An anisotropic transfer matrix approach to profiled optical field propagation through hyperbolic metamaterials

Abstract

We extend the transfer matrix method to study the propagation of beams and arbitrary profiled fields through anisotropic metamaterial slabs, and to demonstrate the negative refractive index property resulting in linear self-focusing of beams in hyperbolic metamaterials. Specifically, the transfer matrix method, commonly used to analyze bi-directional plane wave propagation, is developed to analyze beam propagation. By expressing a Gaussian beam as an angular spectrum of plane waves, an anisotropic transfer matrix, which is also obtained using the eigenvalues mentioned above, can be applied to calculate the beam spectrum at an arbitrary distance of propagation through a hyperbolic metamaterial. With given incident and emergent media, say, air, linear self-focusing within the metamaterial slab and subsequent reimaging in the emergent medium are numerically investigated for one transverse dimensional TM polarized Gaussian beam. Simulation results are compared with results from the unidirectional transfer function approach. The anisotropic transfer matrix method can be used to study beam transmission and reflection at the interfaces, and can be applied to analyze optical propagation through anisotropic metamaterial on uniaxial electro-optic substrates. The technique can be extended to arbitrary initial optical field profiles in one transverse dimension to assess the imaging quality of metamaterial slabs.