The semiclassical approximations to quantum mechanics and wave optics are generally limited to the systems with dimensions that substantially exceed the corresponding  wavelength. Thus, the realm of the semiclassical physics was essentially bypassed by the recent developments in the field of nanophotonics and metamaterials, focused on controlling light on the nanoscale.

However, hyperbolic metamaterials and related devices (such as e.g. the hyperlens), by their very purpose, allow a dramatic wavelength "compression", by orders of magnitude below the free-space value. As a result, the actual wave dynamics inside such nano-systems, remains semiclassical. Here, we present the semiclassical description of these "hyperbolic" nanophotonic systems.