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arXiv:2509.06263 · Physical Review Letters

Phase-Space Nonseparability, Partial Coherence, and Optical Beam Shifts

Yahong Chen, Sergey A. Ponomarenko

Published Oct 21, 2025• 10 citations
arXivHTMLPDF

Abstract

As a paraxial wave packet is reflected or refracted from a planar interface separating two material media, it experiences spatial and angular shifts of its center position with respect to predictions of the geometrical ray picture. These in-plane and out-of-plane beam shifts are known as Goos-Hänchen and Imbert-Fedorov shifts, respectively. We discover a universal link between the phase-space nonseparability of an incident wave packet of any degree of spatial coherence and the reflected beam shifts. We unveil coherence Goos-Hänchen and coherence Hall effects, absent in the fully coherent limit. While the former effect can trigger a pronounced enhancement of the spatial Goos-Hänchen shift, the latter enables control of the spatial Imbert-Fedorov shift, from complete cancellation at a certain incidence angle to dramatic enhancement of the shift to giant magnitudes for nearly incoherent incident wave packets. Our results are equally applicable to optical, x-ray, and neutron, as well as matter waves, and they showcase novel phenomena in wave-matter interactions.

DOI
10.1103/cnvj-6w6f

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As a paraxial wave packet is reflected or refracted from a planar interface separating two material media, it experiences spatial and angular shifts of its center position with respect to predictions of the geometrical ray picture. These in-plane and out-of-plane beam shifts are known as Goos-Hänchen and Imbert-Fedorov shifts, respectively. We discover a universal link between the phase-space nonseparability of an incident wave packet of any degree of spatial coherence and the reflected beam shifts. We unveil coherence Goos-Hänchen and coherence Hall effects, absent in the fully coherent limit. While the former effect can trigger a pronounced enhancement of the spatial Goos-Hänchen shift, the latter enables control of the spatial Imbert-Fedorov shift, from complete cancellation at a certain incidence angle to dramatic enhancement of the shift to giant magnitudes for nearly incoherent incident wave packets. Our results are equally applicable to optical, x-ray, and neutron, as well as matter waves, and they showcase novel phenomena in wave-matter interactions.
We study the classical optics effects known as Goos–Hänchen and Imbert–Fedorov shifts, occurring when reflecting a bounded light beam from a planar surface, by using a quantum-mechanical formalism. This new approach allows us to naturally separate the spatial shift into two parts, one independent on orbital angular momentum (OAM) and the other one showing OAM-induced spatial-versus-angular shift mixing. In addition, within this quantum-mechanical-like formalism, it becomes apparent that the angular shift is proportional to the beams angular spread, namely to the variance of the transverse components of the wave vector. Moreover, we extend our treatment to the enhancement of beam shifts via weak measurements and relate our results to the recent experiments.
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.
The optical analogue of quantum weak measurements has shown considerable promise for the amplification and observation of tiny optical beam shifts, namely Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts. Here, we demonstrate simultaneous weak value amplification of both the angular GH and the IF shifts in partial reflection of a fundamental Gaussian beam at planar dielectric interfaces. We employ pre and postselection schemes with appropriate linear polarization basis states for simultaneous weak measurements and amplification of both of these shifts. The experimentally observed enhancement of the beam shifts and their dependence on the angle of incidence are analyzed/interpreted via theoretical treatment of weak measurements.
The spatial and the angular variants of the Imbert-Federov (IF) beam shifts and the angular Goos-Hänchen (GH) shift contribute in a complex interrelated way to the resultant beam shift in partial reflection at planar dielectric interfaces. Here, we show that the two variants of the IF effects can be decoupled and separately observed by weak value amplification and subsequent conversion of spatial ↔angular nature of the beam shifts using appropriate pre and post selection of polarization states. Such optimized weak measurement schemes also enable one to nullify one effect (either the GH or the IF) and exclusively observe the other. We experimentally demonstrate this and illustrate various other intriguing manifestations of optimized weak measurements in elliptical and / or linear polarization basis. We also present a Poincare sphere based analysis on conversion / retention of the angular or spatial nature of the shifts with pre and post selection of states in weak measurement. The demonstrated ability to amplify, controllably decouple or combine the beam shifts via weak measurements may prove to be valuable for understanding the different physical contributions of the effects and for their applications in sensing and precision metrology.
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 introduce the technique of entangled-beam reflectometry for extracting spatially correlated (magnetic or nonmagnetic) information from material surfaces or thin films. Our amplitude- and phase-sensitive technique exploits the coherent nature of an incoming entangled probe beam, of matter or light waves, undergoing reflection from the surface. Such reflection encodes the surface spatial structure into the probe's geometric and phase-derived Goos-Hänchen shifts, which can then be measured to unveil the structure. We investigate the way these shifts depend on the wave packet widths, and illustrate our technique in the case of in-plane periodic (non)magnetic structures by utilizing spin-path mode-entangled neutron beams.