Finite-thickness slabs of hyperbolic media with tilted optical axes exhibit asymmetry properties for waves propagating upward and downward with respect to slab interfaces. Under certain conditions, asymmetric hyperbolic media acquire extreme permittivity parameters and the difference between upward and downward propagating waves becomes very large. Furthermore, both waves can be perfectly matched with the free space; such a feature makes possible the development of optically ultra thin perfect absorbers. The proposed approach is unified and allows the use of different -negative materials. Of particular interest is the asymmetric hyperbolic medium, made of silicon nanowires, since it can be directly applicable to solar cell systems.