Tunable fiber gratings fabricated in photonic crystal fiber by use of mechanical pressure

The mode-coupling properties of tunable long-period fiber gratings (LPGs) formed in photonic crystal fibers (PCFs) are presented. The mode coupling from the fundamental core mode to a cladding mode of a PCF is obtained by use of periodic mechanical pressure. The strength and the wavelength of the resonant peak are tuned by adjusting the grating period and the pressure applied on the PCF. Contrary to the conventional fiber case, the resonant wavelength of the PCF LPG is decreased by increasing the periodicity.     

Locally-induced permanent birefringence by polymer-stabilization of liquid crystal in cells and photonic crystal fibers

The aim of this work was to induce permanent birefringence both in typical liquid crystal cells and photonic crystal fibers (PCFs) by photo-polymerization. For this purpose three different liquid crystalline materials, namely E7, 5CB, and 6CHBT were combined with a mixture of RM257 monomer and a UV sensitive initiator with the percentage weight less than 10%. Due to the photo-polymerization process it was possible to achieve polymer-stabilized liquid crystal orientation inside LC cells and micro-sized cylindrical glass tubes. In particular, periodic change in spatial molecular orientation was achieved by selective photo-polymerization. Successful results obtained in these simple geometries allowed for the experimental procedure to be repeated in PCFs leading to locally-induced permanent birefringence in PCFs.     

Switchable gratings by spatially periodic alignment of liquid crystals via patterned photopolymerization

Spatially periodic patterning of the anchoring condition of a nematic liquid crystal (NLC) within a polymer matrix via a patterned photopolymerization affords a novel and facile method to prepare electrically switchable diffraction gratings. UV irradiation through a photomask of two comonomers, with opposite tendencies to align the NLC and also with different reactivity ratios, leads to definition of areas with either homeotropic or planar alignment of the NLC. Photopolymerization-induced diffusion of the monomers accounts for the spatial distribution of the concentration of these monomers. The resulting diffraction gratings are switchable under low electric fields and possess structural stability offered by the polymer matrix.     

Differential toolbox to shape dispersion behavior in photonic crystal fibers

We present an analytical procedure to compute the first derivatives of the propagation constants with respect to several structural parameters in photonic crystal fibers (PCFs). From them we can easily evaluate the same derivatives of other directly related magnitudes. The above derivatives provide the trend of the magnitude at issue, which allows us to take advantage of a gradient-based algorithm to shape the properties of the guiding structure. In this way we implement an optimization process to carry out real inverse design in PCFs. We focus our attention on designing PCFs with a specific chromatic dispersion behavior. Likewise, the same approach makes it possible to analyze their fabrication tolerances.     

微结构纤芯对光子晶体光纤基本特性的影响

本文设计了两种具有微结构纤芯的光子晶体光纤（PCFs）——矩形芯和椭圆芯PCFs,利用电磁场散射的多极理论研究了这两种光纤的基本特性.发现在光纤包层气孔不变的情况下,仅通过调节纤芯气孔的大小就可以灵活地调节光纤的双折射、色散和非线性特性.随着纤芯气孔半径r₁的增大,两种纤芯结构的PCFs表现出如下特点：双折射度增大且最大双折射度对应的波长发生红移,零色散波长由一个增加到三个,短波段非线性系数增大而长波段非线性系数减小.r₁=0.4 μm的椭圆芯PCFs的三个零色 关键词： 微结构纤芯光子晶体光纤 双折射 色散 非线性     

Analytical evaluation of bending loss oscillations in photonic crystal fibers

In this paper we present an analytical formula for bending loss oscillations in photonic crystal fibers (PCFs). We follow the approach originally adopted for conventional double-clad fibers and show that it can be applied to PCFs by substituting the structural parameters of the conventional fiber by their PCF counterparts. We then examine the spectral dependence of the critical bending radius and the position of the first order loss peak as a function of structural parameters of the PCF cladding such as the fill factor and the number of hole rings. Finally, we evaluate the precision of the analytical model by comparing the results to finite element calculations for a selection of PCF geometries.     

Grazing-angle scattering of waves in infinitely wide periodic gratings

The approximate method of analysis of grazing-angle scattering (GAS), based on allowance for the diffractional divergence of the scattered wave, is justified and extended to GAS in infinitely wide, slanted, periodic gratings. The analysis has revealed an unusual and strong dependence of the pattern of GAS on small variations of mean structural parameters at the grating boundary. Several times increase of already resonantly large scattered wave amplitudes can be achieved in this case. Sharp resonance-like maximums on the angular dependence of the scattered wave amplitude are predicted inside the grating. The theory is extended to the case of GAS of optical modes guided by a slab with a semi-infinite periodic groove array. Physical interpretation of the obtained results is presented.     

一种阶梯结构的色散平坦光子晶体光纤的研究

以多极法理论为基础,提出了一种阶梯结构的光子晶体光纤.通过改变其内四层的三个结构参量(内两层孔孔径,外两层孔孔径和孔间距),实现色散绝对值在1.1～1.8μm的波段内变化仅为0.05～2 ps/(km·nm)的平坦甚至超平坦的特性.在此情况下对其有效模场面积进行数值模拟,充分展示了达到色散平坦和超平坦时,相对于传统光子晶体光纤,此种结构的光纤对芯区内光场的局域能力有很大程度的增强,其有效模场面积可仅为传统光子晶体光纤的1/30.最后,经过大量的数值计算和理论分析,归纳出若要此种阶梯结构的光纤在1.1～1.8μm的波段内达到色散平坦甚至超平坦特性的设计依据.     

一种新的长周期光纤光栅制作方法

提出了长周期光纤光栅的一种新的制作方法,通过对光纤周期性刻槽并加热拉伸引入纤芯形变,而使得纤芯折射率产生周期性变化。文中给出实验结果,并对其基本原理进行了理论分析。这种长周期光经行光栅可应用于需要宽阻滞滤波器的波分复用系统。     

Controllable grating fabrication by three interfering replicas of single femtosecond laser pulse

The controllable periodic M-shape gratings are fabricated on the surface of silica glass by three coplanar interfering beams from a single femtosecond pulse. The configuration of the M-shape periodic structure is characterized by optical microscopy and atomic force microscopy. The experimental results and the theoretical simulation show that the period and the modulation depth ratio between the neighboring grooves of the fabricated gratings can be controlled by adjusting the collision angles and pulse energy of the three beams, respectively.     

Higher-order extremely asymmetrical scattering

Extremely asymmetrical scattering (EAS) is a type of Bragg scattering in periodic gratings, that occurs when the diffracted order satisfying the Bragg condition (scattered wave) propagates parallel to the grating boundaries. Previous studies were concerned only with first-order EAS that was shown to be a highly unusual type of scattering, characterised by a strong resonant increase of the scattered wave amplitude (i.e. the amplitude of the first diffracted order). In this paper, a rigorous numerical study of higher-order EAS is presented for the case of bulk TE electromagnetic waves in planar holographic gratings of various amplitudes and widths. In particular, it is demonstrated that typical scattered wave amplitudes in higher-order EAS are significantly smaller than those in first-order EAS, and display strongly different dependencies on grating width, grating amplitude, distance from the front grating boundary, etc. Similar to first-order EAS, second-order EAS is shown to be strongly sensitive to small variations of mean structural parameters at the grating boundaries. EAS in non-sinusoidal gratings is investigated in detail with special focus on the transition between first-order EAS and second-order EAS in such gratings. Tolerance of second-order EAS to the presence of the second grating harmonic is analysed. The effect of phase of the second grating harmonic on transitional EAS is investigated. Physical explanation of the predicted effects is presented.     

Pair correlation function and freezing transitions in a two-dimensional system of model ultrasoft colloids

Density functional theory (DFT) of freezing has been used to investigate the freezing transitions in a system of colloidal particles confined to a two-dimensional plane. The particles interact via a model Hertzian type potential of varying softness. The pair-correlation functions (PCFs) needed as input structural information in DFT are calculated by solving hypernetted chain (HNC) integral equation theory. The PCFs thus obtained have been compared with those obtained through experiment and simulations and are found to be in good qualitative agreement. We found that the PCFs are sensitive to the softness of the potential: showing splitting of pair-correlation peak in the harder case and anomalous non-monotonic density dependence in the softer case. Using the common tangent construction method, we have also proposed the fluid-triangular solid phase diagrams in the temperature-density plane. We found that the phase diagram exhibit solid-fluid coexistence region whose thickness decreases with the increasing temperature as well as with increasing softness of the potential. In the temperature and density range of our calculation, DFT fails to produce any reentrance in the phase diagram.     

Optical Texture Super-Lattices Produced by Talbot Effect at Superimposed Gratings

Fresnel diffraction on periodic gratings results in a two-dimensional periodic distribution of light intensity, also known as the Talbot effect. Here this approach is extended to the family of superimposed structures with translational symmetry, which consist of superposed spatial harmonics. The Talbot effect is demonstrated to be valid for superimposed gratings. The considered superimposed gratings provide a wide range of textures of optical super-lattices. These texture super-lattices represent a Talbot carpets with a complex motif, which can be varied by choosing structure parameters. These results provide a new functionality for structuring optical lattices and can find potential applications in a wide range of light–matter interactions.     

Applications of the finite difference mode solution method to photonic crystal structures

The finite difference waveguide mode solution method, which has been popularly employed in the study of waveguide modes on various optical and dielectric waveguides, is utilized to calculate the modal characteristics of photonic crystal fibers (PCFs) and planar photonic crystal waveguides and the band diagrams of two-dimensional photonic crystals. Vector guided modes on both PCFs based on the total internal reflection guiding mechanism ('holey fibers') and those resulting from photonic band gap effect are accurately computed, with their effective indexes and field distributions compared with other methods. Calculated dispersion of a single-core holey fiber and coupled-power behavior of a two-core holey fiber are found to agree with measured results. For applications to band diagram calculation and planar photonic crystal waveguide analysis, the finite difference scheme is modified simply by imposing suitable periodic boundary condition. Numerical results for air-column crystals and dielectric-rod crystals are both found to agree well with calculations using other methods.     

Measurements of mode field diameter and effective area of photonic crystal fibers by far-field scanning technique

We have demonstrated that the correction factor k _n = A _eff/(πw ²), where ω = MFD/2 (MFD: mode field diameter), is above 1.20 for photonic crystal fibers (PCFs) with structural parameters in the range of d/Λ ≅ 0.40 to 0.90 (d/Λ ratio of hole diameter d and pitch Λ). By using the far-field scanning (FFS) technique and the finite difference method, the results of experimental measurements and numerical simulations differed by only 0.9 to 3.0% for two types of PCFs. The finding that k _n ≠ 1.0 for PCFs indicates that their electrical field distribution is non-Gaussian and cannot be determined by assuming a conventional step-index distribution for PCFs. It was also found that the ITU-T Petermann II definition is the most suitable for MFD measurements of PCFs with non-Gaussian distribution.     

Low-loss deposition of solgel-derived silica films on tapered fibers

Films of porous silica are deposited on the uniform waists of tapered fibers in minutes by a modified solgel dip coating method, inducing less than 0.2 dB of loss. The coated tapers are an ideal platform for realizing all-fiber devices that exploit evanescent-field interactions with the deposited porous film. As an example we demonstrate structural long-period gratings in which a periodic index variation in the film arises from the porosity variation produced by spatially varying exposure of the waist to a scanned CO2 laser beam. The long period grating is insensitive to temperature up to 800 degrees C.     

1维介质光栅近场及其衍射的FDTD分析

 应用FDTD方法计算了单色平面波斜入射时1维介质光栅的近场，进而求出介质光栅的衍射效率。借助于周期边界条件，整个计算区域为周期结构的一个单元。考虑入射波在两种介质界面上会产生反射和透射，故在总场边界上引入入射波、反射波和透射波。给出了光栅单元截面为矩形和梯形的算例。该方法可用于斜入射情形下具有复杂结构和任意单元截面的介质栅近场及其衍射特性分析。     

X-ray Bragg diffraction on periodic surface gratings

We report on the X-ray Bragg diffraction analysis of periodic surface gratings on (100) GaAs crystals. We show that the X-ray Bragg diffraction is a very powerful method to investigate ultrafine surface gratings and allow us to determine not only the grating period but, in particular, the width of the grooves and to characterize the quality of the sidewalls, which is not easily possible with optical methods. The X-ray diffraction on surface crystal gratings is analogue to the Fraunhofer diffraction of multiple slits or reflection gratings.     

Talbot interferometry with anisotropic gratings

An interferometer based on the Talbot effect but employing anisotropic gratings is proposed. These gratings are obtained by exposing a Weigert plate with a periodic intensity distribution of polarized light. The phase testing properties of this interferometer are discussed, and some possible extensions are proposed.