Modelling of finite-size grating waveguide filters on the basis of a free-space diffraction approach

The field reflection coefficientR of a high strength and short length waveguide grating section is obtained by resorting to a free-space diffraction approach whereby the waveguide grating is excited by means of a virtual high index prism. The effective index of the guided mode, the coupling coefficient between contradirectionally propagating modes of the grating waveguide as well as the modal field are first obtained in the case of an infinite grating by interpreting the results given by an exact diffraction solution by means of a three-wave coupled mode formalism. These results are then introduced in the coupled wave analysis of the structure of finite extent to provide the field at the entrance of the waveguide grating section where the usual overlap integral with the incident field delivers the reflection coefficient. We neglect only the result of radiation mode propagation. This assumption can be made when the grating section is longer than the propagating length of all the leaky modes.     

Two-dimensional coupled mode equation for grating waveguide excitation by a focused beam

The problem of grating coupling of a focused incident beam under non-normal incidence into a slab waveguide is given a complete three-dimensional (3D) solution. The diffracted field is expressed as the Fourier integral of a regular part and of a singular part resulting from the existence of the coupled guided mode. A suitable expression of the field in the neighborhood of the pole and a rigorous definition of the modal field lead to a generalized coupled mode equation relating the incident field and the two-dimensional (2D) modal field propagating in the plane of the slab waveguide. The phenomenological parameters involved in the coupled wave equation: the propagation constant, the radiation coefficient as well as the modal field shape are derived from the exact treatment of plane wave diffraction in the same structure. The solution of the complete coupling problem is given in the particular case of a Gaussian incident beam, and of a high index step-index waveguide.     

饱和长度对少模光纤光栅影响的数值仿真

对折射率剖面非均匀的少模光纤Bragg光栅(FM-FBG)的反射特性进行了数值仿真，研究了光纤侧面紫外曝光法制作的光纤光栅中饱和长度的影响.用试射法（shooting）数值求解了耦合模方程，得到FM-FBG的反射谱.仿真结果表明，在纤芯和包层边界的最大光致折射率变化量和纤芯吸收因子不变的情况下，随着纤芯折射率变化的饱和长度的增大，LP01和LP11模间的互耦合反射峰呈抛物线形变化,当饱和长度增大到一定值后，互耦合反射峰随饱和长度的增大而逐渐减小并最终消失;同阶LP模的自耦合反射峰随饱和长度的增大而增大.     

Theoretical model of a planar integrated refractive index sensor based on surface plasmon-polariton excitation

A theoretical model of a new integrated planar surface plasmon-polariton (SPP) refractive index sensor is presented and comprehensively investigated. The main principle of operation of this device is based on high efficiency energy transfer between a p-polarized guided mode propagating in a waveguide layer of the structure and the SPP propagating in the opposite direction in a metal layer separated from the waveguide layer by a dielectric buffer. The high efficiency energy transfer is realised by means of a properly designed Bragg grating imprinted in the waveguide layer. This device is compact, free from any moving parts and can easily be integrated into any planar scheme. Our simulations for the sensor operating at the well developed and commercialised telecom wavelengths are based on coupled mode theory.     

金属光栅对表面等离子体波的辐射抑制研究

对金属光栅进行严格耦合波理论计算, 得到了780和1500 nm波长入射光条件下不同光栅调制深度(20-80 nm)对应的反射谱. 根据Fano理论推导了描述反射谱线的经验公式, 最后应用有限元法计算光栅表面近场电场分布, 验证了公式的正确性. 反射谱线公式反映出光栅耦合表面等离子体的各个物理效应, 其中最重要的是反映出光栅在某一调制深度下对表面等离子体反耦合的抑制作用, 这一发现为设计光栅能量约束器件提供了物理依据.     

TM-mode coupling in anisotropic optical waveguides caused by periodic variation optic-axis direction

The problem of mode coupling caused by a small periodic variation of the opticaxis direction in an anisotropic optical waveguide is reduced to a pair of coupled differential equations and an expression for the coupling coefficient is given. For a periodically perturbed section of the waveguide the coupled-mode equations are solved subject to suitable boundary conditions, and the coupling between the forward TM mode and the backward TM mode is analysed. A perturbed section of an anisotropic waveguide acts as a frequency selective reflection filter for TM modes only.     

Long period grating in/on planar and channel waveguides: A theory description

A comprehensive, complete theory suitable for a long period grating (LPG) on/in a planar or channel waveguide is described on the basis of coupled mode theory. The theory aims at key characteristic parameters with respect to the effect of the LPG, including resonance wavelength, transmission power of the guided mode in the waveguide, full-width at half-maximum (FWHM) of the power attenuation band in transmission spectrum of the guided mode, and coupling coefficient between a guided and a coupled mode. The type of the grating including relief and index modulation, different polarization state combinations of the guided mode and the resonant mode, and slanted grating structure are considered in this theory. The influences of the coupling between two guided modes and between a guided mode and a substrate mode are discussed. The role of cladding layer in a long period waveguide grating is demonstrated in particular. Finally, the expressions for the sensitivity of resonance wavelength as a function of external temperature, pressure and surrounding refractive index are derived.     

Theory of gyrotropic ring resonators with counterpropagating modes coupling

The Faraday effect in ring resonators leads to the resonance splitting of clockwise and counter-clockwise propagating modes. In this work we investigate how this resonance splitting influences the ring resonator's behavior if both modes are coupled by a sidewall corrugation of the resonator. Coupled mode theory is used to evaluate the transmission and reflection characteristics of a ring resonator coupled to a waveguide. Based on these evaluations, we characterize a novel ring resonator switch. The resonance of the corrugated gyrotropic resonator coupled to a waveguide can be switched off by the application of the external magnetic field. In this case, the resonance is not shifted, as what typically occurs at small perturbations, but suppressed.     

模式耦合理论在圆周对称长周期光纤光栅建模中的应用

长周期光纤光栅是不同于光纤Bragg光栅的一种光纤光栅器件 ,根据模式耦合理论 ,长周期光纤光栅表现为前向传播的纤芯导模和同向的各阶次包层模式之间的耦合。分析研究了长周期光纤光栅轴向的模场变化。忽略轴向的模式耦合以及包层模式之间的相互耦合作用 ,并认为折射率指数的调制只存在于纤芯中 ,建立了简化的长周期光纤光栅数学模型。对圆周对称轴向均匀型长周期光纤光栅谱特性进行了仿真 ,其结果与实验结果基本吻合 ,表明了简化的数学模型的合理性     

Guided-mode resonances in multimode planar periodic waveguides

<正>Using the effective medium theory and the waveguide eigenvalue equation,we design a multimode planar periodic waveguide.When a plane wave illuminates the grating at the designed angle and wavelength, more than one leaky modes are excited coincidentally.Then the reflection efficiency around this designed angle and wavelength is investigated using a rigorous coupled wave analysis formulation and a gap of reflection peaks is found.Electric field distributions reveal that this high reflectivity gap is due to the coupling between these two coincidentally excited leaky modes.     

Single-material coupling-tolerant semi-planar microresonator using Littrow diffraction

Resonators carved in a single material such as disc, rings, spheres, do not require genuine mirrors since they exploit shape resonances, but they then suffer from poor coupling to standard free-space collimated beams. Exploiting the idea of Littrow resonators combining total internal reflection and grating diffraction, we propose trapezoidal prism-type geometries that include a strong grating on one face, and total internal reflection on the other face. Resonant modes are localized within a length of the same order as the prism thickness, but are well coupled to free-space beams. The resonator core can be seen as a broad waveguide with multimode coupling of “Littrow modes”, a configuration recently pointed out for its capability to produce a “collective” slow-light regime. A more “planar” version, with a saw-tooth input-coupling grating for vertically collimated beam is also proposed.     

分布反馈量子级联激光器光栅反馈特性北大核心CSCD

为探究Bragg光栅结构对TM模反馈特性的影响,利用有限时域差分法对具有TM模的分布反馈(DFB)量子级联激光器Bragg光栅结构进行仿真研究。重点分析了侧向耦合光栅的光学特性以及光栅侧壁倾角对光栅反射谱、损耗的影响及原因,并探究了光栅刻蚀深度及占空比与TM模的耦合系数、损耗的关系。结果表明有效折射率是影响Bragg波长的主要因素,而光限制因子是不同周期的侧向耦合光栅结构耦合系数产生巨大差别的原因,当光栅侧壁倾角90°时镜面损耗最小。光栅周期、占空比、刻蚀深度与耦合系数的关系表明:这些参数不仅影响光栅的相对介电常数,也会对光限制因子产生作用,从而影响耦合系数的大小;耦合系数与刻蚀深度具有正比关系,大周期光栅耦合系数随占空比的变化率较小。对光栅光反馈特性的理论研究有利于提升对DFB量子级联激光器的认识,促进激光器性能的提升和发展。     

Single-Photon Scattering Grating in a Waveguide-Cavity System

We investigate single-photon scattering grating in a one-dimensional waveguide coupled to a cavity embedded with a driven Λ-type three-level atom. The single-photon reflection amplitude and transmission amplitude in the waveguide are obtained via a real-space approach, respectively. By spatially modulating a classical control field to drive the three-level emitter, alternating regions of high reflection and absorption as well as high transmission and absorption of the single photon are generated in both directions of the waveguide, which acts as a kind of scattering grating. The proposed scheme may have the potential for the design of chip-integrated grating.     

Space-charge field of a photorefractive grating in a planar waveguide based on a cubic crystal

We consider the initial stage of formation of photorefractive gratings in planar waveguides based on cubic electrooptic crystals. We have obtained solutions for the components of the space-charge field for arbitrary ratios between parameters characterizing the spatial inhomogeneity of the light interference pattern in the waveguide as well as the diffusion length. The dependence of the component of the space-charge field parallel to the grating vector on its period in the initial section of the recording is also determined by the sum and difference of the transverse propagation constants of the interacting waveguide modes. We show that for waveguide interactions characterized by a small transverse scale of spatial inhomogeneity, the distributions of the space-charge field and the light intensity in the interference pattern are substantially different. These effects must be considered in analysis of the nonlinear interactions occurring in a refractive index grating due to the electrooptical effect. Tomsk University of Control Systems and Radioelectronics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, pp. 65–73, June, 1997.     

介质光栅导模共振耦合波分析

导模共振是由于光栅介质内高级次子波耦合进光栅所支持的泄漏模中,导致传播波能量重新分布的结果.采用严格的耦合波方法,通过分析波导的导波模式,正确估计出弱调制介质光栅导模共振的位置.并对导模共振与光栅厚度、基底厚度以及入射角的关系作了讨论.通过采用抗反射设计,获得了具有对称、低旁带特点的窄带共振峰 关键词： 导模共振 耦合波     

TE0导模干涉刻写周期可调亚波长光栅理论研究

通过棱镜耦合激发非对称金属包覆介质波导结构中的TE₀导波模式, 利用两束TE₀模的干涉从理论上实现了周期可调的亚波长光栅刻写. 分析了TE₀模式的色散关系, 刻写亚波长光栅的周期与激发光源、棱镜折射率、光刻胶薄膜厚度及折射率之间的关系. 用有限元方法数值模拟了金属薄膜、光刻胶薄膜和空气多层结构中TE₀导模的干涉场分布. 研究发现, 激发光源波长越短, TE₀ 模干涉刻写的亚波长光栅周期越小; 光刻胶越厚, 刻写的亚波长光栅周期越小; 高折射率光刻胶有利于更小周期亚波长光栅的刻写. 相较于表面等离子体干涉光刻, 基于TE₀ 模的干涉可在厚光刻胶条件下通过改变激发光源、棱镜折射率、光刻胶材料折射率、特别是光刻胶薄膜的厚度等多种方式实现对亚波长光栅周期的有效调控.     

TE-TE mode coupling at oblique incidence in a periodic dielectric waveguide

The characteristics of reflection of a TE mode into another TE mode in a planar dielectric waveguide with a sinusoidally modulated index are investigated for the general case in which the wavevectors are not aligned with the grating vector. A singular perturbation procedure is used to deduce the asymptotically exact coupled mode equations which govern the interaction. An analysis of the coupled-mode equations has shown the existence of the Brewster phenomenon at the angle of incidence θ_iB=45°. For angles of incidence sufficiently greater than the Brewster angle, the reflection coefficient can be considerably larger than that for the normal incidence. In the spectral response curves of the reflection coefficient, a higher maximum and a smaller base bandwidth are possible for the oblique incidence as compared to that for the normal incidence. The angular sensitivity of the reflection characteristics increases as the angle of incidence changes from the normal incidence to the grazing incidence.     

用耦合波理论求解渐变折射率光纤的传播常数和模式场

本文应用耦合波理论来计算任意渐变折射李光纤的传播常数和模场分布.将无限伸展的抛物型折射率分布光纤作为一个理想波导,任意径向不均匀折射率分布光纤便可以视作该理想波导的微扰,其模场可以展开成一组完备的理想波导模的叠加.然后,模场和传播常数可以通过耦合波方程求得.进一步将一阶微分方程组形式的耦合波方程变换成线性方程组,使计算过程大大简化.文中给出了数值计算结果,并将其与准确值进行了比较.     

Effect of coherence property of incident light on prism waveguide coupling

The accurate reflection coefficient of prism waveguide coupler that takes coherence property of incident light into account is obtained at first. Based on the reflection coefficient, the effect of coherence property of incident light on prism coupling is discussed in this work. It is shown that extra damping in waveguide caused by the coherence property is larger for high-order resonant mode than that for low-order mode. For 100 fs Gaussian pulses incidence, the reflected spectra at different resonant modes are obtained theoretically and experimentally, which show that coherence property has a strong effect on prism coupling at high-order modes.     

Modeling and characterization of fiber Bragg grating for maximum reflectivity

This paper presents the modeling and characterization of an optical fiber grating for maximum reflectivity. Grating length and change in refractive index are the critical parameters in contributing to the performance of fiber Bragg grating. The wavelength chosen for analysis is from the third window to minimize the attenuation. The reflection spectra, bandwidth and side lobes strength were analyzed with different lengths and change in refractive index. The simulations are based on solving coupled mode equations by transfer matrix method that describes the interaction of guided modes.