Abstract
1 Introduction
The quantum spin-Hall state is an electronic surface state with immunity against defects.1 The momentum is locked to the intrinsic spin of electrons, and backward transports are suppressed unless the spin flips.2,3 Analogous phenomena have been widely reported in various uniform and metamaterial waveguides, where theories of universal spin-momentum locking4 and spin-orbit interactions5,6 have been well studied. Uniform waveguides include closed metal waveguides, fibers, and plasmonic metals, where the unidirectional transmission can be realized based on nano-gratings,7 circularly polarized (CP) dipoles or Huygens dipoles8,9 supported by resonant particles.10
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