Transmission Properties of Electromagnetic Waves in Magneto-Electro-Elastic Piezoelectric Electromagnetic Metamaterials

We designed magneto-electro-elastic piezoelectric, electromagnetic (EM) metamaterials (MEEPEM) by using a square lattice of the periodic arrays of conducting wires, piezoelectric photonic crystal (PPC), and split-ring resonators (SRRs). We analyzed the mechanism for multi-field coupling in MEEPEM. The magnetic field of the EM wave excites an attractive Ampere force in SRRs, which periodically compress MEEPEM, and this can create electric polarization due to the piezoelectric effect. The electric field of the EM wave can excite a longitudinal superlattice vibration in the PPC, which can also create electric polarization. The electric polarization can couple to the electric field of the periodic arrays of conducting wires. The coupled electric field will couple to the EM wave. These interactions result in multi-field coupling in MEEPEM. The coupling creates a type of polariton, called multi-field coupling polaritons, corresponding to a photonic band gap, namely, the multi-field coupling photonic band gap. We calculated the dielectric functions, the reflection coefficients, and the effective magnetic permeability of MEEPEM. By using them, we analyzed the transmission properties of EM waves in the MEEPEM. We analyzed the possibility of MEEPEM as left-handed metamaterials and zero refractive index material.