**INHALTE**

We do fundamental research in the field of mesoscopic physics of electronic and optical systems, with a strong focus to turn our findings into trailblazing applications such as smart photonic materials.

A strong motivation of our research are the insights gained in quantum chaos, e.g. how the geometrical shape of a system determines its physical properties. Another focus is the role of interference effects - be it self-interference of the wave function at the system boundary that we found to strongly influence the many-body response in the photoabsorption signal of quantum dots or graphene. In the field of optical mesoscopic systems, we studied in detail the interference effects that lead to deviations from ray optics, namely the Goos-Hänchen shift and Fresenl filtering. That is important for the correct description of optical microcavities - billiards for light and a paradigm example of an open billiards model. Here, light is not confined between two mirrors, but rather by total internal reflection of light travelling along the system boundary in so-called whispering-gallery-type modes. A third motivation for our research comes from the breaking of symmetries that are usually taken for granted, such as the reversal of time. This as well as topological effects in three-dimensional optical microresonators will be the major research focus of the group in the next years. One idea is to use geometric or toplological phases to manipulate and tailor the polarization state of light propagating in curved-space structures.

More information can be found in our publications, on Martin Gutzwiller's Scholarpedia Article on Quantum Chaos, http://www.scholarpedia.org/article/Quantum_chaos, or on Martina Hentschel's Scholarpedia Article on Chaotic Microlasers, http://www.scholarpedia.org/article/Chaotic_microlasers.

Martina Hentschel's **major scientific achievements **are the following (grouped by topic):

**· ** **Electronic mesoscopic systems and graphene**

1. D. Frustaglia, **M. Hentschel,** and K. Richter, Quantum transport in nonuniform magnetic fields:

Aharonov-Bohm ring as a spin switch, **Phys. Rev. Lett. 87**, 256602(1-4) (2001). We showed that spin currents can be controlled by a tiny magnetic field (flux) across the system which proofed to be useful for spintronic applications. (119 citations)

2. **M. Hentschel** and F. Guinea, Orthogonality catastrophe and Kondo effect in graphene, **Phys.** **Rev. B 76**, 115407(1-7) (2007). Many-body effects are at the heart of condensed matter physics. We studied two important (orthogonality catastrophe and the Kondo effect) for mesoscopic systems, here in particular for graphene, and showed their absence at the Dirac point. (96 citations)

**· Optical mesoscopic systems – Fundamentals**

3.** M. Hentschel **and K. Richter, Quantum chaos in optical systems: The annular billiard, **Phys. Rev. E 66**, 056207(1-13) (2002). Optical systems are intrinsically open as light may escape by refraction or by evanescent leakage. We explain the consequences for quantum chaos and ray-wave correspondence. (84 citations)

4. **M. Hentschel,** H. Schomerus, and R. Schubert, Husimi functions at dielectric interfaces: Inside-outside duality for optical systems and beyond, **Europhys. Lett. 62**, 636-642 (2003). The openness of optical systems requires a generalisation of Husimi functions such that incoming, reflected and transmitted rays are properly represented by their wave (Husimi) counterparts.(73 citations)

5. H. Schomerus and **M. Hentschel**, Correcting ray optics at curved dielectric microresonator interfaces: Phase-space unification of Fresnel filltering and the Goos-Hänchen shift,** Phys. Rev.Lett. 96**, 243903(1-4) (2006). Ray optics breaks down for small wavelengths, with additional corrections arising when the interface boundaries are curved. These are essential for an amended ray description of microcavities. (62 citations)

6. P. Stockschläder and **M. Hentschel,** Consequences of a wave-correction extended ray dynamics for integrable and chaotic optical microcavities**, J. Opt. 19**, 125603(1-13) (2017). This paper summarizes ray-wave correspondence and corrections to it in the context of quantum chaos in optical microcavities, including detailed formulae for the Fresnel filtering and Goos-Hänchen correction.

7. J. Wiersig, S. W. Kim, and **M. Hentschel,** Asymmetric scattering and non-orthogonal mode patterns in passive optical micro-spirals, **Phys. Rev. A 78**, 053809(1-8) (2008). This paper marks the beginning of research on non-Hermitian physics in otpical microcavities that meanwhile has taken the community to PT-symmetry and its breaking as well as to the peculiar resonance mode properties at exceptional points and their use in sensing applications. (69 citations)

**· Optical mesoscopic systems – Applications**

8. J. Wiersig and **M. Hentschel,** Combining unidirectional light output and ultralow loss in deformed microdisks, **Phys. Rev. Lett. 100**, 033901(1-4) (2008). Achieving the unidirectional light output that characterizes all lasers from microdisk resonators has long been the holy grail in the field. In this 2008 PRL we predicted that a certain deformation (called Limaçon) will yield directional emission. This was confirmed by four different groups in experiments within one year. The reason is that light coupling out follows the so-called unstable manifold ruling the dynamics in nonlinear (chaotic) systems even, and in particular, when they are open.(177 citations).

9. J. Kreismann, S. Sinzinger, and **M. Hentschel,** Three-dimensional Limaçon: Properties and applications, **Phys. Rev. A 95**, 011801(R)(1-6) (2017). Modelling optical microcavities as two-dimensional billiards is applicable only when their height is small compared to the wavelength. This paper marks the beginning of a systematic study of three-dimensional microresonators in which we find qualitatively new behavior. It is important for applications, in particular we find far-field output tilted away from cross-sectional (two-dimensional) resonator plane*.*

**· Optical mesoscopic systems – Topology**

10. L. B. Ma, S. L. Li, V. M. Fomin, M. Hentschel, J. B. Götte, Y. Yin, M. R. Jorgensen, and O. G. Schmidt, Spin-orbit coupling of light in asymmetric microcavities, Nature Comm. 7,10983(1-6);10983s1(1-9) (2016). The coupling of the two polarisation directions of light in three dimensions induces an intricate interplay between orbital and polarisation (spin) degrees of freedom. This polarisation dynamics depends, e.g., via an anisotropic refractive index, furthermore on the material properties. (10 citations).