127 research outputs found
Frozen water waves over rough topographical bottoms
The propagation of surface water waves over rough topographical bottoms is
investigated by the multiple scattering theory. It is shown that the waves can
be localized spatially through the process of multiple scattering and wave
interference, a peculiar wave phenomenon which has been previously discussed
for frozen light in optical systems (S. John, Nature {\bf 390}, 661, (1997)).
We demonstrate that when frozen, the transmission of the waves falls off
exponentially, and a cooperative behavior appears, fully supporting previous
predictions. A phase diagram method is used to illustrate this distinct phase
states in the wave propagation.Comment: 4 pages and 5 figure
Guiding optical flows by photonic crystal slabs made of dielectric cylinders
We investigate the electromagnetic propagation in two-dimensional photonic
crystals, formed by parallel dielectric cylinders embedded a uniform medium.
The frequency band structure is computed using the standard plane-wave
expansion method, while the propagation and scattering of the electromagnetic
waves are calculated by the multiple scattering theory. It is shown that within
partial bandgaps, the waves tend to bend away from the forbidden directions.
Such a property may render novel applications in manipulating optical flows. In
addition, the relevance with the imaging by flat photonic crystal slabs will
also be discussed.Comment: 5 pages, 5 figure
Theoretical analysis of acoustic stop bands in two-dimensional periodic scattering arrays
This paper presents a theoretical analysis of the recently reported
observation of acoustic stop bands in two-dimensional scattering arrays
(Robertson and Rudy, J. Acoust. Soc. Am. {\bf 104}, 694, 1998). A
self-consistent wave scattering theory, incorporating all orders of multiple
scattering, is used to obtain the wave transmission. The band structures for
the regular arrays of cylinders are computed using the plane wave expansion
method. The theoretical results compare favorably with the experimental data.Comment: 18 pages, 4 page
Evolution of Directional Wave Spectra Through Finite Regular and Randomly Perturbed Arrays of Scatterers
Sonic crystal lenses that obey Lensmaker's formula
This paper presents a theoretical study of the phenomenon of acoustic imaging
by sonic crystals, which are made of two-dimensional regular arrays of rigid
cylinders placed in parallel in air. The scattering of acoustic waves is
computed using the standard multiple scattering theory, and the band structures
are computed by the plane-wave expansion method. It is shown that properly
arranged arrays not only can behave as acoustic lenses, but also the focusing
effect can be well described by Lensmaker's formula. Possible applications are
also discussed.Comment: 4 pages, 5 figure
Acoustic Attenuation by Two-dimensional Arrays of Rigid Cylinders
In this Letter, we present a theoretical analysis of the acoustic
transmission through two-dimensional arrays of straight rigid cylinders placed
parallelly in the air. Both periodic and completely random arrangements of the
cylinders are considered. The results for the sound attenuation through the
periodic arrays are shown to be in a remarkable agreement with the reported
experimental data. As the arrangement of the cylinders is randomized, the
transmission is significantly reduced for a wider range of frequencies. For the
periodic arrays, the acoustic band structures are computed by the plane-wave
expansion method and are also shown to agree with previous results.Comment: 4 pages, 3 figure
Water wave propagation and scattering over topographical bottoms
Here I present a general formulation of water wave propagation and scattering
over topographical bottoms. A simple equation is found and is compared with
existing theories. As an application, the theory is extended to the case of
water waves in a column with many cylindrical steps
Propagation inhibition and wave localization in a 2D random liquid medium
Acoustic propagation and scattering in water containing many parallel
air-filled cylinders is studied. Two situations are considered and compared:
(1) wave propagating through the array of cylinders, imitating a traditional
experimental setup, and (2) wave transmitted from a source located inside the
ensemble. We show that waves can be blocked from propagation by disorders in
the first scenario, but the inhibition does not necessarily imply wave
localization. Furthermore, the results reveal the phenomenon of wave
localization in a range of frequencies.Comment: Typos in Fiures are correcte
Manifestation of photonic band structure in small clusters of spherical particles
We study the formation of the photonic band structure in small clusters of
dielectric spheres. The first signs of the band structure, an attribute of an
infinite crystal, can appear for clusters of 5 particles. Density of resonant
states of a cluster of 32 spheres may exhibit a well defined structure similar
to the density of electromagnetic states of the infinite photonic crystal. The
resonant mode structure of finite-size aggregates is shown to be insensitive to
random displacements of particles off the perfect lattice positions as large as
half-radius of the particle. The results were obtained by an efficient
numerical method, which relates the density of resonant states to the the
scattering coefficients of the electromagnetic scattering problem. Generalized
multisphere Mie (GMM) solution was used to obtain scattering matrix elements.
These results are important to miniature photonic crystal design as well as
understanding of light localization in dense random media.Comment: 4 pages, 2 figure
Theoretical analysis of the focusing of acoustic waves by two-dimensional sonic crystals
Motivated by a recent experiment on acoustic lenses, we perform numerical
calculations based on a multiple scattering technique to investigate the
focusing of acoustic waves with sonic crystals formed by rigid cylinders in
air. The focusing effects for crystals of various shapes are examined. The
dependance of the focusing length on the filling factor is also studied. It is
observed that both the shape and filling factor play a crucial role in
controlling the focusing. Furthermore, the robustness of the focusing against
disorders is studied. The results show that the sensitivity of the focusing
behavior depends on the strength of positional disorders. The theoretical
results compare favorably with the experimental observations, reported by
Cervera, et al. (Phys. Rev. Lett. 88, 023902 (2002)).Comment: 8 figure
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