The exceptional point(EP)is one of the typical properties of parity–time-symmetric systems,arising from modes coupling with identical resonant frequencies or propagation constants in optics.Here we show that in addit...The exceptional point(EP)is one of the typical properties of parity–time-symmetric systems,arising from modes coupling with identical resonant frequencies or propagation constants in optics.Here we show that in addition to two different modes coupling,a nonuniform distribution of gain and loss leads to an offset from the original propagation constants,including both real and imaginary parts,resulting in the absence of EP.These behaviors are examined by the general coupled-mode theory from the first principle of the Maxwell equations,which yields results that are more accurate than those from the classical coupled-mode theory.Numerical verification via the finite element method is provided.In the end,we present an approach to achieve lossless propagation in a geometrically symmetric waveguide array.展开更多
Photonic topological insulators protected by the lattice spatial symmetry(e.g., inversion and rotation symmetry)mainly support single type edge state, interpreted by either valley or pseudo-spin. Here, we demonstrate ...Photonic topological insulators protected by the lattice spatial symmetry(e.g., inversion and rotation symmetry)mainly support single type edge state, interpreted by either valley or pseudo-spin. Here, we demonstrate theoretically, numerically, and experimentally that a type of judiciously designed two-dimensional Kekulé photonic crystal with time reversal symmetry can possess topological valley and pseudo-spin edge states in different frequency bands. Topologically robust transportation of both the valley and pseudo-spin edge states was confirmed by measuring the transmission of straight and z-shaped interface supported edge mode and comparing with bulk modes in the microwave frequency regime. In addition, we show that due to the distinct topological origins, valley and pseudo-spin edge states can be distinguished by examining their end-scattering into the free space. Our system provides an alternative way in manipulating electromagnetic waves with additional degree-of-freedom, which has potential applications for robust and high-capacity waveguiding and multi-mode dividing.展开更多
基金National Natural Science Foundation of China(NSFC)(11274083,61405067)Guandong Natural Science Foundation(2015A030313748)Shenzhen Municipal Science and Technology Plan(JCYJ20150513151706573)
文摘The exceptional point(EP)is one of the typical properties of parity–time-symmetric systems,arising from modes coupling with identical resonant frequencies or propagation constants in optics.Here we show that in addition to two different modes coupling,a nonuniform distribution of gain and loss leads to an offset from the original propagation constants,including both real and imaginary parts,resulting in the absence of EP.These behaviors are examined by the general coupled-mode theory from the first principle of the Maxwell equations,which yields results that are more accurate than those from the classical coupled-mode theory.Numerical verification via the finite element method is provided.In the end,we present an approach to achieve lossless propagation in a geometrically symmetric waveguide array.
基金Shenzhen Science and Technology Program(JCYJ20210324132416040)National Key R&D Program of China(2018YFB1305500).
文摘Photonic topological insulators protected by the lattice spatial symmetry(e.g., inversion and rotation symmetry)mainly support single type edge state, interpreted by either valley or pseudo-spin. Here, we demonstrate theoretically, numerically, and experimentally that a type of judiciously designed two-dimensional Kekulé photonic crystal with time reversal symmetry can possess topological valley and pseudo-spin edge states in different frequency bands. Topologically robust transportation of both the valley and pseudo-spin edge states was confirmed by measuring the transmission of straight and z-shaped interface supported edge mode and comparing with bulk modes in the microwave frequency regime. In addition, we show that due to the distinct topological origins, valley and pseudo-spin edge states can be distinguished by examining their end-scattering into the free space. Our system provides an alternative way in manipulating electromagnetic waves with additional degree-of-freedom, which has potential applications for robust and high-capacity waveguiding and multi-mode dividing.
