14,454 research outputs found
Nonlinear waves in a chain of magnetically coupled pendula
A motivation for the study of reduced models like one-dimensional systems in Solid State Physics is the complexity of the full problem. In recent years our group has studied theoretically, numerically and experimentally wave propagation in lattices of nonlinearly coupled oscillators. Here, we present the dynamics of magnetically coupled pendula lattices. These macroscopic systems can model the dynamical processes of matter or layered systems. We report the results obtained for harmonic wave propagation in these media, and the different regimes of mode conversion into higher harmonics strongly influenced by dispersion and discreteness, including the phenomenon of acoustic dilatation of the chain, as well as some results on the propagation of localized waves i.e., solitons and kinks.Generalitat Valenciana APOSTD/2017/042Umiversitat Politècnica de València PAID-01-14Ministerio de EconomĂa y Competitividad (MINECO), Spain FIS2015-65998-C2-2-PJunta de AndalucĂa 2017/FQM-28
New Analytical Approach for Computation of Band Structure in One-dimensional Periodic Media
In this paper, we present a new approach for the exact calculation of band
structure in one-dimensional periodic media, such as photonic crystals and
superlattices, based on the recently reported differential transfer matrix
method (DTMM). The media analyzed in this paper can have arbitrary profile of
refractive index. We derive a closed form dispersion equation using
differential transfer matrix formalism, and simplify it under the assumptions
of even symmetry and real-valued wavenumber. We also show that under normal
incidence both TE and TM modes must have the same band structure. Several
numerical test cases are also studied and discussed
Local Normal Mode Coupling and Energy Band Splitting in Elliptically Birefringent 1D Magnetophotonic Crystals
An analysis is presented of wave-vector dispersion in elliptically
birefringent stratified magneto-optic media having one-dimensional periodicity.
It is found that local normal-mode polarization-state differences between
adjacent layers lead to mode coupling and impact the wave-vector dispersion and
the character of the Bloch states of the system. This coupling produces extra
terms in the dispersion relation not present in uniform circularly birefringent
magneto-optic stratified media. Normal mode coupling lifts the degeneracy at
frequency band cross-over points under certain conditions and induces a
magnetization-dependent optical band gap. This study examines the conditions
for band gap formation in the system. It shows that such a frequency-split can
be characterized by a simple coupling parameter that depends on the relation
between polarization states of local normal modes in adjacent layers. The
character of the Bloch states and conditions for maximizing the strength of the
band splitting in these systems are analyzed.Comment: 15 pages, 4 figure
Slow light in photonic crystals
The problem of slowing down light by orders of magnitude has been extensively
discussed in the literature. Such a possibility can be useful in a variety of
optical and microwave applications. Many qualitatively different approaches
have been explored. Here we discuss how this goal can be achieved in linear
dispersive media, such as photonic crystals. The existence of slowly
propagating electromagnetic waves in photonic crystals is quite obvious and
well known. The main problem, though, has been how to convert the input
radiation into the slow mode without loosing a significant portion of the
incident light energy to absorption, reflection, etc. We show that the
so-called frozen mode regime offers a unique solution to the above problem.
Under the frozen mode regime, the incident light enters the photonic crystal
with little reflection and, subsequently, is completely converted into the
frozen mode with huge amplitude and almost zero group velocity. The linearity
of the above effect allows to slow light regardless of its intensity. An
additional advantage of photonic crystals over other methods of slowing down
light is that photonic crystals can preserve both time and space coherence of
the input electromagnetic wave.Comment: 96 pages, 12 figure
Modulational Instability in Nonlinearity-Managed Optical Media
We investigate analytically, numerically, and experimentally the modulational
instability in a layered, cubically-nonlinear (Kerr) optical medium that
consists of alternating layers of glass and air. We model this setting using a
nonlinear Schr\"odinger (NLS) equation with a piecewise constant nonlinearity
coefficient and conduct a theoretical analysis of its linear stability,
obtaining a Kronig-Penney equation whose forbidden bands correspond to the
modulationally unstable regimes. We find very good {\it quantitative} agreement
between the theoretical analysis of the Kronig-Penney equation, numerical
simulations of the NLS equation, and the experimental results for the
modulational instability. Because of the periodicity in the evolution variable
arising from the layered medium, we find multiple instability regions rather
than just the one that would occur in uniform media.Comment: 13 pages, 12 figures (several with multiple parts); some important
changes from the page proof stage implemented in this preprint versio
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