Wave-vector diagrams for two-dimensional photonic crystals

Photonic crystals exhibit band gaps, meaning that electromagnetic fields cannot propagate in them for specific ranges of wavelengths and directions. The calculation of band structure diagrams has been intensively studied and is now well understood. In contrast to that, so-called wave-vector diagrams (i.e. dispersion surfaces, depicting the loci of all relevant wave vectors at a fixed wavelength) are less known and used. In principle, they show how the effective index of the structure depends on the direction of propagation. A method to calculate explicitly wave-vector diagrams for two-dimensional photonic crystals is derived which leads finally to quadratic eigenvalue problems. Results for square and triangular lattices are presented and some applications are discussed.     

Wave-vector diagrams for two-dimensional photonic crystals

Photonic crystals exhibit band gaps, meaning that electromagnetic fields cannot propagate in them for specific ranges of wavelengths and directions. The calculation of band structure diagrams has been intensively studied and is now well understood. In contrast to that, so-called wave-vector diagrams (i.e. dispersion surfaces, depicting the loci of all relevant wave vectors at a fixed wavelength) are less known and used. In principle, they show how the effective index of the structure depends on the direction of propagation. A method to calculate explicitly wave-vector diagrams for two-dimensional photonic crystals is derived which leads finally to quadratic eigenvalue problems. Results for square and triangular lattices are presented and some applications are discussed.     

二维光子晶体耦合腔阵列的慢波效应研究

设计了一种六角晶格二维光子晶体耦合腔阵列,平面波展开法计算能带表明,处于禁带中的耦合缺陷腔模的色散曲线在光子晶体平面内所有k矢量方向更加平坦.模拟了横电波沿ΓK方向的透射谱.与光子晶体单缺陷腔相比,耦合腔阵列结构的缺陷腔模透射率提高三个量级以上,而群速度降低一个量级,得到0.007c的结果.该慢波效应在构造微型可调谐光延迟器和低阈值光子晶体激光器等方面具有潜在的应用前景. 关键词： 光子晶体 耦合腔阵列 慢波 透射率     

Two-dimensional function photonic crystals

In this paper, we have studied two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , that can become true easily by electro-optical effect and optical kerr effect. We calculated the band gap structures of TE and TM waves, and found the TE (TM) wave band gaps of function photonic crystals are wider (narrower) than the conventional photonic crystals. For the two-dimensional function photonic crystals, when the dielectric constant functions change, the band gaps numbers, width and position should be changed, and the band gap structures of two-dimensional function photonic crystals can be adjusted flexibly, the needed band gap structures can be designed by the two-dimensional function photonic crystals, and it can be of help to design optical devices.     

Negative refraction and focusing of electromagnetic wave through two-dimensional photonic crystals

The negative refraction of electromagnetic waves in photonic crystals was recently demonstrated experimentally, and the physical properties were analyzed. Microsuperlenses based on two-dimensional photonic crystals were designed and the subwavelength images were observed. In this review, after providing a brief history of the research related to the above phenomena, we will summarize our research works in this field including the method of creating a negative refraction region, generating an absolute negative refraction, the focusing of unpolarized electromagnetic waves, and the effect of interface and disorder on the image by the two-dimensional photonic crystal flat lens. The discussion on the negative refraction and the focusing by high symmetric quasicrystals is also presented.     

磁化等离子体光子晶体缺陷态的研究

采用磁化等离子体的分段线性电流密度卷积时域有限差分(PLCDRC-FDTD)算法研究具有单一缺陷层的一维磁化等离子体光子晶体的缺陷模特性. 从频域角度分析得到微分高斯脉冲的透射率,并讨论该光子晶体的缺陷层厚度、位置、周期常数和等离子体参数对其缺陷模的影响. 结果表明,改变位置和周期常数不会影响缺陷模的频率,改变缺陷层的厚度可以增加缺陷模数,改变等离子体参数能同时影响缺陷模的频率和峰值. 关键词： 磁化等离子体光子晶体 光子晶体 缺陷模 时域有限差分法     

Slow light in photonic crystals waveguide constructed with symmetrically perturbed structure

Symmetrically perturbed photonic crystal waveguide can be constructed by inserting perturbative dielectric rods into photonic crystal waveguide structure with whose rods’ radius distributed according to a certain proportion. Slow light properties in this new structure are studied by using the plane wave expansion method (PWM). In this paper, schemes of adjusting radius of perturbative dielectric rods and adjusting the dielectric constant of perturbative dielectric rods are proposed to optimize slow light properties. The result shows that the scheme for adjusting radius of perturbative rods can realize larger average slow light bandwidth and efficiently control the NDBP value of the waveguide, but it contributes little to obtain smaller group velocity. The scheme for adjusting dielectric constant of perturbative rods can realize smaller group velocity, but can only obtain smaller slow light bandwidth and cannot efficiently enlarge NDBP value of waveguide. Both optimization schemes proposed in this paper realize group velocity that is two magnitudes smaller than the vacuum speed of light meanwhile maintaining large NDBP and low GVD region. Our results provide important theoretical basis for the potential application offered by symmetrically perturbed photonic crystal in future optical networks.     

Slow light engineering in polyatomic photonic crystal waveguides based on square lattice

In this paper, the slow light properties of the polyatomic Photonic Crystal (PhC) which has multiple different air holes in each primitive cell are investigated. A slow light waveguide with “U-type” group index-frequency curve, which results in nearly constant group index over large bandwidth, is achieved using this new photonic crystal geometry based on the square lattice. Also, the radius and position of the innermost rows of small air holes have been modified to investigate the feasibility of controlling the dispersion relation by subtle structural modification. Numerical results demonstrate that decreasing the group velocity effectively and meanwhile maintaining a large Normalized Delay-Bandwidth Product (NDBP) can be achieved by only modifying the radius of the innermost rows of small air holes. Shifting the innermost rows of small air holes toward the waveguide core is highly beneficial to enlarge the slow light bandwidth, but it contributes nothing to the promotion of NDBP. Our results provide important theoretical basis for the potential application offered by the polyatomic photonic crystal in future optical networks.     

可调光子晶体研究进展

可调光子晶体是光子晶体研究中的一个新领域，文章简单介绍了当前可调光子晶体的发展状况，阐述了其调制机理及存在的问题，同时论述了可调光子晶体的发展趋势。     

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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。     

Features of light absorption in chiral photonic crystals with a strong local anisotropy

The interaction of light with a layer of a chiral photonic crystal is considered. Features of the Borrmann effect at a strong anisotropy are studied. The natural polarizations are considered, and it is shown that in the limit δ << 1 (δ = (?₁ ? ?₂)/(?₁ + ?₂), where ?₁ and ?₂ are the principal values of the dielectric permittivity tensor in the plane perpendicular to the medium axis) these polarizations are orthogonal and quasi-circular, while in the limit δ >> 1 they are orthogonal but linearly polarized. It is established that in the general case the chiral photonic crystals show a complete selectivity not to the circular polarizations (as at δ << 1), but to the natural polarizations.     

一维光子晶体光学特性的复平面波展开法研究

应用复平面波展开法对一维光子晶体的光子带隙, 透射特性进行了分析. 通过对色散关系和透射系数的数值计算发现一维光子晶体周期结构个数以及折射率分布对光学晶体透射系数以及光子带隙的影响. 对于含有整数个周期结构的光子晶体有共振点出现在光子帯隙外的频率范围内, 共振点的个数比周期结构个数少1. 带隙倾斜斜率等于折射率的比值. 折射率比值越大, 带隙的范围越大.     

时变非磁化等离子体光子晶体缺陷态研究

采用非磁化等离子体的分段线形电流密度卷积(Current density convolution,JEC)时域有限差分(Finite-dif-ferent time-domain,FDTD)算法研究了具有单一缺陷层的一维时变非磁化等离子体光子晶体的缺陷模特性。以高斯脉冲为激励源,通过由算法公式得到的电磁波透射系数讨论了等离子体上升时间对其缺陷模的影响。结果表明,改变等离子体的上升时间和密度可以获得不同的缺陷模。     

Graphite格子光子晶体带隙的数值模拟

采用平面波展开法模拟计算了由锗圆柱构成的Graphite格子二维光子晶体的带隙结构,发现由空气背景中的介质柱构成的二维Graphite格子结构的光子晶体具有完全光子带隙,并得到了使完全带隙最大化的结构参数。数值计算结果表明,Graphite结构二维光子晶体在填充比从f=0.058到f=0.605连续变化的很大范围内都有完全带隙出现,在低能区出现了Δ=0.053(ωa/2πc)的较大带隙。     

光子晶体器件进展

光子晶体对光具有独特的局域、反射、传导、分束、耦合、调制、慢光等操纵能力,使其成为微/纳光电集成的重要材料之一。介绍了光子晶体的几种重要物理特性——带隙特性、慢光特性、自准直和负折射特性,叙述了光子晶体集成器件方面所取得的最新进展,对光子晶体器件的发展动向做了展望。     

Electromagnetic modes in semi-infinite photonic crystals

In a real photonic crystal, there exist three modes: propagation mode, evanescence mode and surface mode. Using ideal modal, semi-infinite photonic crystals, we study their effects on the transmission spectrum of photonic crystals, respectively. Because there exists only one air–crystal interface in a semi-infinite photonic crystal, no multiple reflection occurs and no evanescent modes and backward-propagating modes exist in this structure. The effects of the evanescence modes are studied by comparing the transmission spectrum of a finite-thickness photonic crystal slab and that of a semi-infinite photonic crystal. In addition, the effects of the backward-propagating modes are investigated using a coated semi-infinite photonic crystal structure. Finally, we study the effects of the surface modes, and find that the transmission spectrum of a semi-infinite photonic crystal is strongly dependent on its termination.     

Negative refraction in photonic crystals

We demonstrate that light propagation in strongly modulated 2D/3D photonic crystals (PhCs) becomes refraction-like in the vicinity of the photonic bandgap, which is contrary to the fact that light propagation in weakly modulated PhCs is very different from refraction and thus the definition of refraction index becomes meaningless. Such a crystal behaves like a material having an effective refractive index controllable by the band structure. This situation is analogous to the effective-mass approximation in electron-band theory. The propagation states having a negative effective index exhibit unusual properties, such as mirror-like imaging effect, image-transfer effect. These properties are confirmed by finite-difference time-domain simulations.     

Vectorial coupled—mode solitons in one—dimensional photonic crystals

We study the dynamics of vectorial coupled-mode solitons in one-dimensional photonic crystals with quadratic and cubic nonlinearities. Starting from Maxwell's equations, the vectorial coupled-mode equations for the envelopes of two fundamental-frequency optical mode and one low-frequency mode components due to optical rectification are derived by means of the method of multiple scales. A set of coupled soliton solutions of the vectorial coupled-mode equations is provided. The results show that a modulation of the fundamental-frequency optical modes occurs due to the optical rectification field resulting from the quadratic nonlinearity. The optical rectification field disappears when the frequency of the fundamental-frequency optical fields approaches the edge of the photonic bands.     

Modelling issues for waveguide photonic crystals and photonic microstructures: A personal view

This paper is primarily an attempt to highlight areas of photonic crystal and microstructure research where there is a need for computer-based modelling. No attempt is made to assess the relative merits of different computational methods. Instead, attention is focussed mainly on engineering issues that, in the author's view, are likely to be important in predicting and analysing the properties of complex device structures built up from photonic crystal building blocks.