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Dual-directional group delays during optical topological transitions in black phosphorus-based asymmetric hyperbolic metamaterials.

We theoretically study the optical properties of TM waves when their magnetic field direction is perpendicular to the armchair and zigzag optical axes of black phosphorus, respectively. It is found that hyperbolic dispersion and elliptic dispersion coexist in periodically arranged black phosphorus multilayers. Interestingly, by tilting the symmetric multilayers to be asymmetric, the elliptical part of the original two dispersions disappears as the wavelength increases. As such only the hyperbolic dispersion remains, showing an optical topological transition. In the region of the topological transition, a large transmitted group delay (3ps) and a reflected group delay (0.2ps) of the TM waves occurs simultaneously. The corresponding group velocities are slowed down to approximately c/1000 and c/100 (c is the speed of light in a vacuum), respectively. This dual-directional group delays significantly increase the wave-matter interaction so that nonreciprocal perfect absorptions can be realized in the mid-infrared band. Such asymmetrical black phosphorus hyperbolic metamaterials can be applied to the directional, tunable, and nonreciprocal perfect absorbers and also to devices based on strong wave-matter interactions.