Infrared non-invasive sub-wavelength microscopy with metamaterials

I demonstrate that hyperbolic metamaterials may provide the solution to the long-standing prob- lem of the fundamental diffraction limit plaguing conventional microscopy and optical imaging sys- tems. Presented here is the formalism of the theory, classical electrodynamics, used to describe the diffraction limit and sub-wavelength imaging using hyperbolic metamaterials. Effective medium theory is then derived and put forth as a design method for such hyperbolic metamaterials. I then outline the design of a planar device based on a hyperbolic metamaterial for use in infrared mi- croscopy, and present numerical simulations to demonstrate the behaviour and performance of the device. The device employs multilayers of InGaAs/AlInAs and is capable of sub-diffraction imaging resolution in the wavelength range of 8.8 - 10.5 μm. I show that high spatial frequency waves, which normally decay in vacuum, are allowed to propagate and reach the far-field in a hyperbolic meta- material. Using a Green’s function formalism to describe optical sources, sub-wavelength imaging capabilities of hyperbolic metamaterials is shown. Finally, potential device applications using the designed metamaterial are motivated.