Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés

Abelès, F.

doi:10.1051/anphys/195012050596

Cited by 516 publications

(165 citation statements)

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“…1.6] reproduce some deliberations probably first thought by Abelés [23] in 1950. Maxwell's equations are written in a cartesian coordinate system and permittivity as well as permeability are allowed to depend on one coordinate.…”

Section: Retro and Prospectsmentioning

confidence: 80%

Electromagnetic Waves in Variable Media

Brösa

2012

Zeitschrift Für Naturforschung A

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Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability, and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one coordinate, general solutions are derived. If the properties depend on two coordinates, geometrically restricted solutions are obtained. Applications to graded reflectors, especially to dielectric mirrors, to filters, polarizers, and to waveguides, plain and cylindrical, are indicated. New foundations for the design of optical instruments, which are centered around an axis, and for the design of invisibility cloaks, plain and spherical, are proposed. The variability of material properties makes possible effects which cannot happen in constant media, e.g. stopping the flux of electromagnetic energy without loss. As a consequence, spherical devices can be constructed which bind electromagnetic waves. Exact Solutions of Maxwell's EquationsThis work originated from a scrutiny for the foundations of quantum mechanics. Do the equations, which Schrödinger considered as the description of the propagation of light, rest upon Maxwell's equations? The answer is no. The study produced analytic methods for the exact solution of Maxwell's equations even if permittivity, permeability, and conductivity vary in space. These methods should be useful to everyone concerned with electromagnetic fields. Thus readers interested in basic physics might read Section 1.1, whereas technicians may begin with Section 1.2. The Foundations of Quantum MechanicsLet us trace the way Schrödinger walked to find the Schrödinger equation. He thought that the propagation of light, if it is construed as propagation of particles, is best described by the eikonal equationSurfaces of equal eikonal s(r) are perpendicular to the light rays everywhere in the space described by the vector of location r. n(r) is the index of refraction. Schrödinger compared this with the Helmholtz equationwhich he considered as the best description of waves. ω denotes the frequency of that wave and c is the velocity of light. The meaning of ψ is not known. Next Schrödinger remembered that there is an eikonal equation for massive particles, too, the Hamilton-Jacobi equationThe mechanical eikonal S(r) has a similar meaning as in ray optics, but its dimension is different. Hence Schrödinger deduced from a comparison of (1) and (3) a mechanical index of refraction n(r) = c 2 h 2 ω 2m(E −V (r)) .The factor in front of 2m(E − V (r)) is an adjustable constant to get dimensions right. That it is related c 2012 Verlag der Zeitschrift für Naturforschung, Tübingen ·

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Section: Retro and Prospectsmentioning

confidence: 80%

Electromagnetic Waves in Variable Media

Brösa

2012

Zeitschrift Für Naturforschung A

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“…with the matrix method, which results in the reflectivity using the propagation of the electric field in the structure. 5,8 Using a fitting algorithm we can change the free parameters in such a way to minimize one of the merit functions M as described by…”

Section: Methodsmentioning

confidence: 99%

Determination of in-depth density profiles of multilayer structures

Kessels

Bijkerk

Tichelaar

et al. 2005

Journal of Applied Physics

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We developed and demonstrate an analysis method in which we calibrate the intensity scale of cross-sectional transmission electron microscopy ͑TEM͒ using Cu K ␣ reflectometry. This results in quantitative in-depth density profiles of multilayer structures. Only three free parameters are needed to obtain the calibrated profiles, corresponding to three TEM image intensity levels. Additionally, the optical indices of the two multilayer materials used and the assumption that the layers are laterally homogeneous are used in the model. The power and the general usefulness of the method is demonstrated using experimental data of W / Si and Mo/ Si multilayer systems with sharp interfaces as well as multilayers of which the interfaces were deliberately intermixed.

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“…30,31 This model deals with SPR components and analytes as stacked layers. Since all layers affect the surface plasmon, the refractive index of each layer is needed for the simulation.…”

Section: Structure Of Ion Pairing Upon Oxidation Of Ferrocenyl Groupsmentioning

confidence: 99%