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In this paper, we numerically investigate the edge plasmons in monolayer black phosphorus. It is found that the complex effective indexes of these modes depend on the molecular configuration of the edge. We have calculated the ratio of the real over the imaginary part of the mode effective index, and the results indicate that such edge modes indeed possess outstanding propagation performances in the mid-infrared. In the case of black phosphorus nanoribbon, it seems that only the anti-symmetric modes have low losses, and may be of use in applications. Compared with those at the edge of monolayer black phosphorus, the propagation performances can be further enhanced due to the mode coupling between the two edges. In the end, the effects of substrates are discussed. Our study shows that monolayer black phosphorus may be regarded as a promising candidate for plasmonic applications in the mid-infrared.

We demonstrate that directional electromagnetic scattering can be realized in an artificial Mie resonant structure that supports electric and magnetic dipole modes simultaneously. The directivity of the far-field radiation pattern can be switched by changing wavelength of the incident light as well as tailoring the geometric parameters of the structure. In addition, we further design a quasiperiodic spoof Mie resonant structure by alternately inserting two materials into the slits. The results show that multi-band directional light scattering is realized by exciting multiple electric and magnetic dipole modes with different frequencies in the quasiperiodic structure. The presented design concept is suitable for microwave to terahertz region and can be applied to various advanced optical devices, such as antenna, metamaterial and metasurface.

a b s t r a c tWe consider the incompressible magnetohydrodynamic (MHD) equations with the coefficients depending on the density and temperature. We prove the existence of unique local strong solutions for all initial data satisfying a natural compatibility condition. The initial density need not be positive and may vanish in an open set.