the cavity can lead to a control over negative and positive GH shift in the reflected and transmitted light beam via the anomalous and normal dispersion of the medium.

DOI
10.1103/physreva.84.053844

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A gain-assisted model is considered to study the Goos-Ha\ifmmode¨\else¨\fi\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\text{a}}a\ifmmode¨\else¨\finchen (GH) shift behavior in the reflected and transmitted light. In this model, a probe light is incident on a cavity containing three-level dilute gaseous atomic medium. The atom-field interaction follows two-photon Raman transitions, and the dielectric susceptibility of the medium exhibits dispersion and gain properties [L. J. Wang, A. Kuzmich, and A. Dogariu, Nature (London) 406, 227 (2000)]. Under appropriate conditions, two gain peaks are observed with anomalous dispersion between the peaks, whereas normal dispersion can be observed at and around the gain maxima. The manipulation of the detuning associated with the probe light field which interacts with the intracavity medium during its propagation through the cavity can lead to a control over negative and positive GH shift in the reflected and transmitted light beam via the anomalous and normal dispersion of the medium.
Control of Goos-H$\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\text{a}}$nchen (GH) shift in reflected and transmitted light is revisited for a Gaussian light incident on a cavity. The intracavity atomic medium follows duplicated two-level atomic configurations where two fields, i.e., a strong control field and a relatively weak probe field are employed [F. A. Hashmi and M. A. Bouchene, Phys. Rev. Lett. 101, 213601 (2008)]. The coherent control is achieved via phase shift $\ensuremath{\phi}$ between control and probe fields. The effect of incident light width on negative or positive GH shifts and distortion in the reflected and transmitted light is investigated.
The influence of the Kerr nonlinearity on the group index of a dispersive intracavity medium is revisited using a Raman gain based scheme to obtain amplitude control of the Goos–Hänchen (GH) shift in the reflected light. The intracavity medium exhibits a Raman gain process which is accompanied by anomalous dispersion, i.e., superluminal pulse propagation (Dogariu et al 2000 Nature 406 277). In the presence of a Kerr field, the gain–dispersion properties of the intracavity medium are modified, which leads to enhancement in the positive and negative group indices of the medium. The behavior of the GH shift in the reflected light due to the enhancement in the group indices in the presence of the Kerr field is investigated, and relatively large positive and negative GH shifts can be obtained.
The negative and positive Goos-H\"anchen (GH) shifts in reflected light are revisited for a partial coherent light incident on a cavity. A three-level dilute gaseous atomic medium, which follows two-photon Raman transitions, is considered in a cavity. The anomalous (negative group index) and normal (positive group index) dispersions of the intracavity medium lead to negative and positive GH shifts, respectively. The effects of beam width, spatial coherence, and mode index of partial coherent light fields are studied on the negative and positive GH shifts. It is observed that the amplitude of negative and positive GH shifts are relatively large for a small range of beam width and for a small value of spatial coherence of partial coherent light beams. The amplitude of GH shifts becomes small for large beam width and spatial coherence of incident light. Further, the distortion in the reflected light field increases when the amplitude of the GH shifts increases and vice versa.
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.
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
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.