Dynamic regulation of nonlocal effect and nonlocal degree in gyromagnetic metamaterials with an applied magnetic field

We report dynamic regulation of nonlocal degree, nonlocal effects and spatial dispersion characteristics for transverse electric (TE) waves in periodic layered gyromagnetic metamaterials (PLGMs) by an applied magnetic field. A nonlocal effective permeability tensor, relying on both frequency and wave vector, is derived by expanding the accurate dispersion relation obtained by the transfer-matrix method (TMM) to high-order terms. The numerical results indicate that the degree of nonlocality of electromagnetic response in such PLGMs is closely dependent on the ratio between the period of PLGMs and the working wavelength. There are giant spatial nonlocality and strong spatial dispersion near the center or boundary of the first Brillouin zone, which leads two or three propagating modes to appear in these regions for a fixed frequency. Interestingly, the degree of nonlocality, nonlocal effects and spatial dispersion properties in such PLGMs can be manipulated dynamically by an applied static magnetic field. In addition, it is possible that a quasi-straight isofrequency contour occurs in the case of linear response. These properties make the PLGMs become excellent candidates for designing photonic devices in information communication, storage, nondiffraction transmission, and so on.