Photonic Crystal Fibers With a General Bravais Lattice

We present a systematic and comprehensive analysis of photonic crystal fibers with a general Bravais lattice and one hole per unit cell. We show how the lack of a proper separation of lattice shape effects from volume rescaling can lead to an incorrect assessment of the impact of lattice shape. We study and compare the endlessly single-mode, waveguide dispersion, and birefringence properties of the fundamental mode across all lattice shapes. For example, we show that the triangular and square lattice shapes offer the largest critical air-hole radius for the endlessly single-mode operation. We identify a general class of PCFs with large birefringence and show that the total birefringence of the fundamental mode is the result of the competition between two opposing effects: the cladding lattice shape and the asymmetry of the core and can vanish for some PCFs with even very nonsymmetric lattices. We show designs for which the birefringence vanishes even with nonsymmetric lattices and cores.     

用于光子晶体光纤研究的超格子构造法

提出应用“超格子构造法”研究光子晶体光纤(PCF)的传输特性。电场用正交完备的厄米-高斯(Hermite-Gauss)函数展开,有中心缺陷的周期性分布的介电常数用两组不同周期的介电常数分布迭加构成超格子，每组介电常数都用余弦函数展开,然后利用波动方程及厄米-高斯函数的正交性。得到光子晶体光纤的传输特性(模场分布、双折射、色散)。模式双折射的大小可用以衡量该算法的精度。     

六角芯高双折射光子晶体光纤

提出了几种六角芯高双折射光子晶体光纤的新型结构,在这些结构中,包层不对称和纤芯不对称都能形成双折射,所有的空气孔都是圆形的,只需调整空气孔的大小、位置就能得到高双折射,这种光纤比椭圆形或矩形空气孔光纤更容易制作.最后,用半矢量平面波法计算模式双折射和波长的关系以及截止波长特性.与全矢量解相比,其带给有效折射率的误差仅约10-5.     

Dependence of birefringence on elliptical-hole orientation in photonic crystal fibers

In this paper, the dependence of birefringence on the orientation of elliptical holes in triangular-lattice elliptical-hole photonic crystal fibers (PCFs) is investigated numerically. A resonant enhancement of birefringence between the anisotropic lattice arrangement and oriented elliptical holes is observed, and the birefringence varies periodically with the elliptical-hole orientation. When the major axes of adjacent elliptical holes are parallel, the birefringence approaches the maximum. Based on the numeric analysis, a novel highly birefringent PCF is proposed, and the maximum modal birefringence of 0.086 is achieved.     

Design of low-confinement-loss and highly birefringent index-guiding photonic crystal fibers

We present a systematic scheme to achieve both high birefringence and low confinement loss in index-guiding photonic crystal fibers （PCFs）, using a structurally-simple PCF with finite number of air holes in the cladding region. By increasing the size of the outermost-ring air holes in the cladding region, highly birefringent PCFs with low confinement loss can be successfully achieved. The design strategy is based on the fact that the modal birefringence of PCFs is dominated by the inner-ring air holes in PCF, which is verified by a full-vector finite element method with anisotropic perfectly matched layers. Numerical results show that modal birefringence in the order of 10-3 and confinement loss less than 0.1 dB/km can be easily realized in the proposed PCF with only four rings of air holes in the cladding region. We expect that such fibers will be much easier to be fabvicated than those with more air holes in the cladding region.     

Highly birefringent index-guiding photonic crystal fibers

Photonic crystal fibers (PCFs) offer new possibilities of realizing highly birefringent fibers due to a higher intrinsic index contrast compared to conventional fibers. In this letter, we analyze theoretically the levels of birefringence that can be expected using relatively simple PCF designs. While extremely high degrees of birefringence may be obtained for the fibers, we demonstrate that careful design with respect to multimode behavior must be performed. We further discuss the cutoff properties of birefringent PCFs and present experimental results in agreement with theoretical predictions on both single- and multimode behavior and on levels of birefringence     

Form-induced birefringence in elliptical hollow photonic crystal fiber with large mode area

We propose a novel type of photonic crystal fiber (PCF), including an elliptical hole in its solid core. We prove the feasibility of such a fiber and investigate both experimentally and theoretically the dependence of its group birefringence on the geometric hole parameters. We show, for the first time, that form-induced birefringence can be achieved in single mode PCFs with large mode area and suggest it as a possible route for the development of polarization maintaining PCF-based LMA fiber devices.     

Polarization-dependent coupling in twin-core photonic crystal fibers

The polarization dependence of light coupling in photonic crystal fibers (PCFs) with sixfold symmetric dual cores and highly birefringent dual cores are numerically investigated. The characteristics of PCF-based couplers, such as coupling length, extinction ratio and form birefringence, are examined as functions of the air-hole size and pitch. The silica bridges between air holes take an important role in the energy transfer across the two cores. We believe that the mechanism of light coupling in PCF-based couplers is different from that of conventional waveguide couplers. The polarization dependent coupling can be reduced by adjusting the air holes around the cores of PCFs. On the other hand, the polarization dependent coupling can be enhanced by introducing high birefringence in the two cores.     

Bending Effects on Highly Birefringent Photonic Crystal Fibers With Low Chromatic Dispersion and Low Confinement Losses

Photonic crystal fibers (PCFs) with elliptical air-holes located in the core area that exhibit high birefringence, low losses, enhanced effective mode area, and low chromatic dispersion across a wide wavelength range have been presented. The effects of bending on birefringence, confinement losses and chromatic dispersion of the fundamental mode of the proposed PCFs have been thoroughly investigated by employing the full vectorial finite element method (FEM). Additionally, localization of higher order modes is presented. Also, effects of angular orientation on bending loss have been reported. Significant improvement on key propagation characteristics of the proposed PCFs are demonstrated by carefully altering the desired air hole diameters and their geometries and the hole-to-hole spacing.     

椭圆芯光子晶体光纤的偏振特性

采用全矢量模型研究椭圆芯光子晶体光纤(photonic crystal fibers,PCFs)的偏振特性。研究表明：椭网芯PCF基模的两个正交偏振态不再简并,模场具有较强的线偏振特性;模式双折射可达10^-3量级,该数值比传统椭圆保偏光纤至少高一个量级;在比传统椭圆保偏光纤更长的波长处获得零走离点和负走离区。椭圆芯PCF的偏振特性与光纤结构参数有较强的依赖关系,通过适当选择光纤的相对孔径和孔距,有望在给定的波长上实现高双折射和零走离单模运转,或设计出高双折射、大走离的单模光纤,为研制高性能保偏光纤提供了一个新的途径。     

Highly Birefringent Photonic Crystal Fibers With Ultralow Chromatic Dispersion and Low Confinement Losses

Highly birefringent photonic crystal fibers (PCFs) with low confinement loss with ultralow and ultraflattened chromatic dispersions at wide wavelength band are presented. The transverse electric field vector distributions of two linearly polarized fundamental modes, their effective indices, modal birefringence, confinement losses and chromatic dispersion of the proposed PCFs are reported by using full-vector finite-element method (FEM). Significant improvements of PCFs in terms of the birefringence, chromatic dispersion and confinement losses are demonstrated by careful investigation of all air holes in each ring, air holes diameters and hole-to-hole spacing. In addition to this, the polarization beat length results of the proposed PCFs are also reported and discussed thoroughly.     

Virtual boundary method for the analysis of elliptically cross-sectional photonic-crystal fibers with elliptical pores

This paper introduces a new semianalytical method for the analysis of propagation characteristics of elliptically cross-sectional photonic-crystal fibers (PCFs) with elliptical pores. This method known as a virtual boundary method (VBM) is based on the equivalency between an actual PCF and a three-layered, transversely inhomogeneous waveguide. The complicated refractive-index profile of the PCF is written as a double Fourier series, and an approximate separable wave equation is found in an elliptical coordinate system for the longitudinal field components. The exact solution to the derived equation is expressed in terms of higher order transcendental functions, such as regular and irregular Coulomb-wave functions and Mathieu functions. After having expressed all the field components, boundary conditions are imposed on the boundaries, and then, a transcendental equation for the propagation constant is derived, which is solved numerically. The validity of the method is ensured by comparing various quantities, such as effective indexes, modal birefringences, and electromagnetic field distributions, with those from an accurate full-vector finite-element method (FEM) simulator, showing relatively good agreement between the results. The method correctly confirms some of the unique PCFs' properties, such as strong localization of light within the fiber and enhancement of modal birefringence as a function of the topology of hole arrangement.     

Design of a new type high birefringence photonic crystal fiber

A High birefringence microstructure fiber with four big elliptical air holes is investigated by using the finite-difference frequency-domain （FDFD） method. Based on the numerical simulations, the influence of the air-hole size and pitch upon the mode birefringence is analyzed. The work may be helpful for the design and fabrication of high birefringence PCFs.     

一种新结构光子晶体光纤的双折射特性研究

在普通正六边形光子晶体光纤的基础上,通过改变x轴方向空气孔的大小及分布构造了一种新结构的光子晶体光纤。利用多极法对该光子晶体基模的模场分布及双折射进行了数值计算,分析了光波长与结构参数对双折射的影响,同时对光子晶体光纤的色散特性进行了研究。结果表明,通过改变x轴方向空气孔的大小以及分布结构使光子晶体光纤比普通六边形结构光子晶体光纤的双折射率明显提高,并且具有较低的宽带反常色散,在光纤双折射效应的应用和光学器件的研制等方面具有独特的优势。     

Determining Properties of Fabricated Index-Guiding Photonic Crystal Fibers Using SEM Micrograph and Mode Convergence Algorithm

We develop a method for modeling properties of fabricated (realistic) air-silica photonic crystal fibers (PCFs). Our approach involves extracting the transverse refractive index (RI) profile of the drawn PCF from its scanning electron micrograph on which is operated a precise and fast mode-analysis recipe based on a finite difference (FD) field convergence scheme. From the digitized scaled RI distribution, we evaluate propagation characteristics of guided modes of PCFs, examining modal shapes, birefringence, dispersion, and other relevant properties. Naturally, our true-structure study of PCFs using FD algorithm exhibits results that are more close to measured data, establishing its practicality as compared with idealized-structure modeling. To demonstrate the efficacy of our method, we investigate some application-specific experimentally drawn PCFs, well known for their study in the literature. The key results that fairly predict experimental measurements are presented. Besides modeling fabricated fibers, this analysis will be very useful to realize PCFs with targeted specifications using feedback of estimation and characterization of trial fabrications.     

PCF-based polarization splitters with simplified structures

We propose novel polarization splitters based on photonic crystal fibers (PCFs), in which the cores of the splitters are nearly nonbirefringent. Different from conventional fiber-based polarization splitters, the birefringence in the new splitters results mainly from narrow silica regions physically connecting the two cores. This means that polarization splitting can be achieved without employing highly birefringent cores, which provides a possibility to greatly simplify the structures of the PCF-based polarization splitters and make them more practical. A 5-mm-long splitter with an extinction ratio of 20 dB has been obtained. We also discuss how the silica regions influence coupling characteristics of the dual-core PCFs and present a design guidance for the polarization splitters based on polarization-dependent coupling.     

Numerical modeling of photonic crystal fibers

Recent progress on numerical modeling methods for photonic crystal fibers (PCFs) such as the effective index approach, basis-function expansion approach, and numerical approach is described. An index-guiding PCF with an array of air holes surrounding the silica core region has special characteristics compared with conventional single-mode fibers (SMFs). Using a full modal vector model, the fundamental characteristics of PCFs such as cutoff wavelength, confinement loss, modal birefringence, and chromatic dispersion are numerically investigated.     

A kind of photonic crystal fiber with high birefringence and low cofinement loss

The triangular-lattice highly birefringent photonic crystal fibers（PCFs） with gradually increasing diameter of the air holes along radial axis are put forward. The modal birefringence, dispersion and confinement loss of the fundamental mode are simulated by full vector Galerkin finite element method（FEM） with a perfectly matched layer（PML）. The results show that this PCF can keep low confinement loss when the rings of air holes are few. When the wavelength is 1.55 μm, the birefringence, the confinement loss of quick-axis and slow-axis are 1.365×10^-3, 0.017 dB/m and 0.051 dB/m, respectively. A new way is proposed to fabricate polarization-mainting fibers with high performance.     

Research on the stability of nearly zero flattened dispersion of photonic crystal fibers

To analyze the stability of nearly zero flattened dispersion, the dispersion deviations for three kinds of PCFs are calculated when the hole diameters deviate from their designed values. Numerical results show that around the wavelength of 1.55 μm, the dispersion deviations of both the PCF with three-fold symmetry core and the PCF with hexagonal lattice are much less than that of the PCF with different hole diameters in different rings. Therefore, the stabilities of nearly zero flattened dispersion of the first two kinds of PCFs are much better than that of the last one. Considering the confinement loss, the PCF with three-fold symmetry core is preferable to practical use.     

Study of Raman amplification properties in triangular photonic crystal fibers

The Raman properties of triangular photonic crystal fibers (PCFs) are analyzed in order to design a fiber for Raman amplification with enhanced performances. By casting the Raman intensity propagation equations, the Raman effective area and the Raman gain coefficient are introduced - two meaningful parameters that take into account the overlap between the pump and signal profiles. The behavior of these two parameters is examined in silica PCFs as a function of the geometrical characteristics of the triangular lattice. The numerical results show that a proper design of the hole diameter and the spacing between air holes can minimize the Raman effective area and maximize the Raman gain coefficient. The paper then focuses on PCFs with a germania-doped core. It is found that, for a given PCF cross section and dimension of the doped region, the Raman gain coefficient increases linearly with germania concentration. Moreover, by enlarging the doped region, it is discovered that a PCF with a germania-doped area internally tangent to the first ring of air holes has a maximum Raman gain coefficient. Finally, the calculated values of the Raman gain coefficient are compared with those of other highly nonlinear fibers presented in the literature, showing that a well-designed triangular PCF can significantly improve Raman gain performance.