Influences of supercell termination and lateral row number on the determination of slow light properties of photonic crystal waveguides

We systematically analyze the effects of the use of an inaccurate supercell termination and an insufficient supercell size of plane-wave expansion method on the dispersion and the slow light properties of the photonic crystal waveguides. The inattentive use of supercells of photonic crystal waveguides appeared in the literature is found to be yielding errors in the dispersion and slow light characteristics of the fundamental guided mode of photonic crystal waveguides. In addition, extra modes appear in the photonic band gap of the photonic crystal waveguide due to inaccurate supercell termination. By examining the field distribution of the modes, the extra modes can be determined and removed from the band diagram. The dispersion, group index and bandwidth characteristics are observed to be less affecting from inaccurate supercell termination as the number of rows adjacent to the waveguide increases. Moreover, the dispersion and the group index-frequency curves of the fundamental guided mode of correctly terminated supercells are found to be converging as the lateral row number along the line-defect is increased.     

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.     

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.     

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.     

High-purity transmission of a slow light odd mode in a photonic crystal waveguide

We demonstrate a novel scheme to control the excitation symmetry for an odd mode in a photonic crystal waveguide and investigate the spectral signature of this slow light mode. An odd-mode Mach-Zehnder coupler is introduced to transform mode symmetry and excite a high-purity odd mode with 20?dB signal contrast over the background. Assisted by a mixed-mode Mach-Zehnder coupler, slow light mode beating can be observed and is utilized to determine the group index of this odd mode. With slow light enhancement, this odd mode can help enable novel miniaturized devices such as one-way waveguides.     

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.     

Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide

We present time-resolved spontaneous emission measurements of single quantum dots embedded in photonic crystal waveguides. Quantum dots that couple to a photonic crystal waveguide are found to decay up to 27 times faster than uncoupled quantum dots. From these measurements beta-factors of up to 0.89 are derived, and an unprecedented large bandwidth of 20 nm is demonstrated. This shows the promising potential of photonic crystal waveguides for efficient single-photon sources. The scaled frequency range over which the enhancement is observed is in excellent agreement with recent theoretical proposals taking into account that the light-matter coupling is strongly enhanced due to the significant slow-down of light in the photonic crystal waveguides.     

Slow light transmission in a photonic crystal power splitter with parallel outputs

In this paper, we investigate coupling of light to slow modes in a photonic crystal power splitter composed of a Y-junction and two 60° bends. First, a combination of two cascaded bends which is commonly used in integrated photonic crystal circuits is studied in slow light frequency regime. We propose a structure that its transmission spectrum covers the high group-index frequencies near the band edge. Also, by structural modifications, high transmission near to 95% is achieved in slow light bandwidth. Next, we study the complete structure of a photonic crystal power splitter with parallel outputs based on a Y-junction integrated with two 60° bends. Using modified bends and reducing sharpness of Y-junction, the efficiency of splitting increases in both high and low group-index frequency bands. The optimized structure has an average efficiency of 82% in slow mode regime. This structure can be used in photonic crystal based slow light devices, such as Mach-Zehnder interferometers.     

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.     

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.     

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.     

Low group velocity in a photonic crystal coupled-cavity waveguide

A two-dimensional photonic crystal coupled-cavity waveguide is designed and optimized, the transmission spectrum is calculated by using the finite-difference time-domain method, and the group velocity of c/1856 is obtained. To our knowledge, this value of group velocity is the lowest group velocity in a photonic crystal waveguide calculated from its transmission spectrum so far. The result is confirmed by the photonic band structure calculated by using the plane wave expansion method, and it is found that the photonic crystal waveguide modes in a photonic band structure are in accordance with those in the transmission spectrum by using the finite-difference time-domain method. The mechanism of slow light in the coupled-cavity waveguide of photonic crystal is analysed.     

光子晶体平面波导与脊波导高效耦合技术的研究

利用一维变周期谐振腔阵列和非线性缓变边界，可以实现光波从脊波导到光子晶体平面波导 （PCW）的高效耦合.基于平面波展开法（PWE）和时域有限差分法（FDTD），深入分析和讨 论了普通脊波导、2D-PCW结构和本征模以及工作模式、缓变边界形状等对耦合效率的影响， 从而得出光波从脊波导到2D-PCW、再返回脊波导的统一图景.指出考虑模式转换和采用缓变 边界条件可以极大提高PCW与脊波导间的耦合效率.对PC-PW边界采用线性和非线性缓变结构 进行了仿真，讨论了边界缓变程度对耦合效率的影响.结果表明，采用模式耦合和PC-PW余弦 缓变边界时的耦合效率在较宽的带宽内超过了95%. 关键词： 光子晶体波导 脊波导 PWE FDTD 耦合边界     

Silicon-based two-dimensional photonic crystal waveguides

A review of the properties of silicon-based two-dimensional (2D) photonic crystals is given, essentially infinite 2D photonic crystals made from macroporous silicon and photonic crystal slabs based on silicon-on-insulator basis. We discuss the bulk photonic crystal properties with particular attention to the light cone and its impact on the band structure. The application for wave guiding is discussed for both material systems, and compared to classical waveguides based on index-guiding. Losses of resonant waveguide modes above the light line are discussed in detail.     

光子晶体波导耦合的波分复用研究

两平行光子晶体单模波导的相互耦合组成一个耦合结构。两本征模的色散曲线相交并出现简并,简并模之间的耦合作用使模式的分布发生了改变。由于耦合的作用,各个波长的光波会在不同的波导中传输。在简并点处两本征模发生解耦合,光波会沿着原来的方向传输。将两个不同耦合长度的光子晶体波导耦合结构集成在一起,就可以组成一个三波长的光子晶体波分复用器。     

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.     

Uniform silicon slow light waveguide

An uniform silicon waveguide is proposed featuring ultralow-dispersion slow light. The core of the waveguide consists of one silicon trip and two pairs of air/silicon strip and the cladding is composed of several alternative silicon and air strips, which form a transverse band gap to confine propagating light in the core. The waveguide has several nearly linear photonic bands in a large frequency range, which can support broadband slow modes with a group velocity of 0.03–0.08c and tolerable group velocity dispersion.     

Waveguide plasmon polaritons in metal-dielectric photonic crystal slabs

The optical properties of arrays of metallic (gold) nanowires deposited on dielectric substrates are studied both theoretically and experimentally. Depending on the substrate, Wood’s anomalies of two types are observed in the transmission spectra of such planar metal-dielectric photonic crystals. One of them is diffraction (Rayleigh) anomalies associated with the opening of diffraction channels to the substrate or air with an increase in the frequency of the incident light. The other type of Wood’s anomaly is resonance anomalies associated with excitation of surface quasi-guided modes in the substrate. Coupling of the quasi-guided modes with individual nanowire plasmons brings about the formation of waveguide plasmon polaritons. This effect is accompanied by a strong rearrangement of the optical spectrum and can be utilized to control the photonic bands of metal-dielectric photonic crystal slabs.     

Coupling into slow-mode photonic crystal waveguides

We study efficient injectors for coupling light from z-invariant ridge waveguides into slow Bloch modes of single-row defect photonic crystal waveguides. Two-dimensional vectorial computations performed with a Bloch mode theory approach predict that very high efficiencies (>90%) can be achieved for injector lengths of only a few wavelengths in length, even for small group velocities in the range of c/100-c/400. This result suggests that photonic crystal devices operating with slow waves can be interfaced with classical waveguides without sacrificing compactness.