Features of the optical response of dielectric crystals with incommensurate phases

Kushnir, O. S.; Lokot, L. O.

doi:10.1134/1.1371358

Cited by 3 publications

(4 citation statements)

References 10 publications

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“…It can be shown that under such Γ-bound, the kinetic energy term in (A12) can induce significant nonlocal effects in (90). One way to realize nonlocal (spatially dispersive) semiconducting metamaterials is to operate with intrinsic semiconductors satisfying (93) by keeping the temperature low and the material pure (undoped) [83].…”

Section: Resonant Nonlocal Semiconductor Domains and The Nonlocal Exc...mentioning

confidence: 99%

“…In general, there has been quite few investigations aimed at going beyond spatial dispersion in homogeneous media. Examples include inhomogeneous plasma, such as those in controlled-fusion reactors [88], cold collisionless magnetoplasma [88], the electrodynamics of nanostructures [89][90][91][92], and incommensurately-modulated superstructures in insulators [76,93].…”

Section: The Locally-homogeneous Model Of Nonlocal Semiconducting Dom...mentioning

confidence: 99%

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On the Topological Structure of Nonlocal Continuum Field Theories

Mikki

2021

Foundations

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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.

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Section: Resonant Nonlocal Semiconductor Domains and The Nonlocal Exc...mentioning

confidence: 99%

Section: The Locally-homogeneous Model Of Nonlocal Semiconducting Dom...mentioning

confidence: 99%

On the Topological Structure of Nonlocal Continuum Field Theories

Mikki

2021

Foundations

View full text Add to dashboard Cite

show abstract

“…In general, there has been quite few investigations aimed at going beyond spatial dispersion in homogeneous media. Examples include inhomogeneous plasma such as those in controlled-fusion reactors [185], cold collisionless magnetoplasma [185], and incommensuratelymodulated superstructures in insulators [12], [186].…”

Section: E the Locally-homogeneous Model Of Nonlocal Semiconducting Domainsmentioning

confidence: 99%

A Superspace Formalism for the Electromagnetism of Generic Nonlocal Continuous Metamaterials: Principal Structures and Applications

Mikki¹

2021

Preprint

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“…In general, there has been quite few investigations aimed at going beyond spatial dispersion in homogeneous media. Examples include inhomogeneous plasma such as those in controlled-fusion reactors [87], cold collisionless magnetoplasma [87], the electrodynamics of nanostructures [88]- [92], and incommensurately-modulated superstructures in insulators [75], [93].…”

Section: F the Locally-homogeneous Model Of Nonlocal Semiconducting Domainsmentioning

confidence: 99%

On the Topology of Nonlocal Field Theories of Material Continua

Mikki¹

2021

Preprint

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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.

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Features of the optical response of dielectric crystals with incommensurate phases

Cited by 3 publications

References 10 publications

On the Topological Structure of Nonlocal Continuum Field Theories

On the Topological Structure of Nonlocal Continuum Field Theories

A Superspace Formalism for the Electromagnetism of Generic Nonlocal Continuous Metamaterials: Principal Structures and Applications

On the Topology of Nonlocal Field Theories of Material Continua

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