Numerical Problems On Waveguides









9-(13-6278) Task 40572. A two-level domain decomposition method with accurate interface conditions for the Helmholtz problem A Vaziri Astaneh, M Guddati International Journal for Numerical Methods in Engineering 107 (1), 74–90 , 2016. AU - Magnanini, Rolando. On the other hand, the purpose of waveguides is to guide electromagnetic energy. 2009-01-01. 2—fields generated on the waveguides at the points that the wave enters the kernel. Pereira(*), J. There have been many numerical studies of microstructure ber based on di-rect numerical calculation of static Maxwell’s equations in order to determine the system’s modes; some of them are also able to capture the attenuation. (Report) by "Elektronika ir Elektrotechnika"; Engineering and manufacturing Equipment performance Evaluation Numerical analysis Research Temperature effects Ultrasonic waves Properties Ultrasound Wave propagation Waveguides Acoustic properties Thermal. CMaxwell equations, different formulations, interfaces, energy and power flow. Linear theory of such waveguides is known for years; see, for example. Numerical methods for calculating the parameters of various types of waveguide structures are described in the monographs and review papers [1,4,6,15]. These classes of problems can be decomposed into two scalar problems like the layerd medium case, by using the pilot potential method. Recent Posts. The Essence of Dielectric Waveguides is a comprehensive overview of the fundamental behavior of dielectric waveguides, essential to interpreting the numerical data results of electromagnetic waveguide problems. Numerical results are found with a projection method. Characteristics of the nonlinear process such as conversion efficiency as well as impact of the multimode character of the waveguide are. Below the waveguide cutoff frequency, it is not able to carry the signals. The researchers worked on an optimization problem: How does one design a waveguide for magnonic circuits to ensure maximum efficiency?. Bibliography: p. A ring sector pumped with. Our numerical experiments show that the pollution primarily has a diffusive effect causing energy loss in the DPG method while phase errors appear less significant. The scheme is tested on several interfaces of homogeneous and periodic media and it is used to. For many years, one of the most commonly used numerical methods for the simula-tion of electromagnetic wave propagation in planar waveguides, is the finite-di↵erence time-domain (FDTD) method [18][23][26]. They are used in many applications. : Antenna Laboratory. The problem arises in the study of light in optical fibers. However, it should be said that most of the methods applied to homogeneous waveguides, are not common and are difficult to implement and apply for specific inhomogeneous structures. Y1 - 2001/7. Conventional three-dimensional finite element analysis has previously been applied to this problem. Video Solution to GATE 2014 Problem - Waveguides - Electromagnetics. Numerical ODE Solvers • Objective: to solve ODE (e. Lecturers: I Prof. Numerical Simulation of Quantum Waveguides Anton Arnold1, Matthias Ehrhardt2 and Maike Schulte3 1 Institut für Analysis und Scientific Computing, TU Wien, Wie dner Hauptstr. Numerical Methods for Ports in Closed Waveguides Christer Johansson Stockholm 2003 Licentiate Thesis Stockholm University Department of Numerical Analysis and. Exercises week 3: Fiber optics and waveguides Problem 1: Numerical aperture (NA) of a slab waveguide. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. on e cient numerical methods to solve these problems. Tell us about Kane Yee and his pioneering work on the numerical solution of Maxwell’s equations. European EMC Products design and manufacture a wide range of radio frequency (RF) shielded Waveguide Vents, specifically for high performance applications. ComputerPhysicsCommunications198(2016)118–127 Contents lists available atScienceDirect ComputerPhysicsCommunications. Electromagnetic Theory Questions and Answers – Smith Chart Manish Bhojasia , a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. WAVEGUIDES Hui-Ming Fang, Chia-Ming Fan, Yan-Cheng Liu, and Sung-Shan Hsiao Key words: least squares Trefftz method, eigenfrequencies problem, Helmholtz equation, boundary-type meshless method. FIMMWAVE combines: methods based on semi-analytic techniques, which allow to tackle efficiently problems with strong variations in refractive index, thin layers, etc. Different types of transitions have been simulated in order to find optimal configurations as well as optimal dimensions of dielectric waveguides for the frequency band of 75-110 GHz. Problems - approximation of Rayleigh or Stoneley waves with nearly incompressible isotropic mate-rials and low order di erence methods. The researchers worked on an optimization problem: How does one design a waveguide for magnonic circuits to ensure maximum efficiency?. They are used in many applications. 056 310 4233 2. Numerical Study of Propagation in Optical Waveguides and Devices: Analytical and Numerical Study of Propagation in Optical Waveguides. Therefore, contour IE techniques seem to be more promising for implementing efficient numerical techniques based on the full-vectorial problem. Abstract-A vector H-field finite-element method has been used for the solution of optical waveguide problems. Both analytical and numerical techniques are used to obtain and analyse solutions. Metal waveguide, dielectric slab waveguide, optical fiber and surface plasmon polariton. [13] for instance). This formulation enables to account for the translational invariance of waveguide problems and leads to a two-dimensional modal problem reduced on the cross-section. This paper is devoted to the numerical solution of the instationary Maxwell equations in singular waveguides. Final Exam. In the case of the interconnection of optical fibers, the problem is reduced to the solution of an iterative series of boundary value problems of the type representing the slab waveguides problem. Numerical interaction of boundary waves with perfectly matched layers in elastic waveguides Kenneth Duru , Gunilla Kreiss y April 10, 2012 Abstract Perfectly matched layers (PML) are a novel technique to simulate the ab-sorption of waves in open domains. We demonstrate the performance of the scheme by showing that the effect of finite cladding on modal confinement loss of rectangular dielectric waveguides increases exponentially fast as the. Ribeiro(*), A. AU - Taflove, Allen. Numerical examples are given for homogeneous andinhomogeneous waveguides, in the homogeneous case the resultsare compared to analytical solutions and the right order ofconvergence is achieved. gation phenomena in the waveguides, are described. The purpose of this study is to develop a new numerical method to solve one-dimensional wave equation for planar waveguides using the Fourier transform and to demonstrate some of its advantages in comparison with the methods exist. For an appropriate membrane geometry, photoluminescence collection efficiencies in excess of 10 % are predicted, exceeding the efficiency of standard free-space collection by an order of magnitude. Recent Posts. • MATLAB codes for 2-D finite-difference (FD) numerical solution of Laplace's equation, based on both iterative and direct solutions of FD equations; potential, field, and charge computations ⋄ MATLAB solutions to nonlinear problems: • Graphical and numerical solutions for a simple nonlinear electric circuit. Research Area: Design and Modeling for Integrated Photonics. A waveguide-pumped 6 mkm-radius ring cavity and it's transmittance Figure 2. The third class of problems includes studies of optical pulse propagation in nonlinear waveguides. The Essence of Dielectric Waveguides is a comprehensive overview of the fundamental behavior of dielectric waveguides, essential to interpreting the numerical data results of electromagnetic waveguide problems. First, in the theory section, a modal field expression and the characteristic equation is derived, which is also valid for higher-order modes. 75 cm in Problem #2, calculate the range of frequencies over which the slab. rectangular waveguides. Abstract: A numerical analysis of an infinite phased array of open rectangular waveguides has been made which includes the effects of wall thickness. The researchers worked on an optimization problem: How does one design a waveguide for magnonic circuits to ensure maximum efficiency?. A wide range of waveguide coverage, from the familiar types (step-index optical fiber and planar) to the more striking (elliptical and. Don't show me this again. Numerical solutions. and Numerical Aspects of Wave Propagation, Gammarth, Tunis, 2013. Masoudi, “Numerical modeling of pulsed optical beams in second order nonlinear waveguides using a Time-Domain Beam Propagation Method”, Integrated Photonics Research Conference, Optical Society of America and IEEE/Lasers and Electro-Optics Society, Monterey, California , June 11—15, 2001. 2) and boundary conditions (2. The guided waves may be radiated away at the end of the waveguide by a horn antenna , which is a flared metal device having the dimensions of the waveguide at one end and opening out to a. The transmission‐line matrix method is a time‐domain numerical method for solving wave problems. System developers will find that. Numerical analysis of optical waveguides with the use of Fourier‐series expansion method combined with perfectly matched layer. Numerical tests indicate the accuracy of the method to be competitive with widely used finite-difference methods for elliptic interface problems. Numerical Approximation of the Streeter-Phelps Equations of River Self-Purification, Sixteenth Annual Conference On Applied Mathematics, University of Central Oklahoma, February 24, 2001. We have built a method which allows to compute the time-dependent electromagnetic field, based on a splitting of the spaces of. Three boundary value problems involving discontinuities in a parallel plate waveguide were solved. Sensors 15 3 4658-4676 2015 Journal Articles journals/sensors/Al-FaqheriITBAR15 10. The solution was then extracted by using ideal. Two cases are examined: (i) the 3D ASA benchmark wedge, and (ii) the 3D Gaussian canyon. Introduction. (recall that traditionally different numerals lemniscate; Aleph zero, etc. In addition to the MOL, I have some past experience with other numerical methods, which includes, the Beam Propagation Method (BPM) and the Finite. Rectangular waveguides are th one of the earliest type of the transmission lines. We implement a local orthogonal transform to transform the irregular waveguide in physical plane into a regular rectangle in computing plane. 39 A hollow rectangular waveguide is to be used to transmit signals at a carrier frequency of 6 GHz. This training material has been developed based on the latest GATE syllabus. 3 At 200MHz a given medium is characterized by σ = 0, µr = 15(1−j3) and εr = 50(1−j1). This paper is devoted to the numerical solution of the instationary Maxwell equations in singular waveguides. matical and numerical methods for planar and peri-odic dielectric waveguides. Other chapters describe the numerical methods for solving guided mode as well as wave propagation problems. The numerical modeling to a boundary value problem and the numerical discretisation of interconnection problems of two slab waveguides are discussed. Circular waveguides have modes that are described in terms of Bessel functions instead of the sines/cosines used for rectangular waveguides. We present an efficient numerical. We developped CAMFR, a comprehensive modelling tool for photonic components, which is freely available from sourceforge. A Comparative Study: Physical Modeling Sound Synthesis Methods. ECE 3065 Homework 7: More Waveguides 1. web; books; video; audio; software; images; Toggle navigation. The transmission-line-matrix method is a time-domain numerical method for solving wave problems. The idea of CSM as a method for solving the prob-lems of wave propagation in irregular waveguides is not new, but in this paper a self-contained and rigorous der-. The filling media studied are uniaxial media and uniaxial media embedded with metamaterial. Journal of Computational and Applied Mathematics 236(18): 4582-4599. While some of the numerical methods, such as the Finite Element Method, the Plane Wave Expansion Method, the Beam Propagation Method-based mode solvers, the Film Mode Matching Method, and the Finite-Difference Method, can be used for finding modes of the arbitrary cross-section and refractive index profile waveguides, others are more specialized. Microwave Engineering - Example Problems - In this chapter, let us have some fun by solving a few numerical problems related to microwaves. Both analytical and numerical approaches are covered. The frequency-domain calculations are carried out. Sponsored by Wright Air Development Center. 8, 1040 Wien, Austria 2 Weierstraß–Institut für Angewandte Analysis und Stochastik, Mohrenstr. Robust optimization of adiabatic tapers for coupling to slow-light photonic-crystal waveguides Ardavan Oskooi,1,∗ Almir Mutapcic,2 Susumu Noda,1 J. 2007 ‹#› efficient power transfer from RF to the beam needed. on e cient numerical methods to solve these problems. 5 Transient problem. This paper is devoted to the numerical solution of the instationary Maxwell equations in singular waveguides. direct numerical solutions of Maxwell’s equations. Section dimensions = 40mm X 60mm. This leads to a very efficient method for the numerical simulation of the waveguide, which can be used, for instance, in optimal shape design. Numerical analysis naturally finds application in all fields of engineering and the physical sciences, but in the 21st century also the life. Studies unsymmetrical bending, shear center, and s. Such a description, however, becomes invalid when interference effects occur, and this is particularly the case for very small waveguide dimensions. The procedure is based on the well-known variational expression for the propagation constant and uses as trial field an expansion in terms of Hermite-Gauss functions. A wide range of waveguide coverage, from the familiar types (step-index optical fiber and planar) to the more striking (elliptical and triangular-core fibers), offers readers a rare in. Tausch and J. 45 NUMERICALANALYSISOFTHEEIGENVALUEPROBLEM OFWAVESINCYLINDRICALWAVEGUIDES by C. The most challenging problem is the design of numerical methods. Most of this work examines cases operating far from any band edge (so the group. Find: (a) η/η0, λ/λ0 and v/v0, where η is the intrinsic impedance and v is the phase velocity (the. The transmission-line-matrix method is a time-domain numerical method for solving wave problems. Validation of the approach for mode excitation in a 1D GRIN, transverse mode beating for non-modal input conditions. Waveguides will only carry or propagate signals above a certain frequency, known as the cut-off frequency. Waveguides are the building blocks of photonic circuits. Several numerical examples are presented to illustrate the method’s efficiency. McCartin Applied Mathematics, Kettering University 1700 West University Avenue, Flint, MI 48504-4898, USA [email protected] Based on the Floquet-Bloch transform and analytic. 3 At 200MHz a given medium is characterized by σ = 0, µr = 15(1−j3) and εr = 50(1−j1). Grading Your grade will be based on, quizzes and exams broken down as follows: Homework. A spectral study of an infinite. A waveguide is a structure that guides waves, such as electromagnetic waves or sound, with minimal loss of energy by restricting the transmission of energy to one direction. An Iterative Adaptive Finite Element Method for Elliptic Eigenvalue Problems. Collection of standard waveguide components. • MATLAB codes for 2-D finite-difference (FD) numerical solution of Laplace's equation, based on both iterative and direct solutions of FD equations; potential, field, and charge computations ⋄ MATLAB solutions to nonlinear problems: • Graphical and numerical solutions for a simple nonlinear electric circuit. Ehrhardt, ed. We find that Luneburg lenses may form efficient waveguides for light propagation and guiding. Indicate the direction of the current on the. Wave propagation in isotropic elastic waveguides has the possibility to support propagating. This paper describes how a minor change in the computer program for loss‐free dielectrics extends the method to include dielectric losses. AU - Blaschak, Jeffrey. 31(7), July 1977, pp [2] T. Waveguides are used at microwave frequencies where dielectric losses in radio cables become excessive; they are therefore used as feeders in radio telescopes. N2 - In this paper, a rigorous method for the analysis of the propagation characteristics of various rectangular waveguides is proposed based on the recent development of the numerical mode matching method for multi-region, vertically stratified media. n 2 n 2 d = 2 a T T k 1 L ig h t A B C O E N E T n 1 Numerical Aperture---Maximum Acceptance Angle 0 max 1 sin(90 ) sin n n c o T D 1 sin 2. The idea of CSM as a method for solving the prob-lems of wave propagation in irregular waveguides is not new, but in this paper a self-contained and rigorous der-. The cross-section method is considered as a method for calculation of the field in a waveguide consisting of two regular waveguides with different cross-sections joined by an irregular domain. They are used in many applications. The rst mathematical existence studies are much more recent, and appear to be limited to guided modes and the continuous spectrum [7]. PY - 1989/3. Accordingly, nite-di erence methods are a natural candidate for the numerical analy-sis of electromagnetic phenomena. Numerical analysis of optical waveguides with the use of Fourier‐series expansion method combined with perfectly matched layer. Duley2 1School of Electronic Science and Engineering, Southeast University, and Key Laboratory of Micro-Inertial. The history of this prob-lem goes back to the engineering analysis of open waveguides in the 1960s (see the references in [37]). Numerical methods for calculating the parameters of various types of waveguide structures are described in the monographs and review papers [1,4,6,15]. We fabricated flexible polymer waveguides by using PDMS elastomer, which has a refractive index of ≈1. 22, which corresponds to incident angles above the critical angle (θ C), enabling total internal reflection at either interface. 1, JANUARY 2009 In the transformed (straight waveguide) problem, the com-ponents and are equal to the co-variantcomponents and inthephys-ical problem. The divergence makes the design of rapidly converging numerical algorithms for vector mode field computations in such waveguides difficult. Numerical study of exact Purcell factors in finite-size planar photonic crystal waveguides V. The proposed algorithm uses the exact expression for the solution to the integral equation for the electromagnetic field in the planar waveguide with. The analytical treatments in Chapters 2 and 3 are quite important to understand the basic subjects of waveguides such as (1) mode concepts and. The Essence of Dielectric Waveguides is a comprehensive overview of the fundamental behavior of dielectric waveguides, essential to interpreting the numerical data results of electromagnetic waveguide problems. ANTENNALABORATORY TechnicalReportNo. Barseghyan (Nuclear Physics Institute, Rez; University of Ostrava, Ostrava, Czech Rep. DIFFERENT NUMERICAL APPROACHES IN THE ANALYSIS OF DIELECTRIC OPTICAL WAVEGUIDES M. Iterative methods for scattering problems in isotropic or anisotropic elastic waveguides Vahan Baroniana, Anne-Sophie Bonnet-Ben Dhiab, Sonia Flissb,, Antoine Tonnoirc aCEA, LIST, Gif-sur-Yvette, France bPOEMS (CNRS-ENSTA Paristech-INRIA, Universit e Paris-Saclay), 828 Boulevard des Mar echaux, Palaiseau, France cINRIA, Universit e Paris-Saclay, 1 Rue Honor e d'Estienne d'Orves, 91120. 45 NUMERICALANALYSISOFTHEEIGENVALUEPROBLEM OFWAVESINCYLINDRICALWAVEGUIDES by C. We suggest a new numerical method that is based on a truncation of the domain and the use of Bloch wave ansatz functions in radiation boxes. Analysis of Ridged Circular Waveguides by the Coupled-Integral-Equations Technique Smain Amari, A variety of numerical techniques have been used to tackle this problem. Tausch [23] for periodic open waveguides, but it was used to deal with the unboundedness of the propagation mediumin the direction(s) transverse to the periodicity direction(s), a much more standard situation than the one we consider in this paper. BONNET-BEN DHIA We show that finding guided waves amounts to solving a family of 2-D eigenvalue problems set in the cross-section of the propagation medium. , Runge-Kutta) – Shooting methods – Finite element/difference methods 4/1/2013 ECE 595, Prof. Study of wave propagation in waveguides, composite and non-homogeneous materials. PY - 1991/1/1. nurnerical analysis. The shielding performance of waveguides is governed by the surface geometry of the apertures (length and width), the aperture depth, the shape, and total number of apertures. @article{osti_22611476, title = {Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections}, author = {Zuo, Peng and Fan, Zheng and Zhou, Yu}, abstractNote = {Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. Waveguide Example based on Cut off frequency 3. The Essence of Dielectric Waveguides is a comprehensive overview of the fundamental behavior of dielectric waveguides, essential to interpreting the numerical data results of electromagnetic waveguide problems. In short, there was a need for a model that was robust, accurate, and efficient. (Report) by "Elektronika ir Elektrotechnika"; Engineering and manufacturing Equipment performance Evaluation Numerical analysis Research Temperature effects Ultrasonic waves Properties Ultrasound Wave propagation Waveguides Acoustic properties Thermal. Waveguide are used at microwave frequencies for the same. Please report any problems with the Mail Feedback Form for correction. An integral approach to the boundary value problem in waveguides is presented. Wilf - University of Pennsylvania, 2002. A method is described whereby complex reflection and transmission coefficients of modes excited at a waveguide junction may be determined by a simple technique utilising a digital computer. If you have had even just a bit of dissatisfaction in reliability test results, please put NTT-AT’s. Analysis of Ridged Circular Waveguides by the Coupled-Integral-Equations Technique Smain Amari, A variety of numerical techniques have been used to tackle this problem. However, it should be said that most of the methods applied to homogeneous waveguides, are not common and are difficult to implement and apply for specific inhomogeneous structures. AU - Taflove, Allen. Numerical interaction of boundary waves with perfectly matched layers in elastic waveguides Kenneth Duru , Gunilla Kreiss y April 10, 2012 Abstract Perfectly matched layers (PML) are a novel technique to simulate the ab-sorption of waves in open domains. 2GeM, ECN, BP 92101, 44321 Nantes, France. In the case of the interconnection of optical fibers, the problem is reduced to the solution of an iterative series of boundary value problems of the type representing the slab waveguides problem. Lecturers: I Prof. Fast Analysis of Gap Waveguides using the Characteristic Basis Function Method and Advanced Green's Function Approaches MASTER's THESIS as part of mandatory clauses in fulfillment of Master's Degree from the Chalmers University of Technology, Gothenburg, Sweden by Pegah Takook Department of Signals and Systems June, 2012. At that time, 2D numerical techniques were used to analyze coaxial waveguides because of their simplicity. Units: (dimensionless) How to cite the article; suggest additional. 2 General techniques 2. Typical difficulties included numerical instabilities for certain types of sound-speed profiles and failures to compute a complete set of ocean modes. AU - Chew, Weng Cho. rectangular waveguides. The cross-section method is considered as a method for calculation of the field in a waveguide consisting of two regular waveguides with different cross-sections joined by an irregular domain. (Author/SK). on orthogonal spectral decompositions and projection operators. With open waveguides, numerical methods must yet face difficulties due to the unbounded nature of the cross-section. While some of the numerical methods, such as the Finite Element Method, the Plane Wave Expansion Method, the Beam Propagation Method-based mode solvers, the Film Mode Matching Method, and the Finite-Difference Method, can be used for finding modes of the arbitrary cross-section and refractive index profile waveguides, others are more specialized. fr Abstract. : Antenna Laboratory. The Essence of Dielectric Waveguides is a comprehensive overview of the fundamental behavior of dielectric waveguides, essential to interpreting the numerical data results of electromagnetic waveguide problems. The book is useful for both theoretical and applied research. ECE 3065 Homework 7: More Waveguides 1. General Problem and Method Numerical Approach Numerical Approach If we want to be more accurate, can include nite ! max corrections for leading terms in Weyl expansion: EWeyl t = 1 e!maxt 1 2 (! maxt)2 + ! t + 1 Area 2ˇt3 1 e!maxt (! maxt + 1) Perimeter 8ˇt2 + C lnt Lev Kaplan (Tulane University) Numerical Computation of Self-Energies QV 2011. 2 Theory of Microwave and Optical Waveguides a closed waveguide, the electromagnetic energy is completely trapped within metallic walls. a numerical method to calculate the optical fields as well as the optical propagation properties of the in- terconnection region of two ideal semi-infinite slab waveguides. , =() ) with greatest accuracy and least computational cost • Categories: – Initial value problems – Boundary value problems • Algorithms: – Euler methods – Higher-order methods (e. Attention is focused on the case of waveguides because numerical problems are generally far greater than for 2-dimensional structures. Numerical ODE Solvers • Objective: to solve ODE (e. In this paper we give the mathematical formulation of the electromagnetic scat-tering problem in terminating waveguides and study with numerical simulations two imaging methods. Circular waveguides Introduction Waveguides can be simply described as metal pipes. Kreiss JCP 2015. Numerical analysis of the eigenvalue problem of waves in cylindrical waveguides By 1934- Chien-hui T'ang and 1920- Yüan-chih Lo Download PDF (2 MB). 45 NUMERICALANALYSISOFTHEEIGENVALUEPROBLEM OFWAVESINCYLINDRICALWAVEGUIDES by C. Literally hundreds of papers have been published on the subject, and even more on the associated problem of finding mode indices or repetencies. 2 General techniques 2. In this case the boundary value problem becomes a classical. New transparent boundary condition for time harmonic acoustic diffraction problem in anisotropic media. The calculation of mode fields in dielectric waveguides is of fundamental importance both in optics and in microwave technology. (If the waveguides are simply butt-coupled without a taper, the transmission goes to zero as the zero-velocity band-edge is approached (Sanchis et al. Variational formulation As mentioned above, our goal is to nd all pairs ( ;(E;E 3)) which satisfy equa-tions (2. AU - Chew, Weng Cho. 1 Introduction We saw in the previous chapter that a Gaussian beam can propagate without beam expansion in an optical medium whose refractive index varies in an appropriate manner in the radial direction. 4 MB) File 2. This approach is deduced from the Kirchhoff's integral formulation of the electromagnetic field. Chapter 9: Electromagnetic Waves 9. on orthogonal spectral decompositions and projection operators. them as additional 'waveguides' • Furthermore, in the linear case, most problems can be solved analytically • Can extend CMT to nonlinear systems (e. Other chapters describe the numerical methods for solving guided mode as well as wave propagation problems. Instruction will be by lectures on the underlying theory, in-depth discussion of numerous practical examples, and hands-on experience in solving. Ask Question Asked 6 years, 6 months ago. FExamples for dielectric optical waveguides. 2 Repeat the previous problem, assuming now that the region z ≥ 0 is filled wiht a poor conductor with εr = 2. Anne-Sophie is interested in waveguides. ) I will discuss the problem of imaging sources/scatterers in random waveguides using measure-ments of the acoustic pressure field recorded at a remote array of sensors, over some time window. These problems consist of MCQs and other numerical answer type. High-Precision Propagation-Loss Measurement of Single-Mode Optical Waveguides on Lithium Niobate on Insulator Jintian Lin 1,y, Junxia Zhou 2,3,y, Rongbo Wu 1,4, Min Wang 2,3, Zhiwei Fang 2,3, Wei Chu 1, Jianhao Zhang 1,4, Lingling Qiao 1 and Ya Cheng 1,2,3,4,5,* 1 State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics. ANTENNALABORATORY TechnicalReportNo. clude the chapter. This method is particularly useful for solving long range wave propagation problems in slowly varying waveguides. For waveguides with arbitrary cross sections, numerical methods are usually used due to the complexity to solve nonlinear Navier equation analytically with arbitrary boundary conditions. As an example, a junction between a homogeneous and an inhomogeneous waveguide is considered for cases where both one and two modes propagate in the inhomogeneous waveguide. Also, the proposed FEM is applicable to waveguides having rectangular and circular cross sections. A rectangular waveguide supports TM and TE modes but. 75 cm in Problem #2, calculate the range of frequencies over which the slab. The idea of CSM as a method for solving the prob-lems of wave propagation in irregular waveguides is not new, but in this paper a self-contained and rigorous der-. Y1 - 1989/3. FIMMWAVE combines: methods based on semi-analytic techniques, which allow to tackle efficiently problems with strong variations in refractive index, thin layers, etc. Chapter 9: Electromagnetic Waves 9. waveguides, building block method, numerical conformal mappings, Schwarz-Christoffel mapping, rounded corners method, approximate curve factors, outer polygon method, boundary curvature, zipper method, geodesic algorithm, acoustic wave scattering, electro-magnetic wave scattering the problem can be solved as a two-dimensional wave. T1 - A study of wave interactions with flanged waveguides and cavities using the on-surface radiation condition method. For an appropriate membrane geometry, photoluminescence collection efficiencies in excess of 10 % are predicted, exceeding the efficiency of standard free-space collection by an order of magnitude. Wednesday, December 3, 2008 4-5pm in 2-151. Waveguides As we saw in Section 7. The Essence of Dielectric Waveguides is a comprehensive overview of the fundamental behavior of dielectric waveguides, essential to interpreting the numerical data results of electromagnetic waveguide problems. Main Researcher: Peter Bienstman. preserver problems involving numerical ranges and numerical radii. MARICA Computer (1959), Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy. Accordingly, nite-di erence methods are a natural candidate for the numerical analy-sis of electromagnetic phenomena. In this paper, we propose a new numerical method for scattering problems in periodic waveguide, based on the newly established contour integral representation of solutions in a previous paper by the author (see [Zhadf]). GSP aims at publishing the state-of-the-art research results, providing the most professional platform for the researchers to prompt their latest discoveries, and connecting the scientists from all over the world in the areas of, but not limited to, mathematics, physics, chemistry, and computational sciences. The filling media studied are uniaxial media and uniaxial media embedded with metamaterial. This paper is devoted to the numerical solution of the instationary Maxwell equations in singular waveguides. Waveguides As we saw in Section 7. 2 we saw that this stored energy is equal to CV2/2. A wide range of waveguide coverage, from the familiar types (step-index optical fiber and planar) to the more striking (elliptical and. This chapter deals with the basic concept of silicon-on-insulator (SOI) slot waveguides, including slot waveguide theory, fabrication steps, and applications. The third class of problems includes studies of optical pulse propagation in nonlinear waveguides. The boundary value problem is then reduced to an initial value problem by one-way reformulation based on the Dirichlet-to-Neumann (DtN) map. This paper proposes a novel numerical approach for waveguide transition problems with the use of the periodic Fourier transform developed by Nakayama [10, 11]. Lecturers: I Prof. Optical waveguide theory APhotonics / integrated optics; theory, motto; phenomena, introductory examples. We prove the existence and a stability estimate for the infinite dimensional version of the proposed problem. 5 Transient problem. problem is reduced to one for the scalar Helmholtz equation by considering a single type of waves, transverse electric or magnetic. Find materials for this course in the pages linked along the left. The FileOpen plug-in is necessary to view the Numerical Recipes books. Introduction. ): Spectrum of the Schrödinger operators in cusps. 1988-11-18 00:00:00 A mode matching method for the analysis of a cylindrical dielectric resonator with arbitrarily shaped cross-section inside a waveguide is presented which allows series expansions of the fields in the region of the dielectric. They stand for certain special field configurations in the transverse plane,. A spectral study of an infinite. The coupled normal mode method is a powerful approach for solving range-dependent propagation problems in underwater acoustics. Tell us about Kane Yee and his pioneering work on the numerical solution of Maxwell’s equations. ENormal modes of dielectric optical waveguides, mode interference. 3) for a given frequency!>0. 22, which corresponds to incident angles above the critical angle (θ C), enabling total internal reflection at either interface. N2 - An efficient scheme based on the bi-Lanczos algorithm has been developed for analysis of the dielectric-waveguide problem. There are different types of waveguides for different types of waves. For more complex shapes, or waveguides with ridges, holes, dents along the way, then it gets messy and we lose one or two of these nice simplifications. The computational complexity can be highly dependent on the acoustic formulation. WAVEGUIDES Hui-Ming Fang, Chia-Ming Fan, Yan-Cheng Liu, and Sung-Shan Hsiao Key words: least squares Trefftz method, eigenfrequencies problem, Helmholtz equation, boundary-type meshless method. N2 - In this paper, a rigorous method for the analysis of the propagation characteristics of various rectangular waveguides is proposed based on the recent development of the numerical mode matching method for multi-region, vertically stratified media. Numerical Implementation of the Cross-section Method for Irregular Waveguides 275 ity, as well as such a problem for homogeneous equa-tion with inhomogeneous conditions at infinity. ), refraction, resonance, phased arrays, and the Doppler effect. The numerical modeling to a boundary value problem and the numerical discretisation of interconnection problems of two slab waveguides are discussed. ECE 3065 Homework 7: More Waveguides 1. The explicit incorporation of. The waveguides obtained had angled walls, and so numerical analysis was undertaken to establish the single mode condition for such trapezoidal structures. Study of wave propagation in waveguides, composite and non-homogeneous materials. We find that Luneburg lenses may form efficient waveguides for light propagation and guiding. A numerical method is proposed to compute high-frequency low-leakage modes in structural waveguides surrounded by infinite solid media. Lecture 26 Dielectric Slab Waveguides In this lecture you will learn: • Dielectric slab waveguides •TE and TM guided modes in dielectric slab waveguides ECE 303 – Fall 2005 – Farhan Rana – Cornell University TE Guided Modes in Parallel-Plate Metal Waveguides z ε µo x ki=−kxx+kzzˆ r kr =kxx +kzzˆ r ki r E r H r kr r Ei Hi ()j k z. Kondratiev1 1. The third class of problems includes studies of optical pulse propagation in nonlinear waveguides. The numerical aperture (NA) of an optical system (e. 2007 ‹#› efficient power transfer from RF to the beam needed. These problems consist of MCQs and other numerical answer type. Typical difficulties included numerical instabilities for certain types of sound-speed profiles and failures to compute a complete set of ocean modes. (If the waveguides are simply butt-coupled without a taper, the transmission goes to zero as the zero-velocity band-edge is approached (Sanchis et al. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. Such structures are encountered in many applications. To describe the fields, we choose a 4-vector composed of the displacements and the horizontal. Finally, a general procedure is proposed for the reformulation of DGFs for common types of waveguides. GNU Octave is software based on a high-level programming language and is primarily intended for numerical computations. load at failure = 2KN. The method starts from a finite element (FE) model of only a short segment of the structure, typically by using existing element libraries and commercial FE packages. Variational formulation As mentioned above, our goal is to nd all pairs ( ;(E;E 3)) which satisfy equa-tions (2. (Report) by "Elektronika ir Elektrotechnika"; Engineering and manufacturing Equipment performance Evaluation Numerical analysis Research Temperature effects Ultrasonic waves Properties Ultrasound Wave propagation Waveguides Acoustic properties Thermal. 5 4 h 1(x) h 2(x) D 0 H D 1 D x⋆ x∗ x˜ xꉱ x˘ Figure 1: Sketch map of a waveguide in ocean acoustics. Waveguide Example based on Cut off frequency 3. • Imaging in Random Waveguides Lecturer: Liliana Borcea (Rice U. Circular waveguides Introduction Waveguides can be simply described as metal pipes. This paper is devoted to the numerical solution of the instationary Maxwell equations in singular waveguides. = (40) (60 3 )/12. An efficient numerical marching scheme is proposed for inverse scattering problems of the Helmholtz equation in waveguides with curved boundaries or interfaces. GWaveguide discontinuities & circuits, scattering matrices, reciprocal circuits. International Journal of Numerical Analysis and Modeling 9(4): 928-949. Kamminga and B. We report on plasmonic waveguides made of a thin metal stripe surrounded on one or both sides by a Kerr nonlinear medium. New propagation regime is found. B : Brush up on mathematical tools: vector calculus, Fourier transform, differential equations, linear problems with homogeneity along a coordinate, a little variational calculus. For 1-dimensional structures there have been applications of the WFE method for free [3] and forced vibration [4] , to rail structures [5] (and, in [6] , using periodic structure theory for a track section. 2 Obtain the expressions of the surface charge and surface current densities on the plates of a parallel plate waveguide for the TM n mode. The proposed algorithm uses the exact expression for the solution to the integral equation for the electromagnetic field in the planar waveguide with. Below the waveguide cutoff frequency, it is not able to carry the signals. Units: (dimensionless) How to cite the article; suggest additional. AU - Chew, Weng Cho. Bonnet-BenDhia (École Nationale Supérieure de Techniques Avancées, Paris, France): A new approach for proving the absence of trapped modes in heterogeneous 2D open media. Numerical methods for calculating the parameters of various types of waveguide structures are described in the monographs and review papers [1,4,6,15]. In the case of the interconnection of optical fibers, the problem is reduced to the solution of an iterative series of boundary value problems of the type representing the slab waveguides problem. On the other hand, the purpose of waveguides is to guide electromagnetic energy. Part 4 provides a balanced presentation of time-varying fields, waves, and applications such as transmission lines, waveguides, and antennas. NUMERICAL PARALLEL COMPUTING Organization Organization: People / Exercises 1. McCartin Applied Mathematics, Kettering University 1700 West University Avenue, Flint, MI 48504-4898, USA [email protected] We suggest a new numerical method that is based on a truncation of the domain and the use of Bloch wave ansatz functions in radiation boxes. German: numerische Apertur. Waveguide Sizes A waveguide is an electromagnetic feed line that is used for high frequency signals. ) A variety of techniques have been employed to select a taper shape for coupling to periodic waveguides. This formulation enables to account for the translational invariance of waveguide problems and leads to a two-dimensional modal problem reduced on the cross-section. treatment of waveguides of inhomogeneous cross sections, but they are strongly singular and numerical algorithms based on them are not very efficient in terms of both computation time and convergence. Now the problem asks to run through all the calculations again sans the cladding (assume its air). The wave and finite element (WFE) method is a numerical approach to the calculation of the wave properties of structures of arbitrary complexity. Imbriale,1 and F. The divergence makes the design of rapidly converging numerical algorithms for vector mode field computations in such waveguides difficult. However, it should be said that most of the methods applied to homogeneous waveguides, are not common and are difficult to implement and apply for specific inhomogeneous structures. Despite this, solving the problem can still be computationally demanding. Also, the basis for the numerical solution of more general problems is given, including the example of the isosceles right triangular guide. This is a rather speci c example of how an optical medium can guide light energy. B : Brush up on mathematical tools: vector calculus, Fourier transform, differential equations, linear problems with homogeneity along a coordinate, a little variational calculus. 25, µr = 1 and σ = 10−4 Sm−1. Depending on their cross section there are rectangular waveguides (described in separate tutorial) and circular waveguides, which cross section is simply a circle. Numerical simulation for scattering problems in perio dic waveguides is an interesting topic, due to its wide applications in optics, nanotec hnology, etc. Method to control light propagation in waveguides invented New technique using nano-antennas to make photonic integrated devices smaller with a broader working wavelength range could transform. Waveguides are used at microwave frequencies where dielectric losses in radio cables become excessive; they are therefore used as feeders in radio telescopes. minimization [27], to mention a few. (If the waveguides are simply butt-coupled without a taper, the transmission goes to zero as the zero-velocity band-edge is approached (Sanchis et al. In order to further reduce the size of the modal problem, this paper presents a SAFE method for waveguides of rotationally symmetric cross-sections. The history of this prob-lem goes back to the engineering analysis of open waveguides in the 1960s (see the references in [37]). Silveira(*), W. High-Precision Propagation-Loss Measurement of Single-Mode Optical Waveguides on Lithium Niobate on Insulator Jintian Lin 1,y, Junxia Zhou 2,3,y, Rongbo Wu 1,4, Min Wang 2,3, Zhiwei Fang 2,3, Wei Chu 1, Jianhao Zhang 1,4, Lingling Qiao 1 and Ya Cheng 1,2,3,4,5,* 1 State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics. For the more complicated inhomogeneouswaveguides with and without striplines, comparison has beendone with results found in literature together with. Two ports are placed at the left and the right side of the structure (along the x-axis) being Source. Several numerical examples are presented to illustrate the method’s efficiency. 5 GHz for its lowest modes. A Comparative Study: Physical Modeling Sound Synthesis Methods. Exercises week 4: Fiber optics and waveguides Problem 1: Numerical aperture (NA) of a slab waveguide. Hughes* Department of Physics, Queen’s University, Kingston, Ontario K7L 3N6, Canada. , Kerr media) or time-varying systems, but generally must use ODE solvers to find numerical solutions • an construct one's own solver in MATLA, or use MTcomb3 on nanoHUB. Question: [20 Points Planar Waveguides A Planar Waveguide Shown In The Picture Was Fabricated By The Epitaxial Growth Of Different Layers Of AlGaAs With Different Aluminum Concentration So That The Outcome Is A Symmetric Slab Waveguide With The Refractive Indices As Shown. AU - Santosa, Fadil. Joannopoulos,3 Stephen P. This tutorial is dedicated to basic properties of circular waveguides. It is observed that the method for large-scale Cauchy problems is computationally efficient, highly accurate, and stable with respect to the noise in the data for the propagating part of a starting field. Analysis of guided-wave problems in substrate integrated waveguides -numerical simulations and experimental results Abstract: In this paper, a novel finite difference frequency domain (FDFD) algorithm is proposed for the analysis of substrate integrated waveguide (SIW) guided-wave problems where the perfectly matched layer (PML) has been chosen. We report an application of the tri-dimensional pseudo-spectral time domain algorithm, that solves with accuracy the nonlinear Maxwell's equations, to predict second harmonic generation in lithium niobate ridge-type waveguides with high index contrast. This leads to a very efficient method for the numerical simulation of the waveguide, which can be used, for instance, in optimal shape design. The transmission‐line matrix method is a time‐domain numerical method for solving wave problems. Numerical method for the solution of waveguide-discontinuity problems the solution of waveguide-discontinuity problems. AU - Blaschak, Jeffrey. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Wave scattering in irregular waveguides is investigated. Research highlights include: prediction and experimental confirmation of the plasmonic nanofocusing effect in tapered gap plasmon waveguides; discovery of channel-plasmons in sharp V-grooves (which have been identified by several groups as being the “ideal” nano-optical waveguide - see follow-up works of Prof. In Chapter 4 we present a mathematical framework which allows us to study the problem of wave propagation in perturbed waveguides. N2 - An efficient scheme based on the bi-Lanczos algorithm has been developed for analysis of the dielectric-waveguide problem. The approach is based on the resolvent method for the Volterra integral equation describing an electromagnetic process. This dissertation will explore the analysis of waveguide discontinuities for the purpose of dielectric filled waveguide filter analysis and design. We report on plasmonic waveguides made of a thin metal stripe surrounded on one or both sides by a Kerr nonlinear medium. One of the Romanian computer pioneers. Gopinath(•) Abstract - The main purpose of this paper is to stablish a comparison between some finite element and finite difference techniques to solve the wave operator together with the boundary. AU - Taflove, Allen. The numerical method used to solve the rel-evant 4D acoustic problems is based on Fourier synthesis of frequency-domain solutions. (7431 views) Lectures on Numerical Analysis by Dennis Deturck, Herbert S. The book introduces theoretical approach to numerical analysis as well as applications of various numerical methods to solving numerous theoretical and engineering problems. The aim of this work is to study the propagation of broadband sound pulses in three-dimensional shallow water waveguides. Power Dividers Propagation Downloads Links Site Map. Judkins Electromagnetics Laboratory, Department of Electrical and Computer Engineering, The University of Arizona, Tucson, Arizona 85721 vices, more-accurate and -realistic numerical simulations of these devices. The electron wave function satisfies the. Variational formulation As mentioned above, our goal is to nd all pairs ( ;(E;E 3)) which satisfy equa-tions (2. Applied Mechanics: AM 6010: Advanced Mechanics of Materials (3) Reviews basic stress-strain concepts and constitutive relations. If the section is 40mmx60mm, find the stress at the failure. The procedure is based on the well-known variational expression for the propagation constant and uses as trial field an expansion in terms of Hermite-Gauss functions. Imaging and wave propagation in random waveguides (3 lectures), Session "Etats de la Recherche", Inverse Problems and Imaging, Soci et e Math ematique de France, Institut Henri Poincar e, 20 - 22 February, 2013. PACS numbers: 41. SOI slot waveguide structures are simulated and characteristic values like the effective. Gudrun is in conversation with Anne-Sophie Bonnet-BenDhia from ENSTA in Paris about transmission properties in perturbed waveguides. Numerical technique usually finds EM field in some region. Type or paste a DOI name into the text box. Barseghyan (Nuclear Physics Institute, Rez; University of Ostrava, Ostrava, Czech Rep. After an introductory chapter outlining the basics of Maxwell's equations, the book includes self-contained chapters that focus on each of the methods. Hollow waveguides are useful for high-power microwaves. Deshpande ViGYAN, Inc. Andreas Adelmann, PSI, Villigen, WBGB/132 Tel. Engineering, Ira A. We report results for 3D vectorial time-harmonic Maxwell problems in waveguides with more than 8000 wavelengths. In order to carry signals a waveguide needs to be able to propagate the signals and this is dependent upon the wavelength of the signal. Attention is focused on the case of waveguides because numerical problems are generally far greater than for 2-dimensional structures. a numerical algorithm similar to that of chapter 2. Then the modified Helmholtz system in computational domain is piecewise solved through a second order numerical marching scheme. Research highlights include: prediction and experimental confirmation of the plasmonic nanofocusing effect in tapered gap plasmon waveguides; discovery of channel-plasmons in sharp V-grooves (which have been identified by several groups as being the “ideal” nano-optical waveguide - see follow-up works of Prof. As most practical problems can be solved by means of numerical techniques, the last part of the book covers the different numerical methods with practical applications and MATLAB® programs. Predicting the influence of axial loads on the wave propagation in structures such as rails requires numerical analysis. Variational formulation As mentioned above, our goal is to nd all pairs ( ;(E;E 3)) which satisfy equa-tions (2. 75 cm in Problem #2, calculate the range of frequencies over which the slab. Introduction. These problems consist of MCQs and other numerical answer type. Lossy boundaries are simulated by imperfect boundary reflections on the transmission lines. The history of this prob-lem goes back to the engineering analysis of open waveguides in the 1960s (see the references in [37]). 2 Computer Experiment—FTIR. The IM is a numerical method developed specifically for the nonlinear isotropic slot waveguides [15, 20], where all the non-null electric field components are present in the Kerr nonlinearity. problem is reduced to one for the scalar Helmholtz equation by considering a single type of waves, transverse electric or magnetic. The numerical aperture (NA) of an optical system (e. Oval waveguide equations are not included due to the mathematical complexity. : Antenna Laboratory. We report results for 3D vectorial time-harmonic Maxwell problems in waveguides with more than 8000 wavelengths. Holzbauer | Waveguides - Lecture 2 2/27/2019 Frank Tecker CLIC – 2 nd Int. 2 we saw that this stored energy is equal to CV2/2. The analysis of high-frequency wave propagation in arbitrarily shaped waveguides requires specific numerical methods. For more complex shapes, or waveguides with ridges, holes, dents along the way, then it gets messy and we lose one or two of these nice simplifications. The problem arises in the study of light in optical fibers. Sensing of gases is a promising area for applications of photonic sensor devices that operate in the mid-infrared spectral range. PY - 2001/7. * student knows about practices in preparing technical reports and in giving peer feedback and is able to prepare a report that combines analytical, measured, and simulated estimates. solving a set of algebraic equations at the interface between two planar waveguides, we. DClasses of simulation tasks: scattering problems, mode analysis, resonance problems. Semi-analytical finite element analysis of elastic waveguides subjected to axial loads. ) I will discuss the problem of imaging sources/scatterers in random waveguides using measure-ments of the acoustic pressure field recorded at a remote array of sensors, over some time window. We present a new variation on existing methods which has its derivation in methods for bifurcation problems, where bordered matrices are used to compute critical points in singular systems. The overall numerical scheme is robust, high-order, and efficient. Numerical Methods for Problems in Unbounded Domains Motivation • Numerical difficulties 03’ • Helmholtz equation in waveguides. Linear preserver results will be surveyed in the next few sections. to existing finite-difference schemes is the high numerical stability and dynamic range of our method, which allows the weak transverse component of the vector field of dielectric waveguides to be calculated with high accuracy. Monochromatic loading. Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). For solving interaction problems with the FDTD method, various techniques have been used in the past to absorb the outgoing. The idea of CSM as a method for solving the prob-lems of wave propagation in irregular waveguides is not new, but in this paper a self-contained and rigorous der-. The waveguides obtained had angled walls, and so numerical analysis was undertaken to establish the single mode condition for such trapezoidal structures. Both analytical and numerical approaches are covered. The idea of CSM as a method for solving the prob-lems of wave propagation in irregular waveguides is not new, but in this paper a self-contained and rigorous der-. ECE 1010 ECE Problem Solving I Chapter 7: Numerical Differentiation 7–16 Numerical Differentiation The derivative of a function is defined as if the limit exists • Physical examples of the derivative in action are: – Given is the position in meters of an object at time t, the first derivative with respect to t, , is the velocity in. Holzbauer | Waveguides - Lecture 2 2/27/2019 Frank Tecker CLIC – 2 nd Int. Our numerical experiments show that the pollution primarily has a diffusive effect causing energy loss in the DPG method while phase errors appear less significant. Introduction to the problem 2-D case Titchmarsh theory 3-D case 2 Uniqueness of solutions Motivations Sommerfeld radiation condition A theorem of uniqueness of solutions 3 Non-rectilinear waveguides Physical motivations Existence of a solution Numerical simulations. Y1 - 2001/7. Jamnejad,1 W. The numerical model also showed damping could potentially be a significant problem in long untapered wire waveguides (>1. Russian Quantum Center (RQC), Skolkovo, Moscow, Russia Figure 1. Rectangular Waveguides Theoretical Information; Design and Analysis. • Hampton, Virginia C. 2009-01-01. Propagation in 1D and 2D waveguides. Numerical implementation of the resulting operator Riccati equation uses a large range step method for discretizing the range variable and a truncated local eigenfunction expansion for approximating the operators. The systemati c analysis of the electromagneti c prop~lg,lli()1l for different measures of random roughness or wavegui de surface is carried out. NUMERICAL PARALLEL COMPUTING Organization Organization: People / Exercises 1. Homogenization techniques. The wave and finite element (WFE) method is a numerical approach to the calculation of the wave properties of structures of arbitrary complexity. The process is tedious as it. This method is particularly useful for solving long range wave propagation problems in slowly varying waveguides. Deshpande ViGYAN, Inc. This type of waveguide is used as a. Two cases are examined: (i) the 3D ASA benchmark wedge, and (ii) the 3D Gaussian canyon. Numerical interaction of boundary waves with perfectly matched layers in elastic waveguides Kenneth Duru , Gunilla Kreiss y April 10, 2012 Abstract Perfectly matched layers (PML) are a novel technique to simulate the ab-sorption of waves in open domains. AU - Chew, Weng Cho. In numerical experiment, two types of nonlinearities are considered and compared: the Kerr nonlinearity and nonlinearity with saturation. Coupled Oscillators Python. Categories: general optics, fiber optics and waveguides. Numerical Linear Algebra with Applications 20:2. A good understanding of propagation, scattering, attenuation and wave-type conversion of regional waves and the availability of analytical/numerical tools. Show that the numerical aperture for a dielectric slab waveguide with refractive indices n1 for the core and n2 for the cladding (n1>n2) is: 2. Hollow metallic pipes are used for this purpose, they do not support TEM waves. The researchers worked on an optimization problem: How does one design a waveguide for magnonic circuits to ensure maximum efficiency?. This paper investigates physiological responses to perceptions of unfair pay. Ribeiro(*), A. Bonnet-Ben Dhia, S. Beck Langley Research Center • Hampton, Virginia National Aeronautics and Space Administration Langley Research Center • Hampton. Numerical Aperture. Numerical technique usually finds EM field in some region. Step 2: Calculation of moment of inertia. A waveguide-pumped 6 mkm-radius ring cavity and it's transmittance Figure 2. 2020 IEEE 21st International Conference on Vacuum Electronics (IVEC) Technical presentations will range from the fundamental physics of electron emission and modulated electron beams to the design and operation of devices at UHF to THz frequencies, theory and computational tool development, active and passive components, systems, and supporting technologies. Basic Electromagnetic Theory The early history of guided waves and waveguides dates back to around the end of the nineteenth century. In the case of the interconnection of optical fibers, the problem is reduced to the solution of an iterative series of boundary value problems of the type representing the slab waveguides problem. It is observed that the method for large-scale Cauchy problems is computationally efficient, highly accurate, and stable with respect to the noise in the data for the propagating part of a starting field. For this kind of problems, solutions are obtained via the Limiting Absorption Principle and we all them LAP solutions. The generalized scattering matrix technique, introduced by Mittra and Pace, was applied to solve these problems. Treysse`dea, C. rectangular waveguides. The computational complexity can be highly dependent on the acoustic formulation. The three kinds of waveguide discontinuities studied were: (1) the metallic step discontinuity, (2) the inhomogeneous E-plane bifurcation, and (3) the trifurcation. Lecture 26 Dielectric Slab Waveguides In this lecture you will learn: • Dielectric slab waveguides •TE and TM guided modes in dielectric slab waveguides ECE 303 – Fall 2005 – Farhan Rana – Cornell University TE Guided Modes in Parallel-Plate Metal Waveguides z ε µo x ki=−kxx+kzzˆ r kr =kxx +kzzˆ r ki r E r H r kr r Ei Hi ()j k z. Of course the fully numerical methods based on finite elements [28,29] or finite differences [30,31] should also be mentioned. Numerical interaction of boundary waves with perfectly matched layers in elastic waveguides Kenneth Duru , Gunilla Kreiss y April 10, 2012 Abstract Perfectly matched layers (PML) are a novel technique to simulate the ab-sorption of waves in open domains. Studies unsymmetrical bending, shear center, and s. The 3D implementation of a hybrid analytical/numerical. Recent Posts. For many years, one of the most commonly used numerical methods for the simula-tion of electromagnetic wave propagation in planar waveguides, is the finite-di↵erence time-domain (FDTD) method [18][23][26]. 1 Simple MSC 74 2. However, because waveguide modeling often uses sophisticated numerical algorithms, you must be familiar with some aspects of the underlying numerics. The first optimization formulation is further employed to design slow light metal-dielectric-metal plasmonic waveguides. 75 cm in Problem #2, calculate the range of frequencies over which the slab. waveguides have been presented in the past using approximate or numerical methods. A method is described whereby complex reflection and transmission coefficients of modes excited at a waveguide junction may be determined by a simple technique utilising a digital computer. Once we have the field pattern, the usefulness is in knowing where the field is strongest - you want to minimize obstructions, and use the best materials. Dielectric waveguides which can lead to problems when coupling light from an optical fiber into the numerical methods like finite differences and fi-. load at failure = 2KN. The waveguides obtained had angled walls, and so numerical analysis was undertaken to establish the single mode condition for such trapezoidal structures. Password requirements: 6 to 30 characters long; ASCII characters only (characters found on a standard US keyboard); must contain at least 4 different symbols;. We fabricated flexible polymer waveguides by using PDMS elastomer, which has a refractive index of ≈1. Instruction will be by lectures on the underlying theory, in-depth discussion of numerous practical examples, and hands-on experience in solving. edu Abstract A perturbation procedure for the modes and cut-off frequencies of. Mathematics Subject Classification: 65N12 / 65M15 / 65M30 Key words: Helmholtz equation / PML / finite element method / waveguide. Kamminga and B. Note that this permittivity and permeability vary withposition,butdonotinvolve ,thetransformedlongitudinal coordinate. Numerical Methods in Photonics presents six of the most frequently used methods: FDTD, FDFD, 1+1D nonlinear propagation, modal method, Green's function, and FEM. 9-(13-6278) Task 40572. The purpose of this study is to develop a new numerical method to solve one-dimensional wave equation for planar waveguides using the Fourier transform and to demonstrate some of its advantages in comparison with the methods exist. Final Exam. Part 4 provides a balanced presentation of time-varying fields, waves, and applications such as transmission lines, waveguides, and antennas. For 1-dimensional structures there have been applications of the WFE method for free [3] and forced vibration [4] , to rail structures [5] (and, in [6] , using periodic structure theory for a track section. After an introductory chapter outlining the basics of Maxwell's equations, the book includes self-contained chapters that focus on each of the methods. Accurate modelling of second order nonlinear effect in optical waveguides using the finite element method. A two-level domain decomposition method with accurate interface conditions for the Helmholtz problem A Vaziri Astaneh, M Guddati International Journal for Numerical Methods in Engineering 107 (1), 74–90 , 2016. The numerical aperture, NA, is defined as Optical Fiber Numerical Aperture The incident light make an angle c with a normal to the core–cladding boundary. This method is particularly useful for solving long range wave propagation problems in slowly varying waveguides. ) Simple analysis - let = c S c L ˝1 = c R c S <1 Then is given by roots of: det 2 2 2 p 2i 2 1 2 2i p 1 2 2 2 2 detR. Calculation of eigenftmctions for optical waveguides using a new numerical approach Takaytiki Yamanaka, Shunji Seki and Kiyoyuki Yokoyama NTT Opto-electronics Laboratories 3-1 Morinosato Wakainiya, Atsugi, Kanagawa 243-01, Japan Abstract : An efficient nvunerical approach has been applied to analyze optical field distributions for optical. ) I will discuss the problem of imaging sources/scatterers in random waveguides using measure-ments of the acoustic pressure field recorded at a remote array of sensors, over some time window. In particular, we are able to prove the existence of a solution for small perturbations of 2-D rectilinear waveguides. Introduction As a result of the vast variety of practical applications of the dielectric filled waveguide in microwave and optical frequencies, the development of methods to solve the associated electromagnetic field problems has attracted the. Two most common approximate techniques are the Marcatili approach [1] and the circular harmonic point matching technique. Problems 361 improving liquid crystal displays, and other products, such as various optoelectronic components, cosmetics, and "hot" and "cold" mirrors for architectural and automotive windows. If you have had even just a bit of dissatisfaction in reliability test results, please put NTT-AT’s. For many years, one of the most commonly used numerical methods for the simula-tion of electromagnetic wave propagation in planar waveguides, is the finite-di↵erence time-domain (FDTD) method [18][23][26]. Length of beam = 2m or 2000mm. 2, 044 632 6141 [email protected] Both analytical and numerical approaches are covered. The new algorithm does not rely. A wide range of waveguide coverage, from the familiar types (step-index optical fiber and planar) to the more striking (elliptical and. A spectral boundary element method for scattering problems Computer Modeling in Engineering and Sciences (CMES), 58, 3,(2010) 221--244. Numerical simulation for scattering problems in perio dic waveguides is an interesting topic, due to its wide applications in optics, nanotec hnology, etc. In addition to the MOL, I have some past experience with other numerical methods, which includes, the Beam Propagation Method (BPM) and the Finite. MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum. Numerical analysis of the eigenvalue problem of waves in cylindrical waveguides. When terrain, wind, and atmospheric effects are taken into account, this problem cannot be solved analytically, and, thus, numerical solutions are required. Waveguides will only carry or propagate signals above a certain frequency, known as the cut-off frequency. This banner text can have markup. The basic principles of electromagnetic theory include electrostatics, electromagnetic induction, magnetic fields of steady currents, etc. Numerical examples are given for homogeneous andinhomogeneous waveguides, in the homogeneous case the resultsare compared to analytical solutions and the right order ofconvergence is achieved. The Essence of Dielectric Waveguides is a comprehensive overview of the fundamental behavior of dielectric waveguides, essential to interpreting the numerical data results of electromagnetic waveguide problems. The numerical modeling to a boundary value problem and the numerical discretisation of interconnection problems of two slab waveguides are discussed. Wave propagation in random waveguides. 1 Prove the reflectance and transmittance formulas (8. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Waveguides conduct microwave energy at lower loss than coaxial cables and are used in microwave communications, radars and other high frequency applications. In this paper, a procedure is developed to reduce the eigenvalue problem for PhC slab waveguides to a nonlinear problem defined on a small surface in the waveguide core. home documentation community source code gallery events try it online donate documentation community source code gallery events try it online donate. The method starts from a finite element (FE) model of only a short segment of the structure, typically by using existing element libraries and commercial FE packages. • MATLAB codes for 2-D finite-difference (FD) numerical solution of Laplace's equation, based on both iterative and direct solutions of FD equations; potential, field, and charge computations ⋄ MATLAB solutions to nonlinear problems: • Graphical and numerical solutions for a simple nonlinear electric circuit. Appears in the select History of Approximation Theory ( Technion Univ.

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