单光子晶体界面介质波导中的慢光效应

研究了单光子晶体界面介质波导中的慢光效应.芯层-空气层界面的全内反射效应以及光子晶体基底的禁带效应共同形成了对光场能量的横向约束.用基于超元胞的平面波展开法计算得到了导模色散曲线,并据此对其色散、群速以及群速色散性质做了详尽分析.由于利用了色散曲线慢光区域内拐点附近低群速色散的部分,该单光子晶体界面介质波导具有良好的慢光特性.对两个不同导模计算得到的平均群速分别为c/98和c/376,可用相对频带宽度分别达到2.1×10-3和4.1×10-4.另外,该慢光结构可以侧向耦合的方式克服光子晶体慢光波导耦合困难的缺点.     

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.     

光子晶体耦合腔光波导慢光结构特性研究

研究了用于光缓存的光子晶体耦合腔光波导的结构对慢光传输特性的影响.详细讨论了微腔间距关于波导禁带、导模带宽、导模传输群速度的具体关系.计算发现,随着微腔之间距离的增加导模显著平坦化,群速度急剧减小.当相邻微腔之间距离为7个晶格常数时,获得了小于2×10~(-4)c的超小群速度.通过长度为13.23 μm的7×7超胞构成的光子晶体耦合腔光波导,产生的最大光延迟超过了400 ps,这比相同长度传统光波导产生光延迟大四个数量级.     

Dispersionless slow light by photonic crystal slab waveguide with innermost elliptical air holes

We report a low-loss photonic crystal slab waveguide formed by deforming the innermost circle air holes in the conventional photonic crystal slab waveguide into elliptical ones. We obtain the photonic bands and group index of guided modes in this photonic crystal waveguide by guided-mode expansion method and investigate the dependence of photonic bands and group index of guided modes on the parameters of the innermost elliptical air holes. The group velocity and group velocity dispersion of this waveguide strongly depend on the innermost elliptical air holes. Photonic crystal slab waveguide with the optimum innermost elliptical air holes possesses a wider single mode region below the light line, in which light can easily propagate without intrinsic loss. At the same time, the guided mode supported by this waveguide has nearly constant group velocity and vanishing group velocity dispersion in a 3-5 nm bandwidth.     

Numerical characterization of nanopillar photonic crystal waveguides and directional couplers

We numerically characterize a novel type of a photonic crystal waveguide, which consists of several rows of periodically arranged dielectric cylinders. In such a nanopillar photonic crystal waveguide, light confinement is due to the total internal reflection. A nanopillar waveguide is a multimode waveguide, where the number of modes is equal to the number of rows building the waveguide. The strong coupling between individual waveguides leads to the proposal of an ultrashort directional coupler based on nanopillar waveguides. We present a systematic analysis of the dispersion and transmission efficiency of nanopillar photonic crystal waveguides and directional couplers. Plane wave expansion and finite difference time domain methods were used to characterize numerically nanopillar photonic crystal structures both in two- and three-dimensional spaces.     

Dual-frequency division de-multiplexer based on cascaded photonic crystal waveguides

A dual-frequency division de-multiplexing mechanism is demonstrated using cascaded photonic crystal waveguides with unequal waveguide widths. The de-multiplexing mechanism is based on the frequency shift of the waveguide bands for the unequal widths of the photonic crystal waveguides. The modulation in the waveguide bands is used for providing frequency selectivity to the system. The slow light regime of the waveguide bands is utilized for extracting the desired frequency bands from a wider photonic crystal waveguide that has a relatively larger group velocity than the main waveguide for the de-multiplexed frequencies. In other words, the wider spatial distribution of the electric fields in the transverse direction of the waveguide for slow light modes is utilized in order to achieve the dropping of the modes to the output channels. The spectral and spatial de-multiplexing features are numerically verified. It can be stated that the presented mechanism can be used to de-multiplex more than two frequency intervals by cascading new photonic crystal waveguides with properly selected widths.     

Anomalous propagation loss in photonic crystal waveguides

Propagation loss can occur in photonic crystal waveguides without complete optical confinement. We employ a highly efficient transfer-matrix method which allows for accurate and reliable extraction of the propagation loss even at an extremely low level. The results for a two-dimensional photonic crystal waveguide shows that the loss exponentially decays via the waveguide wall thickness. An anomalous phenomenon is found where the loss for guided modes near the upper band gap edge can be several orders of magnitude smaller than that for modes in the middle of the band gap. This anomaly can be well explained by the localization degree of guided modes at different frequency domains.     

Special control of the cutoff frequencies in a 2D photonic crystal coupled-cavity waveguide

We show theoretically that the upper and lower cutoff frequencies of the guided band in a 2D photonic crystal coupled-cavity waveguide can be controlled independently or synchronously by changing two configuration parameters of the waveguide simultaneously. The independent control range for the lower and upper cutoff frequencies can be as large as 68.6% and 67.9% of photonic band gap, respectively. The two cutoff frequencies can also be tuned in the same direction over equal distances up to 25.7% of photonic band gap. These results offer an efficient way for designing the various dispersion relations for photonic crystal waveguides.     

Coupling reducing k-points for photonic crystal fiber calculations

When describing localized electromagnetic modes in dielectric waveguides by the planewave method, a supercell geometry must necessarily be adopted. We demonstrate in the present work that the convergence of the calculations with respect to supercell size depends strongly on the choice of the transverse Bloch wave vector, k. We describe a method to derive k-points that minimize the coupling between repeated images of the guided modes in real space. Calculations have been done for a quadratic and a triangular photonic crystal fiber structure. With the new coupling reducing (CR) k-points, the convergence of the eigenfrequencies for both the fundamental and second order modes with respect to supercell size is considerably improved. The general approach outlined may also be applied in the case of three-dimensional photonic crystal structures.     

Optimal tunability of waveguides based on silicon photonic crystals infiltrated with liquid crystals

In this work we study the optimization of the tunability range in waveguides based on two-dimensional silicon photonic crystal infiltrated with liquid crystal. The analyzed structure consists of a two-dimensional silicon photonic crystal with a triangular lattice of circular holes where a line of scatterers in the direction Γ–K has been replaced by a line of circular holes with different radius infiltrated by E7 liquid crystal. To this end, we use the plane-wave expansion method considering anisotropy and modelling supercells to account for the lattice defects that define the waveguide. Finally we study the field distributions of the guided modes in order to analyze their symmetries and confinement.     

Plasmonic crystal waveguides

We study the properties of electromagnetic waves propagating along the waveguides with a periodic core created by alternating metal and dielectric layers, the so-called quasi-one-dimensional plasmonic crystal waveguides. Such waveguides can be symmetric or asymmetric, depending on the cladding or substrate material properties, as well as on the termination of the periodic structure. We analyze the dispersion characteristics as well as the profiles of the guided modes for several types of waveguide structure.     

Broadening compensation for ultrashort pulses in photonic crystals

Extremely large group velocity dispersion of both signs can be achieved at the band edges of guided modes in photonic crystal waveguides. The selection of a proper value and sign of this parameter allows the design of short-length waveguides to compensate for pulse broadening. This pulse broadening can be caused, for instance, when a photonic crystal delay line is introduced. We present a theoretical study of the possibilities of using photonic crystal waveguides as intra-circuital dispersion compensation elements for ultrashort pulses, so the width of a transmitted pulse can be reduced. However, we also demonstrate that recovering the original pulse shape is not possible for these large-bandwidth pulses due to higher-order dispersion terms.     

Tailoring dispersion properties of photonic crystal waveguides by topology optimization

The paper describes a systematic method for the tailoring of dispersion properties of slab-based photonic crystal waveguides. The method is based on the topology optimization method which consists in repeated finite element frequency domain analyzes, analytical sensitivity analyzes and gradient based design updates. The goal of the optimization process is to come up with slow light, zero group velocity dispersion photonic waveguides or photonic waveguides with tailored dispersion properties for dispersion compensation purposes. Two examples concerning reproduction of a specific dispersion curve and design of a wide bandwidth, constant low group velocity waveguide demonstrate the efficiency of the method.     

Improved fake mode free plane wave expansion method

We analyze the origin of the fake modes introduced by the plane wave expansion method with three-dimension (3D) supercell approximation. Through the detailed analysis of the energy distribution of fake modes and real modes, we propose the plane wave expansion-three planar-slab waveguides method to remove the fake modes and obtain the fake mode free band structure of a two-dimensional air hole photonic crystal slab. To the best of our knowledge, this is the first time that such a fake mode free photonic crystal band structure is presented. Our method is also definitely useful in designing other 3D devices.     

一种新型无色散慢光光子晶体薄板波导

利用椭圆形孔替代传统光子晶体薄板波导中邻接波导的最内层两排圆孔构成一种新型低损耗光子晶体薄板光波导.该波导的群速度和群速度色散特性强烈依赖于波导中这两排邻接波导的椭圆孔的特性.借助波导导模展开方法,计算得到波导的能带结构和群指数,并分析了它们与椭圆孔的参数关系.通过优化这些椭圆孔的参数,可以增加光子晶体光波导导模在光锥以下的无固有传输损耗带宽,在2—45 nm 的带宽上实现无色散的常数群速度.这些理论结果将为低损耗低色散慢光波导的设计制造提供理论基础. 关键词： 光子晶体薄板波导 群速度 群指数 群速度色散     

Influence of a holey cladding structure on spectral characteristics of side-polished endlessly single-mode photonic crystal fibers

We experimentally investigate the spectral characteristics of side-polished endlessly single-mode photonic crystal fibers of different polishing depths and radii of curvature that are important to mode field diameter, evanescent coupling, waveguide losses, higher-order mode excitation, and dispersion slopes of photonic crystal fiber components. A polished photonic crystal fiber with a greater polishing depth or a larger radius of curvature shows a more dispersive characteristic. In contrast to conventional single-mode fibers, in photonic crystal fibers the evanescent field is more strongly localized, and the propagating light can be more efficiently guided within the deformed core.     

Evidence of the photonic gap contribution to the guiding mechanism for strongly confined modes in the refractivelike domain

The group index dispersion and birefringence of guided modes supported by straight photonic crystal (PhC) waveguides are theoretically and experimentally investigated as a function of the waveguide width within various reduced frequency domains. Within the photonic gap and far from the Brillouin zone edges, strongly confined modes supported by narrow PhC guides exhibit both a group index and a birefringence larger than those of a deep ridge. These two results evidence the contribution of the photonic gap to the guiding mechanism in the refractivelike domain.     

Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry

We study adiabatic transformation in optical waveguides with discrete translational symmetry. We calculate the reflection and transmission coefficient for a structure consisting of a slab waveguide that is adiabatically transformed into a photonic crystal waveguide and then back into a slab waveguide. The calculation yields high transmission over a wide frequency range of the photonic crystal waveguide band and indicates efficient coupling between the slab waveguide and the photonic crystal waveguide. Other applications of adiabatic mode transformation in photonic crystal waveguides and the coupled-resonator optical waveguides are also discussed.     

基于波导间能量耦合效应的光子晶体频段选择与能量分束器

基于波导间能量耦合效应的光子晶体功率分束器具有结构紧凑、带宽较宽、弯曲损耗低、分光角度大和不受外界电磁场干扰等优点.本文利用时域有限差分方法,理论研究了二维三角晶格光子晶体耦合波导的功率分束特性,设计得出了一种能够在宽频谱范围内针对不同频率区间实现不同分光比的功能器件.在此基础上通过改变耦合区介质柱形状以及输出分支波导与能量耦合波导的连接位置,最终针对三个相邻频率范围内的入射光信号,较好地实现了三均分、二均分、单一输出通道这3种能量分配输出模式.该功能器件具有透过率对比度高、结构紧凑等特性,对于发展全光功能器件在大规模全光复杂集成领域内的实际应用具有一定的促进作用.     

Waveguide mode converter based on two-dimensional photonic crystals

We propose and numerically analyze a novel mode converter based on two-dimensional photonic crystal waveguides with square arrays of cylindrical dielectric rods in air. The mode converter uses small perturbation defects to decouple various modes in the multimode waveguide, thereby permitting propagation of only one mode at any given frequency, which permits one-to-one mode conversion without exciting unwanted modes. The mode converter can efficiently convert a TM0 mode supported in a single-mode photonic crystal waveguide into a TM2 mode supported in the multimode waveguide that is laterally coupled to the single-mode waveguide section for a wide wavelength range. Influences of different sizes and positions of perturbation rods on the band structure of the multimode waveguide are studied.