**4. Conclusions**

In summary, we have introduced a method to obtain geometric mirror planes from the optical *T*-matrix of a scattering object. Accordingly, the optical effects of geometric structures such as metamaterials are analyzed [27]. We applied the procedure to an isolated gold helix and found correlations between the symmetry of its geometric shape and those of the optical response in the long wavelength regime. On the one hand, this confirms the expectation that instrinsic geometric chirality is directly related to an optically chiral response. On the other hand, for shorter wavelengths where higher multipoles are induced, mirror planes derived from the *T*-matrix do not coincide with the geometric mirror plane. This implies light-matter interactions whose symmetry cannot be explained simply by geometric chirality. Our method can be applied to all isolated scattering objects being chiral as the helix or achiral (see Supplementary Materials). It constructively identifies geometric planes of mirror symmetry in their optical response. This approach provides the basis for a detailed analysis of correlations between structural and spectral properties of nano-optical scatterers.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2073-8994/12/1/158/s1 and contain detailed information on *T*-matrix formalism, electromagnetic and geometric chirality coefficients, multipolar analysis, geometric model and optimization as well as the analysis of an achiral scatterer with our method.

**Author Contributions:** Conceptualization, P.G. and K.M.M.; methodology, P.G. and P.-I.S.; software, X.G.-S. and P.-I.S.; resources M.N.-V. and K.M.M.; writing—original draft preparation, P.G.; writing—review and editing, X.G.-S., P.-I.S., K.M.M., M.N.-V. and S.B.; supervision, M.N.-V. and S.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** We acknowledge support from Freie Universität Berlin through the Dahlem Research School. This research was funded by the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie gran<sup>t</sup> number 675745. This research was funded by the EMPIR programme co-financed by the Participating States and from the European Union's Horizon 2020 research and innovation programme under gran<sup>t</sup> number 17FUN01 (BeCOMe). M. Nieto-Vesperinas acknowledges Spanish Ministerio de Ciencia, Innovación y Universidades, grants FIS2014-55563-REDC, FIS2015-69295-C3-1-P, and PGC2018-095777-B-C21.

**Acknowledgments:** We thank Martin Hammerschmidt for in-depth discussions on several topics.

**Conflicts of Interest:** The authors declare no conflict of interest.
