An alternative to conventional spacetime is proposed and rigorously formulated for nonlocal continuum field theories through the deployment of a fiber bundle-based superspace extension method. We develop, in increasing complexity, the concept of nonlocality starting from general considerations, going through spatial dispersion, and ending up with a broad formulation that unveils the link between general topology and nonlocality in generic material media. It is shown that nonlocality naturally leads to a Banach (vector) bundle structure serving as an enlarged space (superspace) inside which physical processes, such as the electromagnetic ones, take place. The added structures, essentially fibered spaces, model the topological microdomains of physics-based nonlocality and provide a fine-grained geometrical picture of field–matter interactions in nonlocal metamaterials. We utilize standard techniques in the theory of smooth manifolds to construct the Banach bundle structure by paying careful attention to the relevant physics. The electromagnetic response tensor is then reformulated as a superspace bundle homomorphism and the various tools needed to proceed from the local topology of microdomains to global domains are developed. For concreteness and simplicity, our presentations of both the fundamental theory and the examples given to illustrate the mathematics all emphasize the case of electromagnetic field theory, but the superspace formalism developed here is quite general and can be easily extended to other types of nonlocal continuum field theories. An application to fundamental theory is given, which consists of utilizing the proposed superspace theory of nonlocal metamaterials in order to explain why nonlocal electromagnetic materials often require additional boundary conditions or extra input from microscopic theory relative to local electromagnetism, where in the latter case such extra input is not needed. Real-life case studies quantitatively illustrating the microdomain structure in nonlocal semiconductors are provided. Moreover, in a series of connected appendices, we outline a new broad view of the emerging field of nonlocal electromagnetism in material domains, which, together with the main superspace formalism introduced in the main text, may be considered a new unified general introduction to the physics and methods of nonlocal metamaterials.
AbstractEmergent electromagnetism in magnets originates from the strong coupling between conduction electron spins and those of noncollinear ordered moments and the consequent Berry phase. This offers possibilities to develop new functions of quantum transport and optical responses. The emergent inductance in spiral magnets is an example recently proposed and experimentally demonstrated, using the emergent electric field induced by alternating currents. However, the microscopic theory of this phenomenon is missing, which should reveal factors to determine the magnitude, sign, frequency dependence, and nonlinearity of the inductance L. Here we theoretically study electromagnetic responses of spiral magnets by taking into account their collective modes. In sharp contrast to collinear spin-density wave, the system remains metallic even in one dimension, and the canonical conjugate relation of uniform magnetization and phason coordinate plays an essential role, determining the properties of L. This result opens a way to design the emergent inductance of desired properties.
The results of studies of the electromagnetic response from composite structures made of a carbon-containing polymer with the inclusion of spherical pores in the bulk of the material and with pyramidal corrugation on the surface of the material are presented. The results of modeling the frequency dependences of the transmission, reflection and absorption coefficients in the EHF range are shown. Samples of composite carbon-containing structures with technological inhomogeneities have been fabricated by 3D printing. Measurements of the electromagnetic response from experimental samples were carried out in the frequency range from 100 to 1000 GHz. At frequencies up to 250 GHz, the inclusion of air pores in the polymer volume reduces the transmission coefficient, practically does not affect the reflection, and increases the absorption. Pyramid corrugated material absorbs more than 99% of radiation in the frequency range from 200 to 635 GHz.
In paper results of research of metamaterial surface based on split-ring resonators obtained by photolithography are presented. Numerical simulation of electromagnetic response of the created structure are shown. Experimental researches of the transmission coefficient using quasi-optical methods of continuous and time-domain spectroscopy in the frequency range from 34 to 200 GHz were carried out. Area of broadband screening in the EHF range has been found.