@article{65316,
  abstract     = {{Metasurfaces are powerful tools for manipulating light using small structures on the nanoscale. In most metasurfaces, near-field couplings are treated as being unfavorable perturbations. Here, we experimentally investigate a structure consisting of sinusoidally modulated silicon waveguides where near-field coupling of local resonances leads to negative coupling, i.e., a negative coupling constant. This gives rise to wave-vector-dependent eigenstates of elliptical, linear, and circular polarizations. In particular, fully circular polarization states are not only present at a single point in momentum space (k-space) but also along a line. This circular polarization line, as well as a linear polarization line, emanates from a polarization degeneracy at the Dirac point. We experimentally validate the existence of these eigenstates and demonstrate the energy-, polarization-, and wave vector dependence of this metasurface as well as its sensitivity to fabrication tolerances. By tuning the incident k-vector, certain polarization-energy eigenstates are strongly reflected, allowing for uses in angle-tunable polarization filters and light sources.}},
  author       = {{Wetter, Helene and Wingenbach, Jan and Rehberg, Falk and Gao, Wenlong and Schumacher, Stefan and Zentgraf, Thomas}},
  issn         = {{2330-4022}},
  journal      = {{ACS Photonics}},
  keywords     = {{metasurface, waveguides, Dirac point, polarization, negative coupling}},
  pages        = {{2128--2133}},
  publisher    = {{American Chemical Society (ACS)}},
  title        = {{{Polarization- and Wave-Vector Selective Optical Metasurface with Near-Field Coupling}}},
  doi          = {{10.1021/acsphotonics.5c02865}},
  volume       = {{13}},
  year         = {{2026}},
}

@article{60298,
  abstract     = {{In this work, we introduce PHOENIX, a highly optimized explicit open-source solver for two-dimensional nonlinear Schrödinger equations with extensions. The nonlinear Schrödinger equation and its extensions (Gross-Pitaevskii equation) are widely studied to model and analyze complex phenomena in fields such as optics, condensed matter physics, fluid dynamics, and plasma physics. It serves as a powerful tool for understanding nonlinear wave dynamics, soliton formation, and the interplay between nonlinearity, dispersion, and diffraction. By extending the nonlinear Schrödinger equation, various physical effects such as non-Hermiticity, spin-orbit interaction, and quantum optical aspects can be incorporated. PHOENIX is designed to accommodate a wide range of applications by a straightforward extendability without the need for user knowledge of computing architectures or performance optimization. The high performance and power efficiency of PHOENIX are demonstrated on a wide range of entry-class to high-end consumer and high-performance computing GPUs and CPUs. Compared to a more conventional MATLAB implementation, a speedup of up to three orders of magnitude and energy savings of up to 99.8% are achieved. The performance is compared to a performance model showing that PHOENIX performs close to the relevant performance bounds in many situations. The possibilities of PHOENIX are demonstrated with a range of practical examples from the realm of nonlinear (quantum) photonics in planar microresonators with active media including exciton-polariton condensates. Examples range from solutions on very large grids, the use of local optimization algorithms, to Monte Carlo ensemble evolutions with quantum noise enabling the tomography of the system's quantum state.}},
  author       = {{Wingenbach, Jan and Bauch, David and Ma, Xuekai and Schade, Robert and Plessl, Christian and Schumacher, Stefan}},
  issn         = {{0010-4655}},
  journal      = {{Computer Physics Communications}},
  publisher    = {{Elsevier BV}},
  title        = {{{PHOENIX – Paderborn highly optimized and energy efficient solver for two-dimensional nonlinear Schrödinger equations with integrated extensions}}},
  doi          = {{10.1016/j.cpc.2025.109689}},
  volume       = {{315}},
  year         = {{2025}},
}

@article{61249,
  author       = {{Ai, Qiang and Wingenbach, Jan and Yang, Xinmiao and Wei, Jing and Hatzopoulos, Zaharias and Savvidis, Pavlos G. and Schumacher, Stefan and Ma, Xuekai and Gao, Tingge}},
  issn         = {{2331-7019}},
  journal      = {{Physical Review Applied}},
  number       = {{2}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Optically and remotely controlling localization of exciton-polariton condensates in a potential lattice}}},
  doi          = {{10.1103/physrevapplied.23.024029}},
  volume       = {{23}},
  year         = {{2025}},
}

@article{60992,
  abstract     = {{Non-Hermitian systems hosting exceptional points (EPs) exhibit enhanced sensitivity and unconventional mode dynamics. Going beyond isolated EPs, here we report on the existence of exceptional rings (ERs) in planar optical resonators with specific form of circular dichroism and TE-TM splitting. Such exceptional rings possess intriguing topologies as discussed earlier for condensed matter systems, but they remain virtually unexplored in presence of nonlinearity, for which our photonic platform is ideal. We find that when Kerr-type nonlinearity (or saturable gain) is introduced, the linear ER splits into two concentric ERs, with the larger-radius ring being a ring of third-order EPs. Transitioning from linear to nonlinear regime, we present a rigorous analysis of spectral topology and report enhanced and adjustable perturbation response in the nonlinear regime. Whereas certain features are specific to our system, the results on non-Hermitian spectral topology and nonlinearity-enhanced perturbation response are generic and equally relevant to a broad class of other nonlinear non-Hermitian systems, providing a universal framework for engineering ERs and EPs in nonlinear non-Hermitian systems.}},
  author       = {{Wingenbach, Jan and Ares Santos, Laura  and Ma, Xuekai and Sperling, Jan and Schumacher, Stefan}},
  journal      = {{Arxiv}},
  publisher    = {{Arxiv}},
  title        = {{{Sensitivity and Topology of Exceptional Rings in Nonlinear Non-Hermitian Planar Optical Microcavities}}},
  doi          = {{10.48550/ARXIV.2507.07099}},
  year         = {{2025}},
}

@article{51105,
  author       = {{Wingenbach, Jan and Schumacher, Stefan and Ma, Xuekai}},
  journal      = {{Physical Review Research, in press}},
  title        = {{{Manipulating spectral topology and exceptional points by nonlinearity in non-Hermitian polariton systems}}},
  year         = {{2024}},
}

@inproceedings{60023,
  author       = {{Wetter, Helene and Gao, Wenlong and Rehberg, Falk and Wingenbach, Jan and Schumacher, Stefan and Zentgraf, Thomas}},
  booktitle    = {{Proceedings of The 14th International Conference on Metamaterials, Photonic Crystals and Plasmonics}},
  issn         = {{2429-1390}},
  location     = {{Toyama, Japan}},
  title        = {{{Dielectric metasurface for wave-vector variant and circular polarization dependent transmission}}},
  year         = {{2024}},
}

@article{61257,
  abstract     = {{<jats:p>Exceptional points (EPs), with their intriguing spectral topology, have attracted considerable attention in a broad range of physical systems, with potential sensing applications driving much of the present research in this field. Here, we investigate spectral topology and EPs in systems with significant nonlinearity, exemplified by a nonequilibrium exciton-polariton condensate. With the possibility to control loss and gain and nonlinearity by optical means, this system allows for a comprehensive analysis of the interplay of nonlinearities (Kerr type and saturable gain) and non-Hermiticity. Not only do we find that EPs can be intentionally shifted in parameter space by the saturable gain, but we also observe intriguing rotations and intersections of Riemann surfaces and find nonlinearity-enhanced sensing capabilities. With this, our results illustrate the potential of tailoring spectral topology and related phenomena in non-Hermitian systems by nonlinearity.</jats:p>
          <jats:sec>
            <jats:title/>
            <jats:supplementary-material>
              <jats:permissions>
                <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement>
                <jats:copyright-year>2024</jats:copyright-year>
              </jats:permissions>
            </jats:supplementary-material>
          </jats:sec>}},
  author       = {{Wingenbach, Jan and Schumacher, Stefan and Ma, Xuekai}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  number       = {{1}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Manipulating spectral topology and exceptional points by nonlinearity in non-Hermitian polariton systems}}},
  doi          = {{10.1103/physrevresearch.6.013148}},
  volume       = {{6}},
  year         = {{2024}},
}