Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physica Scripta

The Goos-Hänchen shift analysis in optical lattices under the parity-time symmetry

Fazal Badshah, Huma Malik, Anwar Ali, Haibo Huang, Ziauddin Ziauddin

Published Jun 28, 2023• 4 citations
Publisher

Abstract

Abstract This article investigates the Goos-Hӓnchen(GH) shift of the reflected light of an ensemble of optical lattices in a cavity. We consider a lambda-type ensemble of three-level atoms to form the optical lattice and apply three fields, two weak fields (probe and microwave) and one strong field. The microwave field transforms the medium into a gain medium, resulting in the optical lattice containing both loss and gain. The co-existence of gain and loss leads to parity-time symmetry in the system. By satisfying the parity-time symmetry condition, we can modify the magnitude of the GH shift. Our results suggest that the GH shift can be controlled in systems exhibiting parity-time symmetry.

DOI
10.1088/1402-4896/ace28f

Related papers

Giant Goos-Hänchen shift using PT symmetry

Ziauddin Ziauddin, You-Lin Chuang, Ray‐Kuang Lee

Influence of $\mathcal{PT}$ symmetry on the Goos-H\"anchen (GH) shift in the reflected light is presented for an ensemble of atomic medium in a cavity, in the configuration of four-level $N$-type ($^{87}\mathrm{Rb}$ atoms) systems driving by two copropagating strong laser fields and a weak probe field. The atom-field interaction follows the realization of $\mathcal{PT}$ symmetry by adjusting the coupling field detunings [J. Sheng et al., Phys. Rev. A 88, 041803(R) (2013)]. A giant enhancement for the GH shift in the reflected light is revealed when the $\mathcal{PT}$-symmetry condition is satisfied.

Physical Review A•Jul 8, 2015•46 citations

Gain-assisted control of the Goos-Hänchen shift

Ziauddin Ziauddin, Sajid Qamar

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.

Physical Review A•Nov 23, 2011•68 citations

Nonreciprocal and enhanced Goos-Hänchen shifts in the cavity-assisted atomic lattice of parity-time antisymmetry

Xiao Liu, Yixin Wang, Jin‐Hui Wu

We propose a scheme for realizing nonreciprocal and largely enhanced Goos-Hänchen (GH) shifts in a lattice of cold atoms exhibiting the parity-time ( P T ) antisymmetric susceptibility when driven by a probe beam and a coupling beam. This atomic lattice in the free space allows to attain unidirectionally detectable nonreciprocal GH shifts for reflected probe beams provided a Bragg bright resonance is tuned to overlap with an exceptional point. Placing this atomic lattice in an optical cavity, we can further attain bidirectionally detectable nonreciprocal GH shifts for reflected probe beams, benefiting from the interplay between a Bragg bright resonance and a cavity dark resonance. Nonreciprocal GH shifts in our cavity-assisted P T -antisymmetric atomic lattice exhibit the advantages of dynamic tunability and reversibility, while enhanced up to hundreds of probe wavelengths, in the case of nonzero detectable reflections.

Optics Express•Feb 18, 2025•5 citations

Giant Goos–Hänchen shift via spontaneous generated coherence

Ziauddin Ziauddin

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.

Journal of Modern Optics•Jul 10, 2015•24 citations

Control of the Goos–Hänchen shifts of a probe light beam using phase tunability of the intracavity medium

Arash Radmehr, Mostafa Sahrai, Hamed Sattari

This paper presents the Goos-Hänchen (GH) shifts of a probe light beam in a fixed cavity configuration containing the three level V-type atomic medium. We found that in the presence of decay-induced interference, the lateral shifts of both the reflected and transmitted probe light beam can easily be controlled just by the relative phase of applied fields. We also discuss the intensity of the applied field on GH shifts of the reflected and transmitted probe light beam.

Applied Optics•Mar 5, 2016•8 citations

Control of the Goos-Hänchen shift using a duplicated two-level atomic medium

Ziauddin Ziauddin, Sajid Qamar

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.

Physical Review A•May 22, 2012•64 citations
Abstract This article investigates the Goos-Hӓnchen(GH) shift of the reflected light of an ensemble of optical lattices in a cavity. We consider a lambda-type ensemble of three-level atoms to form the optical lattice and apply three fields, two weak fields (probe and microwave) and one strong field. The microwave field transforms the medium into a gain medium, resulting in the optical lattice containing both loss and gain. The co-existence of gain and loss leads to parity-time symmetry in the system. By satisfying the parity-time symmetry condition, we can modify the magnitude of the GH shift. Our results suggest that the GH shift can be controlled in systems exhibiting parity-time symmetry.
Influence of PT\mathcal{PT}PT symmetry on the Goos-H\"anchen (GH) shift in the reflected light is presented for an ensemble of atomic medium in a cavity, in the configuration of four-level NNN-type (87Rb^{87}\mathrm{Rb}87Rb atoms) systems driving by two copropagating strong laser fields and a weak probe field. The atom-field interaction follows the realization of PT\mathcal{PT}PT symmetry by adjusting the coupling field detunings [J. Sheng et al., Phys. Rev. A 88, 041803(R) (2013)]. A giant enhancement for the GH shift in the reflected light is revealed when the PT\mathcal{PT}PT-symmetry condition is satisfied.
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.
We propose a scheme for realizing nonreciprocal and largely enhanced Goos-Hänchen (GH) shifts in a lattice of cold atoms exhibiting the parity-time ( P T ) antisymmetric susceptibility when driven by a probe beam and a coupling beam. This atomic lattice in the free space allows to attain unidirectionally detectable nonreciprocal GH shifts for reflected probe beams provided a Bragg bright resonance is tuned to overlap with an exceptional point. Placing this atomic lattice in an optical cavity, we can further attain bidirectionally detectable nonreciprocal GH shifts for reflected probe beams, benefiting from the interplay between a Bragg bright resonance and a cavity dark resonance. Nonreciprocal GH shifts in our cavity-assisted P T -antisymmetric atomic lattice exhibit the advantages of dynamic tunability and reversibility, while enhanced up to hundreds of probe wavelengths, in the case of nonzero detectable reflections.
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.
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.