Nanooptical elements allow for control of the spatial and spectral dispersion of optical fields. Thus, they are ideal to control parametric nonlinear interactions, which depend on the field overlap and the propagation constants of the interacting modes. Our research is focused on parametric  three-wave mixing. Among these second-order nonlinear processes are e.g. second-harmonic generation or spontaneous parametric down-conversion. We aim to theoretically describe such processes in nanostructured environments, design and rigorously simulate structures to allow for experimental observation and finally characterize manufactured samples in the lab. Among the investigated nanostructures are rib waveguides [7], photonic crystal waveguides [8], nanostructured surfaces [9], and monomolecular membranes like molybdenum disulfide.

[7] R. Geiss, S. Saravi, A. Sergeyev, S. Diziain, F. Setzpfandt, F. Schrempel, R. Grange, E.-B. Kley, A. Tünnermann, and T. Pertsch, "Fabrication of nanoscale lithium niobate waveguides for second-harmonic generation," Opt. Lett. 40, 2715 (2015)

[8] S. Saravi, S. Dizian, M. Zilk, F. Setzpfandt, and T. Pertsch, "Phase-Matched Second Harmonic Generation in Photonic Crystal Waveguides," Phys. Rev. A 92, 063821 (2015)

[9] L. Wang, A. S. Shorokhov, P. N. Melentiev, S. Kruk, M. Decker, C. Helgert, F. Setzpfandt, A. A. Fedyanin, Y. S. Kivshar, and D. N. Neshev, "Multipolar third-harmonic generation in fishnet metamaterial," ACS Photonics 3 , 1494  (2016)

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