  Polaritons in strongly anisotropic thin layers have recently captured the
attention in nanophotonics because of their directional propagation at the
nanoscale, which offers unique possibilities for nanooptical applications.
However, exploiting the full potential of anisotropic polaritons requires a
thorough understanding of their properties, including field confinement, energy
and phase propagation direction and losses. Here we fill this critical gap by
providing fundamental insights into the propagation of anisotropic polaritons
in thin biaxial layers. In particular, we introduce a novel methodology that
allows us to represent isofrequency curves of polaritons in strongly
anisotropic materials considering that the real and imaginary parts of the
wavevector are not parallel. In fact, we analytically show that the direction
of the imaginary part of the wavevector is parallel to the group velocity,
which can have different, even perpendicular or opposite, directions with
respect to the phase velocity. This finding is crucial for understanding
polaritonic phenomena in anisotropic media, yet it has so far been widely
overlooked in the literature. Additionally, we introduce a criterion for
classifying the polaritonic modes in biaxial layers into volume and surface
categories, and analyze their dispersion, field structure, and losses. Finally,
we discover the existence of anisotropic transverse electric modes, which can
exhibit natural canalization. Taken together, our results shed light on
hitherto unexplored areas of the theory of electromagnetic modes in thin
biaxial layers. Although exemplified for van der Waals MoO3 layers, our
findings are general for polaritons in other strongly anisotropic biaxial
hyperbolic crystals.
