Two-dimensional Photonic Bandgap Structures Research Articles

Calculation and fabrication of two-dimensional complete photonic bandgap structures composed of rutile TiO2 single crystals in air/liquid

Photoelectrochemical applications of photonic crystals are gathering great interests both from physicists and chemists. Here, we theoretically and experimentally present two-dimensional photonic bandgap (2D-PBG) structures based on rutile titanium dioxide (TiO2) single crystal that is a famous material because of the photoelectrochemical ability. The structures were the arrays of hollow hexagonal rutile TiO2 pillars in contact with air or a typical nonaqueous electrolyte solution, acetonitrile. Since the TiO2 refractive indices exhibit a strong dispersive behavior, the bandgap width was discussed from the viewpoint of the refractive index map that would be helpful for the real application of this structure. The 2D-PBG structures for both infrared light and visible light were fabricated by our established lithography technique for rutile TiO2 with and without Nb doping, i.e., photocatalytic TiO2 and high electron conductive TiO2, respectively. These structures show characteristic absorbance peaks or reflectance dips at wavelengths predicted by our theoretical calculations.

增强光子晶体谐振腔模式选择性的方法分析

Based on analyzing the dispersion characteristics and the global band gaps for general two-dimensional photonic band gap structures formed by triangular arrays of metal posts, we select TE04 at 140 GHz as the operational mode and present the modes distribution diagram in different band gaps. By optimizing the operational point, the number of modes competing with TE04 reduces from 5 to 2. On the other hand, the lattice constant and the radius of metal columns are expanded, thus it can bear more thermal loading. Finally, comparisons are made between electric field distributions of TE04 in different band gaps.

The properties of two-dimensional photonic crystals bandgap structure with rhombus lattice

The relative bandgap ωR of photonic crystals structure with rhombus lattice for both TE and TM modes is studied by the plane wave expansion method. Based on the analysis, a bending waveguide of U type can be easily obtained. The steady-state distribution of the electric field with ω=0.4765(a/λ) of TM mode is given by FDTD method and the transmission is obtained by FFT of the time domain field. All of the sufficient analysis shows the conceptual framework of the proposed rhombus lattice PCs and its great potential application in photonic integration circuit.

一种光子晶体谐振腔的TM模特性

A model of two-dimensional photonic band gap structures resonant cavity is proposed made by GaAs pillars in air with graphite lattice.Its TMy mode formant wavelength changing with stress and temperature is calculated by finite difference time domain method.The results show that no mater what direction for the stress acting on the resonant cavity,there will be a good linear characteristic between the formant wavelength and the stress,the sensitivity responding to stress is 0.013 69 nm/Mpa.Meanwhile,it is found that the sensitivities responding to stress along x and y direction are the same.There is a sectional linear characteristic between the main formant wavelength and temperature for this kind of photonic crystal resonant cavity,and the biggest sensitivity responding to temperature is 1.4 nm/℃.Furthermore,the results show that there is a make-and break key characteristic for the proposed resonant cavity.

Temperature characteristic of photonic crystals resonant cavitycomposed of GaAs pillars with graphite lattice

A model of two-dimensional photonic band gap structure resonant cavity composed of GaAs pillars with graphite lattice is proposed. The variation of its TEy mode formant wavelength with temperature is calculated by finite difference time domain method. The results show that there is a sectional linear characteristic between the main formant wavelength and temperature for this kind of photonic crystal resonant cavity, and the sensitivity responding to temperature is more than 1.60nm/℃. At the same time, the results show that this kind of resonant cavity possesses an excellent characterisitc of frequency switching. Finally, the cause for its switching characteristic is explained by the calculated results.

Fabrication of two-dimensional photonic crystals in a chalcogenide glass

Two-dimensional photonic band gap structures consisting of air holes arranged to form a hexagonal lattice were patterned into chalcogenide glass thin films by Focused Ion Beam (FIB) milling. The dimensional parameters for these structures, namely type of lattice, lattice parameter and radius of the holes, were chosen so as to show a photonic band gap relevant to the infrared range, aiming at their subsequent use in the field of chemical sensing and biosensing. The optical behaviour of these structures was determined by calculating the band structure for the TM (magnetic field in-plane) and TE (electric field in-plane) modes. Furthermore, FIB milling was used to fabricate input and output waveguides coupled to the photonic crystals. The transmission spectra of the resulting structures for the TE and TM modes with two different orientations were also calculated.

Design of high-bandwidth one- and two-dimensional photonic bandgap dielectric structures at grazing incidence of light

We propose one-dimensional photonic bandgap (PB) dielectric structures to be used at grazing incidence in order to obtain an extended bandgap exhibiting considerably reduced reflection loss and dispersion compared to similar structures used at a normal incidence of light. The well-known quarter-wave condition is applied for the design in this specific case, resulting in resonance-free reflection bands without drops in reflection versus wavelength function and a monotonous variation of the group delay dispersion versus wavelength function, which are important issues in femtosecond pulse laser applications. Based on these results we extend our studies to two-dimensional PB structures and provide guidelines to the design of leaking mode-free hollow-core Bragg PB fibers providing anomalous dispersion over most of the bandgap.

Comment on “Analytic and numerical calculations of the dispersion characteristics of two-dimensional dielectric photonic gap structures” [J. Appl. Phys. 99, 063104 (2006)

The article by Samokhvalova et al. [J. Appl. Phys. 99, 026106 (2006)] introduces a solvable analytic model of two-dimensional dielectric photonic band gap structures in the form of rectangular dielectric rods. Here, it is shown that the model is simply a superposition of two one-dimensional models; that is, the authors have, in fact, solved a separable Helmholtz equation.

Characteristics of terahertz slow-wave system with two-dimensional photonic band-gap structure

A terahertz slow-wave system model consists of a photonic crystal with two-dimensional band-gap structure and a slow-wave plate as its periodic unit. The electromagnetic field in the slow-wave system has been numerically simulated. The dispersion relation and the coupled impedance of the backward wave mode in the system have been calculated for a variety of geometric settings. The results indicate that this model would be a promising candidate for the slow-wave system with single stable backward wave mode.

Analysis of a two-dimensional photonic bandgap structure fabricated by an interferometric lithographic system

An interferometric lithographic technique and double exposure method are applied to theoretically and experimentally investigate several kinds of 2D periodic structures. The shape, lattice symmetries, and lattice constants of the 2D structures, for different substrate rotational angles, are obtained from the simulated predictions. The shape of the 2D structures can be varied by controlling the rotational angle of the substrate and the development process, and they are validated experimentally. The variation of the lattice symmetry of the 2D structure with the substrate rotational angle is discussed in detail in relation to the axial angle and lattice constant. It is found that square, circular, rectangular, and elliptical scatterers which are arranged in parallelogram, triangular, and square lattices (with different lattice constants) can be obtained. The photonic bandgaps for each condition are also investigated. When the substrate rotational angles are the same, the normalized frequency (omega a/2 pi c) of photonic bandgap structures with an equal filling factor are very similar regardless of the interference angle. The results are helpful in designing the forbidden frequency when the lattice constant and the scatterer shape can be controlled by the interferometric lithographic technique.

Least action principle for dissipative solitons and its application in two-dimensional PBG structure

Dissipative and coherent effects of X-point solitons are investigated on the basis of dynamic variational formulation in two-dimensional photonic bandgap (PBG) structure of square lattice. Through the least action principle, the result deduced from analyzing soliton parametric equations indicates that dissipative effect leads to not only amplitude decrease but also section expansion of solitons. In addition, co-soliton interaction for negative potential is decreased by dissipation, and bound sate of solitons in x direction is also weakened. Amplitude and period of fluctuation of relative interval between soliton centers increase in x direction, when x increases to some value, relative interval will increase continuously.

DESIGN EQUATIONS OF TWO-DIMENSIONAL DIELECTRIC PHOTONIC BAND GAP STRUCTURES

This paper presents simple formulas for designing different configurations of two-dimensional photonic band gap (PBG) structures. These formulas are obtained by interpolating full wave analysis based on the plane wave expansion method. The design parameters of these formulas include the physical dimensions of the unit cell and the electrical properties of both host and inclusion in the structure. These formulas represent an efficient and fast method to obtain the band gap and the center frequency of different PBG structures.

Nanostructured-porous-silicon-based two-dimensional photonic crystals

Tunable two-dimensional photonic band gap structures were developed, basically consisting of nanometric porous silicon (PS) rods embedded into a silicon matrix, arranged as to form a hexagonal lattice. The optical behavior of these structures was determined by calculating the band structure for the transverse magnetic and transverse electric modes, finding that the optical response can be controlled by independently varying the index of refraction of PS, the radius of the rods, and the lattice parameter. The change in the index of refraction was implemented in the range of 1.4–2.2 by controlling the PS formation parameters. Finally, it can be pointed out that the dependence of the optical behavior of the photonic crystals on polarization can lead to the development of polarization-dependent optoelectronic devices.

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.

Analytical and numerical calculations of the dispersion characteristics of two-dimensional dielectric photonic band gap structures

An exact analytical dispersion relation is derived for transverse-magnetic modes with kz=0 in a particular two-dimensional rectangular photonic band gap structure. The dispersion relation is analyzed, and the dispersion characteristics are determined. Analytical results are compared with results from the Massachusetts Institute of Technology Photonic Band Gap Structure Simulator (PBGSS) code. The error tolerance in the PBGSS code is established. Finally, the attenuations of modes with frequencies in global band gaps are computed analytically.

Electrical modulation of silicon-based two-dimensional photonic bandgap structures

Electrically tunable photonic band gap (PBG) structures hold the potential to become a versatile and compact backbone for optical signal processing. In this letter we report electrical tuning of silicon-based two-dimensional PBG structures infiltrated with liquid crystals. An improved electrode configuration is used to avoid electric field screening by the conductive silicon walls. Electrical tuning using fields well below 1V∕μm is demonstrated experimentally using both polarized light microscopy and reflectance PBG measurements. The structures can be operated with any electro-optic materials and lead to fast and efficient modulators, routers, and tunable filters.

Omnidirectional two-dimensional photonic crystal band gap structures

Omnidirectional (3D) band gaps can evolve in $2\frac{1}{2}$ honeycomb and squared photonic crystal lattices and also in hexagonal crystals [Li and Xia, Phys. Rev. B 64, 153 (2001)]. This study presents a study of the according full parameter space. The calculation of omnidirectional photonic bands is based on the plane wave method for a two-dimensional photonic crystal with an off-plane wave vector ${k}_{z}={k}_{0}\phantom{\rule{0.2em}{0ex}}\mathrm{sin}(\ensuremath{\theta})$. The results are fully respecting the parameters index of refraction, the angle of incidence, as well as the structure radii. Omnidirectional band gaps are found for radii between $R=0.34$ and $R=0.5$, starting with index values from $3.0$ and show maximum relative band gap sizes ranging from $2.7%$ up to $10%$.

The two-dimensional metal photonic band gap structure consisting of a skew lattice in a nonorthogonal coordinate system

The metal photonic band gap structure has potentialities in the areas of high-energy accelerators,microwave vacuum electron devices, and terahertz radiation sources etc. The real space transfer matrix method in a nonorthogonal coordinate system is used to study the two-dimensional metal photonic band gap structure consisting of a skew lattice. A general formula for calculating the complete band gap structure is derived for transverse-electric and transverse magnetic modes, and the influences of the filling fraction, skew angle and cross section of the metal rod on band gap are analyzed. The results are in good agreement with results of other methods in some special cases.

Thermal tuning of silicon‐based one‐dimensional photonic bandgap structures

Thermal tuning of silicon-based one-dimensional photonic bandgap microcavities is demonstrated. Thermally induced spectral shifts are caused by both the host silicon matrix and the optically active material infiltrated inside the photonic bandgap structures. The active material leads to the dominant thermal tuning contribution but the effect of the silicon matrix cannot be neglected. The interaction of the temperature dependence of the host matrix with that of the active material is explored. The general trends revealed by the characterization should be relevant for two-dimensional silicon-based photonic bandgap structures as well as other photonic bandgap materials systems. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Comparison of one- and two-dimensional dielectric reflector geometries for high-energy laser pulse compression

We present a high-efficiency reflective lamellar grating geometry, based on a two-dimensional photonic bandgap structure, that we predict will provide significantly improved resistance to laser-induced damage. Two independent numerical methods are used to compare the performance of this geometry with that of a conventional multilayer dielectric stack.