Lagrangian formulation of electromagnetic fields in nondispersive medium by means of the extended Euler–Lagrange differential equation

Civelek, Cem; Bechteler, Thomas F.

doi:10.1016/j.ijengsci.2008.06.007

Cited by 10 publications

(9 citation statements)

References 8 publications

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“…These drawbacks seem to endorse, in a broader sense, the rather hesitating attitude manifested somewhere [15] in relation to the Lagrangian formulation. Indeed, there are nowadays substantial arguments, given the amount of currently available paradigms [4] worth wider spreading, for trying to revise that stance. The subtle eloquence of Eq.…”

Section: Discussionmentioning

confidence: 99%

“…extensively adopted in the specialised previous literature involving electromagnetic fields (see, for example, [4]). Eq.…”

Section: 2)mentioning

confidence: 99%

“…[3] (see also related papers) and has since continued with strong interdisciplinary connotations to date. A recent survey [4] and a monographic effort [5] are just a pair of examples, among many, clearheadedly proving the above trend. The present paper turns out to be a consequential extension of and an improving effort for those studies.…”

Section: Introductionmentioning

confidence: 99%

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Innovative investigation on ion flows by an ad hoc Lagrangian formulation

Lattarulo

2015

Journal of Electrostatics

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Section: Discussionmentioning

confidence: 99%

“…extensively adopted in the specialised previous literature involving electromagnetic fields (see, for example, [4]). Eq.…”

Section: 2)mentioning

confidence: 99%

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Innovative investigation on ion flows by an ad hoc Lagrangian formulation

Lattarulo

2015

Journal of Electrostatics

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“…Derivation of energy density in metamaterials, or dispersive and absorptive media in a more general sense, can be done in two ways; one is based on the electrodynamic approach [51][52][53][54][55][56], and the other on the equivalent circuit method [57,58]. In recent years, researchers have also tried using the Lagrange formalism to address the problem, and satisfactory results have been obtained [59]. However, it should be noted that the stored energy may not be a correct or useful form in the quantization procedure.…”

Section: Energy Densities In Artificial Metamaterialsmentioning

confidence: 99%

Effective Medium Theory of Metamaterials and Metasurfaces

Jiang¹,

Mei

Cui³

2021

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Metamaterials, including their two-dimensional counterparts, are composed of subwavelength-scale artificial particles. These materials have novel electromagnetic properties, and can be artificially tailored for various applications. Based on metamaterials and metasurfaces, many abnormal physical phenomena have been realized, such as negative refraction, invisible cloaking, abnormal reflection and focusing, and many new functions and devices have been developed. The effective medium theory lays the foundation for design and application of metamaterials and metasurfaces, connecting metamaterials with real world applications. In this Element, the authors combine these essential ingredients, and aim to make this Element an access point to this field. To this end, they review classical theories for dielectric functions, effective medium theory, and effective parameter extraction of metamaterials, also introducing front edge technologies like metasurfaces with theories, methods, and potential applications. Energy densities are also included.

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“…In this paper, we introduce the Lagrangian density [21][22][23] and dissipation function [24] density for the Lagrangian description of the electrodynamics in two kinds of typical dispersive and absorptive metamaterials. The first metamterial we considered is the 'double-negative metamaterial' composed of wires [25] and splitrings [26] array, which can have negative refractive index in some frequency range when both the permittivity and permeability are negative [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Lagrangian dynamics approach for the derivation of the energy densities of electromagnetic fields in some typical metamaterials with dispersion and loss

Luan

2018

J. Phys. Commun.

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The Lagrangians and dissipation functions are proposed for use in the electrodynamics of the doublenegative and chiral metamaterials with finite loss. The double-negative metamaterial considered here is the 'wires and split-rings' periodic structure, while the chiral metamaterial is the 'single-resonance helical resonators' array. For either system, application of Legendre transformation leads to a Hamiltonian density identical to the energy density obtained in our previous work based on the Poynting theorem and the mechanism of the power loss. This coincidence implies the correctness of the energy density formulas we obtained before. The Lagrangian description and Hamiltonian formulation can be further developed for exploring the properties of the elementary excitations or quasiparticles in dispersive metamaterials due to light-matter interactions.

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Lagrangian formulation of electromagnetic fields in nondispersive medium by means of the extended Euler–Lagrange differential equation

Cited by 10 publications

References 8 publications

Innovative investigation on ion flows by an ad hoc Lagrangian formulation

Innovative investigation on ion flows by an ad hoc Lagrangian formulation

Effective Medium Theory of Metamaterials and Metasurfaces

Lagrangian dynamics approach for the derivation of the energy densities of electromagnetic fields in some typical metamaterials with dispersion and loss

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