Untersuchung der Auswirkung von Raumkrümmung auf die Ausbreitung elektromagnetischer Felder durch Beschränkung der Propagation auf zweidimensionale gekrümmte Flächen
Final Report Abstract
As well‐known from general relativity the intrinsic curvature of spacetime traversed by a ray of light alters the latter’s trajectory. This tremendous feature of otherwise homogeneous space is in stark contrast to the modulation of permittivity as utilized in common optics, but hardly accessible in the lab due to the required cosmological masses and distances. Hence, in order to study the impact of space curvature on light propagation in a table top experiment we restrict to the case of two‐dimensional curved surfaces. In the course of this project we focused on surfaces of constant Gaussian curvature, which is defined as the product of the two principal curvatures in one point. Such surfaces resemble the homogeneity and isotropy of Euclidean space with vanishing curvature. Since invoking an effective attractive or repelling force on the plane wave constituents (depending on the sign), the Gaussian curvature dramatically modifies the evolution of a light beam’s envelope by rivaling with beam divergence. The requirement of confining light propagation to curved surfaces demands the deposition of a high refractive index layer acting as a wave guide for light on top of steeply formed substrates without a preferred direction. After overcoming obstacles and drawbacks in the fabrication process we finally achieved a good specimen with the desired quality features. Because of concerns the test sample might be harmed during nonlinear light propagation experiments, the first experiment conducted was Hanbury Brown and Twiss (HBT) type intensity interferometry in curved space. The intensity interferometry technique as brought forward by HBT is based on the measurement of transverse spatial intensity correlation some propagation distance away from the phase modulated light source in order to determine the latter’s angular size. It was the first experiment to survey the most nearby stars and back in its time provoked a controversy about the common conception of quantum mechanics. Never in this context has the impact of space curvature on the evolution of spatial correlation and its implications on the determination of the source’s size been studied. We could show analytically and experimentally that the effective potential invoked by intrinsic curvature on beam propagation strongly modifies the evolution of spatial correlation. For light propagating along a negatively curved surface coherence builds up exponentially and, thus, even faster than in flat space. In contrast, coherence properties of light propagating on positively curved surfaces display an oscillatory behavior. The oscillation of the correlation length is contrary to the common conception of strict gain of coherence during free‐space propagation. Additionally, for specific values of the initial correlation length both the correlation length and the mean envelope field width can remain unchanged during propagation. Subsequent experiments in the nonlinear regime to study soliton formation and stability are still ongoing. Preliminary results suggest that the ion diffusion process utilized to form a waveguiding layer along the surface of the glass figure has changed the nonlinear response of the glass to even smaller values rendering it hard to achieve nonlinear interaction with the laser available in our group. Further experiments are being conducted with a stronger laser. Although not all sub‐projects could be finished in the time frame of this project, we stay confident about their outcome and possible impact on other fields of physics.
Publications
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„Hanbury Brown and Twiss measurements in curved space“, Nature Photonics volume 10, pages 106–110 (2016)
V. H. Schultheiss, S. Batz and U. Peschel
