Breakdown of the effective medium theory: a perspective from Goos-Hänchen shift

The effective medium theory (EMT) provides a simplified framework to calculate the electromagnetic responses and is generally considered exact in the all-dielectric system with deep-subwavelength constituents. In this work, we perform the Goos-Hänchen (GH) shift that invalidates the EMT on the multilayered dielectric structures under the common conditions. This breakdown of the EMT arises from the high sensitivity of the GH shift on the phase and magnitude of Fresnel reflection coefficient. The degree of such breakdown shows strong dependence on the polarization angle of incidence and the layer and filling fraction of the structures. Notably, we find that the GH shift is potentially applicable to nano-meter scale thickness sensing, which cannot be displayed based on EMT in some cases. Our findings will provide useful guidance to reduce the calculation errors of the electromagnetic responses and promote the design of precise metrology devices.