Insight of limitations of effective media theory for metal–dielectric multilayer metamaterials

Effective media theory (EMT) is usually used in the simulations and descriptions of one type of metamaterials which are composed of metal–dielectric multilayer films because of its simplicity and intuitiveness. It is consistent with the rigorous electromagnetic field analysis when the approximation conditions are strictly satisfied. However, there are several noticeable, and sometimes significant failures for the predicted properties that are caused by the approximation dealing with the finite layer of metal/dielectric multilayer structures. These inaccuracies and errors including surface plasmon polaritons (SPPs) spreading angles, reflection properties and interference patterns for SPPs lithography, originate from the differences of isofrequency contours between ideal hyperbolic multilayer structures and the actually fabricated multilayer structures with finite layer of films. Simulation results of EMT with metal/dielectric multilayer structures are analyzed and compared with the rigorous field analysis approach. Being aware of these issues can help to reduce the errors and improve the designs of the plasmonic devices for many applications.