GoosHänchenförskjutning

The Goos–Hänchen effect (Goos–Hänchen-Effekt) describes a lateral displacement of a light beam along an interface after reflection, relative to the position predicted by geometric optics. It is named after Fritz Goos and H. Hänchen, who first reported the phenomenon in 1947 during investigations of total internal reflection at a planar boundary between media with different refractive indices. The effect arises because a real light beam has finite width and a portion of the wave penetrates a short distance into the second medium as an evanescent field; the reflected beam acquires a wavelength- and angle-dependent phase shift, which translates into a shift of the beam’s intensity profile along the interface.

The shift can be described theoretically by the phase of the Fresnel reflection coefficient. In the Artmann approximation, the lateral Goos–Hänchen shift Δ is approximately −(λ/2π) dφ/dθ, where φ is the phase of the reflection coefficient and θ is the angle of incidence in the first medium. The magnitude and sign of the shift depend on polarization (s or p), wavelength, and the refractive indices of the media. The effect is typically on the order of a fraction to several wavelengths and becomes more pronounced near conditions that cause rapid phase variation, such as total internal reflection or resonant structures.

Practically, the Goos–Hänchen shift is relevant in precision optical measurements, metrology, and sensing, where small beam displacements can impact interferometric setups or be exploited to measure refractive indices, film thicknesses, or surface properties. The phenomenon is related to broader discussions of beam shifts in optics and has extensions in multilayer and plasmonic systems.