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.     

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.     

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.     

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.     

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.     

Reflection-free one-way edge modes in a gyromagnetic photonic crystal

We point out that electromagnetic one-way edge modes analogous to quantum Hall edge states, originally predicted by Raghu and Haldane in 2D photonic crystals possessing Dirac point-derived band gaps, can appear in more general settings. We show that the TM modes in a gyromagnetic photonic crystal can be formally mapped to electronic wave functions in a periodic electromagnetic field, so that the only requirement for the existence of one-way edge modes is that the Chern number for all bands below a gap is nonzero. In a square-lattice yttrium-iron-garnet crystal operating at microwave frequencies, which lacks Dirac points, time-reversal breaking is strong enough that the effect should be easily observable. For realistic material parameters, the edge modes occupy a 10% band gap. Numerical simulations of a one-way waveguide incorporating this crystal show 100% transmission across strong defects.     

二维正方晶格光子晶体禁带特性

基于平面波展开法,以碳化硅构成二维正方晶格光子晶体,数值模拟了TE模、TM模二维光子晶体的禁带特性,结果表明,TE模更容易形成光子禁带。同时设计了以碳化硅构成二维正方晶格光子晶体波导,数值模拟了TE模、TM模波导的传输特性和禁带特性,结果表明,TE模构成的波导电磁波能够较好的传播,它们的光子禁带都没有出现。研究结论为光子晶体波导器件的开发提供参考。     

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     

光控二维光子晶体光开关

提出了一种调节液晶光子晶体光子带隙的方法。二维三角介质柱形光子晶体位于2块熔凝石英片之间,在介质柱之间填充各向同性排列的液晶,受偏振紫外光照射后,光诱导液晶分子定向排列,通过光诱导液晶分子取向改变液晶的折射率。数值模拟结果表明：通过外界光场控制所填充的向列相液晶分子的方向可以对这种二维三角形介质柱光子晶体的禁带结构进行调节。该可调光子晶体可控制波导中TM模和TE模的选择性传输,因而可应用于制作全光光开关。     

Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab

Strong coupling between localized particle plasmons and optical waveguide modes leads to drastic modifications of the transmission of metallic nanowire arrays on dielectric waveguide substrates. The coupling results in the formation of a new quasiparticle, a waveguide-plasmon polariton, with a surprisingly large Rabi splitting of 250 meV. Our experimental results agree well with scattering-matrix calculations and a polariton-type model. The effect provides an efficient tool for photonic band gap engineering in metallodielectric photonic crystal slabs. We show evidence of a full one-dimensional photonic band gap in resonant plasmon-waveguide structures.     

Gap maps, diffraction losses, and exciton–polaritons in photonic crystal slabs

A theory of photonic crystal (PhC) slabs is described, which relies on an expansion in the basis of guided modes of an effective homogeneous waveguide and on treating the coupling to radiative modes and the resulting losses by perturbation theory. The following applications are discussed for the case of a high-index membrane: gap maps for photonic lattices in a waveguide; exciton–polariton states, when the PhC slab contains a quantum well with an excitonic resonance; propagation losses of line-defect modes in W1 waveguides, also in the presence of disorder; the quality factors of photonic nanocavities. In particular, we predict that disorder-induced losses below 0.2 dB/mm can be achieved in state-of-the-art samples by increasing the channel width of W1 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.     

二维光子晶体线缺陷结构的光谱辐射特性

光子晶体的禁带特性是该新兴材料的最根本特征。本文运用平面波展开法(PWE)计算了一种正方晶格Si光子晶体材料的禁带特性,并基于该材料设计出一种红外波段的线缺陷光子晶体波导结构。运用时域有限差分法(FDTD)研究了线缺陷二维光子晶体波导宽度对通频带、电场强度及透射能量的影响,研究结果为二维光子晶体波导器件的开发和利用提供了理论支撑。     

Photonic band gap grating in He+-implanted lithium niobate waveguides

In this work, we report the investigation of 2D photonic crystals in lithium niobate associated with waveguiding structures fabricated by He⁺ implantation. From the material point of view, the investigation of PBG structures in lithium niobate is of great interest for optoelectronics technology since this crystal is one of the most important materials widely used in integrated and non linear optics. The choice of the implantation technique to produce the waveguide is motivated by the possibility of having both Transverse Electric (TE) and Transverse Magnetic (TM) guided modes in order to obtain a total photonic band gap (PBG).     

Photonic bands, gap maps, and intrinsic losses in three-component 2D photonic crystal slabs

We obtain the photonic bands and intrinsic losses for the triangular lattice three-component two- dimensional （2D） photonic crystal （PhC） slabs by expanding the electromagnetic field on the basis of waveguide modes of an effective homogeneous waveguide. The introduction of the third component into the 2D PhC slabs influences the photonic band structure and the intrinsic losses of the system. We examine the dependences of the band gap width and gap edge position on the interlayer dielectric constant and interlayer thickness. It is found that the gap edges shift to lower frequencies and the intrinsic losses of each band decrease with the increasing interlayer thickness or dielectric constant. During the design of the real PhC system, the effect of unintentional native oxide surface layer on the optical properties of 2D PhC slabs has to be taken into consideration. At the same time, intentional oxidization of macroporous PhC structure can be utilized to optimize the design.     

Ray Modes in Random Gap Systems

A disordered photonic crystal with spectral degeneracies in the form of Dirac nodes is considered. Disorder can create a random gap at the Dirac nodes, which leads to the formation of random edge modes. We study the distribution of these edge modes and find from symmetry considerations that the discrete anisotropy of the photonic crystal is spontaneously broken for the propagation of photons from a local photon source. This effect can be understood as the spontaneous creation of a ray mode or as the creation of a one‐dimensional waveguide in a two‐dimensional photonic crystal through strong random scattering. The phenomenon must be distinguished from Anderson localization of photons in a single band crystal and can be considered as angular localization, since it creates geometric states rather than confining the photons to an area of the size of the localization length. The propagation of the photon intensity is described by a Fokker‐Planck equation, whose drift term is determined by the spectrum of the photonic crystal near the Dirac node.     

Enhanced photonic band-gap confinement via Van Hove saddle point singularities

We show that a saddle point Van Hove singularity in a band adjacent to a photonic crystal band gap can lead to situations which defy the conventional wisdom that the strongest band-gap confinement is found at frequencies near the midgap. As an example, we present a two-dimensional square photonic crystal waveguide where the strongest confinement is close to the band edge. The underlying mechanism can also apply to any system that is described by a band structure with a gap. In general, the saddle point favors the appearance of a very flat band, which in turn results in an enhanced confinement at band-gap frequencies immediately above or below the flat band.     

Compact and broadband waveguide taper based on partial bandgap photonic crystals

Partial bandgap characteristics of parallelogram lattice photonic crystals are proposed to suppress the radiation modes in a compact dielectric waveguide taper so as to obtain high transmittance in a large wavelength range. Band structure of the photonic crystals shows that there exists a partial bandgap, The photonie crystals with partial bandgap are then used as the cladding of a waveguide taper to reduce the radiation loss efficiently. In comparison with the conventional dielectric taper and the complete bandgap photonic crystal taper, the partial bandgap photonic crystal taper has a high transmittance of above 85% with a wide band of 170 nm.     

Optical confinement of spatial frequencies in the photonic crystal waveguide

The optical confinement of spatial frequencies in the photonic crystal waveguide has been investigated theoretically and simulated numerically. It is found that the enhanced gap confinement is at frequency close to the upper band edge, in contrary to the conventional concept that the strongest optical confinement is found at frequencies near the mid-gap. The anomalous phenomenon may be attributed to a Van Hove saddle point singularity in a band adjacent to a photonic crystal band gap. In general, the saddle point favors the appearance of a very flat band, which in turn causes an enhanced confinement at band-gap frequencies.     

Slight disorder effects in two dimensional photonic crystal structures

In the actual manufacturing process of photonic crystal structure, unavoidable error can generate slight disorder which may influence the performance of photonic crystal based device. In this work, randomly distributional disorders are applied to the air holes in the photonic crystal structure. Based on this, we investigate the influence of the slight disorder on the photonic crystal band structure and the performance of photonic crystal based devices (waveguide and slab cavity). The studies indicate that the slight disorder provides small influence on the band structure of the photonic crystal. But, the random disorder in photonic crystal waveguide may increase transmission loss obviously when the wavelength of the light and the distribution of disorder break the balance of multiple interferences. Also, the slight disorder can reduce the Q factor of the photonic crystal cavity at a certain degree. The studies may provide some useful guides for further photonic crystal device research.