167 research outputs found
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
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
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
Finite frequency external cloaking with complementary bianisotropic media
We investigate the twofold functionality of a cylindrical shell consisting of
a negatively refracting heterogeneous bianisotropic (NRHB) medium deduced from
geometric transforms. The numerical simulations indicate that the shell
enhances their scattering by a perfect electric conducting (PEC) core, whereas
it considerably reduces the scattering of electromagnetic waves by closely
located dipoles when the shell surrounds a bianisotropic core. The former can
be attributed to a homeopathic effect, whereby a small PEC object scatters like
a large one as confirmed by numerics, while the latter can be attributed to
space cancelation of complementary bianisotropic media underpinning anomalous
resonances counteracting the field emitted by small objects (external
cloaking). Space cancellation is further used to cloak a NRHB finite size
object located nearby a slab of NRHB with a hole of same shape and opposite
refracting index. Such a finite frequency external cloaking is also achieved
with a NRHB cylindrical lens. Finally, we investigate an ostrich effect whereby
the scattering of NRHB slab and cylindrical lenses with simplified parameters
hide the presence of dipoles in the quasi-static limit.Comment: 16 pages, 15 figure
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