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.     

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.     

Absolute photonic band gaps in a two-dimensional photonic crystal with hollow anisotropic rods

The plane-wave expansion method is used to calculate photonic band gaps for two structures with hollow anisotropic tellurium (Te) rods. Both structures are found to have absolute band gaps at the low- and high-frequency regions. Compared with the photonic crystal with solid Te rods, the photonic crystal with hollow Te rods has a large absolute band gap at the high-frequency region: for the triangular lattice of oval hollow Te rods, there is an absolute band gap of 0.058w_e (w_e=2πc/a), and for the square lattice of square hollow Te rods, there is an absolute band gap of 0.056w_e.     

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.     

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.     

Properties of the angular gap in a one-dimensional photonic band gap structure containing single negative materials

Properties of the angular gap in a one-dimensional photonic band gap structure containing single negative materials are investigated. This gap forms at oblique incidence due to the total internal reflection into air when the Snell's law breaks down. Its lower edge occurs at the frequency where the refractive index of one or both layers of the structure approaches zero. This gap is found to be highly sensitive to the incident angle and the polarization of the incident light, but is not affected by the thickness ratio of the layers. It is also shown that the electric field gets extremely enhanced at the lower edge of this gap for transverse magnetic polarization. This highly enhanced electric field can be utilized for certain applications.     

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.     

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.     

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).     

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.     

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     

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.     

Large forbidden angles for a two-dimensional photonic crystal of connected-honeycomb lattice

The off-plane band structures of a two-dimensional photonic crystals of connected-honeycomb lattice are calculated by the plane-wave expansion method. To investigate how the band gaps vary with the off-plane angle, an effective refractive-index model is employed to work out the corresponding angular gap map. We find that the connected-honeycomb lattice can provide forbidden angles taking up as much as 58.6% of the solid angle. The result will be helpful in the design of photonics devices incorporating two-dimensional photonic crystal structures.     

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.     

Beaming effect from increased-index photonic crystal waveguides

We study the beaming effect of light for the case of increased-index photonic crystal (PhC) waveguides, formed through the omission of low-dielectric media in the waveguide region. We employ the finite-difference time-domain numerical method for characterizing the beaming effect and determining the mechanisms of loss and the overall efficiency of the directional emission. We find that, while this type of PhC waveguide is capable of producing a highly collimated emission as was demonstrated experimentally, the inherent characteristics of the structure result in a restrictively low efficiency in the coupling of light into the collimated beam of light.     

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.     

Enlargement of complete two-dimensional band gap by using photonic crystal heterostructure

A two-dimensional photonic crystal heterostructure, which consists of two photonic crystals of a square lattice of circular columns with reverse dielectric configurations, is proposed. Photonic band gap properties are calculated using a plane-wave method and the transmission spectra are obtained. After optimization, the relative width of the complete band gap reached 13.8% based on the simple unit-cell shape and crystal lattice. The photonic crystal heterostructure opens up new ways of engineering photonic band gap materials and designing photonic crystal devices.     

Electromagnetic unidirectionality and frozen modes in magnetic photonic crystals

Magnetic photonic crystals are periodic arrays of lossless materials, at least one of which being magnetically polarized. Magnetization, either spontaneous or induced, is associated with nonreciprocal effects, such as Faraday rotation. Magnetic photonic crystals of certain configuration can also display strong spectral asymmetry, implying that light propagates in one direction much faster or slower than in the opposite direction. This essentially nonreciprocal phenomenon can result in electromagnetic unidirectionality. A unidirectional medium, being perfectly transmissive for electromagnetic waves of certain frequency, freezes the radiation of the same frequency propagating in the opposite direction. The frozen mode has zero group velocity and drastically enhanced amplitude. The focus of our investigation is the frozen mode regime. Particular attention is given to the case of weak nonreciprocity, related to the infrared and optical frequencies. It appears that even if the nonreciprocal effects become vanishingly small, there is still a viable alternative to the frozen mode regime that can be very attractive for a variety of practical applications.     

Influence of Kerr nonlinearity on the band structures of two-dimensional photonic crystals

Dynamic modifications of the band structures of two-dimensional photonic crystals composed of Kerr-nonlinear dielectric rods in air forming hexagonal, square and honeycomb lattices are investigated. Calculations are carried out by the method based on the finite-difference time-domain (FDTD) technique for both TM and TE polarizations. The bands in all cases are observed to red-shift with the introduction of nonlinearity. Inspection of the variation of the mid-gap frequencies with source intensity reveals that the red-shift increases as gap number increases, in a manner proportional to the mid-gap frequency in linear regime. The red-shift of mid-gap frequencies is also found to follow the adopted saturable model for the change of relative permittivity with source intensity. Either the so-called dielectric or the air band edges of the gaps are found to be more sensitive to nonlinearity resulting in broadening or shrinking of the gaps. Possible utilizations of the present observations for all-optical device applications, such as wavelength multiplexing, are discussed.