Dispersion relation of surface plasmons near photonic band gaps: Influence of the interaction with light

Abstract

We present an experimental and theoretical study of the photonic band gap in the propagation of surface plasmons (SPs) on periodically corrugated surfaces. Our main purpose is to investigate the case where the band gap width is larger than the energy distance between the SP dispersion curve for a flat surface and the light line. We introduce a physical model of the interaction of light waves with SPs and derive an analytical expression for the SP wave vector near band gaps based on the coupled-mode approach involving three interacting modes (two of them are SP modes and one is a light mode). By using the interferometric measurement we have studied, for the first time, the SP propagation parameters in the vicinity of the photonic band gap (10 μm wavelength region). The predictions of our theory are in good agreement with the experimental data.     

Photonic band gaps in quasicrystal-related approximant structures

Abstract

We propose a method for a systematic investigation of quasicrystal-related approximant structures in view of photonic bandgap applications. A detailed study is presented in the case of approximants formed by dielectric cylinders and constructed from a two-dimensional quasiperiodic lattice with octagonal symmetry. We show that isotropic photonic bandgaps are obtained even for the lowest order approximants generated by successive hyperspace shear. The main Fourier components of the dielectric function, responsible for the first photonic bandgap opening, are derived from the main component set of the quasiperiodic lattice. The magnitudes of the corresponding Brillouin zone vectors are shown to be directly related to the average distance between the planes passing by the dielectric cylinders. In other words, the approximant gap position is rather determined by the fundamental lattice parameters common to the quasiperiodic and approximant structures than by the approximant period. We also show that structure point symmetry is not indispensable for the band gap opening.     

A Polarized Transfer Matrix for Electromagnetic Waves in Structured Media

Abstract

The study of electromagnetic systems with dielectric or magnetic properties that vary spatially on or below the scale set by the wavelength of the radiation considered is of interest both in the field of photonic band gap materials and in that of random multiple scattering media. A key calculation technique in both areas is the transfer matrix. We derive a new transfer matrix, written in the language of scattering between transverse polarized wave states. This could be used in either photonic band calculations or in disordered media calculations. We demonstrate the use of the new transfer matrix to describe transport through a layered random dielectric in the Rayleigh scattering regime. This problem has considerable similarities to that of non-interacting electrons in a one-dimensional random potential. A complete solution for one polarization can be given by the use of group theoretical results. The other polarization exhibits pronounced dipole effects which can easily be calculated to lowest order.     

光子晶体应用于浓度检测的模拟研究

采用平面波展开法数值计算二维光子晶体在TE和TM偏振态下的带隙,给出了光子晶体中的禁带存在的理论依据,选择二维三角晶格光子晶体（GaAs）作为基底,在气孔内填充浓度为一定的待测溶液硫酸铜材料,计算温度为298K情况下介电常数在71．917～62．530变化时,光子晶体在不同偏振模式下的光子禁带结构,结果表明,以硫酸铜的水溶液作为空气圆孔中的介质材料,当溶液质量百分浓度不同时光子带隙（PBG）发生显著变化。     

Control over the spectral position of the band gap of opal photonic crystals

We demonstrate that the width and spectral position of the band gap of opal photonic crystals can be controlled by varying the concentration of solution in the opal pores. An experimental technique is proposed which enables identification of both the first and second photonic band gaps in the reflection spectrum of opal. The ability to observe the second band gap allows a dispersion relation to be derived for the refractive index of the infiltrated substance. The calculations are performed using a model for a one-dimensional periodic layered medium with two refractive indices. We obtain an ω(k) dispersion relation and the reflection spectra of a photonic crystal in the [111] direction at different solution concentrations.     

Localization of Light by a Set of Parallel Cylinders

Abstract

Using a rigorous theory of scattering, numerical evidence of the existence of localized modes in a one-dimensional or a two-dimensional set of circular dielectric rods is given. Particular attention is paid to the transition observed between the phenomena of propagation in periodic structures and localization phenomena in random structures. In particular, we show the strong connection between the phenomenon of a photonic band gap that appears in two-dimensional periodic sets of rods and the phenomenon of Anderson localization which is observed when the periodicity is broken     

Getting effective permittivity and permeability equal to −1 in 1D dielectric photonic crystals

J.B. Pendry (Phys. Rev. Lett., 86 3966 (2000)) mentioned the possibility of making perfect lenses using a slab of left-handed material with relative permeability, permittivity and optical index equal to ?1. This kind of metamaterial has been made in the microwaves domain, using metal and dielectric materials. On the other hand, it has been shown that lenses made using 2D dielectric photonic crystals can generate similar imaging properties, but until now, the image contains only a small part of the incident light. The paper shows, using a very simple analytical model, that 1D dielectric photonic crystals can generate left-handed materials with relative permeability, permittivity and optical index rigorously equal to ?1. Of course, such photonic crystals cannot be used to make perfect lenses, but this conclusion leads to the conjecture that 2D or 3D dielectric photonic crystals could be used in the visible region to realize superlenses.     

Enlarged Photonic Band Gap in Heterostructure of Metallic Photonic and Superconducting Photonic Crystals

We show theoretically that the frequency range of photonic band gap of a hetero-structure which is made of a metallic photonic and superconducting photonic crystal can be enlarged due to the combination of the reflection band properties of the superconductor–dielectric (PC1) and metallic–dielectric (PC2) periodic structures. The transmittance and band structure of the considered structures are calculated using simple transfer matrix method and the Bloch theorem. Beside this, we have also calculated the transmittance of the superconducting photonic structure (PC1), metallic photonic structure (PC2) and heterostructure of metallic photonic and superconductor photonic crystals (PC1/PC2) for TE and TM-mode at the different angles of incidence.     

Analysis of the Filling Pattern Dependence of the Photonic Bandgap for Two-dimensional Systems

Abstract

We investigate in this paper different aspects of the absolute photonic bandgap (PBG) formation for a two-dimensional periodic dielectric structure. In particular we examine how the symmetry of the filling pattern in a periodic dielectric material influences the photonic gap parameters. We present the results of the calculations and discuss the existence of the absolute PBG, the maximization of its width as a function of the parameters of a two-dimensional dielectric crystal as well as the practical technological feasibility of these optimized structures.     

YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−<Emphasis Type="Italic">x</Emphasis></Subscript>/BaTiO<Subscript>3</Subscript> 1D Superconducting Photonic Crystal with Tunable Broadband Response in the Visible Range

Based on the transfer matrix method, we studied theoretically the transmittance of a 1D photonic crystal (PC), consisting of alternating layers of a dielectric material (BaTiO₃) and a superconductor (YBa₂Cu₃O_7?x ). The dielectric properties of this system are described by the two fluid model. We have investigated the transmittance intensity and its bandwidth dependence on the superconductor thickness, incident angle, and temperature in the PC. It was found that the electromagnetic wave propagation can be controlled to be forbidden or allowed in certain wavelengths in the visible and ultraviolet range, and the photonic band gap (PBG) width can also be tuned varying these parameters. We showed that by increasing the thickness of the superconductor layer it is possible to control the number of PBGs in the structure. Also, we found that the frequency ranges of PBGs are sensitive to the incident angle and the polarization of the electromagnetic waves; the bandwidth of PBGs can be notably enlarged by increasing the angle in the TE polarization, but narrowed in the TM one. Additionally, we found that transmission is not markedly affected by temperature variation, but small shifts in the PBGs are presented. We hope these results can be of technical use for developing potential applications in optoelectronic devices.     

Genetic optimization of two-dimensional photonic crystals for large absolute band gaps under light line

A binary genetic algorithm with floating crossover and mutation probabilities is used to design two-dimensional photonic crystals for large absolute band gaps under a light line. The unit cell is composed of a small number of round rods and is arranged in a square lattice. The photonic band structure of each chromosome is calculated by the plane-wave expansion method. Starting from randomly generated photonic crystals, the genetic algorithm finally yielded a photonic crystal with an absolute common band gap of 0.0618(2πc/a) at the mid-frequency of 0.4084(2πc/a).     

A simple perturbative tool to calculate plasmonic photonic bandstructures

We use first order perturbation theory to study the effect of surface plasmon polaritons on the photonic band structure of plasmonic photonic crystals. Our results are based on a simple numerical tool that we have developed to extend the standard frequency domain methods to compute the photonic band structure of plasmonic photonic crystals. For a two-dimensional honeycomb photonic crystal with a lattice constant of 500 nm placed on an aluminium substrate, we show that the band gap for TM modes is enhanced by 13%. Thus a slight variation in the effective dielectric function results in a plasmonic band structure that is not scale-invariant, which is reminiscent of the inherent non-linear properties of the effective dielectric constant.     

Photonic Crystals

Abstract

In this paper, we review the early motivation for photonic crystal research which was derived from the need for a photonic bandgap in quantum optics. This led to a series of experimental and theoretical searches for the elusive photonic bandgap structures: those three-dimensionally periodic dielectric structures which are to photon waves, as semiconductor crystals are to electron waves. We shall describe how the photonic semiconductor can be ‘doped’, producing tiny electromagnetic cavities. Finally, we shall summarize some of the anticipated implications of photonic band structure for quantum electronics and the prospects for the creation of photonic crystals in the optical domain.     

Investigation of TE-polarized photonic band gap properties in matallodielectric photonic crystals composed of metal coated dielectric cylinders

Using the Dirichlet-to-Neumann map method and generalization of this method, we have been able to calculate the photonic band structure of two-dimensional (2D) metallodielectric photonic crystals composed of metal-coated circular dielectric rods. The rods are embedded in an air background with a square array. We are interested in considering transverse electric (TE) mode of electromagnetic waves. The resulting band structures show the existence of photonic band gaps as well as some flat band regions. We theoretically study the effect of the dielectric constant and radius of the dielectric core on the photonic band structures. There are some interesting results compared to the case of solid metallic rods (without dielectric core) such as appearing the new photonic band gaps and a flat band region with the characteristic of cavity modes.     

Band Gap Characteristic and Transmission Spectrum of Ring-shaped Holes Photonic Crystal in THz Range

采用平面波展开法研究了2D三角晶格空气孔型光子晶体的带隙结构和空气环型光子晶体的完全带隙。结果发现空气孔半径R从0.41a到0.49a之间变化时,空气孔型的完全带隙会越大;在同一空气孔半径(R=0.41a~0.47a)下空气环型结构都能得到比空气孔结构更宽的完全带隙,得到最优参数R=0.47a,r=0.133a下的完全带隙为0.1698THz,是空气孔结构的1.15倍。使用时域有限差分法研究了空气环型结构的透射谱,根据计算结果设计了(0.7198~0.8655)THz波段的滤波器。     

Enhancement of Faraday rotation in 3D/Bi:YIG/1D photonic heterostructures

We suggest a new design of magnetophotonic crystals. Microcavity-type magnetic photonic heterostructures exhibiting enhanced magneto-optical Faraday rotation have been fabricated. Such a heterostructure comprises an opal film (3D photonic crystals), a bismuth substituted iron garnet (Bi:YIG) spacer film acting as the defect layer, and a dielectric multilayer (1D photonic crystal). Localized mode was shown to exist in the photonic band gap as a result of resonant interference in heterostructures. The observed enhancement of Faraday rotation was more than three times as compared with that of the Bi:YIG constituent. We have also found that the heterostructures exhibit an unusual polarization-dependent response.     

一维光子晶体的带隙特性研究

一维光子晶体是指介质只在一个方向成周期性排列的材料。利用薄膜光学的特征矩阵法研究了一维光子晶体的禁带特性,分析了填充率变化、厚度的随机扰动对光子带隙的影响。结果表明,随着填充率的变化,各能级的带隙率变化,并且存在一个极大值;厚度的随机扰动对光子带隙也有一定的影响,随机度不同,对光子带隙的影响也不一样。本研究对一维光子晶体的设计与制备有一定的参考价值。     

Photonic band gaps in 12-fold symmetric quasicrystals

The 12-fold symmetric quasicrystal shows great potential as a novel photonic band gap (PBG) structure exhibiting a band gap for relatively low filling fractions and dielectric contrasts. The band gaps are highly homogeneous with respect to the angle of incidence of the incoming light due to the crystal's high degree of rotational symmetry. These crystals have been analyzed using a finite element method developed specifically for modelling PBG structures. We present and discuss quasicrystal structures and their optical properties.     

Symmetry reduction for maximization of higher-order stop-bands in two-dimensional photonic crystals

A large absolute higher-order stop-band is achieved in two-dimensional (2D) photonic crystals of square lattice. A genetic algorithm is used to search through a large number of possible structures. In this algorithm, the unit cell is divided into a grid of square pixels and a 2D binary chromosome is assigned to each filling pattern of the pixels. An initial structure with a small higher-order stop-band is included in the initial population to accelerate the search procedure. This initial structure is formed by breaking the symmetry of the supercell of a photonic crystal having a square lattice of square dielectric rods in air. In the optimization process, the effect of reducing the symmetry of the unit cell on the photonic band-gap is investigated. A structure showing an absolute higher-order band-gap as large as 0.1522(2πc/a) is obtained, which is larger than the values reported so far for photonic stop-bands.     

The design of two-dimensional photonic quasicrystals by means of a fourier transform method

Abstract

We report a method of designing aperiodic photonic quasicrystals. The method is based on the recognition that the Fourier transform of the dielectric structure has a direct influence on the mode spectrum, and can be chosen to enhance the properties of the system. The diffraction of light by, and the band structure of, such modified photonic quasicrystals is investigated and compared to the properties of conventional photonic quasicrystals.