Limits of imaging with multilayer hyperbolic metamaterials

The multilayer hyperbolic metamaterials are known to be capable of imaging with sub-wavelength resolution. In this work performance of these "hyperbolic lenses" is analyzed in depth by employing commonly used transfer matrix method as well as the eigen-mode approach, the latter offering a clear physical insight into the operation of hyperbolic imagers and revealing their fundamental limitations. The resolution of multilayer structures is shown to decrease with the number of layers not only due to increased loss but also because of the severe suppression of large spatial frequencies caused by the cancellation between symmetric and antisymmetric eigen-modes. Additionally, the resolution is strongly affected by the granularity and fill ratio. In the end, hyperbolic metamaterials can create an image with subwavelength resolution only at very close distance to the object and hence limiting their utility.