Hyperbolic Plasmons (HP)

Hyperbolic Plasmon¶

Conductivity Tensor \(\(\begin{pmatrix} \sigma_{xx} & \sigma_{xy}\\ \sigma_{yx} & \sigma_{yy} \end{pmatrix}\)\) We note that the real part of dielectric permittivity is proportional to the \(\text{Im}(\sigma)\), a consequence of current continuity, then, a hyperbolic region appears when, \(\(\sigma_{xx} \ne \sigma_{yy}, \text{ }\text{Im}(\sigma_{xx}) \cdot \text{Im}(\sigma_{yy}) < 0\)\) Only one component of the conductivity tensor is of metallic type. On the other hand, Re(σ), is directly proportional to the optical absorption of the freestanding 2D layer.

The in-plane anisotropy provides the potential to realize HP in Black Phosphorus within the plane of a 2D material. The structural anisotropy in all van der Waals crystals results in a strong optical birefringence. Hyperbolicity is defined as an extreme type of birefringence, whereby the permittivity along orthogonal crystal axes are not just different, but opposite in sign¹

The natural optical anisotropy associated with van der Waals crystals, and the polar nature of many, should in principle offer a broad range of naturally occurring hyperbolic materials covering a very broad spectral range. Strong anisotropy in electron motion along the in-plane (metallic) and out-of-plane (insulating) layered materials can lead to hyperbolicity for specific frequency bands (graphite and magnesium diboride).

Related Links : - Plasma oscillation - Surface Plasmons and Polaritons - HP in Black Phosphorus

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