On the Topology of Nonlocal Field Theories of Material Continua

A fairly general and unified approach to nonlocality in material continua is introduced here. This work aims at proposing new mathematical and conceptual foundations for the emerging topic of nonlocal metamaterials suitable for physicists, engineers, mathematicians, and materials scientists. The text develops an original rigorous theory, a detailed example involving nonlocal semiconductor metamaterials, and extensive literature review and discussion of possible applications of nonlocal metamaterials.

On the Topology of Nonlocal Field Theories of Material Continua

A fairly general and unified approach to nonlocality in material continua is introduced here. This work aims at proposing new mathematical and conceptual foundations for the emerging topic of nonlocal metamaterials suitable for physicists, engineers, mathematicians, and materials scientists. The text develops an original rigorous theory, a detailed example involving nonlocal semiconductor metamaterials, and extensive literature review and discussion of possible applications of nonlocal metamaterials.

Direct-tuning methods for semiconductor metamaterials

Among various tunable optical devices, tunable metamaterials have exhibited their excellent ability to dynamically manipulate lights in an efficient manner. However, for unchangeable optical properties of metals, electromagnetic resonances of popular metallic metamaterials are usually tuned indirectly by varying the properties or structures of substrates around the resonant unit cells, and the tuning of metallic metamaterials has significantly low efficiency. In this paper, a direct-tuning method for semiconductor metamaterials is proposed. The resonance strength and resonance frequencies of the metamaterials can be significantly tuned by controlling free carriers’ distributions in unit cells under an applied voltage. This direct-tuning method has been verified in both two-dimensional and three-dimensional semiconductor metamaterials. In principle, the method allows for simplifying the structure of tunable metamaterials and opens the path to applications in ultrathin, linearly-tunable, and on-chip integrated optical components (e.g., tunable ultrathin lenses, nanoscale spatial light modulators and optical cavities with resonance modes switchable).