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\textsf{\bfseries \Large Mode selection by symmetry and topology}\\[5mm]
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\underline{Henning Schomerus$^{\sst 1}$}\\[5mm]%auteurs
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\item[$^{\sst 1}\!\!$]\emph{Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK}\\[5mm]
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\caption*{Topological photonic systems: (a) Mode guiding in a quasi-one dimensional structure supporting a localised defect state. (b) Sublattice polarisation of Landau levels in strained honeycomb systems. (c) Point defect state in a dimerised Lieb lattice.\label{fig:O2}}
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In systems with suitable symmetries, topologically protected states can arise that are immune to perturbations. I discuss how the properties of such states can be enriched in photonic systems, where one has access to absorption and amplification. In particular, I describe analogues of the chiral symmetry and the charge-conjugation symmetry and elucidate their role for the selective amplification of topological defect states.  This includes the setting of point defects in one dimensional chain\footnote{H. Schomerus, Opt. Lett. \textbf{38}, 1912 (2013).}\footnote{C. Poli, M. Bellec, U. Kuhl, F. Mortessagne, and H. Schomerus,  Nat. Commun. \textbf{6} (2015).} and two-dimensional lattices with flat bands\footnote{C. Poli, H. Schomerus, M. Bellec, U. Kuhl, and F. Mortessagne, arXiv:1512.02284 (2015).}, as well as the case of the sublattice-polarised Landau level in strained honeycomb lattices \footnote{H. Schomerus and N.~Y. Halpern, Phys. Rev. Lett. \textbf{110}, 013903 (2013).}\footnote{C. Poli, J. Arkinstall, and H. Schomerus, Phys. Rev. B \textbf{90}, 155418 (2014).}.


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