499 research outputs found
Modal analysis of wave propagation in dispersive media
Surveys on wave propagation in dispersive media have been limited since the
pioneering work of Sommerfeld [Ann. Phys. 349, 177 (1914)] by the presence of
branches in the integral expression of the wave function. In this article, a
method is proposed to eliminate these critical branches and hence to establish
a modal expansion of the time-dependent wave function. The different components
of the transient waves are physically interpreted as the contributions of
distinct sets of modes and characterized accordingly. Then, the modal expansion
is used to derive a modified analytical expression of the Sommerfeld precursor
improving significantly the description of the amplitude and the oscillating
period up to the arrival of the Brillouin precursor. The proposed method and
results apply to all waves governed by the Helmholtz equations.Comment: 10 pages, 9 figure
Calculation and analysis of complex band structure in dispersive and dissipative two-dimensional photonic crystals
Numerical calculation of modes in dispersive and absorptive systems is
performed using the finite element method. The dispersion is tackled in the
frame of an extension of Maxwell's equations where auxiliary fields are added
to the electromagnetic field. This method is applied to multi-domain cavities
and photonic crystals including Drude and Drude-Lorentz metals. Numerical
results are compared to analytical solutions for simple cavities and to
previous results of the literature for photonic crystals, showing excellent
agreement. The advantages of the developed method lie on the versatility of the
finite element method regarding geometries, and in sparing the use of tedious
complex poles research algorithm. Hence the complex spectrum of resonances of
non-hermitian operators and dissipative systems, like two-dimensional photonic
crystal made of absorbing Drude metal, can be investigated in detail. The
method is used to reveal unexpected features of their complex band structures.Comment: to be submitted for publicatio
Finite Element Analysis of Electromagnetic Waves in Two-Dimensional Transformed Bianisotropic Media
We analyse wave propagation in two-dimensional bianisotropic media with the
Finite Element Method (FEM). We start from the Maxwell-Tellegen's equations in
bianisotropic media, and derive some system of coupled Partial Difference
Equations (PDEs) for longitudinal electric and magnetic field components.
Perfectly Matched Layers (PMLs) are discussed to model such unbounded media. We
implement these PDEs and PMLs in a finite element software. We apply
transformation optics in order to design some bianisotropic media with
interesting functionalities, such as cloaks, concentrators and rotators. We
propose a design of metamaterial with concentric layers made of homogeneous
media with isotropic permittivity, permeability and magneto-electric parameters
that mimic the required effective anisotropic tensors of a bianisotropic cloak
in the long wavelength limit (homogenization approach). Our numerical results
show that well-known metamaterials can be transposed to bianisotropic media.Comment: 26 pages, 8 figure
Phase retrieval of reflection and transmission coefficients from Kramers-Kronig relations
Analytic and passivity properties of reflection and transmission coefficients
of thin-film multilayered stacks are investigated. Using a rigorous formalism
based on the inverse Helmholtz operator, properties associated to causality
principle and passivity are established when both temporal frequency and
spatial wavevector are continued in the complex plane. This result extends the
range of situations where the Kramers-Kronig relations can be used to deduce
the phase from the intensity. In particular, it is rigorously shown that
Kramers-Kronig relations for reflection and transmission coefficients remain
valid at a fixed angle of incidence. Possibilities to exploit the new
relationships are discussed.Comment: submitted for publicatio
Exact Modal Methods
International audienceA rigorous formulation of the Exact Modal Method for lamellar structures is presented. A special attention is paid to the continuation of the electromagnetic field inside a lamellar layer that provides a large class of solutions of Maxwell's equations in presence of lamellar gratings. Next, it is shown that in each lamellar layer, there is a decoupling of the vector field equations into two independent scalar equations, which correspond to those of a multilayered stack. The techniques used for the calculation of the exact modes and eigenvalues are presented in detail. Finally, a numerical illustration shows the efficiency of the method
Quasi-TEM modes in rectangular waveguides: a study based on the properties of PMC and hard surfaces
Hard surfaces or magnetic surfaces can be used to propagate quasi-TEM modes
inside closed waveguides. The interesting feature of these modes is an almost
uniform field distribution inside the waveguide. But the mechanisms governing
how these surfaces act, how they can be characterized, and further how the
modes propagate are not detailed in the literature. In this paper, we try to
answer these questions. We give some basic rules that govern the propagation of
the quasi-TEM modes, and show that many of their characteristics (i.e. their
dispersion curves) can be deduced from the simple analysis of the reflection
properties of the involved surfaces
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