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.     

光子晶体线缺陷波导中的折射率相位移调制增强效应

在传统的基于全内反射原理的低折射率比介质波导所构建的相位移调制型光学器件中,调制区域的长度通常在毫米到厘米量级.由于器件横向尺寸保持在微米量级,因此狭长结构成为了传统光波导器件的典型特征,这限制了光学器件集成度的提高,严重制约了集成光路的进一步发展.光子晶体的出现为高密集成光路的发展提供了一条新的途径.本文使用平面波展开方法计算了光子晶体线缺陷波导中的色散曲线.研究发现:在色散曲线下边缘处,材料折射率的一个微小变化可以引起传输常数的较大变化,如果工作频率点选择在带下边缘附近,则可以大幅度减小相位移调制型器件调制区域的长度.本文使用时域有限差分方法进一步验证这种增强效应,计算结果表明,对于0.46%的折射率变化,光子晶体线缺陷波导中的相位调制长度仅为均匀媒质中相位移调制长度的11.7%.通过以进一步研究,这种增强效应有望应用与高密度集成光路.     

Tunable lightwave propagation in two-dimensional hole-type photonic crystals infiltrated with nematic liquid crystal

Photonic crystals have many potential applications because of their ability to control lightwave propagation. We have investigated the tunability of lightwave propagation in two-dimensional hole-type photonic crystal structures. The linear waveguides can be obtained by the infiltration of liquid crystals into air holes in hole-type photonic crystal with square lattices. The refractive indices of liquid crystals can be changed by rotating the directors of liquid crystals. Therefore, we can control the lightwave propagation in two-dimensional hole-type photonic crystal structures. Such a mechanism of lightwave adjustment should open up a new application for designing components in photonic integrated circuits.     

Design of integrated optical circulator based on photonic crystals

Photonic crystals containing defects produce enhanced Faraday rotation. They have opened up the possibility of fabricating very compact magneto-optics structures. In this work, we have designed a two-dimensional photonic crystal waveguide for use in optical packaging and integrated optical circuits. For design purposes, a temporal coupled mode theory was utilized at the first step. It examined the coupling between cavity and optical ports. After acquiring a general solution, it would be applied to specific problem in hand. Then, optical characteristics of photonic crystal were investigated to design the practical parts such as cavity and waveguides which eventually a triangular crystal lattice of air holes in Bi:YIG (BIG) was considered to be the best candidate. Finally, the results of analytical investigations were evaluated using OptiFDTD software and then were confirmed.     

Photonic band gaps structure properties of two-dimensional function photonic crystals

The tunable two-dimensional photonic crystals band gap, absolute photonic band gap and semi-Dirac point are beneficial to designing the novel optical devices. In this paper, tunable photonic band gaps structure was realized by a new type two-dimensional function photonic crystals, which dielectric constants of medium columns are functions of space coordinates. However for the two-dimensional conventional photonic crystals the dielectric constant does not change with space coordinates. As the parameter adjustment, we found that the photonic band gaps structures are dielectric constant function coefficient, medium columns radius, dielectric constant function form period number and pump light intensity dependent, namely, the photonic band gaps position and width can be tuned. we also obtained absolute photonic band gaps and semi-Dirac point in the photonic band gaps structures of two-dimensional function photonic crystals. These results provide an important theoretical foundation for design novel optical devices.     

Photonic band gap engineering in 2D photonic crystals

The polarization-dependent photonic band gaps (TM and TE polarizations) in two-dimensional photonic crystals with square lattices composed of air holes in dielectric and vice versa i.e., dielectric rods in air, using the plane-wave expansion method are investigated. We then study, how the photonic band gap size is affected by the changing ellipticity of the constituent air holes/dielectric rods. It is observed that the size of the photonic band gap changes with changing ellipticity of the constituent air holes/dielectric rods. Further, it is reported, how the photonic band gap size is affected by the change in the orientation of the constituent elliptical air holes/dielectric rods in 2D photonic crystals.     

1×4光子晶体波导分束器的特性

在完整的二维光子晶体中引入线缺陷,形成了光子晶体波导,光子晶体波导分束器是集成化光学电路的重要组成元件。我们设计了一种线缺陷1×4光子晶体分束器,并且用有限时域差分法研究了它的特性。研究表明,输出端的透射传输特性与入射光的波长和分支的几何形状有关,并且入射波分别相等地流入四个输出端口。为了减少1×4分束器在三个Y型分支区的反射,可以通过调节在分支区的可调介质柱的半径R,使每个输出端口具有很高的透射率。     

An FDTD Analysis of Nonlinear Photonic Crystal Waveguides

We present a modelling technique for analyzing dispersion characteristics of nonlinear photonic crystal waveguides. This technique combines the nonlinear finite-difference time-domain method, based on the numerical simulation of oscillating dipole radiation, with the super cell approach and the periodic boundary conditions. The technique presented makes it possible to calculate the dispersion characteristics of Kerr-like nonlinear photonic crystals waveguides made by removing some scatterers. A numerical tool based on this technique can be used to design various components for integrated optical circuits.     

全矢量有限元模型及其在光波导中的应用

为了研究光波导和光子晶体光纤的模式特性和传输特性,从矢量波动方程出发,推导出了各向异性介质中场微分方程复数泛函表达式,利用棱边/节点混合元离散了该泛函,加入了各向异性介质匹配层边界条件,得到关于传播常量的广义特征值方程.以矩形波导为例,对各向异性介质匹配层边界条件的吸收特性进行了研究,得到了基模以及几个高阶模的场分布、色散曲线和损耗曲线.结果表明该方法可靠有效.对正六边形晶格光子晶体光纤进行了分析.数据表明：光纤有效折射率随空气孔直径或波长的增大而减小,但与空气孔圈数无关;光纤限制损耗(confinement loss)随波长增大近似成指数增大,而增加空气孔直径或者空气孔圈数则可使之显著降低.     

Spectral characteristics of transmission and reflection of photonic-crystal layers containing active dielectric and nanoscale metallic rods

The optical properties of artificial two-dimensional photonic crystals containing various components are studied theoretically and using numerical modeling. The main optical characteristics, such as spectra of transmission and reflection, allowing evaluation of gain properties of a photonic crystal made of neodymium-doped glass, are studied in detail. It is shown that the threshold conditions for oscillation in the studied structures can be achieved via proper choice of their optical characteristics, which allows one to formulate the technical specifications for their manufacturing. Spectral characteristics of photonic crystals containing nanoscale silver rods embedded in a dielectric matrix are studied. Their prospective use as optical filters and polarizers is substantiated. The investigation is conducted using the method of field expansion in terms of plane waves.     

Two-dimensional absolute photonic band gaps in the visible

The most promising two-dimensional photonic crystals are the graphite lattice of dielectric rods in air background and the triangular lattice of air holes in dielectric background. In this paper, we compare their convenience in achieving structures which inhibit the propagation of visible electromagnetic waves. For visible waves, etching is difficult because the structure period must be smaller than the light wavelength. Furthermore, the semiconductor materials whose electronic band gap does not absorb any optical waves have little dielectric constant, which reduces photonic band gap widths. We show, using the Plane Wave Method and the Transfer Matrix Method, that the triangular structure is not appropriate because its gap is too narrow and its dimensions are too small for fabrication. On the other hand, wider gaps and larger dimensions that should be etched easily in wide gap semiconductors make graphite a much more suitable structure.     

An Analytical Model for the Coupling Between the Array Waveguides in AWGs and Star Couplers

The purpose of this paper is to present an accurate analytical solution for the coupling between the array waveguides in arrayed waveguide grating (AWG) devices and star couplers. The results of this analysis will be useful for developing numerical models of AWGs and star couplers, as well as other optical waveguide components containing arrays of coupled waveguides.     

Modal selective tuning in a photonic crystal cavity

We present a way to selectively tune the properties of the degenerated modes confined in a single point defect two-dimensional photonic crystal cavity based on a triangular lattice of air holes. We investigate the dependence of the modal properties of the resonator on the position of the first neighbor holes, showing that it is possible to finely tune the resonant frequency of only one of these two modes and to increase the quality factor of the mode that has no frequency shift. This is achieved by controlling the wavevector components inside the cavity. This approach is a viable strategy for the development and the optimization of several innovative devices based on bi-modal cavity arrays, such as arrays of integrated optical filters and optical read-out sections for biosensing applications.     

The Design of Single Mode Large Cross-section Glass-based Waveguides for Photonic Integrated Circuits

This paper presents our recent simulation results and novel designs of single mode large cross-section glass-based waveguides for photonic integrated circuits (PICs). Simulations were performed using an in-house Finite Difference (FD) based mode solver and the FD Beam propagation Method (FD-BPM). Our simulation results show that this innovative technology could provide a simplified means to couple optical energy efficiently between optical components in a single chip. This would provide the base for the future large-scale integration of optical components in PICs. The novel idea of using single mode large cross-section glass-based waveguides as an optical integration platform is an evolutionary innovative solution for the monolithic integration of optical components, in which the glass-based structures act both as waveguides and as an optical bench for integration. This allows easy and efficient optical coupling between optical components and optical fibres, removing costly and tedious alignment problems and considerably reducing optical coupling losses in PICs. We expect that the glass-based waveguide PICs technology will enable the emergence of a new generation of compact, reliable, high speed, and multifunctional devices.     

Numerical study on characteristic of two-dimensional metal/dielectric photonic crystals

An improved plan-wave expansion method is adopted to theoretically study the photonic band diagrams of twodimensional(2D) metal/dielectric photonic crystals.Based on the photonic band structures,the dependence of flat bands and photonic bandgaps on two parameters(dielectric constant and filling factor) are investigated for two types of 2D metal/dielectric(M/D) photonic crystals,hole and cylinder photonic crystals.The simulation results show that band structures are affected greatly by these two parameters.Flat bands and bandgaps can be easily obtained by tuning these parameters and the bandgap width may reach to the maximum at certain parameters.It is worth noting that the hole-type photonic crystals show more bandgaps than the corresponding cylinder ones,and the frequency ranges of bandgaps also depend strongly on these parameters.Besides,the photonic crystals containing metallic medium can obtain more modulation of photonic bands,band gaps,and large effective refractive index,etc.than the dielectric/dielectric ones.According to the numerical results,the needs of optical devices for flat bands and bandgaps can be met by selecting the suitable geometry and material parameters.     

Optical properties of metamaterial-based devices modulated by a liquid crystal

Due to the fact that it is possible to manipulate light with photonic crystals (PCs), PCs hold a great potential for designing new optical devices. There has been an increase in research on tuning the optical properties of PCs to design devices. We presented a numerical study of optical properties of metamaterial-based devices by liquid crystal infiltration. The plane wave expansion method and finite-difference time-domain method for both TE and TM modes revealed optical properties in photonic crystal structures in an air background for a square lattice. E7 type has been used as a nematic liquid crystal and SrTiO₃ as a ferroelectric material. We showed the possibility of the metamaterials for a two-dimensional photonic crystal cavity on a ferroelectric base infiltrated with a nematic liquid crystal.     

Near-field measurement of amplitude and phase in silicon waveguides with liquid cladding

Heterodyne near-field scanning optical microscopy (H-NSOM) has proven useful as a tool for characterization of both amplitude and phase of on-chip photonic devices in air, but it has previously been unable to characterize devices with a dielectric overcladding, which is commonly used in practice for such devices. Here we demonstrate H-NSOM of a silicon waveguide with a liquid cladding emulating the solid dielectric. This technique allows characterization of practical devices with realistic refractive index profiles. Fourier analysis is used to estimate the effective refractive index of the mode from the measured data, showing an index shift of 0.08 from air to water cladding, which is seen to correspond well to simulations.     

Photonic crystal modelling using a tight-binding Wannier function method

Using the concept of generalized Wannier functions, adapted from the electronic theory of solids, we demonstrate for two-dimensional photonic crystals the existence of a localized state basis and we establish an efficient computational method allowing a tight-binding-like parameter free modelization of any dielectric structure deviating from periodicity. Examples of numerical simulations using this formalism, including modal analysis of microcavities and waveguides are presented to prove the ability of this approach to deal accurately with large scale systems and complex structures. A tight-binding version of the transfer matrix method is proposed to describe the transmission and reflection properties of finite samples of photonic crystals.     

光子晶体传输特性的时域精细积分法分析

将精细积分法应用于时域有限差分法中,提出了一种求解光子晶体传输特性的时域精细积分法,并对其计算精度及稳定性进行了分析.从一阶麦克斯韦方程出发,在空间上采用Yee元胞进行差分离散,结合吸收边界条件及激励源表达式将方程整理为标准的一阶常微分方程组形式.通过时间步长的精细划分和指数矩阵的加法定理,在时间上利用精细积分法对齐次微分方程进行积分求解,并结合激励向量的特解得到空间离散的场分量,最终通过傅里叶变换求得方程的解.利用时域精细积分法对光子晶体进行了实例计算,并将其结果分别与时域有限差分法和四阶龙格库塔法在精度、稳定性等方面进行了比较,结果表明时域精细积分法具有更高的计算精度,并且克服了时域有限差分法以及四阶龙格库塔法在计算稳定性上对时间步长的限制.提出的方法具有精确、稳定的特点,为光子晶体传输特性的研究提供了一种新的有效的分析方法.     

Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals

Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals.