2,733 research outputs found
Gap localization of multiple TE‐Modes by arbitrarily weak defects
This paper considers the propagation of TE‐modes in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a periodic background medium. Both the periodic background problem and the perturbed problem are modelled by a divergence type equation. A feature of our analysis is that we allow discontinuities in the coefficients of the operator, which is required to model many photonic crystals. Using the Floquet–Bloch theory in negative‐order Sobolev spaces, we characterize the precise number of eigenvalues created by the line defect in terms of the band functions of the original periodic background medium for arbitrarily weak defects
Gap Localization of TE-Modes by Arbitrarily Weak Defects
This paper considers the propagation of TE-modes in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a periodic background medium. Both the periodic background problem and the perturbed problem are modelled by a divergence type equation. A feature of our analysis is that we allow discontinuities in the coefficients of the operator, which is required to model many photonic crystals. It is shown that arbitrarily weak perturbations introduce spectrum into the spectral gaps of the background operator
Concept of local polaritons and optical properties of mixed polar crystals
The concept of local polaritons is used to describe optical properties of
mixed crystals in the frequency region of their {\it restrahlen} band. It is
shown that this concept allows for a physically transparent explanation of the
presence of weak features in the spectra of so called one-mode crystals, and
for one-two mode behavior. The previous models were able to explain these
features only with the use of many fitting parameters. We show that under
certain conditions new impurity-induced polariton modes may arise within the
{\it restrahlen} of the host crystals, and study their dispersion laws and
density of states. Particularly, we find that the group velocity of these
excitations is proportional to the concentration of the impurities and can be
thousands of times smaller then the speed of light in vacuum.Comment: 21 pages, 5 figures, RevTex, Phys. Rev. B, 62, 6301 (2000
Localization of Gauge Fields and Monopole Tunnelling
We study the dynamical localization of a massless gauge field on a
lower-dimensional surface (2-brane). In flat space, the necessary and
sufficient condition for this phenomenon is the existence of confinement in the
bulk. The resulting configuration is equivalent to a dual Josephson junction.
This duality leads to an interesting puzzle, as it implies that a localized
massless theory, even in the Abelian case, must become confining at
exponentially large distances. Through the use of topological arguments we
clarify the physics behind this large-distance confinement and identify the
instantons of the brane world-volume theory that are responsible for its
appearance. We show that they correspond to the (condensed) bulk magnetic
charges (monopoles), that occasionally tunnel through the brane and induce weak
confinement of the brane theory. We consider the possible generalization of
this effect to higher dimensions and discuss phenomenological bounds on the
confinement of electric charges at exponentially large distances within our
Universe.Comment: 11 pages, 3 figures, improvements in the presentation, version to
appear in Physical Review
Quantum many-body models with cold atoms coupled to photonic crystals
Using cold atoms to simulate strongly interacting quantum systems represents
an exciting frontier of physics. However, as atoms are nominally neutral point
particles, this limits the types of interactions that can be produced. We
propose to use the powerful new platform of cold atoms trapped near
nanophotonic systems to extend these limits, enabling a novel quantum material
in which atomic spin degrees of freedom, motion, and photons strongly couple
over long distances. In this system, an atom trapped near a photonic crystal
seeds a localized, tunable cavity mode around the atomic position. We find that
this effective cavity facilitates interactions with other atoms within the
cavity length, in a way that can be made robust against realistic
imperfections. Finally, we show that such phenomena should be accessible using
one-dimensional photonic crystal waveguides in which coupling to atoms has
already been experimentally demonstrated
Investigation of localized coupled-cavity modes in two-dimensional photonic band gap structures
Cataloged from PDF version of article.We present a detailed study of the localized
coupled-cavity modes in 2-D dielectric photonic crystals. The
transmission, phase, and delay time characteristics of the various
coupled-cavity structures are measured and calculated. We observed
the eigenmode splitting, waveguiding through the coupled
cavities, splitting of electromagnetic waves in waveguide ports,
and switching effect in such structures. The corresponding field
patterns and the transmission spectra are obtained from the finite-difference-time-domain
(FDTD) simulations. We also develop
a theory based on the classical wave analog of the tight-binding
(TB) approximation in solid state physics. Experimental results
are in good agreement with the FDTD simulations and predictions
of the TB approximation
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