Abstract
We study full vector imaging of two dimensional source fields through finite slabs of media with extreme anisotropy, such as hyperbolic media. For this, we adapt the exact transfer matrix method for uniaxial media to calculate the two dimensional transfer functions and point spread functions for arbitrary vector fields described in Cartesian coordinates. This is more convenient for imaging simulations than the use of the natural, propagation direction-dependent TE/TM basis, and clarifies which field components contribute to sub-diffraction imaging. We study the effect of ordinary waves on image quality, which previous one-dimensional approaches could not consider. Perfect sub-diffraction imaging can be achieved if longitudinal fields are measured, but in the more common case where field intensities or transverse fields are measured, ordinary waves cause artefacts. These become more prevalent when attempting to image large objects with high resolution. We discuss implications for curved hyperbolic imaging geometries such as hyperlenses.
Highlights
(TMM) to calculate the full three-dimensional propagation of fields through finite slabs of extreme uniaxial media
First a spatial Fourier transform along x and y of the vector field components of the image is taken at the input; for each spatial frequency set, fields are projected on the TE/TM basis in which transfer matrices are expressed; the TMM method is used to propagate all spatial frequencies; the inverse transform is used to reconstruct the fields at the other end
While we have used a local model only, as is sufficient in many cases15, this can readily be extended to non-local models22 or used for metal/dielectric multilayer stacks14
Summary
(TMM) to calculate the full three-dimensional propagation of fields through finite slabs of extreme uniaxial media. In contrast to previous studies using TMM, we consider two dimensional images from any object, represented by a known field in Cartesian coordinates. In that work the longitudinal cross coupling was ignored, which, as we show here, becomes of particular importance for near field imaging where it enables the extraction of perfect images. We use this method to analyse imaging transfer functions and two-dimensional point spread functions, as well as imaging artefacts due to ordinary waves, and present strategies to avoid them. The method lends itself to rapid exact calculation of images through slabs of uniaxial materials, and can be extended to exact calculations of images through planar layered hyperbolic media stacks as well as non-local models for wire media
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