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In this talk I will discuss how synthetic photonic materials can be utilized to explore several non-Hermitian symmetries and their topological implications. Although difficult to access in high-energy physics and conventional condensed matter systems, these non-Hermitian symmetries can be realized in photonic materials with carefully arranged gain and loss elements. Therefore, such synthetic photonic materials provide an ideal platform to explore the ramification of these symmetries, including parity-time (PT) symmetry and non-Hermitian particle-hole symmetry, as well as the resulting novel optical phenomena and functionalities.

PT symmetric photonics [1] is one of the fastest growing fields in the past five years. It requires a judiciously balanced refractive index satisfying , i.e., with a symmetric real index modulation and an antisymmetric imaginary index modulation. I will talk about its spontaneous symmetry breaking [2], the coexistence of laser and anti-laser [3], generalized conservation laws for wave propagation, and anisotropic transmission resonances [4]. Particle-hole symmetry imposes a strong restriction on the underlying system in the Hermitian case, which exists, for example, in superconductors and is related to Majorana zero modes. In photonics however, I will show that particle-hole symmetry is ubiquitous in gain and loss modulated systems with two sublattices [5], such as coupled waveguides and a network of optical cavities. As a consequence, there exist a large set of symmetry-protect zero modes, which can be utilized for building a unique single-mode, fixed-frequency, and spatially tunable laser, potentially useful for spatial encoding of telecommunication signals.

[1] Feng, L., El-Ganainy, R. & Ge, L. *Nat. Photon.* **11**, 752 (2017).

[2] Ge, L. & Stone, A. D. *Phys. Rev. X* **4,** (2014).

[3] Chong, Y. D., Ge, L., Cao, H. & Stone, A. D. *Phys. Rev. Lett.* **105,** 53901 (2010).

[4] Ge, L., Chong, Y. D. & Stone, A. D. *Phys. Rev. A* **85,** 023802 (2012).

[5] Qi, B., Zhang, L. & Ge, L. *Phys. Rev. Lett.* **120**, 093901 (2018).