Optical spatial dispersion in terms of Jones calculus

Nastyshyn, Svyatoslav; Bolesta, I.; Tsybulia, S. A.; Lychkovskyy, E.; Fedorovych, Z. Ya.; Khaustov, D.; Ryzhov, Y. V.; Vankevych, P. I.; Nastishin, Yu. A.

doi:10.1103/physreva.100.013806

Cited by 8 publications

(4 citation statements)

References 58 publications

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“…Within nanoscale electrodynamics, nonlocality was treated broadly as an essential feature of microscopic interactions at the nano-and mesoscopic scales [50,53]. Some of the topics reexamined within the framework of a general nonlocal field-matter interaction theory include the applicability of optical reciprocity theorems [101][102][103][104], energy/power balance [105], quantization [106][107][108], operator methods [87], extension of spatial dispersion to include inhomogeneous media [76], and alternative formulations of spatial dispersion in terms of the Jones calculus [109]. The bulk of the available literature on nonlocality is concentrated in the very large area of general field-matter interactions.…”

Section: Appendix A13 General Theories Of Nonlocal Continuamentioning

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: Appendix A13 General Theories Of Nonlocal Continuamentioning

confidence: 99%

On the Topological Structure of Nonlocal Continuum Field Theories

Mikki

2021

Foundations

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“…Eq. (17) shows that, in general, the inequality (which, in their turn, are defined by the components of the transformation matrix J via Eq. ( 18)) reduces the vector amplitude algorithm (17) of the CVIF method to the scalar amplitude algorithm of the SCFIF method [13,14].…”

Section: Amplitude Algorithmsmentioning

confidence: 99%

Jones formalism for image fusion

Khaustov

Ryzhov

et al. 2021

Ukr. J. Phys. Opt.

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We suggest a novel approach for the fusion of visible ( u ) and infrared ( ) images, basing on analogy between the mathematical forms of a Jones vector of elliptically polarized light wave and a complex 2D vector 0   composed of the images u and  . Since there is no restriction on which of the two images should be chosen as a real (or imaginary) component, one can construct 0   in the two forms,    0 of the Jones matrix for optically anisotropic medium. The above analogy with the Jones formalism allows one to synthesize the fused images using three types of the fusion algorithms, 'amplitude', 'azimuth' and 'ellipticity' ones. Varying the components of the J matrix with time, one can synthesize the fused image in a dynamic mode, thus animating the images fused under smoothly varying parameters, which are combinations of the J matrix components.

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“…For example, from the perspective of general thermodynamics, see [29], [30]. Some of the topics reexamined within the framework of a general nonlocal fieldmatter interaction theory include the applicability of optical reciprocity theorems [31]- [34], energy/power balance [35], quantization [36]- [38], operator methods [39], extension of spatial dispersion to include inhomogeneous media [12], and alternative formulations of spatial dispersion in terms of the Jones calculus [40].…”

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

confidence: 99%