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.     

含负折射率材料的一维光子晶体的光学传输特性

采用光学传输矩阵方法,模拟研究了由正折射率材料和负折射率材料交替组成的一维光子晶体的光学传输特性.计算了这种含负折射率材料的一维光子晶体的透射谱和色散关系.结果表明,在正入射时,含负折射率材料的光子晶体的带隙要比传统的光子晶体要大得多,并具有狭窄的透射带,从光学薄膜理论的色散关系出发解释了形成上述现象的原因.讨论了在不同的偏振模式下,光以中心波长入射时,反射率随着入射角度的变化关系.发现含负折射率材料的一维光子晶体具有更好的角度特性,可以用来实现对中心波长的全方位反射.     

Negative refraction in two-dimensional photonic crystals

We present some of our recent results for negative refraction in photonic crystals. The concept of negative refraction in photonic crystals is firstly introduced. Then, the propagation of electromagnetic waves in photonic crystals is systematically studied. By the layer Korringa–Kohn–Rostoker method, the coupling efficiency between external plane waves and the Bloch waves in photonic crystals is investigated. It is found that the coupling coefficient is highly angular dependent even for an interface between air with n=1 and a photonic crystal with effective index n_eff=-1. It is also shown that, for point imaging by a photonic crystal slab, owing to the negative refraction, the influence of the surface termination on the transmission and the imaging quality is significant. Finally, we present results experimentally demonstrating negative refraction in a two-dimensional photonic crystal at optical communication wavelengths. PACS 42.70.Qs; 41.85.Ct; 42.30.Va     

Alternative approach to realize all-angle negative refraction and far-field imaging effects via two-dimensional all-solid photonic crystals

We systematically investigate the band structures, equifrequency surfaces, and the intensity distributions of Poynting vector in two-dimensional Si/SiO₂ all-solid photonic crystals with different lattice types. It is found that all-angle negative refraction with effective refractive index of nearly ? 1 and far-field imaging effects can be achieved from all-solid photonic crystals. And more important thing is that, the all-solid photonic crystals can realize all-angle negative refraction at lower frequencies and provide far-field images with higher quality compared with normal air–dielectric photonic crystals. Such improved performance provides an alternative approach to realize all-angle negative refraction in super-lens and super-prisms applications.     

Negative refraction and left-handed properties in two-dimensional photonic crystals

We report on the negative refraction and left-handed behavior of two-dimensional photonic crystals. For the triangular two-dimensional photonic crystals there are two saddle points and a key point in the first Brillouin zone for the second band, which play important role to determine the refraction phenomena. There is no determined relation between the left-handed behavior and the negative refraction. The refraction phenomena depend on the band structure and the configuration of the incident light. For the first configuration, the first Brillouin zone can be divided into three parts. In part I there are negative refraction and left-handed behaviors. In part II there are normal refraction and left-handed behaviors. In part III there are normal refraction and right-handed behaviors. For the second configuration, the first Brillouin zone can only be divided into two parts. For these complex refraction phenomena, it is meaningless to define the phase refractive index, and it is necessary to define the effective refraction index by a Snell-like formula, and the value of the effective index is determined by the configuration and the band structure.     

Polarization dependent guiding in liquid crystal filled photonic crystal fibers

A theoretical study of nematic liquid crystal filled photonic crystal fibers (LCPCFs) is presented. Detailed investigations including the polarization dependent bandgap formation and the modal properties are given for LCPCFs, in which alignment of the molecules could be controlled by external static electric field. The polarization dependent bandgap splitting caused by the high index difference between the ordinary and the extraordinary dielectric index of nematic liquid crystals provides the possibility of single-mode single-polarization guiding. A polarization operation diagram is proposed to describe the guiding behavior of LCPCFs. The influence of rotation angle ? of the director of liquid crystals on the modal properties is investigated. It is shown that the polarization axis of the guided mode is determined by the rotation angle ?, which could be controlled by external electric field.     

Amphoteric-like refraction in a two-dimensional photonic crystal

High-index contrast photonic crystals possess an intricate photonic band structure that is responsible for surprising phenomena as the surperprism effect, self-collimation, power splitting or negative refraction. Recently, it was reported that at the interface between an isotropic medium and a uniaxial crystal (or between two uniaxial crystals) a phenomenon known as amphoteric refraction, that is, positive as well as negative refraction, can take place. By means of a equifrequency contours analysis and finite-difference time-domain simulations, we show that a two dimensional photonic crystal can also present amphoteric refraction by properly choosing the lattice orientation and the termination. However, total transmission is difficult to achieve because a Bloch mode is excited inside the photonic crystal and the coupling efficiency from this mode to an external plane wave is lower than one.     

Frequency bands of negative refraction in finite one-dimensional photonic crystals

We have discussed theoretically the negative refraction in finite one-dimensional (1D) photonic crystals (PCs) composed of alternative layers with high index contrast. The frequency bands of negative refraction are obtained with the help of the photonic band structure, the group velocity and the power transmittance, which are all obtained in analytical expression. There shows negative transverse position shift at the endface when negative refraction occurs, which is analysed in detail.     

Intensity depending on object distance in a two-dimensional photonic crystal

The propagation of electromagnetic (EM) waves in two-dimensional triangular-lattice photonic crystals (PCs) is investigated through dispersion characteristics analysis and numerical simulation of field pattern. The designed PC structure can exhibit all angle negative refraction in the second band. A flat superlens formed from such a PC has been designed and its imaging properties have been investigated systematically. Good-quality images and focusing, with relative refractive index of ?1, have been observed in this system for TE mode waves. In contrast to the images in near-field region for the lowest valence band, non-near-field images, explicitly following the well-known wave-beam negative refraction law, have been demonstrated. The relation between the intensity of the image and the object distance has also been discussed in this paper. The extensive applications of such a phenomenon to optical devices are anticipated.     

Characteristics of paraxial propagation of a super Lorentz—Gauss SLG01 mode in uniaxial crystal orthogonal to the optical axis

Analytical propagation expression of a super Lorentz-Gauss（SLG） 01 mode in uniaxial crystal orthogonal to the optical axis is derived.The SLG 01 mode propagating in uniaxial crystal orthogonal to the optical axis mainly depends on the ratio of the extraordinary refractive index to the ordinary refractive index.The SLG 01 mode propagating in uniaxial crystals becomes an astigmatic beam.The beam spot of the SLG 01 mode in the uniaxial crystal is elongated in the x-or y-direction,which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index.With the increase of the deviation of the ratio of the extraordinary refractive index to the ordinary refractive index from unity,the elongation of the beam spot also augments.In different observation planes,the phase distribution of an SLG 01 mode in the uniaxial crystal takes on different shapes.With the variation of the ratio of the extraordinary refractive index to the ordinary refractive index,the phase distribution is elongated in one transversal direction and is contracted in the other perpendicular direction.This research is beneficial to the practical applications of an SLG mode.     

Negative refraction and imaging properties of circular photonic crystals

The electromagnetic wave propagation in a two-dimensional (2D) circular photonic crystal (CPC) is investigated. The CPC structure is composed of air holes in the dielectric background material. The finite element method is used to study the optical and propagating properties of the CPC slab. Numerical simulations show that negative refraction and near-field imaging can appear in a 2D CPC slab. We also find that the high-symmetry CPC slab possesses an optics axis along the vertical direction intersecting the symmetric center. As a result, the CPC slab can exhibit an excellent imaging performance when a source is placed on the optical axis.     

Electromagnetic waves in uniaxial crystals with metallized boundaries: Mode conversion,pure reflections,and bulk polaritons

A theory is constructed for the reflection of plane electromagnetic waves in uniaxial crystals with a positive definite permittivity tensor and an arbitrarily oriented metallized boundary. The problem is solved both for general-position orientations corresponding to three-partial reflection and for special conditions allowing two-partial reflections: mode conversions when the incident and reflected waves belong to different sheets of the refraction surface and “pure” reflections when both waves belong to the same sheet. The space of pure reflections is shown to be formed by two types of optical-axis orientations: arbitrary directions in the plane of the crystal surface and in the plane of incidence. The configurations of the conversion surface for optically positive and negative crystals are investigated. A subspace of pure reflections that transform into one-partial bulk polaritons with the energy flux parallel to the surface at grazing incidence has been found. The domain of existence of such bulk eigenmodes is bounded by two “lines” of solutions. These are any directions along the boundary containing the optical axis for ordinary polaritons and the direction along the projection of the optical axis onto the surface at an arbitrary orientation of the axis with respect to the boundary for extraordinary polaritons.     

Characteristics of paraxial propagation of a super Lorentz-Gauss SLG₀₁ mode in uniaxial crystal orthogonal to the optical axis

Analytical propagation expression of a super Lorentz-Gauss(SLG) 01 mode in uniaxial crystal orthogonal to the optical axis is derived.The SLG 01 mode propagating in uniaxial crystal orthogonal to the optical axis mainly depends on the ratio of the extraordinary refractive index to the ordinary refractive index.The SLG 01 mode propagating in uniaxial crystals becomes an astigmatic beam.The beam spot of the SLG 01 mode in the uniaxial crystal is elongated in the x-or y-direction,which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index.With the increase of the deviation of the ratio of the extraordinary refractive index to the ordinary refractive index from unity,the elongation of the beam spot also augments.In different observation planes,the phase distribution of an SLG 01 mode in the uniaxial crystal takes on different shapes.With the variation of the ratio of the extraordinary refractive index to the ordinary refractive index,the phase distribution is elongated in one transversal direction and is contracted in the other perpendicular direction.This research is beneficial to the practical applications of an SLG mode.     

折射率连续周期分布一维光子晶体的带隙分析

微分传输矩阵法(DTMM)可以解析求解一维非均匀介质中的波动方程。用该方法,对几种折射率连续且周期分布的一维光子晶体进行了带隙分析。结果表明,折射率连续变化的一维周期结构也具有明显的带隙特征,折射率变化越平缓,光带隙的宽度越小。对于折射率正弦变化的一维光子晶体,其折射率变化得越剧烈,光子晶体的中心频率越小,带隙越宽;同时,折射率的平均值越大,中心频率越小,带隙越窄。由于材料的物理特性都是连续变化的,同样可以把结构推广到一维周期性功能梯度材料。     

二维光子晶体负折射现象条件及特性研究

结合光子晶体带隙图和等频率线图分析了二维光子晶体中出现负折射现象的条件,得出了负折射现象出现的频率范围.采用有限时域差分法模拟了光在光子晶体界面和内部的传输行为,验证了以上理论所给出的负折射出现的频段,观察到了明显的负折射现象.比较了不同介质、不同晶格结构光子晶体中不同频率的负折射行为.提出一种新结构的六角型二维三角晶格光子晶体分光镜的模型.     

Realization of absolute negative refraction index by a photonic crystal using anisotropic dielectric material

A method to realize absolute negative refraction index -1 with a two-dimensional （2D） photonic crystal is presented by introducing dielectric anisotropy in the photonic crystal material. The band structures of E-polarization mode and H-polarization mode can be adjusted by changing the parameters of materials. Thus the two modes with different polarizations have the same negative refraction index -1 for the same frequency. The results are demonstrated by numerical simulation based on the finite-difference time-domain （FDTD） method.     

All angle negative refraction with the effective phase index of-1

We theoretically studied a left-hand structure based on a two-dimensional (2D) photonic crystal (PC)with a negative refractive index. The propagation of electromagnetic waves in the proposed PC structure is investigated through dispersion characteristic analysis and numerical simulation of field pattern. The designed PC structure can exhibit all angle negative refraction, and the corresponding effective refractive indices along all directions are almost same and close to the ideal value of -1. A flat lens formed from such a PC has been designed and its imaging properties have been investigated systematically.     

Integral equations for photonic-crystal fibers

The integral and integro-differential equations for photonic-crystal waveguides (fibers) with both infinite and finite quasi-periodic dielectric coatings have been obtained, with previous consideration of the equations for 2D periodic photonic crystals with magnetodielectric and metallic inclusions. The corresponding numerical results are presented.     

Tunable broadband isolator based on electro-optically induced linear gratings in a nonlinear photonic crystal

We theoretically propose a broadband optical isolator based on second-harmonic generation in a one-dimensional quadratic nonlinear photonic crystal (NPC) with an embedded defect. An external electric field along the z axis is applied to modulate the NPC refractive index periodically. Complete optical isolation always could be reached with the help of an external field. Influences of the defect position and thickness are discussed. The spectral and power tolerances of the isolator also have been investigated and show high contrast within a wide wavelength range at different power levels.     

LiNbO3:Fe晶体的光折变对喇曼光谱的影响(Ⅱ)

继文献[1]之后,我们又研究了掺Fe浓度为0.07％的LiNbO₃:Fe晶体的光折变对喇曼光谱的影响。发现在x(zx)z和y(zy)z配置下出现异常。这可以由异常声子的极化电场与光折变在晶体中形成的强空间电荷场的相互作用来解释。 关键词：