Explicit finite difference beam propagation method: application to semiconductor rib waveguide Y-junction analysis

A novel explicit finite difference beam propagation method is developed and applied to the analysis of a strongly guiding semiconductor rib waveguide Y-junction. Its accuracy is confirmed by comparison with reported results. This method is much more efficient than the standard beam propagation method for the rib waveguide analysis.<>     

Simulation of three-dimensional optical waveguides by a full-vectorbeam propagation method

Simulations of optical guided waves in three-dimensional waveguide structures by a full vector beam propagation method are described. Two sets of coupled equations governing the propagation of the transverse electric and magnetic fields are derived systematically. Polarization dependence and coupling due to the vectorial nature of the electromagnetic fields are considered in the formulations. The governing equations are solved subsequently by finite-difference schemes. The vector BPM is first assessed for a step-index circular fiber by comparing the numerical results with the exact analytical solutions. The guided modes of a rib waveguide are then investigated in detail. Comparisons among the scalar, semi-vector and full-vector simulations of the rib waveguide are made. Finally polarization rotation of a periodically loaded rib waveguide operated fully based on the vector nature of the electromagnetic waves is modeled and simulated     

Generalized propagation techniques-application to semiconductor ribwaveguide Y-junctions

The simulation of electric fields in strongly guiding semiconductor rib waveguide Y-junctions with a new, general operator identity which yields a series of practical and easily programmed fourth-order accurate propagation algorithms is described. While the methods require 3-6 times the computation time of standard procedures for a given propagation step, they are typically more precise by several orders of magnitude for reasonably small propagation step lengths. The exact ratio of CPU times required to achieve a given accuracy, however, is somewhat problem dependent. It is noted that the procedure has been generalized to all orders     

A rib optical waveguide with cutoff mesa isolation

A rib optical waveguide using the concept of optical cutoff to provide isolation between adjacent waveguides in a photonic integrated circuit is disclosed. Due to the evanescent nature of light propagation in cutoff waveguides, this cutoff mesa rib waveguide permits fabrication of single-moded rib waveguides with minimal self-interference and crosstalk by means of light guided in a remaining slab waveguide. Design rules are given and operation of a single-moded cut-off mesa rib waveguide and an MZI using this waveguide are demonstrated     

Finite element beam propagation method for three-dimensionaloptical waveguide structures

A beam propagation method (BPM) based on the finite element method (FEM) is described for longitudinally varying three-dimensional (3-D) optical waveguides. In order to avoid nonphysical reflections from the computational window edges, the transparent boundary condition is introduced. The present algorithm using the Pade approximation is, to our knowledge, the first wide-angle finite element beam propagation method for 3-D waveguide structures. To show the validity and usefulness of this approach, numerical results are shown for Gaussian-beam excitation of a straight rib waveguide and guided-mode propagation in a Y-branching rib waveguide     

Improved full-vectorial beam propagation method with high accuracy for arbitrary optical waveguides

An improved finite-difference (FD) full-vectorial beam propagation method is introduced for arbitrary optical waveguides with a dramatic improvement in accuracy. This method is developed based on the generalized Douglas scheme and a novel FD formula for the cross-coupling terms which, expressed in explicit form, is independent of specific types of waveguides. The present method is demonstrated for a strongly guiding rib waveguide.     

The design of triple rib waveguide couplers by the discretespectral index method

The operations of three-guide couplers are usually controlled by the width and refractive index of the guides. However, when rib waveguides are used in three-guide couplers and power dividers, we propose to use the dimensions of the ribs as the governing parameters instead. Formulating a new transcendental equation using the discrete spectral index (DSI) method, triple rib waveguide couplers are accurately analyzed for the first time. The new accurate and fast analysis of triple rib waveguides shows that the propagation constants of the various modes are dominantly controlled by the height of the middle rib. A systematic and simple procedure is consequently introduced to design quasi-transverse electric (TE) polarized triple rib waveguide couplers, which ensures maximum power transfer from one outermost guide to the other outermost guide. For triple rib power dividers, the height of the middle rib is found to control the amount of power that can be transferred from the excited middle rib waveguide to the two outer rib waveguides. Maximum power division is achieved when the three ribs of the waveguide are identical     

Analysis of Z-invariant and Z-variantsemiconductor rib waveguides by explicit finite difference beampropagation method with nonuniform mesh configuration

An efficient and simple explicit finite difference beam propagation method (EFD-BPM) incorporating nonuniform mesh is described. The criteria for stability are developed, and it is shown that this algorithm is power conserving when the stability criteria are met. EFD-BPM is applied to the analysis of single and coupled semiconductor rib waveguides and its accuracy is confirmed by comparing the results with the reported results. Nonuniform mesh is found to improve the efficiency of the method significantly for the analysis of weakly guiding waveguide structures. Several coupled rib waveguide structures with curved input and output branching sections are analyzed using both three-dimensional EFD-BPM and two-dimensional finite difference BPM combined with effective index approximation     

Structure optimization of polymeric Mach-Zehnder rib waveguide

The polymeric material is very promising for fabricating the integrated optical waveguide devices. The polymeric op- tical waveguide has become the hotspot because the poly- meric material can offer a series of merits, such as easy integration, rapid resp…     

Radiation modes and step discontinuities in dielectric ribwaveguide

The continuous spectrum of the rib waveguide is derived by a method that ensures orthonormality and completeness of the spectrum. A relatively simple approximation of this continuum for most cases of common interest is obtained. The theory is applied to the abrupt step discontinuity in the E-plane of the rib guide under LSE polarization and to the abrupt termination problem, including radiative effects never before investigated     

SOI波导弯曲损耗影响因素的分析

采用有效折射率方法EIM(effective index method)和二维束传播算法（2D-BPM）对SOI (silicon-on-insulator）波导弯曲损耗的几种影响因素进行了分析. 通过模拟发现弯曲损耗随弯曲半径的增大、波导宽度的增加及内外脊高比的减小而减小. 同时，改进波导结构，例如在弯曲波导外侧刻槽可以减小SOI脊形波导的弯曲损耗.     

GaAs／GaAlAs截止型光波导调制器的设计

利用近似解析方法，详细地讨论了金属覆盖层介质波导在截止点附近的模式传播特种和截止条件，并结合有效折射率方法讨论了脊高和脊宽对脊形波导截止条件的影响，设计了一种双层质结截止型强度调制器。     

Simulation of Tunable Power Multimode Interference Couplers with Deep Rib Structure

The muhimode interference （MMI） couplers, which operate at 1. 55 microns in deep rib InGaAsP/InP waveguide with large lateral confinement and tunable power splitting ratios, are of high interest in integrated optics. The gold contacts are applied on the top of waveguides where tuning is desired and the plasma effect will lead to negative refractive index change. The three-dimensional （3D） finite difference beam propagation method（FD-BPM） is used to model the tunable MMI couplers. The length of a 2 × 2 overlap-MMI is determined by FD-BPM, so the longitudinal position of tuning spots is obtained. The position of gold contacts with two types, the edge-pads or center-pad, are also determined. In our design, the length of MMI is 180 microns. If the width of pads is 50 microns and the refractive index is tuned from 0 to -0. 027, the power ratio is tuned from 50 ： 50 to the maximum 88.5 ： 11.4. For deep rib structure, the effective index（EI） method can not be used to simplify the 3D waveguide to plane waveguide because of its lower precision, and so the direct 3D FD-BPM simulation is necessary for the design of 3D MMI couplers.     

Thermally tunable integrated optical ring resonator with poly-Sithermistor

Doped polysilicon is applied as a thermo-optic heating element to temperature tune the ring resonator based on silicon nitride rib waveguides on silicon. The ring diameter is 2 mm allowing a large free spectral range of 26 GHz. For the first time, a poly-Si resistor is used as a thermistor to measure waveguide temperature. The temperature coefficient of the poly-Si thermistor is 9.5×10^-4/°C. The reproducibility of the temperature measurement is 0.3°C. The finesse of the ring resonator is 77. The propagation loss of silicon nitride rib waveguide is 0.5 dB/cm at the wavelength of 1.312 μm. The temperature tuning of the ring resonator and the in situ supervision of the temperature on chip based on the same poly-Si fabrication process may find use especially in optical sensor applications     

Implicit Yee-mesh-based finite-difference full-vectorial beam-propagation method

A novel Yee-mesh-based finite-difference full-vectorial beam-propagation method is proposed with the aid of an implicit scheme. The efficient algorithm is developed by splitting the propagation axis into two steps. The eigenmode analysis of a rib waveguide is performed using the imaginary-distance procedure. The results show that the present method offers reduction in computational time and memory, while maintaining the same accuracy as the conventional explicit Yee-mesh-based imaginary-distance beam-propagation method. It is demonstrated by the analysis of a polarization converter that the present method can be used for not only the eigenmode analysis but also the propagating beam analysis.     

Efficient beam propagation techniques

It is shown that suitable modifications of the free-space-propagation operator in the standard fast-Fourier-transform beam propagation procedure yield a far more rapid code in the context of semiconductor rib waveguide calculations. The procedure curtails the diffraction experienced by the high-order Fourier components of the electric field and mirrors the structure of the recently introduced finite-difference beam propagation algorithm. It is used to investigate the propagation losses of a Y-junction composed of single-mode rib waveguides and illuminated by its normalized guided mode     

Method for analysing trapezoidal optical waveguides by anequivalent rectangular rib waveguide

The authors present a simple analysis, using first-order perturbation theory, to determine an equivalent rectangular rib optical waveguide that will model the propagation characteristics of a trapezoidal rib optical waveguide. The results obtained from this method show excellent agreement with the results from the more accurate finite element method     

Photobleached refractive index tapers in electrooptic polymer rib waveguides

Photobleached refractive index tapers in electrooptic polymer rib waveguides, which act as two-dimensional optical mode transformers, are investigated. One taper method involves a discrete step mask-shifting scheme with a fixed intensity UV light source. A second method utilizes a gray-scale mask to precisely control the intensity of UV light reaching each portion of the taper. Using a gray-scale mask, adiabatic refractive index tapers can be inscribed into electrooptic polymer waveguides in a single fabrication step with no scanning parts. Optimized taper profiles are derived and applications for their incorporation into passive-to-active waveguide transitions are described.     

Optimization of strongly guiding semiconductor rib waveguideY-junctions

The three-dimensional split-step fast Fourier transform beam propagation method is used to demonstrate that losses associated with a strongly guiding semiconductor rib waveguide Y-junction can be substantially reduced by adding an optimized length of an initial straight broad waveguide segment. It is shown that the resulting transmission is relatively insensitive to the exact waveguide dimensions and in particular to the geometry of the Y-junction vertex     

Vectorial simulation of passive TE/TM mode converter devices on InP

Accurate calculations of polarization rotation at abrupt waveguide interfaces are performed by a vectorial two-dimensional finite difference scheme. It is shown that the small orthogonal component of the vector field in rib waveguides can play an important role in mode polarization rotation. Polarization rotations in mode converters fabricated on InGaAsP/InP by periodically arranged tilted waveguides or periodic loading of the rib are explained by these calculations, and design rules for passive mode converter devices are given