© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Journal of Nonlinear Optical Physics & Materials

Multi-wave mixing dependence Goos–Hänchen shift of structured light in atomic medium

Afsar Ali, Tahirzeb Khan, Syed Zulfiqar, Mohammed Rafi Shaik, Gulzar Khan, Shaukat Ali Khattak, M. Maqbool, Shaik Althaf Hussain

Published Jan 18, 2025• 0 citations

Abstract

The reflection, transmission, and related Goos–Hänchen (GH) shifts of structured light are investigated by multi-wave mixing conditions in this paper. The terms absorption, dispersion, group index, and photon drag rotation of structured light are also studied by multi-wave mixing. The maximum values of group index of [Formula: see text] and rotary photon drag of [Formula: see text] micro-radian are reported in this work. Significant modifications of GH shift in reflection and transmission modes are investigated with azimuthal quantum number of structured light along with multi-wave mixing. Various crater shapes are reported in reflection and transmission modes and with their corresponding GH shifts in reflection and transmission modes. The reflection and transmission GH shifts exhibit a correlation where [Formula: see text]ve reflection GH shift regions correspond to −ve transmitted GH shift regions, and vice versa. The maximum of [Formula: see text]ve and −ve GH shift in reflection and transmission modes is investigated up to [Formula: see text]. The modified GH shifts in reflection and transmission modes have significant applications in high-resolution imaging, sensing, and optical signal processing.

DOI: 10.1142/s0218863525500080

Related papers

Negative and positive Goos-Hänchen shifts of partially coherent light fields

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

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.

Physical Review A•Jan 5, 2015•38 citations

Distortion management of the Goos–Hänchen shifts in reflection–transmission beams

Humayun Khan, Muhammad Haneef

A new scheme focusing on modification and control of distortion in the reflection and transmission of Goos–Hänchen (GH) shifted beams, is discussed. The absorptivity, reflectivity, and transmissivity are measured for the new atomic scheme. The GH-shifted beam is modified by control fields and incident angle. The sum of absorption, transmission, and reflection coefficients is equal to one. For positive reflection GH-shift region, there is negative transmission GH shift. The distortion in the reflected and transmitted beam is controlled with incident angle and control fields. The results discussed in this article show significant applications in micro-optics and nano-optics, acoustics, and plasma physics.

Canadian Journal of Physics•Jul 14, 2017•10 citations

Giant lateral shift in single mode cavity containing four-level sodium atomic medium

Abbas Ghaffar, Rashid Ahmad, Arif Ullah +1 more

Abstract In this work, a four-level sodium atomic medium coupled to a single mode cavity is used to investigate the Goos-Hänchen (GH) shift. Using collective phase of the control fields and intensity of Rabi oscillation, the positive as well as negative GH-shift in transmission and reflection beams are examined. In the transmission beam, a maximum GH-shift of ±6λ is observed. Furthermore, GH-shift in both reflection and transmission beams in a four-level sodium atomic medium is significantly enhanced by photon number density as well as by the cavity coupling strength. By varying the collective phase of the control fields and the probe field frequency, GH-shift in reflection exhibits a maximum value of ±2λ. Our findings may open up significant applications in micro-optics, sensers, photonic crystals and nano processor technology.

Physica Scripta•Oct 15, 2024•5 citations

Coherent control of the Goos-Hänchen shift

Ziauddin Ziauddin, Sajid Qamar, Muhammad Suhail Zubairy

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.

Physical Review A•Feb 22, 2010•19 citations

Coherent control of the Goos-Hanchen shift

Ziauddin, Qamar S., Sajid Qamar, Muhammad Suhail Zubairy

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

•Jan 1, 2010•144 citations

Birefringent lateral Goos-Hänchen effect through chiral medium

Sajid Ullah Khan, Saleh Muhammad, Bakht Amin Bacha +1 more

Abstract Birefringence of lateral Goos-Hänchen (GH) shift in reflection and transmission beams are investigated through four level chiral atomic medium. Significant positive and negative shifts in reflection and transmission birefringence beams are reported under the strength of driving fields. At resonance point, positive birefringent shifts of 2.8 λ and 2 λ are noted in reflection beams. The birefringence lateral GH-shift in transmission beams show contrast behaviors of −2 λ and −2.8 λ at resonance point. A 30% fractional change in birefringent reflection and transmission beams with GH-shift are investigated. These results will play a vital role in the modification of optical heterodyne sensors technology, cloaking devices, image coding, integrated optical technologies and telecom industry.

Physica Scripta•Jul 23, 2020•25 citations

The reflection, transmission, and related Goos–Hänchen (GH) shifts of structured light are investigated by multi-wave mixing conditions in this paper. The terms absorption, dispersion, group index, and photon drag rotation of structured light are also studied by multi-wave mixing. The maximum values of group index of [Formula: see text] and rotary photon drag of [Formula: see text] micro-radian are reported in this work. Significant modifications of GH shift in reflection and transmission modes are investigated with azimuthal quantum number of structured light along with multi-wave mixing. Various crater shapes are reported in reflection and transmission modes and with their corresponding GH shifts in reflection and transmission modes. The reflection and transmission GH shifts exhibit a correlation where [Formula: see text]ve reflection GH shift regions correspond to −ve transmitted GH shift regions, and vice versa. The maximum of [Formula: see text]ve and −ve GH shift in reflection and transmission modes is investigated up to [Formula: see text]. The modified GH shifts in reflection and transmission modes have significant applications in high-resolution imaging, sensing, and optical signal processing.

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.

A new scheme focusing on modification and control of distortion in the reflection and transmission of Goos–Hänchen (GH) shifted beams, is discussed. The absorptivity, reflectivity, and transmissivity are measured for the new atomic scheme. The GH-shifted beam is modified by control fields and incident angle. The sum of absorption, transmission, and reflection coefficients is equal to one. For positive reflection GH-shift region, there is negative transmission GH shift. The distortion in the reflected and transmitted beam is controlled with incident angle and control fields. The results discussed in this article show significant applications in micro-optics and nano-optics, acoustics, and plasma physics.

Abstract In this work, a four-level sodium atomic medium coupled to a single mode cavity is used to investigate the Goos-Hänchen (GH) shift. Using collective phase of the control fields and intensity of Rabi oscillation, the positive as well as negative GH-shift in transmission and reflection beams are examined. In the transmission beam, a maximum GH-shift of ±6λ is observed. Furthermore, GH-shift in both reflection and transmission beams in a four-level sodium atomic medium is significantly enhanced by photon number density as well as by the cavity coupling strength. By varying the collective phase of the control fields and the probe field frequency, GH-shift in reflection exhibits a maximum value of ±2λ. Our findings may open up significant applications in micro-optics, sensers, photonic crystals and nano processor technology.

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 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

Abstract Birefringence of lateral Goos-Hänchen (GH) shift in reflection and transmission beams are investigated through four level chiral atomic medium. Significant positive and negative shifts in reflection and transmission birefringence beams are reported under the strength of driving fields. At resonance point, positive birefringent shifts of 2.8 λ and 2 λ are noted in reflection beams. The birefringence lateral GH-shift in transmission beams show contrast behaviors of −2 λ and −2.8 λ at resonance point. A 30% fractional change in birefringent reflection and transmission beams with GH-shift are investigated. These results will play a vital role in the modification of optical heterodyne sensors technology, cloaking devices, image coding, integrated optical technologies and telecom industry.