Scaling Theory of Wave Confinement in Classical and Quantum Periodic Systems

Completely controlling the propagation of waves in periodic media is a key challenge that is essential for a large variety of applications. An especially interesting type of propagation control is wave confinement, achievable by introducing disorder and functional defects into an otherwise periodic medium [1]. Based on the character of the introduced defect, such waves may exhibit various dimensionalities of confinement, as depicted in Fig. 1.