Quantum to Classical Transitions in Multilayer Plasmonic Metamaterials*

Electromagnetic response of noble metals, transparent conducting oxides, and highly doped semiconductors are all dominated by the dynamics of their free electron plasma. AlInAs/InGaAs heterostructures have emerged as a reliable platform that provides epsilon-near-zero, plasmonic, and hyperbolic responses in the important mid-infrared frequency range. The electromagnetic properties of semiconductor multilayers can be related to the properties of individual layers via effective medium theory (EMT). It is typically assumed that the validity of EMT improves as the layers in metamaterials become thinner. However, quantum-confinement is expected to affect the dynamics of the free charges in ultra-thin layers. In this work, we analyze, experimentally, analytically, and numerically, the optical response of semiconductor designer metal multilayers that undergo transition from bulk to quantum-confined regime. We demonstrate that this transition can be used as a doping-independent control mechanism to engineer the optical response of designer metals and the optical topology of the resulting multilayer metamaterials.