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.     

Optical waveguide dispersion characteristics from the scalar wave equation

The electric and magnetic fields of an optical waveguide are well represented as derivatives of a linearly polarized vector potential. This vector potential obeys a scalar wave equation. Through the use of a variational principle one may obtain good approximations to the dispersion relation, however, without resolution of the birefringence. A simple perturbational approach yields the birefringence. Universal plots may be obtained in this way for TE and TM modes for rectangular channel waveguides with small index discontinuities.     

Birefringent properties of GaAlAs multiple quantum well planaroptical waveguides

Planar GaAlAs optical waveguides in which the waveguide core region is composed of multiple quantum wells are considered. Calculations of optical waveguide dispersion are performed to determine variations in effective refractive indexes for TE and TM modes and in the mode birefringence for large ranges of total waveguide thickness, number, and refractive index of well and barrier layers, and the ratio of well and barrier layer thickness. Ranges of these parameters which yield optical waveguides having unusually high birefringence and optical waveguides supporting single polarization planar propagation only are identified     

High-accurate computation of wave propagation in complex waveguides for microchip optical interconnections

In two-dimensional optical waveguides with the varied refractive index along the transverse direction, the wave propagation is accurately computed. The asymptotic mode solutions are taken as initial guesses for Rayleigh Quotation iteration. More accurate solutions by considering leaky modes and both wave propagation in the transverse electric (TE) and transverse magnetic (TM) are obtained. Numerical simulations demonstrate that the results from Rayleigh Quotation iteration with the asymptotic solutions are better than ones from Lapack solver when the norms of modes are large enough. Thus, it is the best way to combine the two solvers together. This method is particularly useful to the design and simulation of micro waveguide with core layer refractive index fluctuation.     

A wide-angle finite element beam propagation method with perfectlymatched layers for nonlinear optical waveguides

A beam propagation method (BPM) based on the finite element method (FEM) is described for the analysis of both transverse electric (TE) and transverse magnetic (TM) waves propagating in nonlinear optical waveguides. A perfectly matched layer is introduced to avoid spurious reflections from computational window edges. For the wide-angle beam propagation analysis, the Pade approximation is introduced to the differential operator along the propagation direction. In order to improve numerical accuracy and efficiency, a finite element mesh and a reference refractive index are adaptively renewed at each propagation step, and to reduce computational effort for the nonlinear optical waveguide analysis, an iterative algorithm is also introduced. Waveguides with nonlinear self-focusing claddings are analyzed to investigate spatial soliton emission phenomena, and it is confirmed that soliton couplers can be easily constructed     

Numerical analysis of integrated acoustooptic tunable filters withweighted coupling

A numerical approach based on the finite element method (FEM) and the beam propagation method (BPM) is newly formulated for design and modeling of integrated acoustooptic tunable filters (AOTF's) with weighted coupling on a piezoelectric substrate. First, acoustical field profiles in the substrate region and on the substrate surface are separately calculated with FEM and BPM, respectively. These two-dimensional (2-D) profiles are used for constructing three-dimensional (3-D) strain and electric field profiles. Then, from the strains and electric fields the refractive index changes due to acoustooptic (AO) and electrooptic (EO) effects are derived. Finally, by analyzing modified optical waveguides with AO8- and EO-induced changes in refractive indexes using again BPM, optical filter characteristics of AOTF's can be evaluated. Numerical examples are shown for AOTF's with a tapered acoustical directional coupler on a LiNbO₃ substrate     

Local field analysis of bent graded-index planar waveguides

A local field analysis is proposed for bent planar waveguides with arbitrary refractive index profiles. Exact vector wave equations that include the gradient index, or polarization correction, term are derived for both transverse electric and transverse magnetic modes from Maxwell's equations in a local bent coordinate system. The approximate local field and correction to the propagation constants are obtained by perturbation analysis. As an example of the method, an infinitely extended parabolic index profile is studied     

Birefringence suppression of UV-induced refractive index with grooves in silica-based planar lightwave circuits

An effective method for suppressing the birefringence of a UV-induced refractive index change is demonstrated for phase trimming of waveguides in planar lightwave circuits. By employing grooves on both sides of the waveguide to control the UV-induced strain, a significant reduction is achieved from 1.46/spl times/10/sup -4/ to 0.11/spl times/10/sup -4/ in the UV-induced birefringence for a /spl pi/ phase shift averaged between the TE and TM modes in a 2 mm-long waveguide.     

Leaky modes of optical waveguides with varied refractive index for microchip optical interconnect applications – Asymptotic solutions

In two-dimensional optical waveguides with the varied refractive index, approximate analytic solutions of the leaky modes are derived by using an asymptotic analysis for both transverse electric (TE) and transverse magnetic (TM) modes. Numerical simulations show that the asymptotic solutions of the leaky modes are quite close to the exact ones. The results are useful in the eigenmode method, where the leaky modes appear if a perfectly matched layer (PML) is used to terminate the transverse directions of optical waveguides.     

Fabrication and Evaluation of Nano-Scale Optical Circuits Using Sol-Gel Materials With Photo-Induced Refractive Index Variation Characteristics

Nano-scale optical circuits with core thickness of ~ 230 nm and core width of ~ 1 mum were fabricated and evaluated, using the photo-induced refractive index variation sol-gel materials, whose refractive index gradually increases by UV light exposure and baking. Propagation loss of linear waveguides was 1.86 dB/cm for TE mode and 1.89 dB/cm for TM mode at 633 nm in wavelength, indicating that there were small polarization dependences of ~ 0.03 dB/cm. Spot sizes of guided beams along core width direction and along core thickness direction were, respectively, 0.6 and 0.3 mu m for both TE mode and TM mode. Bending loss of S-bending waveguides was reduced from 0.44 to 0.24 dB for TE mode with increasing the bending curvature radius from 5 to 60 mu m. Although the bending loss for TM mode was slightly higher than that for TE mode, the difference was less than 10%. Branching loss of Y-branching waveguides was reduced from 1.33 to 0.08 dB for TE mode, and from 1.34 to 0.12 dB for TM mode with decreasing the branching angle from 80deg to 20deg. From these results, it is concluded that the photo-induced refractive index variation sol-gel materials can realize miniaturized optical circuits with sizes of several tens of microns and guided beam confinement within a cross section area less than 1.0 mum² with small polarization dependences, indicating potential applications to intra-chip optical interconnects.     

Application of Generalized Characteristic Vectors to Problems of Propagation in Clad Inhomogeneous Dielectric Waveguides

A transformation matrix that uses generalized characteristic vectors is used to convert Maxwell's equations into a set of loosely coupled equations for the wave amplitudes. This transformation is suitable for permittivity profiles with turning points. In earlier full-wave solutions to these equations, several special functions that account for the local features of the permittivity profile, especially near the turning points, were used to obtain appropriate expansions of the fields. The transverse field components, the propagation coefficients, as well as the phase and group velocities, are computed for both horizontally polarized (TE) and vertically polarized (TM) modes of the dielectric waveguides using the full-wave approach. These solutions are compared with analytic solutions for waveguides with special permittivity profiles. They are also compared with recently published results based on a perturbational approach.     

Design of optical strip-loaded waveguides with zero modalbirefringence

Integrated optic devices are usually sensitive to the polarization state of light, because the two polarized modes of the waveguides that form the devices in general have different propagation constants and may also suffer from different losses. The performance of such devices becomes unstable when they are connected to single-mode fibers, as the polarization state of the output light from a practical fiber link usually fluctuates in an unpredictable manner. A simple solution could be provided by using waveguides in which the two polarized modes are degenerate, i.e., have equal propagation constants. In this paper, it is shown theoretically with the spectral index method that the quasi-transverse electric (TE) and quasi-transverse magnetic (TM) modes of a properly designed optical strip-loaded waveguide can have equal propagation constants. The conditions for achieving mode degeneracy, or zero modal birefringence, are presented and discussed. Strip-loaded waveguides with degenerate polarized modes can be used potentially for forming polarization-insensitive optoelectronic devices     

Low-loss fluorinated poly(arylene ether sulfide) waveguides withhigh thermal stability

Some novel cross-linkable fluorinated poly(arylene ether sulfides) (FPAESI) were synthesized for use in optical waveguide applications. The materials have high thermal stability, high optical transparency in the infrared communication region, and much less birefringence than other thermally stable fluorinated polyimides. The refractive index of FPAESI after storage at 100°C for 1000 h remains almost constant, demonstrating their thermal stability. Furthermore, the refractive index of the material can be easily controlled by changing the fluorine content of the materials. The propagation loss of channel waveguides, which were fabricated using reactive ion etching was less than 0.42 dB/cm and 0.4 dB/cm at the wavelength of 1.55 μm for TE and TM polarizations, respectively     

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     

An integrated optic adiabatic TE/TM mode splitter on silicon

A compact integrated optic fundamental TE/TM mode splitter, based on the mode-sorting characteristics of an asymmetrical adiabatic Y junction of optical waveguides exhibiting shape birefringence, operating at 1550 nm, is designed, using the discrete sine method (DSM) and the beam propagation method (BPM). The structures are fabricated in a system of SiO₂, SiO_xN_y, and Si₃N ₄ layers, using a low-temperature plasma-enhanced chemical-vapor deposition (PECVD) process, compatible with standard silicon IC processing     

月形波导和加片圆波导的解析分析

采用模匹配方法分析了月形波导和加片圆波导的截止频率。波导中的场采用半数阶Bessel函数展开并令其满足边界条件,从而获得截止频率的特征方程国。根据本文所给公式可求解任意尺寸的月形波导、倒月形波导和加片圆波导的截止频率,并获得稳定的、具有高精度的解。     

Measurement of depolarization ratio and ultimate limit ofpolarization crosstalk in silica-based waveguides by using a POLCR

A polarization optical low coherence reflectometer (POLCR) is described that enables us to excite only the transverse electric (TE) mode of a test waveguide and to measure its Rayleigh backscatter signal distributions in the TE and transverse magnetic (TM) modes at a spatial resolution of 0.3 mm. The depolarization ratios of silica-based waveguides with relative refractive index differences of Δ=0.45 and 0.75% are obtained as 0.14 and 0.10, respectively, by measuring the bias in the ratio between the distributions in the TM and TE modes of each waveguide. By using the depolarization ratios and the Rayleigh backscatter signal levels, we calculate the ultimate polarization crosstalks to be -53 and -51 dB over 1 km, respectively. The actual polarization crosstalks of previously fabricated waveguides are about 50 dB higher than their ultimate limits for the same length of fiber     

Combination of beam propagation method and mode expansionpropagation method for bidirectional optical beam propagation analysis

A combined method of the beam propagation method (BPM) and the mode expansion propagation method (MEPM) is proposed for the analysis of reflections of both transverse electric (TE) and transverse magnetic (TM) polarized waves in waveguiding structures containing longitudinal discontinuities. BPM based on the finite-element method (FEM) is applied to slowly varying regions and MEPM is applied only to regions including abrupt discontinuities. FEM is also utilized for evaluating the eigenmodes necessary for the MEPM analysis. To show the validity and usefulness of the present approach, numerical examples for a semiconductor laser facet with antireflection coating and an optical directional coupler are presented     

Improved Bend Loss Formula Verified for Optical Fiber by Simulation and Experiment

This paper presents an improved curvature loss formula for optical waveguides, which is shown to accurately predict the bend loss of both single-mode and multimode fibers. The formula expands upon a previous formula derived by Marcuse, greatly improving its accuracy for the case of multimode fiber. Also presented are the results of bent fiber simulations using the beam propagation method (BPM), and experimental measurements of bend loss. Agreement among simulation, formula and measurement support the validity of both theoretical methods. BPM simulations showed that the lowest order modes of the bent fiber were reduced to their linearly polarized constituents prior to the onset of significant bend loss. This implies that certain LP mode orientations should propagate with much lower loss than previously expected, and should impact the mode stripping ability of bent large mode area fibers, as employed in fiber lasers and amplifiers.     

Stress-induced polymer waveguides operating at both 1.31 and 1.55 /spl mu/m wavelengths

Metal-defined polymer optical waveguides have been demonstrated for the first time. A metal strip patterned on top of a polymer slab waveguide causes a stress-induced refractive index change, providing lateral optical mode confinement within the core layer. Fabricated waveguides exhibit low propagation loss values of 1.1 dB/cm at 1.31 /spl mu/m and 1.3 dB/cm at 1.55 /spl mu/m for both TE and TM polarisations.