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Physical Review Letters

Quantitative investigation of the effect of resonant absorbers on the Goos-Hänchen shift

E. Pfleghaar, A. Marseille, Antoine Weis

Published Apr 12, 1993• 90 citations
Publisher

Abstract

We report the first observation of a spectral resonance in the lateral displacement (Goos-H"anchen shift) of a laser beam totally reflected from a glass-cesium vapor interface. The line shape and the magnitude of the effect are well described by a model taking atom-wall collisions into account.
DOI
10.1103/physrevlett.70.2281

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Abstract It is proposed to perform an experiment to observe the Goos–Hänchen shift during total reflection from a simple resonant system. The main features of the proposed experimental approach are the use of a resonant system that provides a significant increase in the longitudinal shift of the reflected beam, and the presence of an absorber that stops part of the reflected beam in case of its shift. The main goal of the experiment is to obtain quantitative data that allow the comparison with a theory based on the concept of the reflection time.
The Goos-Hänchen (GH) shift refers to a lateral displacement (from the path expected from geometrical optics) along an interface in totally internal reflection. This phenomenon results from a coherence effect. In order to bring to light the role of coherence, the reflection of partially coherent light fields was investigated within the framework of the theory of coherence. A formal expression for the GH shifts of partially coherent light fields is obtained in terms of Mercer's expansion. It is shown that both the spatial coherence and the beam width have an important effect on the GH shift, especially near the critical angles (such as totally reflection angle). These results are important to observe the GH shifts of the beams with imperfect coherence, like x-ray and matter-wave beams.
In conventional optics for light waves, the pioneering work by Goos-Hänchen in 1947 on the lateral shift (or displacement) of a light beam along the surface of a dielectric boundary under the condition of total reflection has stimulated a large number of studies. The key physics behind the Goos-Hänchen shift is the nature of wave interference. From the perspective of wave optics, the incident beam of a finite transverse width can be viewed as composed of plane wave components, each of which has a slightly different transverse wavevector. Each wave component, after the total internal reflection, undergoes a different phase shift, and the superposition of all the reflected wave components gives rise to the lateral shift of the intensity peak in the reflected beam.
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.
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
When a three-level atomic wavepacket is obliquely incident on a "medium slab" consisting of two far-detuned laser beams, there exists lateral shift between reflection and incident points at the surface of a "medium slab", analogous to optical Goos-Hänchen effect. We evaluate lateral shifts for reflected and transmitted waves via expansion of reflection and transmission coefficients, in contrast to the stationary phase method. Results show that lateral shifts can be either positive or negative dependent on the incident angle and the atomic internal state. Interestingly, a giant lateral shift of transmitted wave with high transmission probability is observed, which is helpful to observe such lateral shifts experimentally. Different from the two-level atomic wave case, we find that quantum interference between different atomic states plays crucial role on the transmission intensity and corresponding lateral shifts.