  Light-matter coupling in van der Waal's materials holds significant promise
in realizing Bosonic condensation and superfluidity. The underlying
semiconductor's crystal asymmetry, if any, can be utilized to form anisotropic
half-light half-matter quasiparticles. We demonstrate generation of such highly
anisotropic exciton-polaritons at the interface of a biaxial layered
semiconductor, stacked on top of a distributed Bragg reflector. The spatially
confined photonic mode in this geometry couples with polarized excitons and
their Rydberg states, creating a system of highly anisotropic polariton
manifolds, displaying Rabi splitting of up to 68 meV. Rotation of the incident
beam polarization is used to tune coupling strength and smoothly switch regimes
from weak to strong coupling, while also enabling transition from one
three-body coupled oscillator system to another. Light-matter coupling is
further tunable by varying the number of weakly coupled optically active
layers. Our work provides a versatile method of engineering devices for
applications in polarization-controlled polaritonics and optoelectronics.
