Elastic Hamiltonians for quantum analog applications

Elastic waves are complex mixtures of transverse and longitudinal oscillations even in isotropic and homogeneous media, in contrast to the quantum, electromagnetic, or acoustic waves which could share the same formalism of Hamiltonian and application techniques. Here, we reformulate the elastic wave equation into a set of polarization-dependent decoupled Hamiltonians, to enable the quantum analogous techniques for higher functionalities. As an application example, we adopt the supersymmetric transformation from particle physics and apply it to elastic Hamiltonians, for the demonstration of spatial- and polarization-selective separation of guided elastic waves. Enabling the application of quantum-analogous techniques under the established elastic Hamiltonian formulation, our approach provides a pathway for controlling elastic waves, not limited to the control of an individual guided mode for arbitrary elastic waves, demonstrated here with supersymmetric technique.