A normalized approach to the design of low-loss optical waveguidebends

A normalized approach for optimal design of abrupt junctions between straight and curved waveguides operating in the whispering gallery mode regime is presented. The optimization includes the widths of both the straight and the curved waveguides, the lateral offset between them, and the bending radius of the curved waveguide. With this approach, optimum bend design is possible from a simple set of formulas or normalized graphs. Predicted transmission losses for optimally designed junctions are well below 0.1 dB     

Calculation of bending losses in dielectric waveguides usingeigenmode expansion and perfectly matched layers

In this letter, we present a different approach to accurately calculate the bending losses in curved dielectric waveguides. It is based on the well-known conformal transformation of the index profile and on vectorial eigenmode expansion, but this time with perfectly matched layer (PML) boundary conditions to accurately model radiation losses. The modal spectrum of these waveguides in the presence of PML is discussed and the method is validated by comparing it to previously published results     

Anomalous radiation loss of curved dielectric ridge waveguides

The radiation loss of curved ridge dielectric waveguides can show an oscillatory dependence on radius for the TM-polarisation. This effect is predicted only by a three-dimensional full vectorial analysis and is confirmed experimentally in S-bend dielectric ridge waveguides     

Low-loss straight and curved ridge waveguides in LPE-grown GaInAsP

Loss measurements on ridge waveguides in LPE-grown GaInAsP at a wavelength of 1.3 mu m are presented. An attenuation of 4.5 dB/cm has been obtained for straight waveguides, and for curved waveguides an excess loss at low as 0.7 dB was found for a 20.8 degrees S-bend with a radius of 300 mu m ( approximately=1.5 dB/90 degrees ).<>     

Numerical optimization procedure for low-loss sharp bends in MgOCo-doped Ti:LiNbO3 waveguides

Recent results provided experimental evidence that losses in bent Ti:LiNbO₃ waveguides can be drastically reduced by using additional titanium and magnesium oxide. We determine an optimization procedure for the index profile in curved sections. The beam propagation method indicates that in optimized bends, losses are orders of magnitude below those of conventional bends. Tolerances in mask alignment and in deposited film thickness are estimated to be well compatible with present technology     

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.     

The impact of CMP and underlying back-end topographical features on losses in deposited dielectric waveguides

The bending losses in rectangular dielectric waveguides deposited on a chemical mechanical polished (CMP) surface above the metal interconnect/interlayer dielectric stack of a processed Si wafer are modeled and estimated. CMP efficiently removes local topography and microroughness, but leaves long-range surface profile undulations due to variations in the metal pattern density. These surface undulations are then transferred to the waveguides deposited on this surface. A beam propagation method (BPM) waveguide simulation program and an equation for bending loss developed by Marcuse have been used to examine the bending losses seen by waveguides deposited on such a surface. In order to simplify the simulation of the bending losses of the waveguides, the undulations are modeled as a series of arcs, which is shown to be a good approximation. It was determined that under typical conditions, the bending losses may be ignored as they are less than 0.1 dB/cm, which is below the range of typical propagation losses for a straight guide.     

Transmission characteristics of germanium thin-film-coated metallichollow waveguides for high-powered CO2 laser light

Various losses such as straight waveguide losses, coupling losses from a CO₂ laser, and bending losses are studied. The authors studied the fact that high-powered CO₂ laser light could be transmitted through germanium-coated waveguides and investigated beam profiles from straight or bent waveguides. To ascertain the application of the waveguide in wavelengths other than 10.6 μm, the authors investigated the wavelength-dependent losses of the waveguide excited by incoherent IR light. As a result, the thickness of the deposited germanium layer can be very precisely obtained     

Circular Bends in Dielectric Frame Beam Waveguides (Short Papers)

An investigation is described on circular bends in beam waveguides constituted by dielectric frames. A uniform bending of the guide axis is obtained by tilting each frame by a small angle; however, due to the phase correction performed by the dielectric frame, the losses introduced by the bending can be made lower than those of an analogously bent iris waveguide. A numerical analysis is performed on the basis of the analogy between beam waveguides and open resonators which permits the assessment, in a number of cases, of the maximum permissible amount of tilting and the corresponding optimum frame dimensions in view of acceptable losses. The losses due to mode conversion are also evaluated when considering the connection between a straight and a curved section of the waveguide.     

Optimized offset to eliminate first-order mode excitation at thejunction of straight and curved multimode waveguides

Applications to equip semiconductor phased-array wavelength demultiplexers with nonbirefringent waveguides are increasing. In several applications, the waveguides are multimodal and elimination of first-order mode excitation is required for their design. The optimized offset for eliminating the first-order mode excitation at the junction of straight and curved waveguides with a two-dimensional (2-D) structure is analyzed theoretically. We assume that the waveguide has a laterally symmetric index profile. By the perturbation method, the offset is obtained to the first order in the inverse of the bending radius. The offset is simply expressed by the effective refractive indices of the straight waveguide     

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.     

Reflection at a Curved Dielectric Lnterface--- Electromagnetic Tunneling

The reflection of a locally plane wave from a curved interface between two nonabsorbing dielectric media is investigated. Our analysis is applicable to an interface of general shape, defined at each point by the two principal radii of curvature. When the wave is incident from the denser medium at angles greater than the critical angle it is only partially reflected, due to a form of electromagnetic tunneling. Generalized Fresnel transmission coefficients and an extension of Snell's law are derived to account for this transmission into the less dense medium. Ray tracing can then be applied to determine such phenomena as the bending losses in optical slab waveguides, and the curvature loss of skew rays within straight optical waveguides of circular cross section.     

Angled-Facet Spot-Size-Converter Integrated Semiconductor Optical Amplifiers Using Asymmetric Twin Waveguide Technology

The extinction ratio (defined as the difference in the optical power between 0-dB fiber-to-fiber loss and the off state level) is enhanced with the introduction of an S-bend waveguide structure using asymmetric twin waveguide techniques for a spot-size converter integrated semiconductor optical amplifier (SSC-SOA) with a polarization-insensitive offset superlattice. Angled waveguides are introduced in order to obtain low facet reflectivity without the need for antireflection coating. A curved waveguide is introduced to connect the angled and straight waveguide, minimizing their coupling loss while achieving a lateral spatial mode filter. The SSC-SOA, operating at 1.62-mum wavelength, achieves an extinction ratio up to 70 dB and a fiber-to-fiber gain of 10 dB using cleaved, flat end single-mode optical fibers.     

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.     

Bends in Nonradiative Dielectric Waveguides

An experimental study was made of bends in the nonradiative dielectric waveguide (NRD-guide) at 50 GHz. The main cause of the bending losses was found to be due to the reflection at the transitions between the straight and curved waveguides rather than due to the radiation. The width of the dielectric strip was experimentally optimized in order to reduce the reflection, and a bend with a curvature radius as small as one guide wavelength could be realized. The experimental results are examined theoretically. The theory implies that the NRD-guide has a favorable tendency to suppress not only the radiation but also the reflection at the curved sections. It is also shown that the field maximum moves outwards or inwards from the mean path of the curved guide according to whether the dielectric strip is wider or narrower than a certain critical width. This critical width can be adopted as a design criterion for a low loss, very sharp NRD-guide bend.     

Coupling of surface waves by two crossed dielectric waveguides

The coupling of surface waves by two crossed dielectric slab sections with curved transition waveguides is investigated by the method of staircase approximation. the coupling problem of the nonuniform structure is analyzed in terms of the scattering of incident surface wave by the crossed structure as a whole. The scattering characteristics of the crossed waveguides are calculated with a particular attention directed to the effect of radiation due to bending of the curved transition waveguides on coupling properties of the structure. Some useful guidelines for the design of the coupling structures are thereby suggested.     

基于贝塞尔函数数值求解平面光波导的弯曲损耗

为了数值求解平面光波导的弯曲损耗,首先给出了平面弯曲光波导的传输模型。基于这种模型,使用基于求解贝塞尔函数的方法数值求解出平面光波导的弯曲损耗。为了验证该方法的准确性,将计算得到的弯曲损耗结果与以往的实验结果相比较,结果表明,在弯曲半径较大的情况下两者基本吻合。     

The method of lines applied to planar transmission lines incircular and elliptical waveguides

The method of lines (MOL) is utilized to analyze a class of planar transmission lines with circular or semicircular/elliptical metallic shielding. The authors show how the general MOL principles can be modified so that curved boundary structures can be included. Dispersion diagrams are presented for microstrip and slotline structures with curved metallic shielding as well as for their suspended counterparts in circular and elliptical waveguides. Results show that some of the structures have potential applications at millimeter-wave frequencies because losses in circular waveguide enclosures are generally lower than those in rectangular waveguides     

基于热光效应的1×4聚合物数字光开关

提出了基于热光型聚合物的集成有S弯曲光衰减器的1×4 Y分叉数字光开关.利用开关与光纤阵列耦合用的S弯曲,将其设计成可变光衰减器,这使得器件更紧凑,并获得低串扰和大分叉角.在小于200mW的驱动功耗下,器件串扰可低至-35dB.     

Monolithic integration of curved waveguides and channeled-substrate DH lasers by wet chemical etching

Integration of AlGaAs/GaAs curved waveguides and other two-dimensional waveguides with DH lasers and detectors is demonstrated. Devices are fabricated from LPE AlGaAs/GaAs layers by wet chemical etching processes. Differential transfer efficiencies ofeta_{t}= 5percent are routinely achieved in a structure consisting of an integrated laser, a 90° curved waveguide with 150μm radius, and a detector, for the case where one laser mirror is etched and one cleaved. This value iseta_{t}= 4percent if both mirrors are etched. A comparison of waveguide attenuation between straight and curved rib waveguides is given, along with the transfer characteristics of curved waveguides. The loss coefficient of curved rib waveguides with 150-μm radius is about two times that of a straight waveguide of the same length. The fabrication and properties of channeled-substrate crescent (CSC) lasers and detectors with transverse single-mode confinement, monolithically integrated by means of passive CSC interconnecting waveguides, is also described.