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Materials with nontrivial topological properties may also be found in standard optical systems like photonic crystals and waveguide arrays. Many of these systems are characterized by a well-defined topological winding number (also known as the Brouwer degree). We pick several interesting optical model systems to show that the winding number is a very simple topological concept, which can often be guessed intuitively.
However, even for minor modifications of the standard topological model systems the use of the simplest types of winding numbers is no longer justified. Thus, we also present ongoing research to employ other intuitive topological concepts.
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Alexander Quandt, "Optical topological materials and winding numbers," Proc. SPIE 11461, Active Photonic Platforms XII, 1146115 (20 August 2020); https://doi.org/10.1117/12.2567486