Array Of Dielectric Cylinders Research Articles

Spatial observation of highly directional radiation from a compact 3D photonic-crystal antenna in Ku band

A three-dimensional compact prototype of a photonic crystal directive antenna is constructed for beam steering and directional radiation in the microwave. Experiments demonstrate that the array of dielectric cylinders placed in a U-shape open metal cavity can be profitably exploited to act as a high-efficiency splitting directive antenna in particular modes. Highly directional radiation has been observed at the fundamental electromagnetic resonance of band edge crystal with a maximum gain of 20.73 dBi and an aperture efficiency of 49.77%. The side-lobes on the E-plane (yoz) are almost constrained in −20 dB benefitting from the band edge lattice-induced resonance on the H-plane (xoy), suppressing the effect of aperture diffraction, and retaining high directivity performance in space. The detected half-power beam widths on the E-plane and H-plane are 7.7° and 8.9°, respectively, agreeing well with the simulations. Different from traditional orientation approaches, the photonic crystal antenna delivers performance of high directivity gain with compact structure, facile preparation, low cost, and high efficiency, which make it suitable for spatial information transmission and modulation and offer potential applications in remote sensing and wireless communication.

Beam focusing in reflections from flat subwavelength diffraction gratings

We predict that narrow beams, reflecting from flat subwavelength diffraction gratings, can focus. The effect is shown for the beams of electromagnetic radiation; however, it should be observable for beams of waves of arbitrary nature (microwaves, surface plasmons, and acoustic and mechanical waves). We present analytical estimations of the focusing performance obtained by multiple scattering calculations and demonstrate the focusing effect numerically for an optical system (reflections from an array of dielectric cylinders), using the finite-difference time-domain calculations.

Two-dimensional scattering of a plane wave from a periodic array of dielectric cylinders with arbitrary shape

A two-dimensional scattering of a plane wave from a periodic array of dielectric cylinders with arbitrary shape using the multigrid-moment method is examined. The scattered field is expressed in terms of the integral form by an infinite summation of the surface integral over the cross section of the reference cylinder. The integral form is converted into the matrix equation by using the moment method. The integration in the elements of the matrix equation is evaluated by the lattice-sums technique to obtain a precise solution. The multigrid method is applied to the matrix equation to improve the CPU time. The CPU time and the residual norm are examined numerically for a given number of iterations and cycle indices. Then the effects of shape and material of the periodic structure on the power reflection coefficient of the fundamental Floquet mode are shown. In addition, the results indicate the effect of changing the relative permittivity of the dielectric coated body and the reflection coefficient.

Time-domain analysis of bandgap characteristics of two-dimensional periodic structures by use of a source-model technique

We introduce a time-domain source-model technique for analysis of two-dimensional, transverse-magnetic, plane-wave scattering by a photonic crystal slab composed of a finite number of identical layers, each comprising a linear periodic array of dielectric cylinders. The proposed technique takes advantage of the periodicity of the slab by solving the problem within a unit cell of the periodic structure. A spectral analysis of the temporal behavior of the fields scattered by the slab shows a clear agreement between frequency bands where the spectral density of the transmitted energy is low and the bandgaps of the corresponding two-dimensionally infinite periodic structure. The effect of the bandwidth of the incident pulse and its center frequency on the manner it is transmitted through and reflected by the slab is studied via numerical examples.

Terahertz demonstrations of effectively two-dimensional photonic bandgap structures

We demonstrate effectively two-dimensional (2D) terahertz (THz) photonic bandgap (PBG) structures for transverse electromagnetic (TEM) mode propagation within metal parallel plate waveguides (PPWG). The 2D-PBG structures consisting of square arrays of dielectric cylinders were characterized by THz time-domain spectroscopy (THz-TDS). THz photonic bandgaps were observed, as determined by the 160 mum lattice constant, the 65 mum diameter, and the dielectric constant of the cylinders. The experimental measurements were fitted with excellent agreement to 2D theory, confirming that for TEM mode propagation, effectively 2D propagation experiments can be achieved within the bounded space of the PPWG.

A Simple Modification of Three-dimensional 90°-bent Periodic Dielectric Waveguides

A 3D periodical dielectric waveguide (PDWG) is a linear array of dielectric cylinders or holes. It becomes more and more promising in integrated optics because PDWG occupies less area on a chip than a common photonic crystal waveguide (PCWG). In this paper, a new and simple type of 3D 90°-bent PDWG is proposed to improve the transmission characteristics by shifting only one cylinder to another place. The finite-difference time-domain (FDTD) simulations demonstrate that the transmission efficiency can be obviously increased.

Microwave localization due to defects in the arrays of dielectric cylinders: Multiple scattering approach

Microwaves propagation and scattering by dielectric cylinders in an uniform and defected media are simulated by using multiple scattering method. Formation of localized state due to the presence of a defect is observed in our simulations. Our theoretical results are compared with the previous experimental findings, yielding quantitative agreements in the transmission coefficients for a certain range of frequencies. In addition, our results point out some possible inconsistency in the experimental observations.

Effect of point defect geometry on localized defect modes in two-dimensional photonic crystals

A numerical study of point defect modes in two-dimensional square array of dielectric cylinders in air is presented. Three kinds of defect are considered, namely, circular, square and rectangular, respectively. The results show that for square defects, the defect modes are only dependent of the defect filling fraction F d , regardless of the defect orientations. Further evidence shows that the defect modes for square defects have almost the same features as those of the circular defects having the same defect filling fraction, exhibiting the independence of these two geometries. However, for the rectangular defects, the defect modes show a dependence on their geometry. When the aspect ratio of the rectangle defect is big enough, the defect modes exhibit the splitting feature. This provides a way to split the degenerate defect modes.

Negative-refraction-like behavior revealed by arrays of dielectric cylinders.

We investigate the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel dielectric cylinders embedded in a uniform medium. The transmission of electromagnetic waves through prism structures is calculated by the standard multiple scattering theory. The results demonstrate that, in certain frequency regimes and when the propagation inside the scattering media is not considered, the transmission behavior mimics the negative refraction expected for a left-handed material. This feature may illusively lead to the conclusion that a negative refraction is observed and it obeys Snell's law of negative refraction. Possible implications for current experimental and theoretical studies of negative refraction are also discussed.

Disorder effects on the imaging of a negative refractive lens made by arrays of dielectric cylinders

By a numerical simulation based upon multiple scattering theory, we confirm that, for certain frequencies, crystal structures formed by dielectric cylinders embedded in parallel in a uniform medium can indeed act as a negative refractive lens. Some agreement with and differences from previous studies are elaborated upon. The refractive index is also estimated from ray optics approximation. The tolerance of the lens to positional disorders is then discussed.

Anderson localization of electromagnetic waves in confined dielectric media

Anderson localization of electromagnetic waves in random arrays of dielectric cylinders confined within a planar metallic waveguide is studied. The disordered dielectric medium is modeled by a system of randomly distributed two-dimensional electric dipoles. An effective theoretical approach based on the method of images is developed. A clear distinction between isolated localized waves (which exist already in finite media) and the band of localized waves (which appears only in the limit of the infinite medium) is presented. The Anderson localization emerging in the limit of an infinite medium is observed both in finite-size scaling analysis of transmission and in the properties of the spectra of some random matrices.

Localized defect modes in a two-dimensional triangular photonic crystal

By using a finite-difference time-domain numerical method based on introducing an oscillating dipole at a proper position in a two-dimensional photonic crystal consisting of an array of dielectric cylinders, we numerically solve the inhomogeneous wave equation discretized in both space and time to calculate the eigenfrequency and the eigenfunction of a localized defect mode. We study the spatial distribution of the electric field and the radiated power associated with the defect modes produced by introducing a defect cylinder into an otherwise periodic two-dimensional triangular photonic crystal. We have obtained excellent agreement for the defect mode of ${A}_{1}$ symmetry created by removing a single cylinder from the center of the region of cylinders arrayed in a triangular lattice with the experimental result of Smith et al. [J. Opt. Soc. Am. B 10, 314 (1993)]. We have also examined systems in which defect states are introduced by varying the radius of a single cylinder and when both the dielectric strength and the radius of the defect cylinder are changed. The calculated values of the donor and acceptor levels associated with the exponentially decaying defect modes of ${A}_{1}$ symmetry induced by changing the radius are in good quantitative agreement with the nondegenerate donor and acceptor levels obtained by the supercell method within the plane-wave approach reported recently by Feng et al. [Jpn. J. Appl. Phys. 36, 120 (1997)].

The rotational effect on the multiple scattering of a linear array of dielectric cylinders with finite conductivities

The rotational effect on the multiple scattering of a linear array of dielectric cylinders with finite conductivities

Analytical approach to localization of electromagnetic waves in two-dimensional random media.

Localization of electromagnetic waves in two-dimensional random media is studied analytically. A simple but realistic model, based directly on the Maxwell equations, is developed. Almost perfect localization is predicted in sets of randomly distributed two-dimensional dipoles which are linearly coupled to the electric field of the incident wave. Striking qualitative similarities are observed between our results and effects found experimentally in microwave localization by random arrays of dielectric cylinders [R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, and S. L. McCall, Nature (London) 354, 53 (1991)].

Iterative focusing in a parallel planar array of dielectric cylinders

Comparisons of experimental data with theory for the diffracted fields behind a parallel planar array of dielectric cylinders indicate the importance of iterative focusing in explaining field anomalies.

Microwave lens matching by simulated quarter-wave transformers

The reflections from the surface of a dielectric lens may be cancelled by a quarter-wavelength layer of refractive index intermediate between that of air and the lens medium. The possibility of simulating a quarter-wave matching section by perturbing the boundary of the lens is described in this paper. Some of the configurations considered are corrugated surfaces, arrays of dielectric cylinders, and arrays of holes in the dielectric surface. In each case, a match may be obtained at a given frequency and angle of incidence by the proper adjustment of the depth of the perturbation, and of one other parameter such as the width of a groove.