Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task

Modal reflection, transmission and loss of deeply etched Bragg waveguide gratings were modelled by six European laboratories using independently developed two-dimensional (2D) numerical codes based on four different methods, with very good mutual agreement. It was found that (rather weak) material dispersion of the SiO₂/Si₃N₄ system does not significantly affect the results. The existence of lossless Floquet–Bloch modes in deeply etched gratings was confirmed. Based on reliable numerical results, the physical origin of out-of-plane losses of 1D or 2D photonic band gap structures in slab waveguides is briefly discussed.     

Influence of parameters on light propagation dynamics in optically induced planar waveguide arrays

The diffraction and refraction of light beam in optical periodic structures can be determined by the photonic band-gap structures of spatial frequency. In this paper, by employing the equation governing the nonlinear light propagations in photorefractive crystals, we study the photonic band-gap structures, Bloch modes, and light transmission properties of optically induced planar waveguide arrays. The relationship between the photonic band-gap structures and the light diffraction characteristics is discussed in detail. Then the influence of the parameters of planar waveguide arrays on the band-gaps structures, Bloch modes, and linear light transmissions is analyzed. It is revealed that the linear light transmission properties of waveguide arrays are tightly related to the diffraction relationships determined by band-gap structures. And the Bloch modes corresponding to different transmission bands can be excited by different excitation schemes. Both the increases of the intensity and the period of the array writing beam will lead to the broadening of the forbidden gaps and the concentration of the energy of the Bloch modes to the high-index regions. Furthermore, the broadening of the forbidden gaps will lead to separation and transition between the Bloch modes of neighboring bands around the Bragg angle. Additionally, with the increase of the intensity of the array writing beams, the influences from light intensity will tend to be steady due to the saturation of the photorefractive effect. Supported by the Youth for Northwestern Polytechnical University (NPU) Teachers Scientific and Technological Innovation Foundation, the NPU Foundation for Fundamental Research, and the Doctorate Foundation of NPU (Grant No. CX200514)     

基于布里渊区谱的二维光子晶格线性缺陷模式分析

结合均匀光子晶格的衍射关系和晶格中正负缺陷的布里渊区谱特性,探讨了光诱导二维光子晶格中线性缺陷模式的形成条件,对布里渊区中各点的缺陷模式进行了模拟分析,并得到了光子带隙结构中“嵌入点”X₁点的正、负缺陷模式.结果表明：对于二维缺陷,只有当衍射关系曲面中沿两个正交的横向波矢方向同时为正常（反常）衍射的区域才能存在正（负）缺陷模式;而对于一维缺陷,只要在一个横向波矢方向上存在正常（反常）衍射的区域就可以支持正（负）缺陷模式,因此在某些特殊点处,正和负的缺陷模式可以同时存在.X₁点正缺陷模式的存在预示着自聚焦非线性同样可以支持带内孤子.研究结果有助于对光子晶格中晶格孤子（特别是带内孤子）的理解和进一步研究. 关键词： 光诱导光子晶格 光子带隙 线性缺陷态     

Extremely low optical transmittance in the stopbands of photonic crystals

We demonstrate extremely low transmittance characteristics of photonic crystals (PhCs) with a finite thickness in specific photonic bandgaps (PBGs) through numerical simulation, and clarify its origin. Some of the PhCs support decaying Bloch eigenmodes, whose propagation constant (real part of the Bloch wavenumber) as well as their decay constant (imaginary part) changes with frequency inside the bandgap. Such a class of modes can interfere destructively at the exit end of the crystal depending on their round-trip phase change, which creates comb-like valleys in their transmission spectra.     

Optical surface Bloch modes of complete photonic bandgap materials as a basis of optical sensing

Surface Bloch modes induced on three-dimensional dielectric photonic crystals with a complete photonic bandgap are evanescently decaying states at surfaces and have large field overlap with low-index media, resulting in narrow spectrum linewidth and simultaneously a large resonance shift due to a perturbation of the refractive index in the background media. Surface Bloch resonance states are analyzed for (001), (100), and (110) woodpile surface planes. Low-loss, high-sensitivity surface Bloch modes are also analyzed on a flat-top (001) woodpile planar surface. These analyzed surface Bloch modes are confined in a subwavelength scale and are expected to form a basis set used for optical resonance sensing.     

基于高折射率断环结构的全固光子带隙光纤的设计

设计了基于断环结构的全固光子带隙光纤,其背景材料为熔石英而断环结构由若干掺杂的高折射率介质柱构成.基于平面波展开法计算得到的态密度图和Bloch模场分布表明,该种光纤中的一个高阶带隙可以得到调节并被极大展宽,带隙调节的基本原理是断环可以同时控制包层介质柱的线偏振模式的角向和径向模式阶数.研究表明,断环中的介质柱数目决定了受影响最小的一组线偏振模式的最高角向阶数,而带隙宽度受介质柱尺寸影响很大.这一宽的高阶带隙可以用来设计带隙中心分别在800和1550 nm、带宽分别为488和944 nm的全固光子带隙光纤 关键词： 全固光子带隙光纤 光子带隙 光纤设计 平面波展开法     

Si-based two-dimensional photonic crystals coupled to one-dimensional Bragg mirrors

Planar two-dimensional photonic crystals can be combined with a one-dimensional Bragg mirror to control the quality factor and out-of-plane coupling of optical Bloch modes. We have investigated the optical properties of such structures fabricated on silicon. The photonic crystals are fabricated in the upper Si layer deposited on top of quarter-wave thick SiO₂-polycrystalline Si layers. The optical properties are probed by the room-temperature photoluminescence of Ge/Si self-assembled islands as an internal source. We show that an enhancement of the quality factor can be obtained by controlling the thickness of the silicon upper layer in which the two-dimensional photonic crystal is etched and by controlling the air filling factor of the photonic crystal. Quality factors of 2200 around 1100 nm are obtained by this method for defect-free photonic crystals with a square lattice pattern. The experimental results are supported by three-dimensional finite-difference time-domain (FDTD) calculations of the radiated modes for the investigated structures.     

Electromagnetic modes in semi-infinite photonic crystals

In a real photonic crystal, there exist three modes: propagation mode, evanescence mode and surface mode. Using ideal modal, semi-infinite photonic crystals, we study their effects on the transmission spectrum of photonic crystals, respectively. Because there exists only one air–crystal interface in a semi-infinite photonic crystal, no multiple reflection occurs and no evanescent modes and backward-propagating modes exist in this structure. The effects of the evanescence modes are studied by comparing the transmission spectrum of a finite-thickness photonic crystal slab and that of a semi-infinite photonic crystal. In addition, the effects of the backward-propagating modes are investigated using a coated semi-infinite photonic crystal structure. Finally, we study the effects of the surface modes, and find that the transmission spectrum of a semi-infinite photonic crystal is strongly dependent on its termination.     

与色散介质毗邻的一维半无限光子晶体表面态

运用Bloch定理和传输矩阵方法,研究了与色散介质毗邻的由两种材料组成的半无限一维光子晶体局域表面态的电场和色散关系.和以空气为背景的一维光子晶体相比,毗邻色散介质的光子晶体表面模色散曲线在一定堆积次序下会在较低的带隙中发生断开,较高带隙中的表面模群速度在不同堆积次序下会有很大差异.当与色散介质毗邻的物质折射率较大时,较高带隙中的表面模群速度较小;与色散介质毗邻的物质折射率较小时,较高带隙中表面模的群速度较大.     

Room temperature operation of a deep etched buried heterostructure photonic crystal quantum cascade laser

High power single mode quantum cascade lasers with a narrow far field are important for several applications including surgery or military countermeasure. Existing technologies suffer from drawbacks such as operation temperature and scalability. In this paper we introduce a fabrication approach that potentially solves simultaneously these remaining limitations. We demonstrate and characterize deep etched, buried photonic crystal quantum cascade lasers emitting around a wavelength of 8.5 μm. The active region was dry etched before being regrown with semi‐insulating Fe:InP. This fabrication strategy results in a refractive index contrast of 10% allowing good photonic mode control, and simultaneously provides good thermal extraction during operation. Single mode emission with narrow far field pattern and peak powers up to 0.88 W at 263 K were recorded from the facet of the photonic crystal laser, and lasing operation was maintained up to room temperature. The lasing modes emitted from square photonic crystal mesas with a side length of 550μm, were identified as slow Bloch photonic crystal modes by means of three‐dimensional photonic simulations and measurements.

     

光子晶体微腔中高偏振单偶极模的研究

三角晶格排列的光子晶体微腔中的偶极模式是简并的,通过改变其晶格的对称性可以消除模式简并.晶格的整体形变破坏了晶格对称性从而影响光场的分布,同时还改变了电磁场的偏振分布.晶格整体形变使得简并的偶极模式分离成x极和y极偶极模式.通过计算分析发现分离后的模式具有良好的偏振特性,从而为实现单偏振光子晶体激光器提供了一种很好的途径.文中针对光子晶体薄板结构的微腔,主要计算了偶极模中x极偶极模式在不同拉伸时以及不同填充因子情况下的Q值,并分别计算了x关键词： 光子晶体 偶极模 品质因子 偏振度     

对称型单负交替一维光子晶体的能带结构

构造了(AB)^N(BA)^N对称型两种单负材料交替一维光子晶体,利用传输矩阵法进行数值模拟.结果表明：这种单负交替对称型一维光子晶体具有一种特殊带隙结构,该带隙不敏感于入射角和晶格的无序性.在该带隙内出现了两个隧穿模,该隧穿模不敏感于入射角的改变和晶格的无序性,但能带及带隙内的隧穿模却敏感于晶格标度和周期数的变化;随着入射角的改变,带隙两侧的隧穿模趋于简并.这些特性对在利用此结构光子晶体设计双重超窄带滤波器时,具有一定的参考价值. 关键词： 光子晶体 单负材料 光子带隙     

有效抑制光子晶体加载矩形谐振腔中模式竞争的方法

研究了光子晶体加载矩形谐振腔,针对传统光子晶体加载无法完全抑制模式竞争的问题,提出了特性阻抗和介质加载方法进行改进,完全实现了谐振腔的高次模式的单模工作,为抑制高次模式工作的谐振腔中模式竞争的问题提供了一种新方法.在此基础之上,采用解析方法以及高频仿真软件HFSS,设计了一个采用TM₅₃₀高次模式工作的传统光子晶体加载的谐振腔,进一步采用了该新方法对其进行改进,并深入分析了采用这种方法抑制模式竞争的物理原因.计算结果表明,新方法能有效抑制模式竞争,实现谐振腔的高次工作模式的单模工作. 关键词： 光子晶体 谐振腔 模式竞争 特性阻抗     

周期性层状结构材料中光子带隙的形成

结合经典电磁场理论和Bloch定理,讨论了光波在周期性层状结构材料中传播的色散关系,并通过传输矩阵方法得到光波的透射谱,指出在周期性层状结构中波阻抗是形成光子带隙的本质因素.     

Out-of-plane scattering in 1-D photonic crystal slabs

We present a detailed study of out-of-plane scattering losses in a 1D approximation of 2D photonic crystal slabs. In 2D photonic crystals with a waveguide structure in the third dimension, the periodic structure (in a lot of applications a 2D arrangement of holes etched through the core and cladding) will cause light to scatter out of the waveguide plane. We studied the out-of-plane scattering losses of these holes using a 2D approximation of this 3D structure, with etched slots instead of holes. Our simulation techniques included mode expansion with PML and FDTD. We will present the influence of the refractive index contrast between core and cladding of the layered structure. We show that the losses increase with higher index contrast between core and cladding, but that with very high index contrasts and under the right circumstances light can be coupled into lossless Bloch modes.     

手征材料构成的简立方光子晶体光子带结构计算——平面波法

发展了适于计算由手征材料组成的光子晶体的光子带结构的平面波法。在此基础上，研究了由手征材料组成的简立方光子晶体的光子带结构。计算表明：手征材料“球形原子”在电介质中排列所组成的科立方光子晶体和电介质“球形原子”在手征材料中排列所组成的简立方光子晶体，不仅都存在光子带隙，而且存在截止频率，在该频率以下的区域无传播模存在，本语文认了这种光子晶体的潜在应用。     

Modified phase matching conditions for second harmonic generation in a finite one-dimensional photonic crystal near the bragg condition: Weak and strong diffraction

Enhanced noncollinear second harmonic generation in a finite one-dimensional photonic crystal is analyzed theoretically under conditions of pump field localization near the Bragg reflection. It is shown numerically that phase-matched second-harmonic generation can be implemented in a finite one-dimensional photonic crystal that does not satisfy the conventional phase-matching conditions calculated for effective Bloch modes with narrow spectral lines. The intensity of the generated second-harmonic signal exceeds the second-harmonic intensity attained under the conventional phase-matching conditions by more than an order of magnitude. This phenomenon is explained by interference between Bloch modes having similar amplitudes, wavenumbers, and spectral widths. Since the spatial spectra of waves propagating in a bounded medium have finite widths, the broadened spectral lines of proximate effective Bloch modes resulting from Bragg diffraction of waves tuned to the first transmission resonances near the photonic bandgap edge overlap, merging into a spectral profile with center shifted relative to the original effective Bloch wavevectors. This effect leads to modified phase matching conditions for second harmonic generation in a finite photonic crystal, which are written for the centers of the spectral profiles resulting from modal overlap, rather than for individual effective wavevectors. Substantially different phase matching conditions are obtained for weakly and strongly diffracted beams, whereas conventional phase matching conditions hold only for transmitted signals in the case of weak diffraction.     

填充比和格点方向对二维三角晶格光子晶体带隙的影响

采用有限元法,计算了二维三角晶格椭圆形格点空气孔型光子晶体的TE、TM模式的带隙结构。通过对椭圆形空气孔格点的大小、方向进行改变,研究了填充比、格点方向对带隙的影响。计算结果表明,在空气孔型光子晶体中TE模式更容易形成带隙;不同填充比情况下,格点方向对TE模式和TM模的带隙变化都具有不同影响;不论格点方向如何变化,均未出现完全带隙。     

二维函数光子晶体

光子晶体是由两种或两种以上不同介电常数材料所构成的周期性光学纳米结构.光子晶体结构可分为一维、二维和三维,其中二维光子晶体已成为研究的热点.可调带隙的二维光子晶体可以设计出新型的光学器件,因此,对它的研究具有重要的理论意义和应用价值.本文提出的二维新型函数光子晶体可以实现光子晶体带隙的可调性.所谓二维函数光子晶体,即组成它的介质柱的介电常数是空间坐标的函数,它不同于介电常数为常数的二维常规光子晶体.二维函数光子晶体是通过光折变非线性光学效应或电光效应使介质柱的介电常数成为空间坐标的函数.运用平面波展开法给出了TE和TM波的本征方程,由傅里叶变换得到二维函数光子晶体介电常数ε(r)的傅里叶变换ε(G),其傅里叶变换比常规二维光子晶体的复杂.计算发现当介质柱介电常数为常数时,其傅里叶变换与常规二维光子晶体的相同,因此二维常规光子晶体是二维函数光子晶体的特例.在此基础上具体研究了二维函数光子晶体TE波和TM波的带隙结构,其介质柱介电常数函数形式取为ε(r)=k·r+b,其中k,b为可调的参数.并与二维常规光子晶体TE波和TM波的带隙结构进行了比较,发现二维函数光子晶体与二维常规光子晶体TE波和TM波的带隙结构有明显的区别,二维函数光子晶体的带隙数目、位置以及宽度随参数k的变化而发生改变.从而实现了二维函数光子晶体带隙结构的可调性,为基于二维光子晶体的光学器件的设计提供了新的设计方法和重要的理论依据.     

Observations of band structure and reduced group velocity in epitaxial GaN–sapphire 2D photonic crystals

We report experimental results for the band structure of 2-dimensional triangular photonic crystals of air holes in an epitaxial group III–nitride waveguide film. Surface coupling techniques enable the observation of sharp resonance dips in the transmission spectra due to a resonance phenomenon between the incident light and Bloch modes of the photonic crystal. The position of the dips has been measured as a function of angle of incidence and the photonic band structure has been successfully constructed by the measurement. Corresponding Bloch-mode group velocities have also been obtained. Received: 28 May 2001 / Published online: 23 October 2001