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Annual Methodological Archive Research Review

The Localized Goos Hänchen Shift In Reflection And Transmission Via Sodium Atomic Medium

Murad Ali, Shoaib Akmal, Umair Khatab, Waqar Ahmad, Muhammad Shoaib, Mehran Ahmad, Raees Muhammad Fawad

Published Aug 22, 2025• 0 citations
Publisher

Abstract

In this work, we investigate the manipulation of the Goos-Hänchen (GH) shifts, referring to the lateral displacement of light beams at planar interfaces, in a global sodium atomic vapor medium by utilizing its tunable optical characteristics under the coherent control fields and the variable incident angles (0.6rad≤θ≤0.8rad). We achieve this by accurately manipulating probe detuning and control field intensities using a technique called 'electromagnetically induced transparency (EIT)'. EIT is a quantum interference effect that makes a medium transparent to a probe beam. By combining a near-resonant probe beam with transitions in the sodium atoms [D₂ line (5S1/2​→5P3/2)​], we obtain remarkable amplification of absorption, reflection, and transmission with spatially shifted beams that present up to ±4λ bidirectional GH shifts in reflection and ±2λ in transmission. The non-ideal normalization condition (∣T∣2+∣R∣2+∣A∣2<1) results from the redistribution of energy due to these shifts and indicates that established efficiency bounds no longer apply in coherent media. The GH-shifted beams astonishingly also maintain uniform intensity profiles at large displacements. Here, then, angular-dependent reflection pivots peak around critical angles, and transmission shifts are dynamically tunable, all emphasizing the atomic susceptibility gradients as key shapers for beam steering. These observations reveal unprecedented promise in applications, such as super-precision optical measurement, sub-wavelength displacement detection, and refractive index measurement, thus making sodium atomic vapors a tunable platform for advanced photonic devices with unique and high sensitivity. Keywords: Goos-Hänchen shift, Sodium atomic vapor, Atomic coherence, Beam displacement sensing, Optical susceptibility modulation

DOI
10.63075/12m08v08

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In this work, we investigate the manipulation of the Goos-Hänchen (GH) shifts, referring to the lateral displacement of light beams at planar interfaces, in a global sodium atomic vapor medium by utilizing its tunable optical characteristics under the coherent control fields and the variable incident angles (0.6rad≤θ≤0.8rad). We achieve this by accurately manipulating probe detuning and control field intensities using a technique called 'electromagnetically induced transparency (EIT)'. EIT is a quantum interference effect that makes a medium transparent to a probe beam. By combining a near-resonant probe beam with transitions in the sodium atoms [D₂ line (5S1/2​→5P3/2)​], we obtain remarkable amplification of absorption, reflection, and transmission with spatially shifted beams that present up to ±4λ bidirectional GH shifts in reflection and ±2λ in transmission. The non-ideal normalization condition (∣T∣2+∣R∣2+∣A∣2<1) results from the redistribution of energy due to these shifts and indicates that established efficiency bounds no longer apply in coherent media. The GH-shifted beams astonishingly also maintain uniform intensity profiles at large displacements. Here, then, angular-dependent reflection pivots peak around critical angles, and transmission shifts are dynamically tunable, all emphasizing the atomic susceptibility gradients as key shapers for beam steering. These observations reveal unprecedented promise in applications, such as super-precision optical measurement, sub-wavelength displacement detection, and refractive index measurement, thus making sodium atomic vapors a tunable platform for advanced photonic devices with unique and high sensitivity. Keywords: Goos-Hänchen shift, Sodium atomic vapor, Atomic coherence, Beam displacement sensing, Optical susceptibility modulation
A metal-clad waveguide backed by a coherent atomic medium is proposed to achieve tunable giant spatial and angular Goos-H\"anchen (GH) shifts. With a metal layer of appropriate thickness, a large GH shift can occur simultaneously for transverse-magnetic- and transverse-electric-polarized light beams when the waveguide modes are resonantly excited. The phase change and dip slope of the reflection coefficient around the resonance angle are closely related to the system's internal damping, which depends on the absorption of the medium. Then based on the quantum coherence effect, the spatial and angular shifts can be greatly enhanced by adjusting the parameters of the atomic system. The lateral displacement can also be switched from positive to negative or vice versa via coherent control of the absorption by the medium. Moreover, the dependence of the resonance angle of the guided mode on the refractive index makes the peak position of GH shifts tunable. The proposed scheme provides more flexibility for manipulating the spatial and the angular GH shifts, and it has potential applications in optical switches, beam steering, etc.
We propose an efficient scheme to manipulate the Goos–Hänchen (GH) shift of a reflected beam from a metal-clad waveguide, where a coherent atomic medium with a Λ -type configuration is employed as the substrate. Using experimentally achievable parameters, we identify the conditions under which spontaneously generated coherence (SGC) allows us to enhance the spatial and angular GH shifts of the reflected beam. With the help of SGC, the relative phases of the probe and control fields can alter the absorption gain and refractive index of the atomic medium, thereby manipulating the magnitudes, signs, and positions of the spatial and angular shifts. Furthermore, the spatial and angular GH shifts can be coherently controlled via adjusting the incoherent pumping rate and the intensity of the control field. Our proposal provides an avenue for the manipulation of spatial and angular GH shifts and potential applications in optical switching and optical steering.
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-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 We present a new scheme to report on the effects of a five-level chiral atomic medium on the lateral Goos–Hänchen (GH) shift in Gaussian probe beams via Kerr nonlinearity (KNL) and local field effects. The physical realization of birefringence in absorption, dispersion, reflection and transmission beams is investigated, with special emphasis on the manipulation of absolute and fractional change in lateral GH shifts in birefringence transmission and reflection beams, via local fields and Kerr nonlinearity. We have employed a semiclassical atomic density-matrix formalism so as to obtain the expression for electric and magnetic susceptibilities of the chiral medium and the corresponding chirality coefficients in conjunction with Kerr and local fields, both separately and in combination. Stationary-phase theory is used to compute GH shift from the calculated birefringent reflection and transmission coefficients of probe beams. A negative and positive GH shift is observed in reflection and transmission beams, respectively, subjected to local field and Kerr effect. In contrast, a positive GH shift is observed in both reflection and transmission beams in the presence of both local field and Kerr effects. The local and Kerr fields also alter the divergence angle between left and right circularly polarized birefringence beams. GH shift depends on incident angle and probe detuning. The anisotropy of medium is lessened by switching ON the Kerr field in the medium. We observed a positive fractional change of ±30% in the GH shift in the birefringence reflection beam in the presence of a local field without KNL, while a 20% fractional GH shift was observed in the presence of both local field and KNL effects. Our results suggest promising applications in nonlinear optical, plasmonic and biophotonic devices for the manipulation of light propagation and optical signal processing.
We present a scheme for enhancing Goos-Hänchen shift of light beam that is reflected from a coherent atomic medium in the Kretschmann-Raether configuration. The complex permittivity of the medium can be coherently controlled and has significant influence on the surface plasmon resonance (SPR) at the metal-medium interface. By tuning the atomic absorption, the internal damping of SPR system can be modulated effectively, thereby leading to giant positive and negative lateral displacements. The refractive index of medium determines the SPR angle. Thus the peak position of the beam shift becomes tunable. As the optical response of the coherent medium depends on the intensity and detuning of the controlling fields, we are able to conveniently manipulate the magnitude, the sign, and the angular position of Goos-Hänchen shift peaks.