Dispersion properties of planar Bragg waveguides

We reformulate the leaky mode condition of planar Bragg waveguides as two simple, separate conditions on the propagation constant; a phase match condition and a loss formula. These relations enable efficient numerical calculations of the mode properties. Furthermore, we use the phase match condition as a starting point to discuss the dispersion of waveguides with advanced cladding structures. In particular, we point out that chirped claddings, where the effective reflection point is dependent on frequency, do not give dispersion characteristics significantly different from metallic waveguides or waveguides with periodic claddings.     

Doubly resonant single-layer bandpass optical filters

A bandpass filter based on guided-mode resonance effects in a single-layer periodic waveguide is presented. Strong refractive-index modulation is used to support the excitation of a resonance pair in which leaky waveguide mode TE0 is excited by the second diffraction order and TE2 by the first diffraction order. It is shown that one resonance provides a broad low-transmission band, whereas the other supplies the transmission peak through its asymmetrical line shape. A bandpass filter with central wavelength at 1.55 microm is presented to demonstrate this concept.     

Superbending effect in two-dimensional graded photonic crystals

We study the superbending effect in a two-dimensional graded photonic crystal (GPC) for both TE and TM modes. We show that the lateral beam shift is extremely sensitive to the wavelength for the TM mode but not TE mode, indicating the potential in designing some special superbending devices, for example, TE/TM splitter and polarization-indifference waveguide at prescribed wavelengths.     

金属包层对称平面单轴晶体波导的模式场(Ⅱ)

对于晶体光轴平行于波导界面的结构,讨论了光在金属包层对称平面单轴晶体波导(波导层是单轴晶体,两个波导界面均为金属)内的传输特性.解析地得到了这种结构下波导模式场的精确解.模式场的性质因单轴晶体的性质不同而异.对于正单轴晶体,波导的主模是横电波,任何频率的光波均可激励该模式;当频率满足一定条件时,波导内传输单模,否则,将激励起高阶模式.高阶模既非TE波,也非TM波,而是两者耦合而成的混合模.对于负单轴晶体,波导的主模是一种混合模,该模式同样可被任何频率的光波所激励;当频率满足一定条件时,波导内传输单模,否则 关键词： 平面金属波导 单轴晶体 模式场 混合模     

Reconstruction of extraordinary refractive index profile of O ion-implanted LiNbO3 single-mode channel waveguide based on beam propagation method and image processing

A method bases on beam propagation method and image processing is brought forward to reconstruct the extraordinary refractive index profile of the ion-implanted single-mode channel waveguide in lithium niobate. Channel waveguide is formed by O²⁺ ion implantation at three energies of (3.0, 3.6 and 4.5 MeV) and respective doses of (1.8, 2.2 and 4.8) × 10¹⁴ ions/cm² in vacuum at room temperature. Only one enhanced-index mode is observed for extraordinary light at 1539 nm by prism-coupling method. TRIM’98 code is used to simulate the damage profile in channel waveguide. The modes pattern of TE and TM are measured by use of end-face coupling method.     

对称平面单轴晶体金属波导的模式场(1)

由于平面各向异性介质金属波导的重要应用,本文讨论了光在对称平面单轴晶体金属波导(波导层是单轴晶体,两个波导界面均为金属)内的传输特性.对于晶体光轴位于波导界面法方向与传输方向构成的平面内的特殊波导结构,利用麦克斯韦方程组并结合单轴晶体的性质,精确解出了波导模式场.结果表明:1)此种特殊结构波导内存在横电波(TE)和横磁波(TM);2)TM波的坡印廷矢量与波矢方向不在一条直线上;3)波导层为负单轴晶体时波导主模是TE波主模,而波导层为正单轴晶体时波导主模是TM波主模.     

Self-consistent theory of cyclotron autoresonance maser in a uniform planar waveguide

A general dispersion relation for the cyclotron autoresonance maser (CARM) that takes into account self-consistent couplings between TE, TM and ac space charge perturbations in a uniform planar waveguide is derived. The dispersion relation predicts enhanced growth rate due to ac space charge effects. Results from computer simulations of a planar CARM amplifier are presented to support this finding.     

Sensitivity enhancement in TE mode nonlinear planar optical waveguide sensor with metamaterial layer

The dispersion equation of the TE mode nonlinear planar optical waveguide with metamaterial layer was derived, and the sensitivity of the waveguide sensor was analyzed. The influences of structural parameters on the sensitivity of the waveguide sensor were investigated. We verify that the waveguide sensor with metamaterial layer can dramatically enhance the sensitivity compared with other waveguide sensors.     

Guided modes in slab waveguides with a left handed material cover or substrate

We study guided modes propagating along a dielectric slab waveguide with a left handed material (LHM) cover or substrate. The dispersion relation is derived by using normalized waveguide parameters. An analytical method is then proposed to calculate the universal dispersion curves. Different from a slab waveguide with a LHM core, we find that guidance properties are strongly dependent on dielectric permittivity ε and magnetic permeability μ of the substrate and cover layers. For oscillating guided modes, fundamental zero order mode is not always absence, sometimes it exists in a restricted range of normalized propagation constant. First order mode behaves as other higher order modes and exists up to infinite high frequency. Higher order modes have no double degeneracy in the case of LHM cover layer. For surface guided modes, the existence and the type of the mode solutions with respect to different parameters are classified systematically and discussed in detail. Unlike a slab waveguide with a LHM core where the dispersion curve of TE₁ surface mode continues with that of oscillating TE₁ mode, the dispersion curve of TE₁ surface mode continues with that of oscillating TE₀ mode. It seems that the two different kinds of modes compensate each other to form one whole mode. Both TE and TM guided modes are discussed.     

New method for calculating the spectra and radiation losses of leaky waves in multilayer optical waveguides

The efficiency of a new method for calculating the spectrum and attenuation coefficient of leaky electromagnetic modes is demonstrated with multilayer planar optical waveguides the guiding properties of which are determined by antiresonant reflection from the multilayer cladding (antiresonant reflecting optical waveguides) rather than by total internal reflection from the core-cladding interface as in standard optical waveguides. The new method applies to calculation of both electromagnetic modes in dielectric waveguides and electron quantum states in multibarrier semiconductor heterostructures. The characteristics of multilayer waveguides calculated by the new method are compared with published data obtained from a complex dispersion relation by the transfer matrix method. As an example, the wavelength dependence of the radiation losses for the first TE mode of a planar optical waveguide containing 52 pairs of layers is calculated.     

Analysis and calculation of planar waveguides with two-dimensionally periodic interface

General two-demensionally periodic interface (2DPI) model are proposed to describe a class of two-dimensionally periodic structure. Rigorous mode matching techniques show that the existence of 2DPI introduces only one scalar set of Fourier coefficients in terms of which the general formulation of mode voltages and currents on the both side of 2DPI can be established. Any planar waveguide with arbitrary number of periodic and flat interfaces can then be analyzed. The dispersion curves are presented and compared with those from other models.The Project supported by National Science Foundation of China.     

Characterization of optical waveguide in Nd: GdVO4 by triple-energy oxygen ion implantation

We report on the optical planar waveguide formation and modal characterization in Nd: GdVO₄ crystals by triple oxygen ion implantation at energies of (2.4, 3.0, and 3.6 MeV) and fluences of (1.4, 1.4, and 3.1)  × 10¹⁴ions/cm². The prism-coupling method is used to investigate the dark-mode property at wavelength of 632.8 nm. The refractive index profiles of the waveguide are reconstructed by an effective refractive index, n_eff method. The modal analysis shows that the fields of TE modes are well restricted in the guiding region, which means the formation of nonleaky waveguide in the crystal.     

Full-vectorial analysis of bending waveguides using finite difference method based on H-fields in cylindrical coordinate systems

A full-vectorial (FV) analysis of optical dielectric waveguide bends by using finite difference (FD) method in terms of magnetic field components is developed in a local cylindrical coordinate system. The perfectly matched layer absorbing boundary conditions via the complex coordinate stretching technique are incorporated into the FV wave equations for effectively demonstrating the leaky nature of waveguide bends, and a six-point FD scheme is constructed to approximate the cross-coupling terms for improving the convergent behavior. The leaky modes of a typical rib waveguide bend are calculated and the complex propagation constants and the field patterns for TE- and TM-like modes are obtained. Solutions are good agreement with those from the film mode matching method, which shows the validity and utility of the established method.     

紧凑型圆极化模式转换器

 提出了一种结构紧凑的、能将圆波导TM01模或同轴波导TEM模转换为圆极化TE₁₁模的高功率微波模式转换器。该转换器由前后2个十字转门波导结对接组成,前者首先把圆波导TM₀₁模转变为4个矩形波导中的TE₁₀模,4个矩形波导的长度不等;后者再把4个经过不同相位延迟的矩形波导TE₁₀模转变为圆波导中的圆极化TE₁₁模。对所设计的1.75 GHz模式转换器进行了仿真研究,在中心频率上,该模式转换器转换效率为99%,轴比为0.03 dB;在1.575~1.900 GHz的频率范围内,转换效率大于90%,轴比小于2.5 dB,对应带宽为18.6%。     

A Simple Bi-directional Mode Expansion Propagation Algorithm Based on Modes of a Parallel-plate Waveguide

The bi-directional mode expansion propagation algorithm (BEP) is known to be an accurate and efficient method for modelling field distribution in high-index contrast waveguide structures with strong back-reflections like Bragg gratings and photonic crystals. The main difficulty of this method is that for lossy structures, the propagation constants of modes are to be searched in the complex plane. To speed-up this procedure, a two-step algorithm for eigenmode calculation based on the expansion into the modes of an empty metallic waveguide has recently been proposed. Proper truncation rules possessing good convergence of the expansion method for both TE and TM modes have also been recently published. In this contribution, both these approaches are combined in the development of an extremely simple version of the two-dimensional BEP method that makes use of the field expansion into the eigenmodes of a parallel-plate waveguide. The method is strictly reciprocal and appeared to be computationally reliable also for strongly lossy structures. High numerical stability is ensured using the scattering matrix formalism, and an efficient method of calculating Bloch modes for symmetric as well as asymmetric periodic waveguide structures is adopted. A wide range of applicability of the method is demonstrated by a few examples.     

各向异性色散左手材料平面波导的导模特性(英文)

对芯层为左手材料而内外包层都是普通材料的非对称三层平面波导TE振荡模进行了分析.在考虑左手材料色散和各向异性的情况下,从Maxwell方程组出发,得到了TE振荡模的色散方程和功率流分布,并且画出了相应的色散曲线.我们找到了8个TE振荡模,而且包括基模.随着模阶数的增加,模色散曲线右移,功率流曲线下移.但是,随着波导厚度的增加,色散曲线左移,功率流曲线上移.此外,TE振荡模有反常色散特性和负的群速,这正揭示了左手材料的本质特性.     

Supermode dispersion and waveguide-to-slot mode transition in arrays of silicon-on-insulator waveguides

In this Letter, we report group index measurements of the supermodes of an array of two strongly coupled silicon-on-insulator waveguides. We observe coupling-induced dispersion that is greater than the material and waveguide dispersion of the individual waveguides. We demonstrate that the system transforms from supporting the two supermodes associated with two coupled waveguides to the single mode of a slot waveguide within the investigated spectral range. During the cutoff of the antisymmetric supermode, an anti-crossing between the symmetric TM and antisymmetric TE supermodes has been observed.     

各向异性色散左手材料平面波导的导模特性

对芯层为左手材料而内外包层都是普通材料的非对称三层平面波导TE振荡模进行了分析.在考虑左手材料色散和各向异性的情况下,从Maxwell方程组出发,得到了TE振荡模的色散方程和功率流分布,并且画出了相应的色散曲线.我们找到了8个TE振荡模,而且包括基模.随着模阶数的增加,模色散曲线右移,功率流曲线下移.但是,随着波导厚度的增加,色散曲线左移,功率流曲线上移.此外,TE振荡模有反常色散特性和负的群速,这正揭示了左手材料的本质特性.     

Vectorial electromagnetic modes in V-shaped dielectric waveguides with application to quantum wire devices

The properties of V-shaped optical dielectric waveguides are investigated in detail using a vectorial finite element method. The fundamental modes exhibit extremely tight, heart shaped near field patterns. The maximum intensity of the fundamental mode is found to be vertically shifted with respect to the geometrical center of the waveguide. Fundamental and higher order mode properties are extensively studied, including mode patterns, dispersion curves and polarization properties. The local mode polarization of the two fundamental modes varies from a horizontal (vertical) orientation at the groove center to TM (or TE respectively) far in the side wings. The optimal design of waveguides for GaAs/AlGaAs quantum wire diode lasers and Quantum Confined Stark Effect modulators grown on V-grooved substrates is discussed.     

Goos-Hänchen induced vector eigenmodes in a dome cavity

We demonstrate numerically calculated electromagnetic eigenmodes of a 3D dome cavity resonator that owe their shape and character entirely to the Goos-H?nchen effect. The V-shaped modes, which have purely TE or TM polarization, are well described by a 2D billiard map with the Goos-H?nchen shift included. A phase space plot of this augmented billiard map reveals a saddle-node bifurcation; the stable periodic orbit that is created in the bifurcation corresponds to the numerically calculated eigenmode, dictating the angle of its 'V.' A transition from a fundamental Gaussian to a TM V mode has been observed as the cavity is lengthened to become nearly hemispherical.