On the limits of laminates in diffusive optics

Laminate metamaterials lead to anisotropic material properties, which can be tailored by the contrast between the two ingredient materials within the laminate. Such tailored anisotropies are, for example, required to realize advanced invisibility cloaks, wormhole architectures, or analogues of negative refraction. The physics and mathematics of laminates is very well established in the context of the diffusion equation and mathematical equivalents thereof, such as the heat conduction equation, the electrical conduction equation, electrostatics, magnetostatics, and laminar fluid dynamics. However, the validity of the diffusion equation is often stressed for disordered optical media, because sufficiently large transmission of light is requested. As a result, the condition that all relevant transport mean free path lengths need to be small compared to all relevant geometrical dimensions, may not be fulfilled. Monte Carlo simulations can grasp the physics of this transition regime between diffusive and ballistic optics. Here, we present corresponding numerical simulations for laminates. On this basis, we discuss the resulting fundamental limitations and trade-offs for laminates.