研究期間：10108~10207;In this project “Study on the electrodynamics and acoustodynamics of dispersive metamaterials”we will study the electrodynamics/acoustodynamics of dispersive-lossy metamaterials. Our study includes the following items: 1. We will first derive the formulas of effective energy density in dispersive electromagnetic metamaterials. From these formulas we can know what the appropriate field variables are. From the known equations of motion for these field variables we can find the Lagrangian density by trial and error method. The equations of motion are then identified as the Euler-Lagrangian equations. The corresponding canonical momentum of every field variable can be derived from this Lagrangian density, and then we can find the Hamiltonian density using the Legendre Transformation. The Hamiltonian density should be the same as the energy density or plus a divergence term. 2. For acoustic metamaterials we will follow the procedures of 1 to find the Langrangian density and Hamiltonian density, and then study their acoustodynamics. 3. If the metamaterials are lossy, we will find the dissipation function. 4. For the system that we can find the Hamiltonian, we will study the quantized version of the system. This research may provide useful insight or knowledge for further studying the quantum optics that is related to metamaterials. 5. We will study the propagation behaviors of electromagnetic/acoustic signals in dispersive metamaterials. The research results may provide useful insight or knowledge for the study of communication system/Integrated optics system using metamaterials.
