Inspired from electronic systems, topological photonics and polaritonics aims to engineer optical devices with robust properties in metamaterials. A popular model was proposed by Wu and Hu for realizing a bosonic Z2 topological crystalline insulator with “robust” edge states, which led to intense studies including extensions to polaritons. Utilizing topology in photonic designs can lead to robust optical propagation with promising implications for integrated photonics. However, detailed analyses using topological quantum chemistry tools reveal that the Wu-Hu model is topologically trivial but is a higher order topological photonic insulator (Phys Rev. Lett, 131, 053802 (2023). Therefore, the waveguided edge mode in the Wu-Hu model cannot host robust helical states, as previously believed. We are exploring new ways of incorporating nontrivial topology in photonic systems where the excitations are bosonic in nature. We will discuss our efforts in incorporating quantum geometry in photonic systems by utilizing fragile topology. Our efforts and challenges to realize fragile topological photonic and polaritonic lattices will be discussed.
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