1,851 research outputs found
Exact solution of lossy asymmetrical coupled dielectric slab waveguides
This paper gives an exact characteristic equation for asymmetrical coupled dielectric slab waveguides with losses in both the guiding and surrounding regions. For the lossless case the solution of a single transcendental equation is all that is required for the evaluation of the propagation constant
Formation Mechanism of Guided Resonances and Bound States in the Continuum in Photonic Crystal Slabs
We develop a formalism, based on the mode expansion method, to describe the
guided resonances and bound states in the continuum (BICs) in photonic crystal
slabs with one-dimensional periodicity. This approach provides analytic
insights to the formation mechanisms of these states: the guided resonances
arise from the transverse Fabry-P\'erot condition, and the divergence of the
resonance lifetimes at the BICs is explained by a destructive interference of
radiation from different propagating components inside the slab. We show BICs
at the center and on the edge of the Brillouin zone protected by symmetry, as
well as BICs at generic wave vectors not protected by symmetry.Comment: 12 pages, 3 figure
Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity
We consider a sub-wavelength periodic layered medium whose slabs are filled
by arbitrary linear metamaterials and standard nonlinear Kerr media and we show
that the homogenized medium behaves as a Kerr medium whose parameters can
assume values not available in standard materials. Exploiting such a parameter
availability, we focus on the situation where the linear relative dielectric
permittivity is very small thus allowing the observation of the extreme
nonlinear regime where the nonlinear polarization is comparable with or even
greater than the linear part of the overall dielectric response. The behavior
of the electromagnetic field in the extreme nonlinear regime is very peculiar
and characterized by novel features as, for example, the transverse power flow
reversing. In order to probe the novel regime, we consider a class of fields
(transverse magnetic nonlinear guided waves) admitting full analytical
description and we show that these waves are allowed to propagate even in media
with since the nonlinear polarization produces a
positive overall effective permittivity. The considered nonlinear waves
exhibit, in addition to the mentioned features, a number of interesting
properties like hyper-focusing induced by the phase difference between the
field components.Comment: 12 pages, 7 figure
The exact theory for scattering of waves by thick holes in a slab and other objects with non-separable geometries
The theory for scattering of electromagnetic waves is developed for scattering objects for which the natural modes of the field inside the object do not couple one-to-one with those outside the scatterer. Key feature of the calculation of the scattered fields is the introduction of a new set of modes. As an example, we calculate the reflected and transmitted fields generated by an electromagnetic plane wave that impinges upon a multilayer slab of which the layers are stacked perpendicular to the boundary planes. As this is the geometry of a thick plate with slits our theory encompasses the exact scattering theory of electromagnetic waves by a thick plate with slits.
On wave propagation in inhomogeneous systems
We present a theory of electron, electromagnetic, and elastic wave
propagation in systems consisting of non-overlapping scatterers in a host
medium. The theory provides a framework for a unified description of wave
propagation in three-dimensional periodic structures, finite slabs of layered
structures, and systems with impurities: isolated impurities, impurity
aggregates, or randomly distributed impurities. We point out the similarities
and differences between the different cases considered, and discuss the
numerical implementation of the formalism.Comment: 12 page
Spontaneous-emission rates in finite photonic crystals of plane scatterers
The concept of a plane scatterer that was developed earlier for scalar waves
is generalized so that polarization of light is included. Starting from a
Lippmann-Schwinger formalism for vector waves, we show that the Green function
has to be regularized before T-matrices can be defined in a consistent way.
After the regularization, optical modes and Green functions are determined
exactly for finite structures built up of an arbitrary number of parallel
planes, at arbitrary positions, and where each plane can have different optical
properties. The model is applied to the special case of finite crystals
consisting of regularly spaced identical planes, where analytical methods can
be taken further and only light numerical tasks remain. The formalism is used
to calculate position- and orientation-dependent spontaneous-emission rates
inside and near the finite photonic crystals. The results show that emission
rates and reflection properties can differ strongly for scalar and for vector
waves. The finite size of the crystal influences the emission rates. For
parallel dipoles close to a plane, emission into guided modes gives rise to a
peak in the frequency-dependent emission rate.Comment: 18 pages, 6 figures, to be published in Phys. Rev.
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