Characterization of internal order of colloidal crystals by optical diffraction

We report the results of the optical characterization of photonic crystals consisting of close-packed arrays of polymeric monodispersed microspheres. The excellent agreement of the diffraction peak wavelengths with Bragg's law enables a precise determination of the sphere diameter. Optical diffraction is used to assess the quality of the internal order of colloidal crystals and to identify optimum growth conditions. This work leads to an estimate of the average free propagation distance of light, which is limited by incoherent scattering due to lattice imperfections, of up to 30 lattice constants.     

Photonic Bandgap Deformation in a Nonideal Synthetic Opal Photonic Crystal

The Bragg diffraction in synthetic opal as a 3D photonic crystals has been analyzed using the weak disorder model in various approximations. For a one-domain crystal, the photonic bandgap is calculated in the regime of reflection along the 〈111〉 axis. In the multidomain case, a considerable expansion of the photonic bandgap, the emergence of asymmetry, and the photon band shift to the short-wavelength region are demonstrated. The results are compared with experimental dependences.     

Photonic properties of two-dimensional high-contrast periodic structures: Numerical calculations

The photon properties of two-dimensional periodic structures formed by infinite homogeneous dielectric cylinders packed in a square lattice have been investigated theoretically. Depending on the dielectric contrast between the cylinders and the surrounding medium, the photonic band structure, transmission spectra of crystals with a finite number of layers, and spectra of Mie scattering by an isolated cylinder have been calculated. The calculations have been performed for the TE polarization. The transformation of photonic stop-bands corresponding to Bragg and Mie resonances has been analyzed using the obtained data. The main effect consists in “castling” energy positions of the Bragg stop-bands and Mie stop-bands. For low-contrast photonic crystals, the low-frequency region of the energy spectrum is determined by Bragg stop-bands, and Mie stop-bands are located higher in energy. With an increase in the dielectric contrast, the energy of Mie stop-bands decreases, and they intersect the region of Bragg stop-bands weakly varying in the TE polarization and form the low-energy region of the spectrum.     

Anomalous coherent backscattering of light from opal photonic crystals

We studied coherent backscattering (CBS) of light from opal photonic crystals with incomplete band gaps. We observed a dramatic broadening of the CBS cone for incident angles close to the Bragg condition in the crystals. We modify the conventional CBS theory to incorporate Bragg attenuation resulting from the photonic band structure. By fitting the CBS data with the modified theory, we extract both the disorder-induced light mean-free path and the Bragg attenuation length of the inherent opal photonic crystal.     

Interference of additional modes in spectra of opal-like photonic crystals in the multiple diffraction regime

The mechanisms of formation of Bragg reflectance and transmittance spectra have been investigated for films of three-dimensional opal-like photonic crystals. Attention has been drawn to the fact that the spectra exhibit an additional short-period interference structure of the novel type due to the multiple Bragg diffraction of light. The spectra have been calculated in the framework of the dynamical three-wave diffraction model taking into account strong spatial modulation of the dielectric function. It has been found that short-period oscillations appear in the spectra due to the spatial quantization of additional modes with a low group velocity.     

基于Bragg反射面结构的衍射光栅设计与研究

基于Bragg反射光栅是一维光子晶体的一种特例结构,本文提出利用一维光子晶体带隙理论进行Bragg反射光栅设计.通过光学仿真软件OptiFDTD对Bragg反射光栅的宽度及倾斜角度误差的仿真分析,发现Bragg光栅齿刻槽宽度变化在10%范围、倾斜角度10°以内不会引起Bragg光栅衍射效率的明显变化,说明Bragg反射光栅具有较高的工艺误差容限;根据一维光子晶体带隙理论,设计了一种罗兰圆结构的Bragg衍射双光栅结构模型,实现了两个频段之间的衍射分光,优化分析结果表明:当第一套光栅中Bragg周期层数为6、第二套光栅Bragg周期层数为10时,两频段波长的衍射效率均可以达到70%左右,明显高于传统深刻蚀的衍射光栅.基于本设计的波分复用器是一种尺寸小、衍射效率高的新型EDG波分复用器,为未来高效密集型EDG波分复用器发展提供了一种新的设计思路.     

Propagation of polarized light in opals: Amplitude and phase anisotropy

The interaction of linearly polarized light with photonic crystals based on bulk and thin-film synthetic opals is studied. Experimental transmission spectra and spectra showing the polarization state of light transmitted through opals are discussed. A change in polarization is found for waves experiencing Bragg diffraction from systems of crystallographic planes of the opal lattice. It is shown that the polarization plane of the incident linearly polarized wave at the exit from photonic crystals can be considerably rotated. In addition, incident linearly polarized light can be transformed to elliptically polarized light with the turned major axis of the polarization ellipse. Analysis of polarization states of transmitted light by using the transfer-matrix theory and homogenization theory revealed good agreement between calculated and experimental spectra.     

Optical Anisotropy of Photonic Crystals of Cubic Symmetry Induced by Multiple Diffraction of Light

The optical spectra of Bragg reflection from opal-like photonic crystals under conditions of the resonant enhancement of the multiple diffraction of light have been studied experimentally and theoretically using the photonic crystal structures prepared of monodisperse polystyrene globules. It is shown that the reflection signal registered in mutually orthogonal configurations of the polarizer and analyzer is related to the intrinsic optical anisotropy of the crystals and is a specific manifestation of the multiple Bragg diffraction in three-dimensional photonic crystals.     

Formation of bcc-Ni thin film on GaAs(100) substrate and phase transformation from bcc to fcc

Ni thin films are prepared on GaAs(100) single-crystal substrates at room temperature by using an ultra-high vacuum radio-frequency magnetron sputtering system. The growth behavior and the crystallographic properties are studied by in-situ refection highenergy electron diffraction and pole-figure X-ray diffraction. In an early stage of film growth, a metastable bcc Ni(100) single-crystal film is formed on GaAs(100) substrate, where the bcc structure is stabilized through hetero-epitaxial growth. With increasing the film thickness, fcc crystals coexist with the bcc(100) crystal. High-resolution cross-sectional transmission electron microscopy shows that the film consists of a mixture of bcc and fcc crystals and that a large number of planar faults exist parallel to the fcc(111) close-packed plane. The results indicate that the bcc structure starts to transform into fcc structure through atomic displacement parallel to the bcc{110} close-packed planes.     

Bragg反射齿型平面凹面衍射光栅性能研究

本文基于Bragg反射光栅是一维光子晶体的一种特例结构, 提出利用一维光子晶体理论进行Bragg衍射光栅的设计并对其性能进行研究分析. 根据一维光子晶体理论, 建立了罗兰圆结构的凹面椭圆Bragg蚀刻衍射光栅, 研究了TE/TM模式下器件的分光特性以及入射角度改变对器件角色散造成的影响; 同时, 文中对比了空气介质型和金属铝线型椭圆Bragg蚀刻衍射光栅的光学性能. 研究结果表明: 选择合适的器件参数, 可以实现TE/TM模式下1.465-1.615 μm范围内波长衍射效率在95% 以上, 且空气介质型结构光栅的通道均匀性要优于金属铝线型结构光栅; 入射角在30°-60°范围内变化时, 相同入射角度下, TM模式下器件角色散大于TE模式. 基于Bragg衍射光栅设计的波分复用器是一种尺寸小、衍射效率高的新型EDG 波分复用器, 为未来密集型EDG波分复用器发展提供了一种新的设计思路.     

Bragg rods and multiple X-ray scattering in random-stacking colloidal crystals

Synchrotron small-angle x-ray diffraction images of random-stacking-induced Bragg scattering rods are obtained in a wide range of wave vectors from a single colloidal crystal. The results reveal a strong multiple scattering effect, which leads to new features in the diffraction pattern-secondary Bragg rods. We argue that dynamic x-ray diffraction is rather common for high-quality colloidal photonic crystals and should be taken into account.     

Applied electric field to fabricate colloidal crystals with the photonic band-gap in communication waveband

The macropore silica colloidal crystal templates were assembled orderly in a capillary glass tube by an applied electric field method to control silica deposition. In order to achieve the photonic band gap (PBG) of colloidal crystal in optical communication waveband, the diameter of silica microspheres is selected by Bragg diffraction formula. An experiment was designed to test the bandgap of the silica crystal templates. This paper discusses the formation process and the close-packed fashion of the silica colloidal crystal templates was discussed. The surface morphology of the templates was also analyzed. The results showed that the close-packed fashion of silica array templates was face-centered cubic (FCC) structure. The agreement is very good between the experimental data and the theoretical calculation.     

Multiple higher-order stop gaps in infrared polymer photonic crystals

Engineering of stop gaps between higher photonic bands provides an alternative to miniaturization of photonic crystals. Femtosecond laser microfabrication of highly correlated void channel polymer microstructures results in photonic crystals with large stop gaps and a multitude of higher-order gaps in the mid- and near-infrared spectral regions. The gap wavelengths obey Bragg's law. Consistent with theory, varying the woodpile structure unit cell allows for tuning the number of higher-order gaps, and transitions from mere resonant Bragg scattering to stop band total reflection are observed.     

三维光子晶体典型结构完全禁带的最佳参数理论分析

基于平面波展开法，理论分析了晶格结构、填充率、介电常数比等因素对fcc，diamond，woodpile三种三维光子晶体典型结构完全禁带的影响.三种结构中，fcc结构由于高对称性导致的能级简并，只适用于密堆积排列的反蛋白石结构；diamond结构非常容易产生高带隙率的完全禁带，并且可以通过调节多项参数得到所需的完全禁带；woodpile结构参数调节范围比较宽，为实验制备带来方便.对于不同的三维光子晶体结构，随着介电常数比的增大，完全禁带的宽度和带隙率也会随着增大.还发现了一些以前未引起注意的现象. 关键词： 三维光子晶体 完全禁带 介电常数比 带隙率 平面波展开法     

Fabrication of silica/zinc oxide core–shell colloidal photonic crystals

We have fabricated three-dimensional ZnO photonic crystals by the self-assembly of SiO₂/ZnO core–shell microspheres of diameter 180–220 nm by means of a vertical deposition method. The organized crystals adopt a uniform close-packed hexagonal structure with long-range order and a high filling fraction. They exhibit strong partial photonic band gaps at 565–688 nm in the transmission spectrum and a broadened band edge emission at 383 nm in the photoluminescence spectrum. For comparison with these ZnO photonic crystals, we have also prepared pure silica crystals of the same dimensions. The photonic band gaps of the former have been found to be shifted to a longer wavelength by about 200 nm compared to those of the latter as a result of the higher refractive index of ZnO. This approach provides an efficient, economical alternative means of obtaining other, more complicated photonic crystals. PACS 82.70.D; 61.46.w; 61.82.Rx; 68.37.Hk     

New approaches for the fabrication of photonic structures of nonlinear optical materials

We revisited two different strategies to fabricate 1D photonic crystals of nonlinear optical dielectric materials based on ultrafast laser ablation of the surface of an RbTiOPO₄ crystal, and selective etching of ferroelectric domains of the surface of a periodically poled LiNbO₄ crystal. We evaluated their behaviour as Bragg diffraction gratings. We also presented the recent advances we developed in a new procedure of fabrication of 2D and 3D photonic crystals of KTiOPO₄ (KTP) grown on the surface of a KTP substrate by liquid phase epitaxial means within the pores of a silicon macroporous template. Optical, structural, morphological, and compositional characterization for the photonic crystals produced through this technique are presented.     

两类单负材料组成的一维半无限光子晶体反射谱

运用传输矩阵方法和Bloch定理计算了两类单负材料组成的一维半无限光子晶体反射谱,与有限多层结构通带中振荡的反射谱相比,半无限结构的反射谱曲线是光滑的,是有限周期结构反射谱振幅取平均的结果,可用来估计通带中的反射率.研究半无限结构的反射谱,有利于分析带隙的位置和宽度,结果表明,由两类单负材料组成的光子晶体中,不仅存在零有效位相带隙,还存在角度带隙,尤其发现高频处的Bragg带隙也是一个全方位带隙.     

169Tm-A new candidate for monochromatization of synchrotron radiation by nuclear Bragg diffraction

Thulium containing crystals with appropriate structure should be feasible for monochromatizing synchrotron radiation by nuclear Bragg diffraction. Thulium iron garnet and thulium gallium garnet were investigated by MB-transmission spectroscopy. The evaluated hyperfine interactions are discussed with respect to the crystal structure. The occurrence of pure nuclear reflections is predicted and theoretical time spectra are calculated by the dynamical theory of MB-optics.     

Coupled-wave formalism for optical waveguiding by transverse Bragg reflection

A formalism is presented for optical waveguiding by means of Bragg reflection. The theory provides analytic expressions for field modal profiles, dispersion, and attenuation. Waveguiding in line defects of photonic bandgap crystals, a special case of the theory, is used as an example. Quantized allowed widths of the guiding channel are predicted.