Scalar BPM analyses of TE and TM polarized fields in bent waveguides

We have applied the effective index method to reduce the two-dimensional (2-D) refractive index profile into the 1-D refractive index structure and modified the wave equations to obtain the paraxial wave equations. Then, transverse electric (TE) and transverse magnetic (TM) polarized fields in the curved single-mode planar waveguides are analyzed by using the scalar beam-propagation method (BPM) employing the finite-difference method with a slab structure. The bending loss in bent waveguides is analyzed for optical fields obtained from the BPM and comparisons are made between the loss for the waveguides with various radius of curvature and refractive index difference. The outward shift of the optical field, which is generated at the connection between a straight and a bent waveguide, is obtained from the results of calculation of location of the maximum optical intensity. The transition loss can be reduced by introducing an optimized inward offset at a straight-to-bend junction. The birefringence for TE and TM polarized fields in bent waveguides is calculated from the phase difference of the optical fields. The wavelength shift due to the birefringence of TE and TM polarized fields in bent waveguides is also calculated.     

“Total” internal reflection of a beam-wave at a curved interface

The partial transmission of a cylindrical wave at a cylindrical interface between two different media is discussed, and is used as the basis for a new derivation of a power transmission formula previously derived for locally-planewaves by Snyder and Love. The formula is applied to the case of a Gaussian beam wave, and the relevant power transmission coefficient is obtained. The power transmission coefficient for a beam wave incident on a plane interface is also derived. It is shown that leakage due to spread of the angular plane-wave spectrum beyond the critical angle may well be much greater than that due to curvature when the radius of the curvature is large.     

Study and Design of Spiral Bent Waveguide Configuration

A new version of the scalar transverse electric（TE） wave equation in the bent waveguide is introduced. Then. TE polarized field in curved single-mode waveguides is analyzed by using the finite- difference beam propagation method（FD-BPM）. The bending loss in bent waveguides is gotten for the optical fields obtained from BPM and comparisons are made among losses of the waveguides with various curvature radiuses, refractive index differences and cross sections. Based on the results, the design of spiral bent waveguide configuration is proposed as follows： refractive index difference being of 0. 007, both width and thickness of waveguides being of 6 μm, the curvature radius in the spiral centre being of 4 mm, and the bending loss coefficient of the designed spiral bent waveguide being of 0. 302 3 dB/cm.     

Bending losses of multimode optical fibres

The bending loss of rays within circular and slab multimode optical waveguides is determined using only Snell's laws, the generalised Fresnel transmission coefficient and the Goos-Haenchen shift. The generalised transmission coefficient accounts for radiation losses, due to curvature, not included in Fresnel's classical laws.     

Generalised Fresnel's law for loss due to curvature

Many rays, predicted by Fresnel's laws to be totally reflected from a curved interface between two dielectric media, are only partially reflected. We derive a generalised Fresnel transmission coefficient to account for this loss. Our transmission coefficient applies to an arbitrary surface; e.g. one defined by two arbitrary radii of curvature. It can be used to determine radiation loss from bent and straight circular optical fibres.     

Analysis of a phase mismatched three waveguide coupler with an optical amplifier

A novel optical amplifier is proposed and analyzed. This device consists of three parallel waveguides and each has a slightly different propagation constant, that is, each waveguide is slightly phase mismatched and couplings among these waveguides are weak. Two adjacent waveguides are passive and the third one is active and all end facets of waveguides are antireflection coated, so that optical feedback can be eliminated and the active waveguide is a traveling wave type amplifier. Because of a phase mismatched configuration, this device can be used to tap optical signals without much power reduction in optical transmission lines. Signals coming into the device are weakly coupled to the active waveguide via the passive waveguide in between and they are amplified through the active waveguide. Characteristics of this device are studied and parameters which are required to design the device are also given as an example.     

Analysis of butt coupling in photonic Crystals

We present a detailed analysis of butt coupling from conventional dielectric waveguides into photonic crystal waveguides. Closed-form expressions for the reflection and transmission matrices based on an eigenmode expansion technique are derived and validated by means of simulations. We use them to investigate butt-coupling losses in two kinds of photonic crystal structures: one formed by rods with a higher refractive index than the surrounding medium and the other formed by air holes inserted in a high-refractive-index medium. The origin and difference of coupling losses between the two photonic crystal structures is analyzed and discussed. We show that, although the coupling efficiency is much worse in the former structure, it can be significantly improved by choosing the optimum interface position that minimizes the mode impedance mismatch. Furthermore, the dependence of coupling efficiency on frequency is also analyzed. Finally, we also relate some traditionally used approximate formulas to our rigorous expressions.     

Ray Methods for Trapped and Slightly Leaky Modes in Multilayered or Multiwave Regions

Ray-optical techniques presented previously by the authors for study of mode propagation in homogeneously filled waveguides are extended to accommodate multilayered regions and regions capable of supporting multiple wave species. Emphasis is placed on a self-consistent ray treatment which illustrates alternative methods for dealing with ray coupling at boundaries and with the presence of multiple wave types, either in a single layer or in adjacent regions. Both closed and open structures are analyzed, with discussion of the latter limited to modes with small leakage due either to duct inhomogeneities or to curvature. Examples include layered dielectric waveguides with a straight or circular axis, and compressible plasma waveguides which are illustrative of media wherein two wave species (electromagnetic and electroacoustic) can propagate.     

AlGaAs-based two-dimensional photonic crystal slab with defectwaveguides for planar lightwave circuit applications

An AlGaAs-based near-infrared 2-D photonic crystal (PC) with an air-bridge structure featuring defect waveguides has been developed. For the sample without defect waveguides, measurements of the optical transmission characteristics in the wavelength range from 850 nm to 1100 nm showed a deep attenuation due to a bandgap with 30-35 dB attenuation and transmittance of nearly 100% for the guided modes. Optical propagation properties of defect waveguides were obtained by two methods: measurements of transmission spectra and plan-view observations of the optical beam trace along the waveguide with an infrared-vidicon camera. 3-D finite-difference time-domain simulations for the band structure and transmission spectra in the air-bridge slab with and without defect waveguides have revealed the appearance of four defect propagation modes specific to the defect waveguide, between two slab modes for the defect-free photonic crystal slab. These defect modes were experimentally identified in the measured transmission spectra     

Modal matching applied to a discontinuity in a planar surface waveguide

A modal-matching method is used to evaluate the transmission and reflection coefficients at a junction between two planar surface waveguides. Results are obtained for parameters which represent the junction between a solid-state laser and a planar optical waveguide. Favourable comparison is made with results obtained from an integral-equation method.     

Radiation losses from sinusoidal serpentine bends in optical waveguides

Radiation losses due to curvature in optical waveguides with sinusoidal bends are found in terms of the amplitude and period of the fluctuation. For tolerable loss, the critical factor is the minimum radius of curvature, i.e. the radius of curvature at a point of maximum deviation.     

弯曲光波导端面修饰的设计方法

光波导的弯曲损耗一直是集成光学中一个值得人们重视的问题,为有效地减小光波导弯曲损耗,弯曲光波导的设计成为集成光学波导设计中的一个重要内容.本文在弯曲光波导保形变换方法的基础上,应用几何光学分析方法给出了波导弯曲损耗产生的简洁的物理图像,从而深入地分析了弯曲损耗产生的根本原因,并由此提出了弯曲光波导端面修饰的设计方法.理论分析表明,与传统的弯曲的光波导设计相比,该种设计方法可以有效地减小导波的模式泄漏,从而减小波导弯曲损耗.尤其是在弯曲光波导曲率半径、材料折射率等参数被设定的情况下,该种设计方法成为一种有效的设计方法.     

对称结构光子晶体表面Tamm态的光学性质

利用传输矩阵理论和等效原理,从能级的角度研究对称结构光子晶体表面Tamm态的光学性质,结果表明:在有限排列周期结构光子晶体中,介质表面可支持表面Tamm态的存在,且轴向传播时通带中出现TM和TE偏振的能级简并现象,离轴传播时从通带边缘分离出来的非简并能级被局域于光子晶体表面而形成了光学Tamm态；表面Tamm态内存在很强的局域电场,而且局域电场在介质界面处分布最强；表面Tamm态内的能量输运,对于低折射率介质可正反两方向输运,且输运速度快,对于高折射率介质只能正向输运,且输运速度较慢,故在高折射率介质界面处形成很强的局域光场。对称结构光子晶体表面Tamm态光学性质可为光子晶体光波导和表面波传感器的研究和设计提供指导。     

Design of a nanoelectromechanical high-index-contrast guided-wave optical switch for single-mode operation at 1.55 /spl mu/m

A design is presented for a nanoelectromechanical optical switch based on the horizontal deflection of an input waveguide to align with one of two output waveguides. The use of high-index (GaAs) strip waveguides surrounded by air, designed to be single-mode at 1.55 /spl mu/m, significantly decreases device dimensions as compared to previous designs. Design tradeoffs between optical and mechanical properties of the device are discussed. By means of three-dimensional numerical simulations, optical transmission is optimized for two different design strategies: butt and parallel coupling. High polarization-independent transmission (over 90%) is predicted for realistic design parameters.     

GaAs/GaAlAs curved rib waveguides

Curved dielectric optical waveguides suffer from radiation loss due to bending. To minimize the bending loss and reduce the radius of curvature, it is necessary to fabricate guides which provide strong optical confinement. This paper gives a brief review of curved waveguide analysis and presents some experimentally measured loss values for GaAs/GaAlAs curved rib waveguides. The rib waveguides, fabricated using ion beam milling, have a large rib height and are tightly guided structures. When corrected for reflection losses and input coupling efficiency, a minimum loss of approximately 3 dB has been achieved for a multimode 90° curved guide with a radius of curvature of 300 μm, and 8.5 dB for a single-mode curved guide with a radius of curvature of 400 μm. It is believed that most of this residual loss is not radiation loss due to bending, but rather scattering loss due to rib wall imperfections.     

Optical transmission losses in polycrystalline silicon strip waveguides: Effects of waveguide dimensions, thermal treatment, hydrogen passivation, and wavelength

Signal propagation delays dominate over gate delays in the ever-shrinking ultra large scale integrated (ULSI) circuits. Consequently, silicon-based monolithic optoelectronic circuits (SMOE) with their light speed signal propagation can provide unique advantages for future generations of microprocessors. For such SMOE circuits, we need optical interconnects compatible with silicon technology. Strip waveguides consisting of polycrystalline silicon (polySi) clad with SiO₂ offer excellent optical confinement and ease of fabrication that are ideal for such interconnect applications. One major challenge with using this material system, however, is its insertion loss. In this paper we provide techniques for minimizing optical transmission losses in polySi strip waveguides. Our previous work using polySi strip waveguides, showed an optical transmission loss of 15 dB/cm at λ=1.55 μm, which is a communication wavelength of choice in optical fibers because it represents an absorption minimum. Similar measurements in crystalline silicon strip waveguides¹ yielded transmission losses of less than 1 dB/cm. Hitherto, in decreasing loss from 77 dB/cm to 15 dB/cm, we had minimized loss from surface scattering by improving the film surface morphology, and decreased bulk absorption with hydrogen passivation. In this paper we report a further reduction in the residual bulk loss from 15 dB/cm to 9 dB/cm. By experimenting with different waveguide core dimensions, we find that the contribution of bulk loss towards net transmission loss decreases with waveguide core thickness. Additionally, high temperature treatment provides strain relief in the polySi, decreasing transmission loss. Annealing in an oxygen ambient is not recommended because it always increases transmission loss. Hydrogen passivation improves transmission, attributable to passivation of light-absorbing dangling bond defect sites present at polySi grain boundaries. Together, these methods have resulted in the lowest measured loss value of 9 dB/cm at λ=1.55 μm. Since integrated SiGe and Ge photodetectors are more efficient at shorter wavelengths like λ=1.32 μm, transmission loss is also measured at λ=1.32 μm. Losses at the two wavelengths (1.32 μm and 1.55 μm) are similar when defects and stress in the waveguides are minimized.     

基于三平行光子晶体波导的多功能功分器研究

采用时域有限差分法研究三平行光子晶体直波导的传输特性及模场分布,结合耦合模理论计算光子晶体波导的耦合系数.计算结果表明,在高频段(0.33～0.42)(ωa/27πc)的范围内两耦合波导与主波导表现出相互的能量交换,实现光耦合,耦合系数随入射波频率增加而减小;而在低频段(0.31～0.33)(ωa/2πc)的范围内,两耦合波导与主波导的传输谱图同步变化,耦合波导的传输光强均约为入射光强的四分之一.最后,提出一种采用固定波导耦合长度同时实现超微结构光均分器及1/4功分器的方案,当耦合长度取L_c=(2n+1)π/2 K时,两耦合波导可将高频段相应入射波实现均分,同时将低频段中的任意入射波实现1/4功分.

Abstract：

The propagating characteristics and mode profiles of three parallel photonic crystal waveguides are studied by using finite-difference time-domain method, and the coupling coefficient between the parallel photonic crystal waveguides is obtained with coupled-mode theory. Numerical results demonstrate that for a high frequency range of (0.33～0.42)(ωa/ 2πc), they exchange energy with each other and the optical coupling is realized, the coupling coefficient decreased with the increase of input frequency; while at a low frequency range of (0.31 ～0.33) (ωa/2πc), the mode profiles of the coupling waveguides and main waveguide are changed synchronously, and the coupling waveguides propagating intensity occupies a quarter of the incident intensity. Finally, a solution realizing the ultracompact optical power equalizer and 1/4 optical beam splitter is proposed using a certain coupling length, when the coupling length is L_c= (2n+1)π/2 K, the corresponding incident wave with high frequency can be equalized, meanwhile the wave power with arbitrary frequency at low frequency can be quartered within the two coupling waveguides.     

Lateral wave propagation in a wedge shaped region

Lateral wave propagation in a wedge shaped region is examined. The geometry consists of two media, the lower one of which is bounded from below by a conducting plate. The plate intersects the interface between the two media from below at an oblique angle. The transmitting antenna is an infinite, time harmonic, electric line source located close to the interface between the two media, and oriented to make the problem two dimensional. The wavenumber of the upper medium has a magnitude which is much greater than that of the lower medium. The lateral wave travels downward from the source into the second medium, along the interface, and back up to the point of observation in the first medium. The problem cannot be easily solved in closed form as the boundary conditions at the interface do not permit solution by separation of variables techniques. An approximate analytical method is therefore used in which the two media are separated from one another at each step of an iterative procedure using impedance boundary conditions. The simpler single medium problems which result are more amenable to analysis. The lateral wave field is expressed either as a modal series or image series depending on the angle the plate makes with the interface and on the location of the source and receiver. The decay of the wave in the direction parallel to the interface is shown to be algebraic, even in the presence of the plate. The results are valid subject to the restrictions that the source and receiver are close to the interface and are not too close to each other or the edge of the plate. There will be other waves present which are not considered in this paper if the upper region is not conducting, although the expression for the lateral wave remains valid.     

Non-evanescent adiabatic directional coupler

A directional coupling mechanism based on an adiabatic coupling between three optical modes is suggested. The optical power transfer between two waveguides which are far apart is mediated by adiabatic coupling between zero-order optical modes of the individual waveguides and a high-order intermediate mode. The analytical model for an adiabatic three-mode coupling based on a scalar wave equation is presented. The directional coupling via the adiabatic mode coupling between copropagating modes is described and compared with a nonadiabatic directional coupling assisted by periodic perturbation. It is shown that adiabatic directional coupling has much less sensitivity to the mode parameters and to the wavelength     

Low-loss single-mode GaAs/AlGaAs miniature optical waveguides withstraight and bending structures

Low-loss single-mode GaAs/AlGaAs miniature optical waveguides fabricated for use in monolithically integrated optical circuits are discussed. The propagation characteristics of these waveguides with straight and S-bending structures have been investigated at wavelengths of 1.30 and 1.55 μm. The lowest propagation losses are estimated to be 0.58 dB/cm and 0.69 dB/cm at wavelengths of 1.30 and 1.55 μm, respectively. The total loss of an S-bending waveguide with a curvature radius of 2 mm and with a lateral displacement of 200 μm was 0.61 dB and 0.46 dB at wavelengths of 1.30 and 1.55 μm. The fabricated single-mode strip-loaded waveguides proved to be suitable for application of the semiconductor waveguide into monolithically integrated optical circuits