Effect of transition waveguides on dielectric waveguide directionalcouplers

The coupling of energy between two curved dielectric waveguides is investigated by the staircase approximation method, which combines the building-block approach of multimode network theory with a rigorous mode-matching procedure. Particular attention is directed toward two major effects of transition waveguides on the performance of directional couplers composed of dielectric waveguides: one is the change in the coupling length, the other is the radiation loss. The coupling problem is analyzed in terms of the scattering of an incident guided mode by the coupler structure as a whole. Numerical results are given to illustrate the coupling characteristics of various structures and to establish useful guidelines for the design of directional couplers     

Rigorous Analysis of Wide-Band Directional Coupler Using Π-Shape Dielectric Waveguide

Wide-band directional couplers using П-Shape dielectric waveguide in the parallel coupling region are investigated in detail by a rigorous mode matching method, both the eigenvalue problem of the coupled П-guide and the coupling characteristics of curved transition structure are solved accurately. Particular attention is directed toward the effects of transition waveguides on the scattering and coupling performance of the coupler to give useful guidelines for the design and optimization consideration. Finally, a 3-dB directional coupler is proposed with quite constant coupling factor (within ±0.5dB) throughout a wide frequency band from 34 GHz to 40 GHz.     

Full-wave analysis of cross-aperture waveguide couplers

This paper presents a full-wave analysis of coupling between rectangular waveguides through a cross-aperture. The rigorous mode-matching method is used to derive the generalized scattering matrix of a waveguide T-junction having a crossed waveguide as the side arm. Two three-port T-junctions are then cascaded together to form a number of cross-aperture couplers. The analysis method can handle both broad-wall and narrow-wall, both parallel and crossed coupling structures. Our numerical results for a variety of couplers are in good agreement with those obtained by Ansoft's HFSS     

圆柱共形缝隙阵

给出用圆弧弯波导耦合馈电的圆柱共形阵设计原理，重点是弯波导与扇面形直波导列之间的耦合孔列计算。耦合孔列同时控制辐波导的激励强度和补偿由于柱面缝隙射线程长度不等所引的相位差。     

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.     

Compound coupling slots for arbitrary excitation of waveguide-fedplanar slot arrays

A resonant coupling slot cut in the common broad wall of two crossed rectangular waveguides is analyzed. The slot is offset from the center line and tilted with respect to the longitudinal axis of the main waveguide, whereas it is centered-tiled in the branch waveguide. It is shown that the slot offset and tilt control the branch waveguide excitation amplitude with a phase variability of 360°. Pertinent integral equations are developed, taking into account finite wall thickness. The integral equations are solved for the slot aperture electric field using the method of moments. Dominant mode scattering by the slot in both waveguides is obtained     

Enhancement of power transfer in periodic array of optical waveguides via intermediate Bloch states

A directional coupling mechanism between different waveguides in a periodic array of waveguides is suggested. The optical power transfer between two different waveguides is mediated by the coupling between zero-order modes of two of the waveguides and the second band of the periodic structure. Analytical solutions for the no-detuning (narrow band) and far-from-resonance cases are presented. The far-from-resonance case is shown to resemble a simple two-mode system with complete optical power transfer between the two waveguides, coupled by localized gratings. The transfer is mediated by the second band of the periodic structure. The transition length depends strongly on the shape of the perturbation, and depends exponentially on the distance between the waveguides, yet it allows us to transfer power from one waveguide to another at such distances, for which the transition via conventional directional tunneling mechanism is impossible. Our analytical results are supported by numerical calculations carried out for a model problem with realistic parameters.     

Fields in Waveguide Bends Expressed in Terms of Coupled Local Annular Waveguide Modes

The fields in waveguide bends with arbitrary curvature and cross section are expressed in terms of "local" annular modes. The coupling between the local mode amplitudes is derived by evaluating the differential scattering coefficients between two adjacent infinitesimal annular waveguides. Comparison of these solutions with an earlier analysis of the problem shows that the coupling terms for the local annular modes are smaller for gradually curved bends since they are proportional to the derivative of the curvature. Furthermore, the significant scattered annular modes are bunched more tightly about the incident mode. The coupled differentiaI equations for the annular mode amplitudes may therefore be solved by considering relatively fewer scattered modes.     

Coupling Characteristics of Nonradiative Dielectric Waveguides

An analytical method is presented for predicting coupling characteristics of dielectric strips in the nonradiative dielectric waveguide. Starting with an approximate but very accurate expression for the coupling coefficient between parallel dielectric strips, the scattering coefficients for nonuniform coupling structures are derived in simple closed-form expressions by taking the effect of the field deformation at the curved sections into account. The coupling coefficient of the nonradiative dielectric waveguide is found to be so large compared to those of other dielectric waveguides that complete power transfer can be attained with coupled polystyrene bends having a curvature radius as small as 20 mm at 50 GHz. The theory was verified experimentally for various coupling structures. As an application toward millimeter-wave integrated circuits, 0-dB couplers, quadrature hybrid couplers, and an in-phase power divider were constructed based on the present analysis. A comparison of theory and experimental data of these fabricated coupling circuits suggests that the effect of the nondegenerate modes in the straight and curved guides must be included in the analysis to further improve the theory.     

Coupling characteristics of two rectangular dielectric waveguides laid in different layers

The coupling characteristic of rectangular dielectric waveguides which lay in different, parallel layers and one waveguide crossed over the other one are studied. Step-like approximation and the variational method are used for calculating the coupling coefficient which varies with axial distancez. Electromagnetic field expression for the dielectric waveguide mode of rectangular cross section is newly introduced and used. Calculated coupling characteristics are compared with experimental results carried on 50 GHz band. The principle of crossed waveguides leads us to the new design concept of "multilayered integrated circuit."     

Integration of magnetooptical waveguides onto a III-V semiconductorsurface

Optical waveguides fabricated on a yttrium iron garnet (YIG) substrate are integrated onto a semiconductor surface by using ridge waveguides patterned onto a prefabricated recess in the YIG surface. The recess separates the waveguides from the semiconductor substrate with an air-gap. This structure makes it possible to avoid coupling light within the YIG waveguides into the semiconductor substrate which has a higher refractive index. The excess optical loss due to the coupling can be as low as ⩽0.1 dB/cm with a 1-μm-wide air-gap. The calculated coupling loss is confirmed by comparing the guided TE and TM modes     

Hollow dielectric waveguide for distributed feedback lasers

Hollow dielectric waveguides with gas-filled core and a dielectric tube seem promising as laser structures. The tube fulfills the dual role of a guidance structure for the electromagnetic radiation as well as that of a container for the plasma of the gas laser. Feedback for laser oscillation is achieved by providing coupling between forward- and backward-traveling modes by means of periodic ripples of the inner surface of the hollow dielectric tube. This paper is devoted to the derivation of the coupling coefficients between two guided modes that are coupled by ripples in the tube wall. The calculation is based on the model of a slab waveguide. Expressions for the leaky-mode losses and the scattering losses inevitably introduced by the coupling mechanism are also presented.     

A theoretical study of semiconductor integrated etalon interference lasers--Part I: Waveguiding properties and intermodal coupling analysis

We present a theoretical study of semiconductor interferometric lasers, having a resonator with curved and straight segments, in two parts. In this first part, the wave equation in a curved dielectric waveguide is solved by applying the conformal transformation method to develop design criteria for curved optical waveguides in integrated optics. An intermodal coupling analysis at the junction discontinuity between a curved and straight waveguide is carried out to define a scattering matrix representing lateral mode conversion and internal reflection at the junction. The results of the theoretical analysis reveal two important consequences: 1) an extremely low internal reflection coefficient for the fundamental lateral mode, and 2) an increased internal reflection into higher order lateral modes. This phenomenon leads us to the conclusion that the interferometric effect in integrated etalon interference lasers is caused by the participation of higher order lateral modes into the resonance process.     

Improving the characteristics of rectangular waveguide branchingsby cylindrical obstacles

The scattering matrix of a transition between one or two parallel rectangular waveguides and a larger rectangular waveguide which contains two metallic or dielectric cylinders is investigated by means of the orthogonal expansion method. Mathematical programming is applied in order to improve the characteristics of the branchings. Reflection at a rectangular step discontinuity can be reduced by 30 dB using metallic or dielectric obstacles. Using Teflon cylinders, coupling of a transition can be reduced by 40 dB without debasing reflection. Physical interpretations are given with the help of field patterns     

Higher order mode coupling effects in the feeding waveguide of a planar slot array

The effect of internal higher order modes in the feeding waveguide of a planar slot array is investigated. Both the centered-inclined coupling slot and the longitudinal-transverse coupling slot are considered. Method of moments solutions to pertinent coupled integral equations are investigated for arrays of coupling slots of the centered-inclined and longitudinal-transverse types between a main waveguide and crossed branch waveguides. It is demonstrated that, by including the TE/sub 20/ mode coupling in the analysis, most of the higher order mode effects can be accounted for in reduced height waveguides, whereas in waveguides of standard height there may be a small additional effect arising from the TE/sub 01/ mode coupling.<>     

Propagation loss in single-mode GaAs-AlGaAs microring resonators:measurement and model

We report propagation loss measurements in single-mode GaAs-AlGaAs racetrack microresonators with bending radii from 2.7 μm to 9.7 μm. The experimental data were found to be in good agreement with a physical-loss model which accounts for the bending loss, the scattering loss due to surface roughness on the waveguide sidewalls, and the transition loss at the straight-to-bend waveguide junctions. The model also enables us to identify the dominant loss mechanisms in semiconductor microcavities. We found that for racetracks with large bending radii (greater than 4 μm, in our case) the loss due to surface-roughness scattering in the curved waveguides dominates, whereas for small-radius rings, the modal mismatch at the straight-to-bend waveguide junctions causes the biggest loss. This result suggests that circular-shaped rings are preferable in the realization of ultrasmall low-loss microcavities. We also show that the round-trip propagation loss in small-radius racetrack microresonators can be minimized by introducing a lateral offset at the straight-to-bend waveguide junctions     

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.     

Analysis of coupling between two parallel dielectric waveguides

The coupling between two parallel dielectric waveguides with a finite coupling length is investigated. The ends of the waveguides are tapered in order to reduce the scattering losses. It is shown that the taper sections can be utilized to achieve an effective coupling which is insensitive to the coupling length, thus, providing a much greater tolerance for the design and manufacturing of coupling devices.     

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.     

Scattering at a Junction of Two Waveguides with Different Surface Impedances

We consider junction of two cylindrical waveguides and derive the scattering matrix when a single mode is incident in one of the two waveguides. We are interested primarily in the case of two corrugated waveguides with different longitudinal impedances, but the analysis applies also to waveguides with nonzero transverse impedances. It is shown that, under certain general conditions the infinite set of equations specifying the junction scattering coefficients can be solved exactly by the residue-calculus method. Very simple expressions are then obtained between the scattering coefficients and the propagation constants gamma/sub n/ and y/sub i/ of the modes in the two waveguides. These expressions, obtained previously only in special cases, are direct consequences of certain simple relations derived here for the coupling coefficients between the modes of the two waveguides. In those cases in which the scattering coefficients cannot be determined exactly, we determine them approximately by a perturbation analysis.