Radiation from an oscillating point dipole from a photonic crystal layer of dielectric nanocolumns

The radiation pattern and intensity of the electromagnetic radiation from a point dipole source (e.g., a semiconductor quantum dot) located inside a photonic crystal layer consisting of a periodically ordered array of dielectric nanocolumns have been calculated. It has been shown that the main features of radiation can be explained considering a simple model of the interaction of the dipole with Fabry-Perrot resonances of eigenmodes of the photonic crystal layer. The total power of radiation and radiation pattern strongly depend on the position of the dipole, orientation of its dipole moment, and frequency of oscillations.     

On transmittance and localization of the electromagnetic wave in two-dimensional graphene-based photonic crystals

Two-dimensional graphene-based photonic crystal (GPC) formed by a periodic array of the homogeneous dielectric cylinders etched in the alternating graphene and dielectric layers and its inverse counterpart are considered. The transmittance of the photonic crystal is obtained. The waveguide due to the localization of the electromagnetic wave on the lattice defect that breaks the translational symmetry of the GPC of two different topologies is studied. The different topologies of GPC are characterized by different photonic band structures with different widths of photonic band gaps (PBG) and provide different frequencies for the localized electromagnetic wave due to the defect. The frequencies of the localized mode for both type of the GPC, located inside the lowest PBG, are in the range of THz or tens of THz depending on the topology of the GPC. It is shown that the photonic band gap always can be tuned by changing the chemical potential of graphene to provide formation of the localized photonic mode due to the defect. The technological advantages of the GPC, as well as the opportunity to tune the PBG and the frequency of the localized electromagnetic wave in the terahertz region of spectrum for the GPC are discussed.     

Graphene-based one-dimensional photonic crystal

A novel type of one-dimensional (1D) photonic crystal formed by an array of periodically located stacks of alternating graphene and dielectric stripes embedded into a background dielectric medium is proposed. The wave equation for the electromagnetic wave propagating in such a structure is solved in the framework of the Kronig-Penney model. The frequency band structure of the 1D graphene-based photonic crystal is obtained analytically as a function of the filling factor and the thickness of the dielectric between the graphene stripes. The photonic frequency corresponding to the electromagnetic wave localized by a defect of the photonic crystal formed by an extra dielectric placed in the position of one stack of alternating graphene and dielectric stripes is obtained.     

Non compact single-layers of dielectric spheres electromagnetc behaviour

Single layer of dielectric spheres is a recognized model for the basic understanding of some aspects of photonic crystals. Here we present a systematic study of the effect of compacting in the electromagnetic transmission of dielectric spheres monolayers. Experiments were performed in the microwave domain (from 10 GHz to 30 GHz) with glass spheres of high dielectric permittivity ε = 7. Time Domain Finite Integration (TDFI) calculations were also accomplished. Experimental data and TDFI calculations agreement provides a double check on the lack of experimental artefacts and the correctness of simulation settings. Following the evolution of the lower frequency spectral peak with layer compacting ratio, we established three different electromagnetic regimes. For the higher and lower compacting ratio regimes, the peak frequency matches isolated sphere pure resonances, while for intermediate values of compacting, some transition between these two modes takes place. Extending the study to the complete frequency range, we find that sphere single layers transmission spectra become closer to isolated sphere scattering calculations as the compacting ratio is decreased. However as the agreement remains imperfect even for our lowest compacting measurable layer, we conclude that some structure contribution cannot be neglected even for low compact layers.     

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.     

The ballistic dimer resonance in the one-dimensional disordered photonic crystals

The propagation of electromagnetic waves in one-dimensional disordered dielectric layer stack is studied theoretically using the transfer matrix formalism. The presence of the dimer unit cells inside a host photonic crystal, as the intentionally short range disorder correlation, provides predicted dimer resonances, leading to the break down of the Anderson localization. However while suitably adjusting the intrinsic defect unit cell parameters (i.e. the defect dielectric constants), the light can be transmitted on larger localization length through a ballistic canal, opening up possibilities for performing better tailored ballistic optical filters. Moreover, by increasing the rate of disorder (i.e. the defects concentration and/or the length of the system) the quality of the transmission around the ballistic resonance can be improved with the smoother corresponding allowed mini bands.     

二维非晶光子材料的缺陷态

应用多重散射方法计算了二维介质柱构成的非晶光子材料的缺陷态。在非晶光子材料中抽掉不同位置的圆柱会产生频率不同的缺陷模，但缺陷模的能量都是非常局域的，能量基本上集中在以缺陷波长1／3为半径的圆内。这表明非晶光子材料中形成的缺陷模不仅具有周期性光子晶体的缺陷模的强局域化特征，同时缺陷模更富于变化。     

电磁波在周期介质中的传播及二维光子晶体的光子带结构

光子晶体是光学与凝聚态物理交叉的新领域,也是近年来应用物理学的一个重要研究领域,它是一种由介电常数高的(低的)介质在另一种介电常数低的(高的)背景介质中周期排列所组成的人造多维周期结构材料,能够产生光子带隙。频率落在带隙内的光在晶体里沿任何方向都不能传播,因而具有能够抑制原子、分子的自发辐射等诱人的光电子学特性,在基础研究和实际应用上都有着巨大的潜力。本文在这一领域里进行了富有成效的研究,获得了很好的结果。主要有:(1)利用平面波展开方法来计算二维光子晶体的带隙结构。首先,我们设计正方晶胞的二维光子晶体模型。设x₃方向为介质柱的轴方向,二维周期结构在x₁-x₂平面上。晶胞的晶格常数为a,半径为r,介质柱和空气柱的介电常数分别为ε_a=17和ε_b=1,a>2r。设计的核心思想是通过降低光子晶体结构的对称性,消除光子能带在晶体的布里渊区高对称点上的本征简并。(2)对于二维光子晶体的电磁波理论及周期介质中的Bloch波解做了详细的推导,给出了光子晶体中禁带存在的理论依据。同时以正方格子晶格的二维光子晶体为例,验证了电介质在空气圆孔中的排列存在E偏振和H偏振的光子带隙重叠区,称为绝对光子带隙。对于二维的光子晶体,两种本征偏振模式的光子能带结构可以独立地调节,以实现两者的光子带隙的最优重叠, 从而大大提高了二维光子晶体的完全带隙宽度。     

Correlation between single-cylinder properties and bandgap formation in photonic structures

The origin of frequency gaps in the dispersion relation of periodic, quasi-periodic, and random photonic structures consisting of different arrangements of dielectric cylinders has been investigated. For TM polarization it was found that the formation and properties of gaps are strongly affected by Mie resonances of a single cylinder. Both the spectral position and size depend on the properties of this single scatterer. In contrast, for TE polarization no correlation between the scattering properties and bandgap formation was found, as Mie resonances are spectrally not well separated. For the inverted structure consisting of air cylinders in a dielectric material, the frequency gaps depend on the spatial arrangement of the cylinders because no pronounced Mie resonances exist in this case.     

Graphene-based photonic crystal

A novel type of photonic crystal formed by embedding a periodic array of constituent stacks of alternating graphene and dielectric discs into a background dielectric medium is proposed. The photonic band structure and transmittance of such photonic crystal are calculated. The graphene-based photonic crystals can be used effectively as the frequency filters and waveguides for the far infrared region of electromagnetic spectrum. Due to substantial suppression of absorption of low-frequency radiation in doped graphene the damping and skin effect in the photonic crystal are also suppressed. The advantages of the graphene-based photonic crystal are discussed.     

Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence

The near field solution for the scattering of a plane monochromatic electromagnetic wave by an ensemble of parallel infinite dielectric cylinders at perpendicular incidence is presented in this paper. The solution is given for the calculation of the electric and magnetic near fields and the Poynting vector. A MATLAB program has been developed to solve the near field formulas which is introduced and validated. The near to far field transition as well as formation and transport of photonic nanojets have been calculated for multiple cylinder scattering.     

Classification of electromagnetic resonances in finite inhomogeneous three-dimensional structures

We present a simple and unified classification of macroscopic electromagnetic resonances in finite arbitrarily inhomogeneous isotropic dielectric 3D structures situated in free space. By observing the complex-plane dynamics of the spatial spectrum of the volume integral operator as a function of angular frequency and constitutive parameters, we identify and generalize all the usual resonances, including complex plasmons, real laser resonances in media with gain, and real quasistatic resonances in media with negative permittivity and gain.     

The electromagnetic Brillouin precursor in one-dimensional photonic crystals

We have calculated the electromagnetic Brillouin precursor that arises in a one-dimensional photonic crystal that consists of two homogeneous slabs which each have a single electron resonance. This forerunner is compared with the Brillouin precursor that arises in a homogeneous double-electron resonance medium. In both types of medium, the precursor consists of the components of the applied pulse that have their frequencies below the lowest of the two electron resonances. In the inhomogeneous medium however, the slab contrast starts affecting the precursor field after a certain rise time of the precursor: its spectrum starts to peak at the geometric scattering resonances of the medium whereas minima appear at the Bragg-scattering frequencies.     

Hybrid waveguide-plasmon resonances in gold pillar arrays on top of a dielectric waveguide

We propose a hybrid waveguide-plasmon system consisting of gold pillar arrays on top of a dielectric waveguide. The formation of extraordinary transmissions induced by the hybrid waveguide-plasmon resonances is investigated by rigorous coupled-wave analysis. The characteristics of the hybrid resonances can be predicted by introducing the photonic crystal slab theory. Extremely narrow absorption peaks and the electromagnetically induced transparency-like optical property are demonstrated in our hybrid system.     

Observation of phase-matched electromagnetic scattering in an active dielectric cylinder

A theoretical investigation of oblique plane-wave electromagnetic scattering in an active dielectric cylinder predicted the existence of anomalous resonances at discrete plane-wave angles of incidence. These resonances may be understood as being due to a leaky-wave phase-matching boundary condition. Experiments were performed with active dielectric cylinders to confirm the existence of discrete resonances. Cross coupling between TE and TM modes was clearly detected for both active and passive scattering. Enhancement of active scattered field intensities was observed in experiments with finite-diameter pump and probe laser beams. Optical pumping of a dye solution was used to provide the gain.     

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).     

Effect of Fabry‐Perot resonances in disordered one‐dimensional array of alternating dielectric bi‐layers

We study numerically and analytically the role of Fabry‐Perot resonances in the transmission through a one‐dimensional finite array formed by two alternating dielectric slabs. The disorder consists in varying randomly the width of one type of layers while keeping constant the width of the other type. Our numerical simulations show that localization is strongly inhibited in a wide neighborhood of the Fabry‐Perot resonances. Comparison of our numerical results with an analytical expression for the average transmission, derived for weak disorder and finite number of cells, reveals that such expression works well even for medium disorder up to a certain frequency. Our results are valid for photonic and phononic one‐dimensional disordered crystals, as well as for semiconductor superlattices.     

Transverse or off-axis localization of electromagnetic waves in random one- and two-dimensional dielectric systems which are periodic on average

We study the transverse or off-axis localization of electromagnetic waves for several different random dielectric systems which are periodic on average. Unlike previous scalar wave treatments of transverse localization, in the present work we present results based on a full vector treatment of the electromagnetic fields based on Maxwell's equations. In a first system, we consider a random semi-infinite array of slabs with plane waves or finite beams of electromagnetic waves obliquely incident on the slab surfaces. The localization of the fields in a region near the surface of illumination is studied as a function of the oblique angle of incidence. In a second system, an array of semi-infinite slabs with random thickness is considered with an incident finite beam of electromagnetic waves initially directed parallel to the slab surfaces. The spreading of the beam width is computed as it propagates through the array of semi-infinite slabs. In a final system, we consider a semi-infinite array of random dielectric rods (2D system) with obliquely incident plane waves. The localization length of the plane-wave fields is computed as a function of the oblique angle of incidence and as a function of the strength of the disorder of the dielectric medium. All the random media we consider, when averaged over their randomness, are periodic on average. The above systems are studied for both p- and s-polarizations of incident electromagnetic waves, and the difference in the transverse localization of the electromagnetic field for these two polarizations is determined.     

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用时域有限差分法研究了电磁波在等离子体光子晶体中的传播特性。数值模拟中使用完全匹配层吸收边界条件,计算了电磁波通过等离子体光子晶体的反射和透射系数。讨论了等离子体密度、等离子体温度、介电常数比和引入缺陷层对等离子体光子晶体光子带隙的影响。