Darmstadt 2008 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 53: Poster Photonik

Q 53.7: Poster

Thursday, March 13, 2008, 16:30–19:00, Poster C2

Linear and nonlinear optics in curved space — •Sascha Batz, Henrike Trompeter, and Ulf Peschel — Max Planck Research Group of Optics, Information and Photonics, Günther-Scharowsky-Str. 1 / Bau 24, 91058 Erlangen

In the past nonlinear optics was restricted to homogenous Euclidean space. However, completely new effects occur if the curvature of space starts to play a role. In optics we can investigate related phenomena if we abandon one spatial dimension and restrict wave propagation to a two-dimensional manifold. Using the tools provided by the theory of general relativity we established a mathematical model for the propagation of light on a curved surface with arbitary curvature. Here we focus on surfaces with constant Gaussian curvature. A sphere with a film waveguide on it is an example for a space of constant positive curvature. Here already the linear wave propagation deviates from that in flat space. It is characterized by periodic refocusing caused by a quantization into discrete modes with constant wavenumber spacing. If the power is increased solitons appear as nonlinear extension of these discrete linear modes. They show a distinct stability behavior deviating considerably from that of their counterparts in flat space. The theoretical model developed to describe wave propagation on curved surfaces shows some interesting similarities with nonlinear systems e.g. dispersion management in optical fibers and solitons in trapped Bose-Einstein condensates. Symmetry transformations derived for wave propagation in curved space can likewise be applied to other systems, thus generating new solutions.