Refraction In Photonic Crystals Research Articles

Refocusing resolution based on negative refractive-photonic crystal group with Ag defects for target detection and imaging

Negative refractive-photonic crystal (NR-PC) lenses that can exceed the diffraction limit of focus resolution for imaging and target detection in the near field have gotten more and more special attention in recent years. Three flat lens groups with Ag defects based on NR-PC are designed, and the focusing imaging in the NR-PC three flat lens groups is concluded with the extension of Snell’s law, and the influence on the resolution for a target detection dynamic scanning scheme is simulated by using the finite difference time domain method. An optimal-doped structure with Ag defects is achieved by different simulation combinations. The refocusing resolution 0.18834λ is achieved in the optimal structure and there is approximately a 0.06806λ improvement in the refocusing resolution compared to those undoped with Ag (0.2564λ); it also possesses distinct smaller side-lobes than a single flat lens doped with Ag. This means the optimal detecting ability for the three NR-PC flat lens groups with Ag defects is more improved than that for a single undoped and doped with Ag. This is significant for the perfect imaging being achieved for a particle structure.

Experimental demonstration in X-band of dual-negative refraction in photonic crystals

The effect of dual-negative refraction (DNR) in a photonic crystal (PhC) is demonstrated experimentally in X-band (8–12 GHz) for the first time. The two-dimensional PhC sample is made of highly pure Al2O3 ceramic cylinders close packed in air with a triangular lattice structure. The frequency regions of DNR are predicted by the analyses of wave vector diagrams. Experiments of anomalous refraction in PhCs are carried out in a near-field scanning system to demonstrate the theory and numerical results. The experimental measurements of electric field (real part and spatial intensity) for DNR are in good agreement with the numerical simulations. This work demonstrates that the unique feature of photonic crystals can be realized experimentally in different frequency regions which are proportional to the lattice constant of the PhC. Due to the large design flexibility, we believe this result will be promising for application in the range of optical devices.

On the use of NR-PC flat lens for square target detection and imaging by lens-combined scanning scheme

In the paper, target detection and imaging from refraction photonic crystal (NR-PC) slab lens is studied by the finite-difference time-domain (FDTD) method. Numerical simulation shows that, there is a transmission peak with a value far greater than unit, resulting from the mini-forbidden bands and resonance excitation at the resonance frequency of 0.3068 (a/λ). When a target is placed at the focus point (F2) of the NR-PC lens, its image and great amplitude could be formed in the vicinity of the point source through the focusing of backscattered optical wave from the target. Further investigation demonstrates that the lens-combined scanning scheme provides higher refocusing resolution than lens-fixed and non-dynamic scanning scheme for square target detection and imaging.

Dual-negative refraction in photonic crystals with hexagonal lattices

We present a dual-negative refraction effect based on the overlapping bands in a two-dimensional triangular photonic crystal formed by holographic lithography. Under certain conditions, one incident plane wave launched into this photonic crystal can be dispersed into two negative refracted waves at the same frequency and the same perpendicular polarization state with different phase velocities and group velocities. We find that this dual-negative refraction behavior can be easily manipulated by adjusting the incident angle, the frequency of incident wave and the filling ratio of the PhC. This special effect can be applied to realize wave-front division and optical interference in optical holography. Based on this effect, a double focusing imaging phenomenon has been achieved by the PhC slab. These unique features may show great impacts on both fundamental physics and optical device applications.

Highly refractive three-dimensional photonic crystals for optical sensing systems

We investigate optical properties of three-dimensional photonic-crystal systems consisting of spherical nanoparticles of styrene copolymer with methacrylic acid closely packed into a face-centered cubic lattice. The effective refractive index of such structures is shown to be much higher than effective refractive indices typical of synthetic-opal-type photonic crystals. Highly refractive photonic-crystal systems combined with diffuse light scattering components radically improve the sensitivity of optical sensing elements within a broad frequency range.

Efficient tunable negative refraction photonic crystal achieved by an elliptic rod lattice with a nematic liquid crystal

Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation. We have investigated the electromagnetic wave propagation inside an elliptic rod PC slab by means of finite-difference time-domain simulations. The band structure of the PC composed of elliptic rod in the square and triangular lattices is studied by solving Maxwell's equations using the plane wave expansion method. Numerical simulations show that the refractive angle can be tuned greatly by rotating the directors of elliptic rod in the PC slab. Furthermore, an optical switch based on elliptic rod PC structures with nematic liquid crystals was proposed. In the on/off switching system, the partial band gap can be controlled when the normalized operation frequency is 0.28. The modulation induced by liquid crystals created a sharp switching in the photonic devices. Such a mechanism of negative refraction PCs should open up a new application for designing components in photonic integrated circuits.

Optical imaging superresolution by a negative refraction anisotropic photonic crystal

Abstract Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation. We have investigated the focusing of electromagnetic wave propagation inside an anisotropic PC slab by means of finite-difference time-domain simulations. The PC structure composed of air cylinders in the anisotropic–dielectric medium is studied by solving Maxwell's equations using the plane wave expansion method. Numerical simulations show that the optical imaging resolution can be improved greatly in the square lattices consisting of anisotropic–dielectric background. Such a mechanism of negative refraction PCs should open up a new application for designing components in optical imaging systems.

Uncoupled modes and all-angle negative refraction in walled honeycomb photonic crystals

Left-handed materials have superlensing effects that enable them to surmount the optical diffraction limit. A photonic crystal is able to mimic some properties of all-angle left-landed materials. In this study, the all-angle negative refraction criteria of photonic crystals are evaluated. The MIT Photonic-Bands program is employed to calculate the band structure of walled honeycomb photonic crystals, and the finite-difference time-domain method is used to provide a snapshot of the electric field distribution inside and outside the honeycomb photonic crystals. The results indicate that the all-angle negative refraction phenomena of the honeycomb photonic crystals are correlated with the orientation of the photonic crystals. Furthermore, the role of the uncoupled modes varies based on their orientation to the all-angle negative refraction photonic crystals, in one case assisting negative refraction and in the other case preventing it. The results suggest that symmetric properties should not be ignored when considering the negative refraction of photonic crystals.

Improvement of optical imaging resolution by a negative refraction photonic crystal with a solid immersion lens

Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation. We have investigated the solid immersion lens (SIL) technology in imaging system based on negative refraction PCs and analyzed the influence of refractive index and geometric parameters of SIL on imaging resolution. In the finite element method calculation, the resolution of our optical system has improved greatly. The high performance of imaging resolution was achieved with shorter radius and larger refractive index of SIL. Furthermore, the effects of the three kinds of SILs at the same radius were analyzed. Such a mechanism of negative refraction PCs and SILs should open up a new application for designing components in optical imaging systems.

Theoretical Study of Light Refraction in Three-Dimensional Photonic Crystals

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A rigorous theory for solving general 3-D photonic crystal refraction problem is developed. The power flow direction and transmission intensity of each mode refracted at a periodic surface are rigorously analyzed and determined from matrix equations. We further illustrate how to apply our method to design a low-index-contrast 3-D superprism structure that exhibits efficient transmission over a wide angular scanning range at wavelengths near 1550 nm. </para>

Optical switches based on partial band gap and anomalous refraction in photonic crystals modulated by liquid crystals

Optical switches using two transmission properties in triangular photonic crystals infiltrated with liquid crystals (LCs) are investigated for incorporation in wave-guided structures for planar lightwave circuits. The two devices employ partial band gap and anomalous refraction, which are based on the anisotropic characteristics of LC reorientation under applied fields. These switches have been designed and their parameters have been analyzed by the plane wave and finite-difference time-domain calculations. In the on/off switching system, the partial band gap can be controlled when the normalized operation frequency is 0.27. The anomalous refraction can be modulated to deflect a light beam with a maximum deflection angle ~57 degrees when the frequency is 0.3. The tunability induced by LCs can create a sharp switching in the photonic devices.

Rigorous analysis of diffraction gratings of arbitrary profiles using virtual photonic crystals

A new approach is developed to calculate diffraction efficiency for a dielectric grating with an arbitrary refractive index profile. By treating a one-dimensional grating as a segment of a virtual two-dimensional (2D) photonic crystal, we exploit a rigorous theory of photonic crystal refraction and calculate the diffraction efficiencies. We expand, analytically in many cases, the dielectric function of the grating into 2D Fourier series. We find the eigenmodes for the virtual photonic crystal, and then use these eigenmodes to match the boundary conditions by solving a set of linear equations. In two such simple steps, the diffraction efficiencies can be computed rigorously without slicing the grating into thin layers.

Towards focusing using photonic crystal flat lens

AbstractWe report on the numerical simulation and fabrication of a two-dimensional flat lens based on negative refraction in photonic crystals. The slab acting as a lens is made of an hole array (operating at the wavelength of 1.5 μm) etched in a InP/InGaAsP/InP semiconductor layer. We first study the key issues for the achievement of a negative refractive index taking advantage of folding of dispersion branches with main emphasis in dispersion properties rather than the opening of forbidden gaps. The diffraction and refraction regimes are analysed according to the comparison of the wave-vector with respect to the relevant dimensions of the hole array. In the second stage, we illustrate technological challenges in terms of e-beam lithography on a sub-micron scale and deep reactive ion etching for an indium phosphide based technology.

Refraction and rightness in photonic crystals

We present a study on relation between the refraction and rightness effects in photonic crystals applied on a 2D square lattice photonic crystal. The plane wave (the band and equifrequency contour analyses) and FDTD calculations for both TM and TE modes revealed all possible refraction and rightness cases in photonic crystal structures in the first three bands. In particular, we show for the first time, a possibility of the left-handed positive refraction. This means that left-handedness does not necessarily imply negative refraction in photonic crystals.

New evidences of negative refraction in photonic crystals

To verify the behavior of negative refraction in photonic crystals, we design a point source imaging system in which a point source is placed at a distance in front of photonic crystals slab. The distance is equal to the thickness of the slab. By numerical simulation based on the finite-difference time-domain (FDTD), the light beam inside the slab just focuses from one side to the other side of the slab and makes a clear image. Our result proves that negative refraction occurs inside PC for a certainty on special condition.

Numerical study of anomalous refraction in photonic crystals

We present a theoretical study of light propagation through photonic crystal (PhC) structures using an effective medium approximation based on equifrequency surface calculations. The procedure is illustrated by calculating bending, splitting and focusing phenomena in a slab of two-dimensional PhC using a Fourier imaging technique. In the passband above the first stop band, wave propagation was found to depend dramatically on both light frequency and incident direction. This propagation anisotropy leads to very large negative refraction along the [11] crystal direction. Light emitted from a line source outside the PhC slab can be focused, divided into subbeams inside the PhC, bent negatively, and refocused again on the other side the slab. The results agree well with the field calculated using a finite-difference time-domain method and can be straightforwardly applied to more complicated PhC structures, such as three-dimensional PhC structures. The imaging properties of a PhC slab are also discussed.

Theory of light refraction at the surface of a photonic crystal

A rigorous theory is developed for light refraction by a photonic crystal (PC) with arbitrary lattice-type and surface orientation. First, the refraction of a planar wave incident upon a photonic crystal surface is analyzed. We rigorously prove the equal partition of propagating PC modes by a surface under a general condition. The concept of surface-orientation-dependent mode degeneracy has been proposed and its relationship to quasi-periodic surfaces unfolded. With modes partitioned and the degeneracy properly recognized, a subset of the solved PC modes is identified to uniquely represent all PC modes that can be excited by an incident wave. The refraction problem can thus be rigorously solved in the plane-wave formulation. Essentially, we need to solve the field in only a single cell on the surface to solve the refraction problem. We further discuss the case where a Bloch wave illuminates the surface from inside a photonic crystal, which enables us to compute the transmissions along a complete light path through a series of interfaces. In addition, the transmission of a Gaussian beam is discussed, and the insertion loss formulas are presented. Other realistic beam profiles are discussed for designing photonic crystal devices. With all these issues solved, a complete theoretical framework of the photonic crystal refraction and transmission has thus been established. The theory has been applied to design a wavelength-division multiplexing demultiplexer that exhibits lower than $3\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$ loss over a $25\text{\ensuremath{-}}\mathrm{nm}$ spectrum. In examining the refraction by a quasiperiodic surface, a slight change of surface orientation is predicted to split one beam into an infinite number of beams.

Negative refraction in two-dimensional photonic crystals

We present some of our recent results for negative refraction in photonic crystals. The concept of negative refraction in photonic crystals is firstly introduced. Then, the propagation of electromagnetic waves in photonic crystals is systematically studied. By the layer Korringa–Kohn–Rostoker method, the coupling efficiency between external plane waves and the Bloch waves in photonic crystals is investigated. It is found that the coupling coefficient is highly angular dependent even for an interface between air with n=1 and a photonic crystal with effective index neff=-1. It is also shown that, for point imaging by a photonic crystal slab, owing to the negative refraction, the influence of the surface termination on the transmission and the imaging quality is significant. Finally, we present results experimentally demonstrating negative refraction in a two-dimensional photonic crystal at optical communication wavelengths.

Negative-refraction phenomenon at multiple frequency bands from electromagnetic crystals

Negative refraction in photonic crystals at the lower bandgap edges has been identified by many researchers. In this paper, we experimentally demonstrate that such negative refractions can also be found in an electromagnetic crystal consisting of metallic wires at multiple frequencies in the passbands in addition to the lower edges of bandgap. The experimental results are in very good agreement with the simulations. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 45: 465–469, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20854

Analysis of wave propagation in a two-dimensional photonic crystal with negative index of refraction: plane wave decomposition of the Bloch modes

This work presents a comprehensive analysis of electromagnetic wave propagation inside a two-dimensional photonic crystal in a spectral region in which the crystal behaves as an effective medium to which a negative effective index of refraction can be associated. It is obtained that the main plane wave component of the Bloch mode that propagates inside the photonic crystal has its wave vector k' out of the first Brillouin zone and it is parallel to the Poynting vector ( S' ? k'> 0 ), so light propagation in these composites is different from that reported for left-handed materials despite the fact that negative refraction can take place at the interface between air and both kinds of composites. However, wave coupling at the interfaces is well explained using the reduced wave vector ( k' ) in the first Brillouin zone, which is opposed to the energy flow, and agrees well with previous works dealing with negative refraction in photonic crystals.