On the application of Kramers-Kronig relations to media with spatial dispersion

Musienko, T; Rudakov, V.S.; Solovev, L. E.

doi:10.1088/0953-8984/1/37/020

Cited by 6 publications

(4 citation statements)

References 7 publications

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“…The formulation, discretization, and solution of surface integral equations for nonlocal plasmonic materials were also attempted in [121,122], where the reduction of the electromagnetic problem to a finitematrix form was achieved using the RWG basis functions. Moreover, specialized methods were proposed for various possible scenarios involving nonlocal field-matter interactions, such as nonlocal dielectric profile retrieval from measurable data [123], iterative solutions of nonlocal wave equations [124,125], applications of the derivative expansion method to nonlocal plasma analysis [126], application of Kramers-Kronig relation method [127], application of the Pade approximation to homogenization [128].…”

Section: Boundary Conditions In Nonlocal Metamaterialsmentioning

confidence: 99%

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: Boundary Conditions In Nonlocal Metamaterialsmentioning

confidence: 99%

On the Topological Structure of Nonlocal Continuum Field Theories

Mikki

2021

Foundations

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“…Surface integral equations for nonlocal plasmonic materials were also proposed in [61], [62], with discretizstion done using the RWG basis functions. Moreover, specialized methods were proposed for various possible scenarios involving nonlocal field-matter interactions, such as nonlocal dielectric profile retrieval from measurable data [63], iterative solutions of nonlocal wave equations [64], [65], applications of the derivative expansion method to nonlocal plasma analysis [66], application of Kramers-Kronig relation method [67], application of the Pade approximation to homogenization [68],…”

Section: Review Of Nonlocal Electromagnetism and An Outline Of The Present Work A Survey Of The Literature On Nonlocal Metamaterialsmentioning

confidence: 99%

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

Mikki¹

2021

Preprint

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“…Next, the real part of the dielectric function is discussed. The real part of dielectric function can be extracted from the imaginary part of the dielectric by using Kramer-Kroning relation [47]. The calculated spectra for the real part of dielectric function for a doped system with and without vacancy defects are shown in figures 7(a) and (b), respectively.…”

Section: Optical Propertiesmentioning

confidence: 99%

Ab initio study of optoelectronic and magnetic properties of Mn-doped ZnS with and without vacancy defects

Khan¹,

Shi²,

Ullah³

et al. 2019

J. Phys.: Condens. Matter

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The effect of vacancy defects on optoelectronic and magnetic properties of Mn-doped ZnS have been systematically investigated using first principle approaches. A single Mn substitution at Zn site induces a spin-polarized ground state in pure ZnS with total magnetization 5 . Our results for magnetic coupling show that the coupling between Mn spins in pure Mn doped ZnS is antiferromagnetic under the super-exchange mechanism. The existence of native defects has a great influence on the magnetic ground state of Mn-doped ZnS. In particular, a p -type defect such as Zn vacancy play a crucial role in stabilizing ferromagnetic ground state while n-type defect, such as S vacancy, has no effect on the magnetic ground state i.e. the interaction between two Mn spins with S-vacancy remain antiferromagnetic. Furthermore, optical properties such as dielectric functions, absorption coeffiecients, reflectivity and transmissitivity for Mn doped systems with and without vacancy defect were also studied, and we found that an absorption peak was obtained in the infrared region which is attributed to the defect states introduced by Zn vacancy in the system. In a S-vacancy defect system, the peaks in the near infrared and visible region are due to donor states introduced by S vacancy defect and these peaks are produced by electrons flipping from a spin up state to a spin down state. Finally, we also correlated the magnetic interactions with the d–d optical transition in pure Mn-doped ZnS and found that the d–d transitions during optical absorptions are red shifted and blue shifted in FM and AFM coupled Mn ions pair, which is in good agreement with the experimental observations. This study may help to understand the behavior of optical and magnetic properties of DMS under vacancy defects.

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On the application of Kramers-Kronig relations to media with spatial dispersion

Cited by 6 publications

References 7 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

Ab initio study of optoelectronic and magnetic properties of Mn-doped ZnS with and without vacancy defects

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