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。     

Tunneling of electromagnetic waves through a barrier with a periodic structure

The propagation of an electromagnetic wave through a barrier with a periodic structure is considered. An interesting manifestation of electromagnetic wave tunneling through a barrier with a periodic structure is revealed. Specifically, it is theoretically and experimentally shown that, when an electromagnetic wave passes through a medium with a periodic structure in the diffraction mode within a photonic band gap, the field in the medium is localized near its boundaries. Theoretical calculations have been performed for a cholesteric liquid crystal layer of finite thickness and for a 1D photonic crystal. The experiment was carried out with perfect Si single crystals in reflection from the $ (2\bar 20)$ (2\bar 20) and $ (4\bar 40)$ (4\bar 40) planes using MoK _α X rays.     

Novel spatial solitons in light-induced photonic bandgap structures

The study of wave propagation in periodic systems is at the frontiers of physics, from fluids to condensed matter physics, and from photonic crystals to Bose-Einstein condensates. In optics, a typical example of periodic system is a closely-spaced waveguide array, in which collective behavior of wave propagation exhibits many intriguing phenomena that have no counterpart in homogeneous media. Even in a linear waveguide array, the diffraction property of a light beam changes due to evanescent coupling between nearby waveguide sites, leading to normal and anomalous discrete diffraction. In a nonlinear waveguide array, a balance between diffraction and self-action gives rise to novel localized states such as spatial “discrete solitons” in the semi-infinite (or total-internal-reflection) gap or spatial “gap solitons” in the Bragg reflection gaps. Recently, in a series of experiments, we have “fabricated” closely-spaced waveguide arrays (photonic lattices) by optical induction. Such photonic structures have attracted great interest due to their novel physics, link to photonic crystals, as well as potential applications in optical switching and navigation. In this review article, we present a brief overview on our experimental demonstrations of a number of novel spatial soliton phenomena in light-induced photonic bandgap structures, including self-trapping of fundamental discrete solitons and more sophisticated lattice gap solitons. Much of our work has direct impact on the study of similar discrete phenomena in systems beyond optics, including sound waves, water waves, and matter waves (Bose-Einstein condensates) propagating in periodic potentials.     

Novel spatial solitons in light-induced photonic bandgap structures

The study of wave propagation in periodic systems is at the frontiers of physics, from fluids to condensed matter physics, and from photonic crystals to Bose-Einstein condensates. In optics, a typical example of periodic system is a closely-spaced waveguide array, in which collective behavior of wave propagation exhibits many intriguing phenomena that have no counterpart in homogeneous media. Even in a linear waveguide array, the diffraction property of a light beam changes due to evanescent coupling between nearby waveguide sites, leading to normal and anomalous discrete diffraction. In a nonlinear waveguide array, a balance between diffraction and self-action gives rise to novel localized states such as spatial “discrete solitons” in the semi-infinite (or total-internal-reflection) gap or spatial “gap solitons” in the Bragg reflection gaps. Recently, in a series of experiments, we have “fabricated” closely-spaced waveguide arrays (photonic lattices) by optical induction. Such photonic structures have attracted great interest due to their novel physics, link to photonic crystals, as well as potential applications in optical switching and navigation. In this review article, we present a brief overview on our experimental demonstrations of a number of novel spatial soliton phenomena in light-induced photonic bandgap structures, including self-trapping of fundamental discrete solitons and more sophisticated lattice gap solitons. Much of our work has direct impact on the study of similar discrete phenomena in systems beyond optics, including sound waves, water waves, and matter waves (Bose-Einstein condensates) propagating in periodic potentials.      

Spin waves in periodic magnetic structures—magnonic crystals

Propagation of spin waves (SWs) through a periodic multilayered magnetic structure is analyzed. It is assumed that the structure consists of ferromagnetic layers having the same thickness but different magnetizations. The wave spectrum obtained contains forbidden zones (stop bands) in which wave propagation is prohibited. Introduction into the structure of the ferromagnetic layer with a different thickness breaks the structural symmetry and leads to a localization of the SW mode with the frequency lying in the stop band. Reflection of the wave by the structure of the finite length and transmission of the wave through the structure are also investigated. Numerical calculations of the wave dispersion and the transmission coefficients for symmetrical periodic structures as well as the structures with a defect are presented. Drawing an analogy from photonic crystals known in optics, such magnetic structures can be called one-dimensional (1-D) magnonic crystals (MCs). The possibilities of existence of the 2-D MCs are also discussed.     

On the theory of diffraction of light in photonic crystals with allowance for interlayer disordering

Electrodynamic Green’s functions are used to construct an analytical theory of the Bragg diffraction of polarized light in photonic crystals having a close-packed structure. For opal-based photonic crystals, the Bragg diffraction intensity is calculated with allowance for permittivity periodic modulation and for the presence of an optical crystal boundary and interlayer disordering, which usually appears during sample growth. A comprehensive study is made of the effect of the structure disorder caused by the random packing of growth layers on diffraction. For a random constructed twinned fcc structure, the average structure factor and the scattering (diffraction) cross sections (which are dependent on the linear polarization of the incident and scattered waves) are calculated. Numerical examples are used to show that the theory developed can be applied to analyze and process experimental diffraction patterns of real photonic crystals having a close-packed structure disordered in one direction.     

Conical diffraction and gap solitons in honeycomb photonic lattices

We study wave dynamics in honeycomb photonic lattices, and demonstrate the unique phenomenon of conical diffraction around the singular diabolical (zero-effective-mass) points connecting the first and second bands. This constitutes the prediction and first experimental observation of conical diffraction arising solely from a periodic potential. It is also the first study on k space singularities in photonic lattices. In addition, we demonstrate "honeycomb gap solitons" residing in the gap between the second and the third bands, reflecting the special properties of these lattices.     

聚苯乙烯微粒光子晶体的反常透过特性

在实验上发现了3μm聚苯乙烯(PS)小球光子晶体在350nm至900nm波长上的透过率的周期扰动.根据透过率曲线的周期扰动的峰谷值判断，这种周期性透过率特性是基于PS小球的whispering-gallery-mode(WGM)共振，而不是源于米氏散射或布拉格衍射.实验表明，周期性排列 小球在非带隙区域对光的传输同样有一定的影响.这一结果对光子晶体薄膜的应用提供了新 的可能性. 关键词： 光子晶体 透过率 whispering-gallery-mode共振     

Enhancement of stimulated emission in 12-fold symmetric quasi-crystals

In this paper, we investigate the stimulated emission in a 12-fold symmetric quasiperiodic photonic crystal. The stimulated emission peaks in the quasiperiodic photonic crystal are more abundant and stronger than those in a periodic crystal. Also, more stimulated emission peaks appear as the crystal size and the gain increase, and some frequencies of the peaks are independent of the incident direction. These phenomena may be due to wave localization in the quasiperiodic photonic crystal. PACS 42.70Qs; 42.25Bs; 32.80.-t     

单轴应力对一维镜像光子晶体光子局域态透射峰的影响

利用传输矩阵法研究了镜像异质三周期一维光子晶体中的光子局域态随单轴应力发生变化的特性. 对于镜像异质三周期光子晶体, 由于其镜像结构, 破坏了光子晶体的有序性, 产生了一个缺陷态, 使其在较宽的光子禁带中心有一个光子局域态透射峰. 研究表明: 当对镜像异质三周期光子晶体施加单轴应力时, 其中的光子局域态透射峰会随着应力的改变而发生剧烈的变化. 当外部微弱的机械应力施加到光子晶体上时, 对光子晶体形成一个拉伸应变, 拉伸应变引起光子晶体结构的变化, 进而大幅度影响光子局域态透射峰的透射率.结果表明: 透射峰的透射率明显受单轴应力的影响. 这些特性可为用此结构的光子晶体设计超高灵敏度压力传感器提供理论参考. 关键词： 光子晶体 单轴应力 光子局域态 传输矩阵     

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.     

Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials

The elastic coupling between the a-SiO2 spheres composing opal films brings forth three-dimensional periodic structures which besides a photonic stop band are predicted to also exhibit complete phononic band gaps. The influence of elastic crystal vibrations on the photonic band structure has been studied by injection of coherent hypersonic wave packets generated in a metal transducer by subpicosecond laser pulses. These studies show that light with energies close to the photonic band gap can be efficiently modulated by hypersonic waves.     

二维斜三角晶格光子晶体完全带隙研究

在二维正三角晶格光子晶体的基础上,通过改变晶体的晶格基矢构造了一种全新的周期结构。该周期结构的最小周期单元不再是传统意义上的等边三角形,而是一种更为优化的斜三角形结构。利用平面波展开法理论模拟了二维斜三角晶格光子晶体完全带隙的情况,发现所设计结构的完全带隙宽度是二维正三角晶格光子晶体完全带隙宽度的4.3 2倍。分析了介质柱宽度,介质柱旋转角度以及相对介电常数对所构造结构的完全带隙的影响,所得结果对二维光子晶体的理论研究和实际应用有所帮助。为任意角度的二维光子晶体集成波导的研究和制作提供了理论基础。     

Dispersion of light in opal photonic crystal

The selective reflection spectra of films prepared from the photonic crystal, i.e., synthetic opal, are investigated. It is revealed that the refractive index changes at the boundaries of the photonic band gap. The wave vector is renormalized as a result of the interaction of the light wave with the periodic structure of the crystal, and the dependence of the frequency on the photon wave vector deviates from a linear behavior. The band gap determined from these data is approximately equal to 1.7 × 10¹⁴ Hz.     

用转移矩阵法数值研究二维正方介质柱光子晶体的传输特性

利用转移矩阵方法对二维正方介质柱光子晶体的传输特性进行了研究,数值计算研究了不同晶格、同一晶格柱体截面面积不同、放置方位角不同时光子晶体的传输特性。数值结果表明光子禁带的宽度与中心频率和晶格结构有很大关系,正方晶格更易形成平坦光子禁带,柱体截面面积大,则形成的禁带较宽,在其他因素相同的条件下柱体放置的方位角对光子禁带有重要影响。数值研究表明在正方介质柱下设计宽平坦光子禁带时,可以首先考虑正方晶格结构,其次设法使柱体截面尽量大一些,最后可通过柱体放置方位角来微调光子禁带的宽度与中心频率以达到设计要求。     

From the inverted pendulum to the periodic interface modes

The physics of the spatial propagation of monochromatic waves in periodic media is related to the temporal evolution of the parametric oscillators. We transpose the possibility that a parametric pendulum oscillates in the vicinity of its unstable equilibrium position to the case of monochromatic waves in a lossless unidimensional periodic medium. We develop this concept, that can formally applies to any kind of waves, to the case of longitudinal elastic wave. Our analysis yields us to study the propagation of monochromatic waves in a periodic structure involving two main periods. We evidence a class of phonons we refer to as periodic interface modes that propagate in these structures. These modes are similar to the optical Tamm states exhibited in photonic crystals. Our analysis is based on both a formal and an analytical approach. The application of the concept to the case of phonons in an experimentally realizable structure is given. We finally show how to control the frequencies of these phonons from the engineering of the periodic structure.     

Fabrication of two-dimensional elliptic photonic lattices in photorefractive crystal by optical induction method

We fabricate two-dimensional elliptic photonic lattices in iron-doped lithium niobate photorefractive crystal for the first time with optical induction method. The experimental setup of our method is very simple and flexible without complicated optical adjustment system. We analyze and verify the two-dimensional elliptic photonic lattices by plane wave guiding, far field diffraction pattern imaging, and Brillouin-zone spectroscopy. Induced elliptic photonic lattices can stably exist for a long time in the iron-doped lithium niobate crystal. The induced two-dimensional elliptic photonic lattices might offer an easy method to study generic band gap phenomena in anisotropic periodic structures.     

Band structure of superconducting photonic crystals

The band structure of a two-dimensional superconducting photonic crystal is investigated. This crystal is considered a periodic system of nonoverlapping cylinders that have a circular cross section and are infinite in length. The results are obtained using the method of plane wave expansion of eigenfunctions. The photonic band structure is analyzed for two temperatures, namely, in the vicinity of the superconducting transition point and far from it. The two-dimensional superconducting photonic crystal is found to have complete and incomplete band gaps at low temperatures. As the temperature increases, these band gaps shift toward the short-wavelength range.     

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.     

Linear and nonlinear properties of photonic crystal fibers filled with nematic liquid crystals

We investigate linear and nonlinear light propagation in the photonic crystal fibers infiltrated with nematic liquid crystals. Such a photonic structure, with periodic modulation of refractive index, which could be additionally controlled by the temperature and by the optical power, allows for the study of discrete optical phenomena. Our theoretical investigations, carried out with the near infrared wavelength of 830 nm, for both focusing and defocusing Kerr-type nonlinearity, show the possibility of the transverse light localization, which can result in the discrete soliton generation. In addition, we present the preliminary experimental results on the linear light propagation in the photonic crystal fiber with the glycerin-water solution and 6CHBT nematics, as the guest materials.