Band structure of comb-like photonic crystals containing meta-materials

We study the transmission properties and band structure of comb-like photonic crystals (PC) with backbones constructed of meta-materials (negative-index materials) within the frame of the interface response theory. The result shows the existence of a special band gap at low frequency. This gap differs from the Bragg gaps in that it is insensitive to the geometrical scaling and disorder. In comparison with the zero-average-index gap in one-dimensional PC made of alternating positive- and negative-index materials, the gap is obviously deeper and broader, given the same system parameters. In addition, the behavior of its gap-edges is also different. One gap-edge is decided by the average permittivity whereas the other is only subject to the changing of the permeability of the backbone. Due to this asymmetry of the two gap-edges, the broadening of the gap could be realized with much freedom and facility.     

Optical properties of one-dimensional photonic crystals containing graded materials

The optical properties of an one-dimensional photonic crystal containing graded materials are studied theoretically. The graded layers have space dispersive permittivity and magnetic permeability which vary along the direction perpendicular to the surface of the layer. The gradation profiles of permittivity are studied in detail. We show that the structure possesses forbidden band gaps in its transmission spectra and the gradation profiles of permittivity affect the band gaps significantly. For the exponential gradation profile ε₁(x) = α e^βx, the number of the band gaps increases and the total frequency region corresponding to the gaps becomes large with increasing parameter β. On the other hand, the position of band gaps can be changed by the adjustment of the gradation profiles even if possessing same volume-average permittivity in the graded layers. Therefore, we can achieve suitable photonic band gaps by choosing gradation profiles of permittivity.     

Properties of defect modes in one-dimensional photonic crystals containing a graded defect layer

The properties of defect modes in one-dimensional photonic crystals (PCs) containing a graded defect layer are studied theoretically. The relative permittivity and magnetic permeability of the graded defect layer vary continuously along the direction perpendicular to the surface of the layer. The effect of the linear gradation profiles of the relative permittivity and permeability are studied in detail. It is shown that the defect modes appear inside the forbidden band gaps in its transmission spectra and the gradation profiles of the relative permittivity and permeability affect the defect modes significantly. By changing the gradation parameters, the intensity and position of the defect modes can be tuned. Therefore, introducing a graded defect layer in one-dimensional PCs provides possible mechanism for tuning the defect modes. This may be useful in the design of channeled filters.     

Engineering absolute band gap in anisotropic hexagonal photonic crystals

We analyze the band gap spectra of two-dimensional anisotropic photonic crystals created by a hexagonal lattice of rods covered by an interfacial layer (e.g. tellurium tubes). Using the plane-wave numerical expansion method, we study the modification of the band gap spectrum when the rods are infiltrated with other material, and discuss the optimization strategies leading to the maximum value of the absolute band gap.     

Tunable full band gap in two-dimensional anisotropic photonic crystals infiltrated with liquid crystals

We analyze the tunability of full band gap in two-dimensional photonic crystals created by square and triangular lattices of anisotropic tellurium rods in air background, considering that the rods are infiltrated with liquid crystal. Using the plane-wave expansion method, we study the variation of full band gap by changing the optical axis orientation of liquid crystal.     

Absolute band gap properties in two-dimensional photonic crystals composed of air rings in anisotropic tellurium background

We analyze the band gap spectra of two-dimensional photonic crystals created by square, triangular and honeycomb lattices of air rings with different geometrical shapes and orientations in anisotropic tellurium background. Specifically, five different shapes of rings (circular, hexagonal, elliptical, rectangular and square) are considered. Using the numerical plane wave method, we discuss the maximization of the absolute photonic band gap width as a function of air ring parameters with different shapes and orientations in three types of lattices.     

Tunable multichannel filter in photonic crystal heterostructure containing permeability-negative materials

A tunable multichannel filter is demonstrated theoretically based on a one-dimensional photonic crystal heterostructure containing permeability-negative material. The filtering properties of the photonic crystal filter, including the channel number and frequency, can be tuned by adjusting the structure parameters or by a pump laser. The angular response of the photonic crystal filter and the influences of the losses on the filtering properties are also analyzed.     

Photonic band gap effect in one-dimensional plasma dielectric photonic crystals

Propagation of electromagnetic waves in one-dimensional plasma dielectric photonic crystals, the superlattice structure consisting of alternating plasma and dielectric materials, is studied theoretically using transfer matrix method. Numerical calculation is presented for plasma-air finite and infinite periodic structures. The results of photonic band gap characteristics are discussed in terms of plasma density, plasma width, and number of unit cells (N).     

Large forbidden band in one-dimensional multi-layered structure containing exponentially graded materials

In the present communication, we have presented band spectra and reflectance properties of one-dimensional multi-layered structure containing dielectric exponentially graded and simple dielectric layers. This study has been performed theoretically by using transfer matrix method. In this paper we have taken the multi-layered structure where refractive index of odd layers is varying continuously along the direction perpendicular to the surface of the layer in exponential form. The effect of the graded profiles are studied and compared with the conventional multi-layered structure of suitable contrast of refractive indices in detail. In this study the materials are considered as non-magnetic and layers other than the graded are taken to be homogeneous and isotropic dielectric medium of constant refractive index. It has been found that the introduction of graded layers enhanced the forbidden band gaps and affects the reflectance of electromagnetic wave spectra significantly. By changing the grading profiles and the contrast, we obtained the forbidden band gaps and the reflectance of such structural change accordingly. Therefore, introducing a graded exponential layer of dielectric in the one-dimensional multi-layered structure provides possible mechanism for enhancing the reflectance as well as the forbidden gap in the optical region. Such multi-layered structure may be useful in the design of a broadband filter.     

Complete evanescent tunneling gaps in one-dimensional photonic crystals

Complete band gaps are found in one-dimensional photonic crystals composed of negative-permittivity and negative-permeability materials. The mechanism of these complete band gaps, unlike the Bragg complete gaps formed by interferences of forward/backward propagating waves, originate from the evanescent wave tunneling in the single-negative materials is reported for the first time. Moreover, it is also reported for the first time that both Bragg complete gaps and evanescent wave tunneling complete gaps exist in a three-constituent one-dimensional photonic structure simultaneously.     

Narrow transmission bands of quasi-1D comb-like photonic waveguides containing negative index materials

Using the interface response theory, we investigate the band structure and transmission of quasi-1D comb-like photonic waveguides with side branches composed of negative index materials. Numerical results exhibit the existence of discrete modes in band structure. These discrete modes are corresponding to narrow transmission bands which separated by large forbidden band in the transmission spectrum. Meanwhile it is shown that the narrow transmission bands become narrower with the increase of the number of side branches. The above properties are still maintained when the negative index materials are dispersive and lossy.     

Multichannel filtering properties of photonic crystals consisting of single-negative materials

The multichannel filtering properties have been investigated by means of the transfer-matrix method in the one-dimensional periodic structures containing two kinds of single-negative materials. Two sets of comb-like filtering channels appear simultaneously on the two sides of the bandgap with zero-effective phase. One is omnidirectional in the low frequency, and the other is angle-sensitive in the high frequency. The multichannel filtering properties of the structures, such as the channel number, the central frequencies and quality factors, may be modified by adjusting the period number and the layer thicknesses. It thus provides a simple way to design multichannel filter with specific channels.     

Imaging Properties of a Rectangular-Lattice Metallic Photonic-Crystal Slab

We report the imaging properties of a two-dimensional rectangular-lattice photonic crystal （PC） slab consisting of rectangular metallic rods immersed in a dielectric background. By simulating the electromagnetic wave propagation through such a PC slab with the finite-difference time-domain method, we find that a point source placed in the vicinity of the PC slab can form a good-quality image through the slab. The frequency region where a good-quality image is formed can be controlled by choosing the direction along which the PC slab surface normal is placed.     

Band-gap properties of two-dimensional low-index photonic crystals

We study the band-gap properties of two-dimensional photonic crystals created by a lattice of rods or holes conformed in a symmetric or asymmetric triangular structure. Using numerical plane-wave method, we calculate a minimum value of the refractive-index contrast for opening both partial and full two-dimensional spectral gaps for both TM- and TE-polarized waves. We also analyze the effect of ellipticity of rods and holes and their orientation on the threshold value and the relative size of the band gaps.     

The effect of etching interfacial layers on the absolute photonic band gap in two-dimensional photonic crystals

The photonic band structures of two-dimensional (2D) photonic crystals with etched interfacial layers between air rods and the background dielectric is studied theoretically. The effect of etching interfacial layers on absolute photonic band gap (PBG) is analyzed quantitatively. Numerical calculations are carried out based on Maxwell's equations and the plane-wave expansion method. It is shown that the physical property of interfacial layers influence the absolute PBG, and the existence of interfacial layers cannot enlarge the largest absolute PBG of an ideal case without interfacial layers.     

Negative refraction in a honeycomb-lattice photonic crystal

In this paper we theoretically investigate a photonic crystal with dielectric rods in a honeycomb lattice. Two left-handed frequency regions are found in the second and third photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Subwavelength imaging by the photonic crystal flat lens are systematically studied by numerical simulations using the multiple scattering method. Different from the photonic crystals with noncircular dielectric rods in air, this structure is almost isotropic at the optimal frequency for superlensing. As a comparison, flat slab focusing is also demonstrated at other frequencies in the two left-handed regions.     

Amphoteric-like refraction in a two-dimensional photonic crystal

High-index contrast photonic crystals possess an intricate photonic band structure that is responsible for surprising phenomena as the surperprism effect, self-collimation, power splitting or negative refraction. Recently, it was reported that at the interface between an isotropic medium and a uniaxial crystal (or between two uniaxial crystals) a phenomenon known as amphoteric refraction, that is, positive as well as negative refraction, can take place. By means of a equifrequency contours analysis and finite-difference time-domain simulations, we show that a two dimensional photonic crystal can also present amphoteric refraction by properly choosing the lattice orientation and the termination. However, total transmission is difficult to achieve because a Bloch mode is excited inside the photonic crystal and the coupling efficiency from this mode to an external plane wave is lower than one.     

Tunable band gaps in electro-optical photonic bi-oriented crystals

Electrically induced birefringence is studied in photonic bi-oriented crystals in terms of molding lightflow in optical devices. In photonic bi-oriented crystals, misorientation of dielectric anisotropic grains results in a dielectric contrast at the grain boundaries. The translational periodicity of the optical constants depends upon a regular network of twisted dielectrics. Due to the anisotropy of the bicrystalline structure the direction of light propagation determines the dielectric contrast at the grain boundaries. In a specific crystallographic arrangement the optical properties of the bi-oriented crystal can be tuned by the electro-optical effect: the periodic dielectric contrast is electrically induced and photonic bandgaps are generated by applying external electric fields. The geometrical requirements for tunable photonic bicrystals are evaluated based on materials employed for electro-optical applications. Tunable photonic bi-oriented crystals may be candidates for fast optical switches, modulators and multiplexers in the optical communication network. Received: 5 July 2001 / Revised version: 3 August 2001 / Published online: 15 October 2001     

Optical switching applications of ZnSe/MgF2 photonic band gap structures based on thermal nonlinearities

We investigate a thermo-optical device based on a ZnSe/MgF₂ multilayer and demonstrate the modulation of its optical reflectance around the band edge. An electrically induced temperature increase is responsible for the change of the refractive indices of the layers. As a result, the reflection spectrum shifts and the reflected signal decreases. The structure was grown using a thermal evaporation technique, and was designed in such a way that a band edge appears at 632.8 nm, i.e. accessible to a low-power He–Ne laser. The reflection characteristics were investigated as a function of the applied voltage and we found that the photonic band edge shifts by a maximum of 7 nm for an applied voltage of 90 V. Furthermore, different sets of measurements have shown that the spectral shift depends on the voltage squared, thus allowing experimental data analysis in terms of the thermally driven optical nonlinearity.     

The Sommerfeld precursor in photonic crystals

We calculate the Sommerfeld precursor that results after transmission of a generic electromagnetic plane wave pulse with transverse electric polarization, through a one-dimensional rectangular N-layer photonic crystal with two slabs per layer. The shape of this precursor equals the shape of the precursor that would result from transmission through a homogeneous medium. However, amplitude and period of the precursor are now influenced by the spatial average of the plasma frequency squared instead of the plasma frequency squared for the homogeneous case.