Rigorous analysis of numerical methods: a comparative study

For any photonic device simulation, the accuracy of the numerical solution not only depends on the methods being used but also on the discretization parameters used in that numerical method. In this work, Finite Element Method and Finite Difference Time Domain Method based on Maxwell’s equations were used to simulate optical waveguides and directional couplers. As the solution accuracy may also depend on the index contrast used in such photonic devices, the characteristics of low-index contrast Germanium doped Silica and high-index contrast Silicon Nanowire Waveguides were analyzed, evaluated and benchmarked. Numerical results to benchmark Directional Couplers are also reported in this paper

Loss and Dispersion Analysis of Microstructured Fibers by Finite-Difference Method

The dispersion and loss in microstructured fibers are studied using a full-vectorial compact-2D finite-difference method in frequency-domain. This method solves a standard eigen-value problem from the Maxwell’s equations directly and obtains complex propagation constants of the modes using anisotropic perfectly matched layers. A dielectric constant averaging technique using Ampere’s law across the curved media interface is presented. Both the real and the imaginary parts of the complex propagation constant can be obtained with a high accuracy and fast convergence. Material loss, dispersion and spurious modes are also discussed

Design and Characterization of Silicon-on-Insulator Passive Polarization Converter with Finite-Element Analysis

As optical fiber systems evolve to higher data rates, the importance of polarization control and manipulation steadily increases. Polarization manipulating devices, such as polarization splitters and converters, can be realized by introducing material anisotropy or geometric asymmetry. Compared to active devices, passive polarization converters are more simply fabricated and controlled; therefore they have attracted increasing attention during the past two decades. However, materials employed in previous polarization rotating waveguides are mainly limited to low index-contrast III-V semiconductors such as InP and GaAs. Such III-V devices possess large radiation loss, large curvature loss, and low coupling efficiency to single-mode fibers; in addition, due to the weak optical confinement, the device spacing has to be large, which prevents high-density and large-scale integration in optoelectronic integrated circuits (OEIC) and planar lightwave circuits (PLC). In this dissertation, the silicon-on-insulator (SOI) technology is introduced to the design and fabrication of passive polarization rotators (PR). Efficient and accurate full-vectorial finite-element eigenmode solvers as well as propagation schemes for characterizing novel SOI PRs are developed because commercial software packages based on finite-difference techniques are inefficient in dealing with arbitrary waveguide geometries. A set of general design procedures are accordingly developed to design a series of slanted-angle polarization converters, regardless of the material system (SOI or III-V), outer-slab layer configuration (symmetric or asymmetric), and longitudinal loading (single- or multi-section). In particular, our normalized design charts and simple empirical formula for SOI polarization converters are applicable to a wide range of silicon-guiding-film thickness, e. g. , from 1 to 30 μm, enabling fast and accurate polarization rotator design on most commercial SOI wafers. With these procedures, in principle 100% polarization conversion efficiency can be achieved by optimizing waveguide geometric parameters. A novel configuration with asymmetric external waveguiding layers is proposed, which is advantageous for fabrication procedure, manufacturing tolerance, single-mode region, and conversion efficiency. By etching along the crystallographic plane, the angled-facet can be perfectly fabricated. Completely removing external waveguiding layer beside the sloped sidewall not only simplifies production procedures but also enhances fabrication tolerances. To accurately and efficiently characterize asymmetric slanted-angle SOI polarization converters, adaptive mesh generation procedures are incorporated into our finite-element method (FEM) analysis. In addition, anisotropic perfectly-matched-layer (PML) boundary condition (BC) is employed in the beam propagation method (BPM) in order to effectively suppress reflections from the edges of the computation window. For the BPM algorithm, the power conservation is strictly monitored, the non-unitarity is thoroughly analyzed, and the inherent numerical dissipation is reduced by adopting the quasi-Crank-Nicholson scheme and adaptive complex reference index. Advantages of SOI polarization rotators over III-V counterparts are studied through comprehensive research on power exchange, single-mode condition, fabrication tolerance, wavelength stability, bending characteristics, loss and coupling properties. The performance of SOI PRs is stable for wavelengths in the ITU-T C-band and L-band, making such devices quite suitable for DWDM applications. Due to the flexible cross-section of SOI polarization converters, the coupling loss to laser diodes and single mode fibers (SMF) can be designed to be very small and can be further reduced by a tapered waveguide with cross-sections always satisfying the single-mode criteria. Slanted-angle SOI polarization rotators display asymmetric bending characteristics and permit extremely small curvatures with negligible radiation loss when the angled-facet is located at the outer bend radius. Moreover, SOI polarization rotators can be manufactured with low-price processing techniques that are fully compatible with CMOS integrated circuits (IC) technology, and thus can be integrated on both photonic and electronic chips. Experimental verifications have shown good agreement with theoretical analysis and have confirmed the promising characteristics of our novel asymmetric SOI polarization converters. Similar asymmetric-outer-slab geometry has recently been employed by peer researchers to fabricate high performance III-V polarization rotators. We therefore believe that results in this dissertation will contribute much to related research fields

A High-Order Numerical Method for the Nonlinear Helmholtz Equation in Multidimensional Layered Media

We present a novel computational methodology for solving the scalar nonlinear Helmholtz equation (NLH) that governs the propagation of laser light in Kerr dielectrics. The methodology addresses two well-known challenges in nonlinear optics: Singular behavior of solutions when the scattering in the medium is assumed predominantly forward (paraxial regime), and the presence of discontinuities in the % linear and nonlinear optical properties of the medium. Specifically, we consider a slab of nonlinear material which may be grated in the direction of propagation and which is immersed in a linear medium as a whole. The key components of the methodology are a semi-compact high-order finite-difference scheme that maintains accuracy across the discontinuities and enables sub-wavelength resolution on large domains at a tolerable cost, a nonlocal two-way artificial boundary condition (ABC) that simultaneously facilitates the reflectionless propagation of the outgoing waves and forward propagation of the given incoming waves, and a nonlinear solver based on Newton's method. The proposed methodology combines and substantially extends the capabilities of our previous techniques built for 1Dand for multi-D. It facilitates a direct numerical study of nonparaxial propagation and goes well beyond the approaches in the literature based on the "augmented" paraxial models. In particular, it provides the first ever evidence that the singularity of the solution indeed disappears in the scalar NLH model that includes the nonparaxial effects. It also enables simulation of the wavelength-width spatial solitons, as well as of the counter-propagating solitons.Comment: 40 pages, 10 figure

Advances in beam propagation method for facet reflectivity analysis

Waveguide discontinuities are frequently encountered in modern photonic structures. It is important to characterize the reflection and transmission that occurs at the discontinuous during the design and analysis process of these structures. Significant effort has been focused upon the development of accurate modelling tools, and a variety of modelling techniques have been applied to solve this kind of problem. Throughout this work, a Transmission matrix based Bidirectional Beam Propagation Method (T-Bi-BPM) is proposed and applied on the uncoated facet and the single coating layer reflection problems, including both normal and angled incident situations. The T-Bi-BPM method is developed on the basis of an overview of Finite Difference Beam Propagation Method (FD-BPM) schemes frequently used in photonic modelling including paraxial FD-BPM, Imaginary Distance (ID) BPM, Wide Angle (WA) BPM and existing Bidirectional (Bi) BPM methods. The T-Bi-BPM establishes the connection between the total fields on either side of the coating layer and the incident field at the input of a single layer coated structure by a matrix system on the basis of a transmission matrix equation used in a transmission line approach. The matrix system can be algebraically preconditioned and then solved by sparse matrix multiplications. The attraction of the T-Bi-BPM method is the potential for more rapid evaluation without iterative approach. The accuracy of the T-Bi-BPM is verified by simulations and the factors that affect the accuracy are investigated

Characterisation of silicon photonics devices

Silicon based integrated circuits has been dominating the electronics technology industry in the last few decades. As the telecommunications and the computing industry slowly converges together, the need for a material to build photonics integrated circuits (PIC) that can be cost-effective and be produced in mass market has become very important. This thesis describes and outlines the characteristics of high index contrast waveguides as a building blocks that can be designed, fabricated and employed on devices in silicon photonics. Initially in this work, a fully vectorial H-field based finite element method has been used to obtain the modal characteristics of high index contrast bent waveguide to get a better understanding of the curved section. Through the beam propagation method, the propagation losses and the spot-size along the propagation distance are obtained when a mode from the straight guide is launched into a bent guide. It is also learnt that mode beating exists at the junction of a straight-to-bent waveguide, in which higher order modes will also be generated. It will be shown in this work that power do exchange between the two polarization states, therefore the polarization conversion, the power losses and the bending losses will be investigated. It will also shown in here that by applying lateral offsets with coupled waveguides of unequal widths, the insertion loss can be reduced. Secondly, for a high index contrast waveguide such as the silicon strip waveguide with a nanoscale cross-section, modes in such waveguide are not purely TE or TM but hybrid in nature, with all the six components of their E and H-fields being present. Therefore a detail analysis of the modal field profiles along with the Poynting vector profile will be shown. The effects of waveguide's width and height on the effective indices, the hybridness, the modal effective area and the power confinement in the core or cladding has been studied. Furthermore the modal birefringence of such strip waveguide will be shown. It will be presented that for a strip waveguide with height of 260 nm, single mode exists in the region of the width being 200 nm to 400 nm and that the modal effective is at its minimum when width is around 320 nm for both polarization states. Thirdly, a compact polarization rotator with an asymmetric waveguide structure design, suitable for fabrication that does not require a slanted side wall or curved waveguide is considered in this work. It will be shown in here that due to the hybrid nature of the asymmetric waveguide design, maximum polarization rotation (from TE to TM) will be achieve by enhancing the non-dominant field profile of both polarized fundamental mode. As the modal hybridness and the propagation constants of both polarized modes will be obtained, the half-beat length, polarization conversion and polarization cross-talk will be calculated by using the FEM and the least squares residual boundary method (LSBR). It is learnt that a compact single stage polarization rotator with a device length of 48 μm with more than 99% of polarization conversion is achieved in this work. Finally, a study of vertical and horizontal slot waveguide will be shown. Based on silicon strip waveguide, a detail modal characteristics of E and H-fields along with the Poynting vectors are presented. It will be shown that for slot waveguide, high power confinement and power density will be achieved in the slot area. It will be presented that by optimising the waveguide and slot dimension, the performance of the power confinement and power density in the slot region can be improved

Parallel numerical methods for analysing optical devices with the BPM

In this work, some developments in the theory of modelling integrated optical devices are discussed. The theory of the Beam Propagation Method (BPM) to analyse longitudinal optical waveguides is established. The BPM is then formulated and implemented numerically to study both two and three-dimensional optical waveguides using several Finite-Difference (FD) techniques. For the 2-D analysis, comparisons between the performance of the implicit Crank Nicholson (CN), the explicit Real Space (RS) and the Explicit Finite-Difference (EFD) are made through systematic tests on slab waveguide geometries. For three-dimensional applications, two explicit highly-parallel three-dimensional FD-BPMs (the RS and the EFD) have been implemented on two different parallel computers, namely a transputer array (MIMD type) and a Connection Machine (SIMD type). To assess the performance of parallel computers in this context, serial computer codes for the two methods have been implemented and a comparison between the speed of the serial and parallel codes has been made. Large gains in the speed of the parallel FD-BPMs have been obtained compared to the serial implementations; both methods, in their parallel form, can execute, per propagational step, a large problem containing 106 discretisation points in a few seconds. In addition, a comparison between the performance of the transputer array and the Connection Machine in executing the two FD-BPMs has been discussed. To assess and compare the two methods, three different rib waveguides and three different directional couplers have been analysed and the results compared with published results. It has been concluded from testing these methods that the parallel EFD-BPM is more efficient than the parallel RS-BPM. Then, the linear parallel EFD-BPM was extended to model nonlinear second harmonic generation process in three-dimensional waveguides, where the source field is allowed to deplete, using the transputer array and the Connection Machine

Modeling and Simulation of Photonic Crystal Fibers and Distributed Feedback Photonic Crystal Fiber Lasers

A photonic crystal fiber (PCF) is comprised of a solid or air core surrounded by periodically arranged air holes running along the length of the fiber, which guides light in a fundamentally new way compared to conventional optical fibers, affecting almost all areas of optics and photonics. To analyze the dispersion and loss properties of PCFs, a two-dimensional (2D) finite-difference frequency-domain (FDFD) method combined with the technique of perfectly matched layer (PML) is developed. The propagation constant and loss can be obtained with accuracies in the orders of ∼10-6 and ∼10 -3, respectively. The Bragg fiber is a kind of PCF with alternate layers surrounding a solid or air core. To improve the performance of the above algorithm, a 1D FDFD method in the cylindrical coordinates is proposed to fully utilize the rotational symmetry property of the Bragg fiber. In addition to improving the accuracy, this method reduces the computation region from 2D to a straight line, significantly relieving the computation burden. A second method, called Galerkin method, is also developed under cylindrical coordinates. The mode fields are expanded using orthogonal Laguerre-Gauss functions; and the method is accurate and stable. However, it cannot do the loss analysis. For photonic-band-gap-guiding PCFs, the properties of the confined modes are closely related to the band structures of the cladding photonic crystals. Therefore, a third FDFD method using periodic boundaries is developed in a generalized coordinate system. Various lattice geometries are analyzed in the same manner, and the results are comparable to those obtained by the plane wave expansion method which is commonly used in the literature. Finally, a theoretical model for analyzing distributed feedback (DFB) PCF lasers has been presented. Two structures are investigated: PCFs with triangular lattice (TPCF) and PCFs made of capillary tube (CPCF). The modeling and simulation of erbium-doped and erbium/ytterbium (Er/Yb) co-doped DFB lasers are aimed at finding suitable PCF geometry to achieve low threshold and high output power. Various steps involved in this model are: (1) the properties of PCFs are analyzed by the FDFD method; (2) the Bragg grating is investigated by coupled mode theory; (3) the coupled wave equations are solved by transfer matrix method; and (4) Er atom is modeled as a three-level medium while energy transfer between Yb and Er atoms is considered for Er/Yb co-doped fiber. It is found that a CPCF laser with a smaller mode area is useful for lower-threshold applications and both of CPCF and TPCF lasers with larger mode areas are suitable for high-power operation