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Search Results: 1 - 10 of 10888 matches for " Pierre Hillion "
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Pedestrian Analysis of Harmonic Plane Wave Propagation in 1D-Periodic Media  [PDF]
Pierre Hillion
Journal of Modern Physics (JMP) , 2011, DOI: 10.4236/jmp.2011.24027
Abstract: The propagation of TE, TM harmonic plane waves impinging on a periodic multilayer film made of a stack of slabs with the same thickness but with alternate constant permittivity is analyzed. To tackle this problem, the same analysis is first performed on only one slab for harmonic plane waves, solutions of the wave equa- tion. The results obtained in this case are generalized to the stack, taking into account the boundary condi- tions generated at both ends of each slab by the jumps of permittivity. Differential electromagnetic forms are used to get the solutions of Maxwell’s equations.
Wave Propagation in Nanocomposite Materials  [PDF]
Pierre Hillion
Journal of Electromagnetic Analysis and Applications (JEMAA) , 2010, DOI: 10.4236/jemaa.2010.27053
Abstract: Electromagnetic wave propagation is first analyzed in a composite material mde of chiral nano-inclusions embedded in a dielectric, with the help of Maxwell-Garnett formula for permittivity and permeability and its reciprocal for chirality. Then, this composite material appears as an homo-geneous isotropic chiral medium which may be described by the Post constitutive relations. We analyze the propagation of an harmonic plane wave in such a medium and we show that two different modes can propagate. We also discuss harmonic plane wave scattering on a semi-infinite chiral composite medium. Then, still in the frame of Maxwell-Garnett theory, the propagation of TE and TM fields is investigated in a periodic material made of nano dots immersed in a dielectric. The periodic fields are solutions of a Mathieu equation and such a material behaves as a diffraction grating.
Pulsed Sound Waves in a Compressible Fluid  [PDF]
Pierre Hillion
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.210167
Abstract: The propagation along oz of pulsed sound waves made of sequences of elementary unit pulses U (sin τ) where U is the unit step function and τ = kzωt is analyzed using the expansion of U (sin τ) and of the Dirac distribution δ (sin τ) in terms of τ where n is an integer. Their properties and how these pulsed sound waves could be generated are discussed.
Schrödinger Equation with a Cubic Nonlinearity Sech-Shaped Soliton Solutions  [PDF]
Pierre Hillion
Optics and Photonics Journal (OPJ) , 2012, DOI: 10.4236/opj.2012.23026
Abstract: We first analyze the sech-shaped soliton solutions, either spatial or temporal of the 1D-Schr?dinger equation with a cubic nonlinearity. Afterwards, these solutions are generalized to the 2D-Schr?dinger equation in the same configuration and new soliton solutions are obtained. It is shown that working with dimensionless equations makes easy this generalization. The impact of solitons on modern technology is then stressed.
TE, TM Fields in Toroidal Electromagnetism  [PDF]
Pierre Hillion
Applied Mathematics (AM) , 2013, DOI: 10.4236/am.2013.41006

We analyze the behaviour of TE, TM electromagnetic fields in a toroidal space through Maxwell and wave equations. Their solutions are discussed in a space endowed with a refractive index making separable the wave equations.

Reflection from a flat dielectric film with negative refractive index
Hillion, Pierre;
Brazilian Journal of Physics , 2007, DOI: 10.1590/S0103-97332007000800005
Abstract: we analyse the reflection of a tm electromagnetic field first on a flat dielectric film and second on a veselago film with negative refractive index, both films being deposited on a metallic substrat acting as a mirror. an incident harmonic plane wave generates inside a conventional dielectric film a refracted propagating wave and an evanescent wave that does not contribute to reflection on the metallic substrat so that part of the information conveyed by the incident field is lost. at the opposite, inside a veselago film, evanescent waves are changed into outbursting waves reflecting on the metallic substrat and participating to the total reflected field from the metallic film without loss if information.
Spinor and Hertzian Differential Forms in Electromagnetism
Pierre Hillion
PIER M , 2011, DOI: 10.2528/PIERM10111501
Abstract: The purpose of this paper is to extend to spinor electromagnetism the differential forms, based on the Cartan exterior derivative and originally developed for tensor fields, in a very compact way. To this end, differential electromagnetic forms are first compared to conventional tensors. Then, using the local isomorphism between the O (3,C) and SL (2,C) groups supplying the well known connection between complex vectors and traceless second rank spinors, they are generalized to spinor electromagnetism and to Proca fields. These differential forms are finally expressed in terms of Hertz potentials.
Impedance Boundary Conditions on a Chiral Film
Pierre Hillion
PIER , 2004, DOI: 10.2528/PIER03061101
Abstract: Using a technique borrowed from Idemen [1] and requiring the Fourier transform of the , -components of the electric and magnetic fields, we obtain the impedance boundary conditions for electromagnetic plane waves withh orizontal, vertical and arbitrary polarization incident on a infinite, smooth, chiral film located at = 0 and deposited on a metallic substrate. As an application, we discuss the scattering of harmonic plane waves and of a finite beam on sucha film.
Coherent Field Approximation of Plane Wave Scattering from 1D-Rough Mirrors
Pierre Hillion
PIER M , 2010, DOI: 10.2528/PIERM09011202
Abstract: For an harmonic plane wave impinging on a perfectly reflecting smooth plane the total field, incident and reflected, satisfying on this plane a Dirichlet or Neumann boundaray condition, has an integral representation that we extend to the specular reflection from a perfectly reflecting rough plane. To make this generalization possible, some constraints must be imposed on the wavelength of the incident field and on the rough amplitude to make the diffuse field negligible so that only the coherent field is important and we may use the fact that the coherent power is identical to that of a smooth surface. This generalized integral representation supplies an approximation of the coherent field valid far from the rough plane. We limit the discussion to acoustic, TE, TM electromagnetic wave incident on 1D-perfectly reflecting rough planes with roughness described by zig-zag functions piecewise linear with opposite slop on adjacent intervalls.
Electromagnetism with Nanodoped Charges and Currents
Pierre Hillion
Applied Physics Research , 2012, DOI: 10.5539/apr.v4n1p156
Abstract: We analyze the solutions of Maxwell’s equations in a 2D-medium with nano doped static and moving charges and currents, doping being made of delta Dirac dots.
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