二维光子晶体点群对称对不可约布里渊区的影响

采用平面波展开法,研究了二维光子晶体点群对称对不可约布里渊区的影响。在单柱体二维光子晶体单胞中增加一个柱体,设计成不同点群对称操作数的对称结构,计算了最低5条能带的本征频率值在第一布里渊区的分布图。结果表明:在计算二维光子晶体的能带结构时,如果光子晶体的点群对称操作数为n,所取的不可约布里渊区应为整个第一布里渊区的1/n。     

Flat superlens by using negative refraction in two-dimensional phononic crystals

We experimentally and theoretically demonstrated a flat superlens by negative refraction imaging for acoustic waves in a two-dimensional phononic crystal. The sample consists of a square array of steel cylinders immersed in water. The dispersion surfaces at the first band for this sample are nearly circular around point M in the first Brillouin zone, which makes the index of the negative refraction for the phononic crystal sample be well defined for all angles of incidence. Both the observed negative refraction behavior and imaging effect are in excellent agreement with numerical simulations by the Multiple Scattering Theory method.     

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.     

Anisotropic photonic crystals: Generalized plane wave method and dispersion symmetry properties

This article presents a generalized vector plane wave expansion method, applicable to isotropic and anisotropic periodic dielectric media of arbitrary geometry and dimension. The influence of anisotropic material orientation on the symmetry properties of photonic crystal dispersion surface is discussed. It is shown that the overall Brillouin zone symmetry is formed by the intersection of the photonic crystal lattice symmetry and the symmetry determined by the anisotropic material orientation. This work explains how to define the irreducible Brillouin zone of a two-dimensional anisotropic photonic crystal and demonstrates that doing it correctly allows one to avoid erroneous results, when calculating band gap diagrams of anisotropic photonic crystals. With the help of the methods presented, the possibility of controlling the band gaps of anisotropic photonic crystals by means of external electric field is shown.     

Negative Refraction in One-Dimensional Photonic Crystals with Tilted Interface

We investigate the wave propagation through the tilted interface of one-dimensional photonic crystals. Negative refraction can be realized by excitation of the Bloch states in the extended Brillouin zone with suppressed reflection. Equi-frequency surface analysis shows that the positive refraction, negative refraction or birefringence in this configuration can be achieved under a proper incident angle, which is confirmed by finite-difference timedomain simulations. The results may be useful in applications in the new devices based on one-dimensional photonic or optical waveguide arrays.     

Uncoupled photonic band gaps

We theoretically investigated the symmetry properties of the modes in two-dimensional square lattice photonic crystals in order to study phenomena that would enable new frontiers in the applications of photonic crystals. Using group theory, symmetry analysis of the photonic crystals bands has been done. Particular attention was given to the search for the uncoupled B modes that cannot be excited by the external plane wave because they are symmetry forbidden. The existence of the uncoupled modes enabled to define new physics phenomena: uncoupled photonic band gaps. For the frequency ranges inside the uncoupled photonic band gaps, zero transmission is obtained. Therefore, there are two different types of photonic gaps in the photonic crystals: photonic band gaps and uncoupled photonic band gaps. The appearance of uncoupled photonic band gaps in photonic crystals could at least improve the application of the existing photonic materials and structures or even enable the usage of new ones for devices like waveguides, filters, and lasers.     

Physics and applications of photonic crystals

In this article, we investigate how the photonic band gaps and the variety of band dispersions of photonic crystals can be utilized for various applications and how they further give rise to completely novel optical phenomena. The enhancement of spontaneous emission through coupled cavity waveguides in a one-dimensional silicon nitride photonic microcrystal is investigated. We then present the highly directive radiation from sources embedded in two-dimensional photonic crystals. The manifestation of novel and intriguing optical properties of photonic crystals are exemplified experimentally by the negative refraction and the focusing of electromagnetic waves through a photonic crystal slab with subwavelength resolution.     

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.     

Acoustic backward-wave negative refractions in the second band of a sonic crystal

Acoustic negative refractions with backward-wave (BW) effects were both theoretically and experimentally established in the second band of a two-dimensional (2D) triangular sonic crystal (SC). Intense Bragg scatterings result in the extreme deformation of the second band equifrequency surface (EFS) into two classes: one around the K point and the other around the point of the reduced Brillouin zone. The two classes can lead to BW negative refractions (BWNRs) but with reverse negative refraction dependences on frequencies and incident angles. Not only BWNR but BW positive refraction can be present at EFSs around the K point, so it is possible to enhance the resolution of acoustic waves with a subdiffraction limit regardless of refractions, which is no analogy in both left-handed material and SCs' first band. These abundant characters make refractions in the second band distinguished.     

Negative refractive behavior of a two-dimensional negative-index photonic crystals using a wave vector diagram method

We have theoretically studied the negative refractive behavior and the focusing effect in a two-dimensional square-lattice photonic crystal made of air rods in a dielectric background. Detailed explanations are given for the effect of the negative refraction, and the imaging of the plano-concave lens is shown by the use of a wave vector diagram formalism. The typical negative refractive behavior is demonstrated by considering the Bloch mode with the wave vector inside the first Brillouin zone, because only those wave vectors inside the first Brillouin zone of multiple Brillouin zones have a definite meaning. The single propagating beam is analyzed by the use of the wave vector diagram formalism following the folding of the wave vectors. Good-quality focusing of a plane wave can be realized by using a photonic crystal plano-concave lens, while a plane wave is formed by a point source placed at the focal point. Our results are in good agreement with the experimental ones shown for a negative-index plano-concave lens by Vodo et al. [Appl. Phys. Lett. 86 (2005) 201108]. Finally, we also have shown the focusing behavior of a plane wave and a Gaussian pulse by a plano-concave lens structure with high-index modulation instead of air in the concave region.     

Modulation of photonic band structures with dielectric anisotropy

By the multiple scattering method and the extended Mie theory, we have calculated the photonic band structure of the photonic crystals consisting of the dielectric spheres with uniaxial/biaxial anisotropy. The results demonstrate that for fcc lattice structure there exist two partial photonic band gaps which does not appear in the isotropic case. Among them, the lower one, lying between the second and the third bands, exists in one third of the first Brillouin zone, while the upper one, opening between the fourth and fifth bands, can appear simultaneously in the rest two thirds of the first Brillouin zone. The effects of anisotropy on the band structures are studied as well, which suggests the biaxial anisotropy are much more flexible than the uniaxial anisotropy in modulating the band structures.     

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.     

Tunable reducibility of Brillouin zone and bandgap width in elliptical nanowire arrays

Rotating elliptical nanowire arrays as two-dimensional photonic crystals has been proposed and studied in this Letter. The analysis of the four lowest energy bands and the first bandgap width of some examples illustrates that the rotation and configuration of the primitive cell can have effects on the reducibility of the Brillouin zone.As the central element's orientation changes, the irreducible Brillouin zone could be expanded to the whole first Brillouin zone. Special attention has been paid to the nanowire arrays with adjacent elements perpendicular to each other, and the irreducible Brillouin zone unexpectedly retracted back to the 1/8 of the first Brillouin zone though the symmetry of elements is lower than that of the square lattice. Meanwhile, the first bandgap width of the perpendicular array can be adjusted by the rotation of each primitive element.     

二维复式声子晶体中基元配置对声学能带结构的影响

研究了二维复式声子晶体中基元配置对其声学能带结构的影响,发现当声子晶体的基元配置改变时,声子晶体的不可约布里渊区也会改变,而且部分能带的极值不再在高对称线上.特别地,在某些基元配置下,不可约布里渊区扩大为整个第一布里渊区.因此,对于对称性较高的复式晶格声子晶体,可用通常的方法得到能带结构,而对于对称性较低的复式晶格结构声子晶体,只有采用对整个第一布里渊区进行研究的方法,才能获得可信的能带结构及带隙.     

Band gap properties of two-dimensional photonic crystals with rhombic lattice

A new structure of two-dimensional photonic crystals (PCs) with rhombic lattice is proposed in this paper. It provides more flexibility in the design of photonic crystal devices and makes the designer be able to choose a more suitable lattice angle to satisfy different demands. The first Brillouin zone (1st BZ) of this structure is discussed and the general wave vectors are derived. The plane wave expansion (PWE) method is used to analyze the band gap properties. The impact of different lattice angels on the band gaps is analyzed, and the band gap map is also given.     

正方介质柱光子晶体中异常传输现象研究

研究了电磁波在二维正方介质柱光子晶体中的传输,发现处于第一频带部分带隙的电磁波在不同界面切割方向上不同角度入射时可分别产生全反射及复杂异常折射现象如自准直现象、负折射现象.首先利用平面波展开法从理论上研究正方介质柱正方晶格光子晶体的频带结构及等频线,然后通过时域有限差分法来仿真研究光子晶体在第一频带部分带隙的传输特性.当光子晶体的界面切割沿着ΓX方向时,由于光子晶体内无本征模能够被有效地激发,入射波束被完全反射,这与光子带隙导致的全反射具有本质的不同;当光子晶体的界面切割方向沿着ΓM时,归因于其扁平的等频线,一定角度范围内入射的波束在光子晶体内几乎沿同方向传输即产生自准直现象.     

Experimental determination of the band structure of photonic crystals of colloidal silica spheres

A photonic band structure of colloidal crystals of silica spheres is analytically determined by a band model with three fitting parameters: the sphere size, the effective refractive index, and the band-gap. Optical properties of the crystals annealed at various temperatures were characterized by a procedure similar to X-ray diffraction technique, and the width of photonic band-gap measured from the transmission spectra experimentally servers as an additional check on the validation of the model. The photonic band structures defined by the band-gap, the refractive index, and the Brillouin zone are obviously superior to the use of the Bragg's expression involving simple zone folding.     

Negative refraction and imaging beyond the diffraction limit by a two-dimensional left-handed metamaterial

We report our experimental results on two-dimensional left-handed metamaterials (LHM) exhibiting negative refraction and subwavelength imaging. Transmission and reflection spectra of LHM are studied and a left-handed transmission band is observed at the frequencies where both dielectric permittivity and magnetic permeability are negative. Impedance matching is verified both with the experiments and simulations. The two-dimensional LHM structure is verified to have a negative refractive index. We employed three different methods to observe negative refraction; refraction through prism-shaped LHM, beam shifting method, and phase shift experiments. We further demonstrated subwavelength imaging and resolution using LHM superlenses. The effect of thickness on the resolving power is investigated experimentally.     

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     

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.