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

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

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

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

Bandgaps in the propagation and scattering of surface water waves over cylindrical steps

Here we investigate the propagation and scattering of surface water waves by arrays of bottom-mounted cylindrical steps. Both periodic and random arrangements of the steps are considered. The wave transmission through the arrays is computed using the multiple scattering method based upon a recently derived formulation. For the periodic case, the results are compared to the band structure calculation. We demonstrate that complete band gaps can be obtained in such a system. Furthermore, we show that the randomization of the location of the steps can significantly reduce the transmission of water waves. Comparison with other systems is also discussed.Comment: 4 pages, 3 figure

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

Anisotropic mass density by two-dimensional acoustic metamaterials

We show that specially designed two-dimensional arrangements of full elastic cylinders embedded in a nonviscous fluid or gas define ( in the homogenization limit) a new class of acoustic metamaterials characterized by a dynamical effective mass density that is anisotropic. Here, analytic expressions for the dynamical mass density and the effective sound velocity tensors are derived in the long wavelength limit. Both show an explicit dependence on the lattice filling fraction, the elastic properties of cylinders relative to the background, their positions in the unit cell, and their multiple scattering interactions. Several examples of these metamaterials are reported and discussed.Torrent Martí, D.; Sánchez-Dehesa Moreno-Cid, J. (2008). Anisotropic mass density by two-dimensional acoustic metamaterials. New Journal of Physics. 10. doi:10.1088/1367-2630/10/2/023004S10Sánchez-Pérez, J. V., Caballero, D., Mártinez-Sala, R., Rubio, C., Sánchez-Dehesa, J., Meseguer, F., … Gálvez, F. 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Solitary osteochondroma of the twelfth rib with intraspinal extension and cord compression in a middle-aged patient

<p>Abstract</p> <p>Background</p> <p>Osteochondroma is a disease of growing bone and thus typically presents in younger patients. It has rarely been described in middle-aged and elderly patients. Data on the occurrence of osteochondroma show that the reported incidence of costal osteochondroma is very low. Moreover, costal osteochondroma arising at the costovertebral junction with neural foraminal extension and spinal cord compression is extremely rare.</p> <p>Case presentation</p> <p>This study reports the case of a 58-year-old patient with a solitary osteochondroma of the 12th rib with intraspinal extension and spinal cord compression. The clinical history, plain radiographs, computed tomography (CT), magnetic resonance imaging, and pathologic findings of the reported patient have been reviewed. The relevant medical literature has also been reviewed. The patient was treated with surgery for complete tumour excision to avoid tumour recurrence. After surgery, the patient's symptoms improved. An additional CT scan obtained at 1 year after surgery did not show any evidence of recurrence.</p> <p>Conclusions</p> <p>This patient is the oldest patient reported to have this rare form of costal osteochondroma. The age of the patient and the erosion of the adjacent bones raised clinical suspicion of malignancy; therefore, surgical management involved complete tumour excision with thoracolumbar fixation and fusion.</p