Large photonic band gaps and strong attenuations of two-segment-connected Peano derivative networks

In this Letter, based on ancient Peano curves we construct four kinds of interesting Peano derivative networks composed of one-dimensional (1D) waveguides and investigate the optical transmission spectra and photonic attenuation behavior of electromagnetic (EM) waves in one- and two-segment-connected networks. It is found that for some two-segment-connected networks large photonic band gaps (PBGs) can be created and the widths of large PBGs can be controlled by adjusting the matching ratio of waveguide length and are insensitive to generation number. Diamond- and hexagon-Peano networks are good selectable structures for the designing of optical devices with large PBG(s) and strong attenuation(s).     

二维光子晶体禁带特性研究

采用平面波展开法对二维光子晶体分别在E和H极化下的带隙进行了计算. 考虑了填充比、晶格结构、介电常数对最大绝对帯隙的影响. 结果表明,不论是正方晶格还是三角晶格,TM模在介质柱型光子晶体中更容易形成带隙;TE模在空气孔型光子晶体中更容易形成带隙. 填充比一定,最大绝对帯隙宽度并非随着介电常数增大总是增大,而是存在一个峰值. 相对介电常数一定,最大绝对帯隙宽度随填充比的变化也存在一个峰值. 不论空气孔型还是介质柱型结构,三角晶格比正方晶格更容易形成帯隙. 关键词： 平面波展开法 TE模 TM模 最大绝对帯隙     

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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。     

大带隙的二维各向异性椭圆介质柱光子晶体

用平面波展开方法及时域有限差分法计算了各向异性介质材料碲形成的椭圆柱光子晶体的带隙结构.计算表明,选取适当的椭圆长短轴以及晶格常数可以形成约0.051ωe(ωe=2πcLy,Ly为沿长轴的晶格常数)的大带隙,而且在高能区域也出现了一个小的禁带.分析表明,该光子晶体大禁带对工艺上可能引起的轴长及晶格常数的偏离具有很好的稳定性. 关键词： 光子晶体 各向异性 平面波展开方法 时域有限差分法     

Robust photonic band gap from tunable scatterers

We show theoretically and experimentally that photonic band gaps can be realized using metal or metal-coated spheres as building blocks. Robust photonic gaps exist in any periodic structure built from such spheres when the filling ratio of the spheres exceeds a threshold. The frequency and the size of the gaps depend on the local order rather than on the symmetry or the global long range order. Good agreement between theory and experiment is obtained in the microwave regime. Calculations show that the approach can be scaled up to optical frequencies even in the presence of absorption.     

Transformation optics with photonic band gap media

We introduce a class of optical media based on adiabatically modulated, dielectric-only, and potentially extremely low-loss, photonic crystals (PC). The media we describe represent a generalization of the eikonal limit of transformation optics (TO). The basis of the concept is the possibility to fit some equal frequency surfaces of certain PCs with elliptic surfaces, allowing them to mimic the dispersion relation of light in anisotropic effective media. PC cloaks and other TO devices operating at visible wavelengths can be constructed from optically transparent substances such as glasses, whose attenuation coefficient can be as small as 10 dB/km, suggesting the TO design methodology can be applied to the development of optical devices not limited by the losses inherent to metal-based, passive metamaterials.     

Temperature effect on photonic band gap in polymer photonic lattices

Using the transfer matrix method we have studied the effect of the temperature on the appearance, the width, and the location of the photonic band gap (PBG) for the air cylinders embedded in a slab of vinyl chloride polymer. For two different lattice parameters we have found that the behaviour of this polymer with respect to the temperature in the visible region is strongly different from that of the far-infrared region. Furthermore, results of comparison in the far-infrared region with the PBG material which is constructed with methylpentene polymer are reported.     

Synthesis and photonic band gap characterization of high quality photonic crystal heterostructures

High quality photonic crystal heterostructures with a thin titania planar defect layer between its two constitutional photonic crystals were fabricated and their structural and optical properties were analyzed. The results suggest that the thin planar defect layer is beneficial to separate the two constitutional photonic crystals from each other and to reduce the roughness of the interface. The quality of the resulting photonic crystal heterostructures is improved largely and the main features of the photonic band gaps of the two constitutional photonic crystals are inherited. The predominant optical quality of these heterostructures (e.g. deep double photonic band gaps and steep photonic band edges) may afford new flexibility and functionality for engineered photonic behavior in practical devices such as late-model light-operated switches.     

低频和高频区域内大禁带的二维各向异性光子晶体

采用一种改进的平面波展开法,运用一种有效的设计二维各向异性光子晶体的方法,在低频和高频区域内获得了具有较大禁带的两种二维光子晶体.低频区域内,找到具有最大禁带宽度的光子晶体的禁带宽度为Δω=0076(2πca),中心频率为0769(2πca)(这里的a为晶格常量).高频区域内,找到的光子晶体的最大禁带宽度为Δω=01(2πcα),中心频率为1653(2πca).同时在低频区域内,发现一种很简单的正方网格结构,它的禁带宽度为Δω=00574(2πca),禁带宽度与禁带的中心频率之比为Δωωc=11782%. 关键词： 光子晶体 平面波展开法 各向异性材料 完全禁带     

Modulation of four-wave mixing via photonic band gap

The dressed four-wave mixing （FWM） in a four-level S5Rb atomic system, experimentally demon- strated in this paper, is comprised by two coexisting processes. One is emission signal due to enhanced nonlinear via electromagnetically induced transparency （EIT）. The other is the Bragg reflection of probe beam because of the created photonic band gap （PBG）, which is affected by both linear and third-order nonlinear susceptibility. Moreover, we have demonstrated that different experimental parameters can significantly influence the measured signal with flexibly controlled PBG. These studies are found useful for understanding the fundamental mechanisms in generated FWM processing.     

Analysis of photonic band gap structure for the design of photonic devices

A detailed analysis, based on Kronig–Penney model and finite-difference time-domain (FDTD) method, is used to explain the air-filling factor effect on the optical properties of defect-free photonic crystals. By the use of the Kronig–Penney model, we calculated the photonic band structure for electromagnetic waves in a structure consisting of a periodic square array of dielectric rods of lattice constant a separated by air holes. Gaps in the resulting band structures are found for waves of both polarisations. We analysed the air-filling factor effect on both polarisations in low and high frequency regions. It is shown that the frequency of the lower TE (transverse-electric) band edge is independent of the air-filling factor in the low frequency region. The opposite behaviour holds for the upper band edge, growing rapidly with the air-filling factor. Using the FDTD we simulated the electric field as the pulse propagates through the structure. The results of both approaches are compared, and the operation characteristics of the measuring air-filling factor device are described. We investigate the optical properties of a single and two defects incorporated in the PC, which can be potentially applied to ultra small surface-emitting-type channel drop filter. It is shown that the frequency and polarisation of the dropped light can be controlled by changing the size and/or shape of the defect. The electric field distribution calculations show that the electric field for a given frequency is located only at the defect, which means that each defect can detect only its corresponding wavelength. To cite this article: F. Ouerghi et al., C. R. Physique 5 (2004).     

Nonlinear wave interaction in photonic band gap materials

We present detailed analytical and numerical studies of nonlinear wave interaction processes in one-dimensional (1D) photonic band gap (PBG) materials with a Kerr nonlinearity. We demonstrate that some of these processes provide efficient mechanisms for dynamically controlling so-called gap-solitons. We derive analytical expressions that accurately determine the phase shifts experienced by nonlinear waves for a large class of non-resonant interaction processes. We also present comprehensive numerical studies of inelastic interactions, and show that rather distinct regimes of interaction exist. The predicted effects should be experimentally observable, and can be utilized for probing the existence and parameters of gap solitons. Our results are directly applicable to other nonlinear periodic structures such as Bose–Einstein condensates in optical lattices.     

Photonic band gap failure in photonic crystal devices

The photonic crystal is an artificial material with periodic dielectric constant and the key factor to preserve their band features is its periodicity. When the number of periods of photonic crystal is decreased the photonic band gap cannot prevent the light of the corresponding frequencies from propagating in photonic crystal, in another word, photonic band gap will be failure. The minimum periods of photonic crystal device which can keep photonic band gap effective in miniaturization process is analyzed, the transmittance spectrum is calculated by the Finite-difference time-domain algorithm (FDTD) [1], the minimum periods is got in the simulation and the reason which affects the minimum periods is analyzed in this paper.     

具有光子晶体带隙结构的返波振荡器的初步研究

 提出了一种新型的具有光子晶体带隙（PBG）结构的返波振荡器（BWO）,利用PBG禁带对BWO工作及输出微波模式进行调制,抑制低次模式,工作在高次模式。通过数值模拟给出了介质柱PBG结构的能带图、禁带限制模式电场分布和周期慢波结构的色散关系曲线,选择晶格常数为0.31 cm,介质柱半径为0.12 cm,介电常数为4.0的三角格子PBG结构可以实现在Ka波段的单一类TM03模式工作,在36～40 GHz的频率范围内,器件可以工作在返波状态,周期长度为0.4 cm。     

具有光子晶体带隙结构的返波振荡器的初步研究

提出了一种新型的具有光子晶体带隙（PBG）结构的返波振荡器（BWO）,利用PBG禁带对BWO工作及输出微波模式进行调制,抑制低次模式,工作在高次模式。通过数值模拟给出了介质柱PBG结构的能带图、禁带限制模式电场分布和周期慢波结构的色散关系曲线,选择晶格常数为0.31 cm,介质柱半径为0.12 cm,介电常数为4.0的三角格子PBG结构可以实现在Ka波段的单一类TM03模式工作,在36～40 GHz的频率范围内,器件可以工作在返波状态,周期长度为0.4 cm。     

Superluminal propagation in plasma photonic band gap materials

Electromagnetic wave propagation in one-dimensional plasma photonic crystal (PPC) made of alternate thin layers of two materials namely plasma and dielectric materials is theoretically studied. Dispersion relation is obtained. Group velocity, effective group index, reflectivity and superluminal behavior have been studied. The study of the reflectivity plot shows that the designed structure works as a perfect reflector/mirror in a certain range of frequency. Left-right and up-down symmetries (and flip-flop) are observed when we study the variation of group velocity with frequency. Abnormal behavior of group velocity (negative) inside the PPC structure creates the superluminal propagation of electromagnetic waves. The marked existence of symmetries may be exploited for directional switching in optical circuits.     

Diffraction effects in guided photonic band gap structure

The concept of the photonic band gap (PBG) structures stems from ideas of Yablonovitch. The idea is to design components so that they affect the properties of photons, in much the same way that ordinary semiconductor crystals affect the properties of electrons. In fact, the PBG structures forbid propagation of photons for a particular range of energy. They can be used to realise optical filters with large stop band and sharp transmission resonance. In the guided PBG structures, the existence of diffractive effects in the vertical dimension could limit the quality factor of such filters. In this paper, we have investigated the origin of diffraction losses in one-dimensional guided PGB structures using 2D and 3D numerical tools. We propose an analytical approach based on Bragg diffraction relation to explain these losses phenomenon. From this approach, the influence of some design parameters on the electromagnetic behaviour and the spectral response of PBG resonators will be explained.     

Three-dimensional photonic quasicrystal with a complete band gap

The band structure of three-dimensional cubic approximants of a photonic quasicrystal has been determined by numerical calculation. The approximants of different orders appear to have large, almost isotropic, band gaps in a wide range of relative permittivity values. The existence of the complete band gap in the photonic quasicrystal with the six-dimensional bcc lattice is shown.     

Experimental investigation of photonic band gap in one-dimensional photonic crystals with metamaterials

Composite right/left-handed transmission lines with lumped element series capacitors and shunt inductors are used to experimentally realize the one-dimensional photonic crystals composed of single-negative metamaterials. The simulated and experimental results show that a special photonic band gap corresponding to zero-effective-phase (zero-_φeff${\phi }_{\mathrm{eff}}$) may appear in the microwave regime. In contrast to the Bragg gap, by changing the length ratio of the two component materials, the width and depth of the zero-_φeff${\phi }_{\mathrm{eff}}$ gap can be conveniently adjusted while keeping the center frequency constant. Furthermore, the zero-_φeff${\phi }_{\mathrm{eff}}$ gap vanishes when both the phase-matching and impedance-matching conditions are satisfied simultaneously. These transmission line structures provide a good way for realizing microwave devices based on the zero-_φeff${\phi }_{\mathrm{eff}}$ gap.     

Properties of omnidirectional photonic band gap in one-dimensional staggered plasma photonic crystals

In this paper, the properties of the omnidirectional photonic band gap (OBG) realized by one-dimensional (1D) photonic crystals (PCs) with a staggered structure which is composed of plasma and isotropic dielectric layer have been theoretically studied by the transfer matrix method (TMM). From the numerical results, it has been shown that such OBG is insensitive to the incident angle and the polarization of electromagnetic wave (EM wave), and the frequency range and central frequency of OBG can be effectively controlled by adjusting the plasma frequency, the average thickness of plasma layer, the average thickness of dielectric layer and staggered parameters, respectively. The frequency range of OBG can be notably enlarged with increasing the plasma frequency, average thickness of plasma layer, respectively. Moreover, the bandwidth of OBG can be narrowed with increasing the average thickness of dielectric layer. Changing staggered parameters of dielectric and plasma layer means that the OBG can be tuned. It is shown that 1D plasma dielectric photonic crystals (PPCs) with such staggered structure have a superior feature in the enhancement of frequency range of OBG compared with the conventional 1D binary PPCs. This kind of OBG has potential applications in filters, microcavities, and fibers, etc.