Wave Optics Module User’s Guide Wave Optics Module User’s Guide © 1998–2018 COMSOL Protected by patents listed on www.comsol.com/patents, and U.S. Patents 7,519,518; 7,596,474; 7,623,991; 8,457,932; 8,954,302; 9,098,106; 9,146,652; 9,323,503; 9,372,673; and 9,454,625. Patents pending. This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement (www.comsol.com/comsol-license-agreement) and may be used or copied only under the terms of the license agreement. COMSOL, the COMSOL logo, COMSOL Multiphysics, COMSOL Desktop, COMSOL Server, and LiveLink are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see www.comsol.com/trademarks. Version: COMSOL 5.4 Contact Information Visit the Contact COMSOL page at www.comsol.com/contact to submit general inquiries, contact Technical Support, or search for an address and phone number. You can also visit the Worldwide Sales Offices page at www.comsol.com/contact/offices for address and contact information. If you need to contact Support, an online request form is located at the COMSOL Access page at www.comsol.com/support/case. Other useful links include: • Support Center: www.comsol.com/support • Product Download: www.comsol.com/product-download • Product Updates: www.comsol.com/support/updates • COMSOL Blog: www.comsol.com/blogs • Discussion Forum: www.comsol.com/community • Events: www.comsol.com/events • COMSOL Video Gallery: www.comsol.com/video • Support Knowledge Base: www.comsol.com/support/knowledgebase Part number: CM023501 Contents Chapter 1: Introduction About the Wave Optics Module 10 About the Wave Optics Module . 10 What Problems Can You Solve? . 11 The Wave Optics Module Physics Interface Guide . 12 Common Physics Interface and Feature Settings and Nodes . 13 Selecting the Study Type . 14 The Wave Optics Module Modeling Process . 16 Where Do I Access the Documentation and Application Libraries? . 16 Overview of the User’s Guide 20 Chapter 2: Wave Optics Modeling Preparing for Wave Optics Modeling 24 Simplifying Geometries 25 2D Models . 25 3D Models . 26 Using Efficient Boundary Conditions . 27 Applying Electromagnetic Sources . 28 Meshing and Solving. 28 Periodic Boundary Conditions 30 Scattered Field Formulation 32 Modeling with Far-Field Calculations 34 Far-Field Support in the Electromagnetic Waves, Frequency Domain Interface. 34 The Radiation Pattern Plots . 35 CONTENTS | 3 Maxwell’s Equations 41 Introduction to Maxwell’s Equations . 41 Constitutive Relations . 42 Potentials. 44 Electromagnetic Energy . 44 Material Properties . 45 About the Optical Materials Database . 47 Boundary and Interface Conditions . 47 Phasors . 48 Special Calculations 50 S-Parameter Calculations. 50 Far-Field Calculations Theory . 53 References . 54 S-Parameters and Ports 55 S-Parameters in Terms of Voltage and Electric Field . 55 S-Parameter Calculations. 56 S-Parameter Variables . 56 Port Sweeps/Manual Terminal Sweeps and Touchstone Export . 56 Lossy Eigenvalue Calculations 57 Eigenfrequency Analysis . 57 Mode Analysis . 59 Reduced Order Modeling 61 Adaptive Frequency Sweep Using Asymptotic Waveform Evaluation (AWE) Method . 61 Frequency Domain, Modal Method . 63 Electromagnetic Quantities 64 Chapter 3: Wave Optics Interfaces The Electromagnetic Waves, Frequency Domain Interface 68 Domain, Boundary, Edge, Point, and Pair Nodes for the 4 | CONTENTS Electromagnetic Waves, Frequency Domain Interface . 75 Wave Equation, Electric . 77 Initial Values . 82 External Current Density . 82 Far-Field Domain . 82 Far-Field Calculation . 83 Polarization . 84 Perfect Electric Conductor . 84 Perfect Magnetic Conductor . 85 Port. 86 Circular Port Reference Axis . 93 Diffraction Order . 93 Periodic Port Reference Point . 95 Electric Field . 96 Magnetic Field . 97 Scattering Boundary Condition . 97 Reference Point . 100 Impedance Boundary Condition . 101 Surface Current Density . 103 Surface Magnetic Current Density . 103 Transition Boundary Condition . 104 Periodic Condition . 106 Magnetic Current . 107 Edge Current . 108 Electric Point Dipole . 108 Magnetic Point Dipole . 108 Line Current (Out-of-Plane) . 109 The Electromagnetic Waves, Transient Interface 110 Domain, Boundary, Edge, Point, and Pair Nodes for the Electromagnetic Waves, Transient Interface . 111 Wave Equation, Electric . 113 Initial Values . 116 Drude-Lorentz Polarization . 116 The Electromagnetic Waves, Time Explicit Interface 118 Domain, Boundary, and Pair Nodes for the Electromagnetic Waves, Time Explicit Interface . 119 CONTENTS | 5 Wave Equations . 120 Initial Values . 122 Electric Current Density . 123 Magnetic Current Density . 123 Electric Field . 123 Perfect Electric Conductor . 124 Magnetic Field . 124 Perfect Magnetic Conductor . 124 Surface Current Density . 125 Scattering Boundary Condition . 125 Flux/Source . 126 Background Field . 126 Far-Field Domain . 127 Far-Field Calculation . 127 The Electromagnetic Waves, Beam Envelopes Interface 129 Domain, Boundary, Edge, and Point Nodes for the Electromagnetic Waves, Beam Envelopes Interface . 134 Wave Equation, Beam Envelopes . 136 Polarization . 137 Initial Values . 138 Electric Field . 138 Field Continuity . 139 Magnetic Field . 139 Matched Boundary Condition . 139 Scattering Boundary Condition . 140 Surface Current Density . 142 Theory for the Electromagnetic Waves Interfaces 144 Introduction to the Physics Interface Equations . 144 Frequency Domain Equation . 144 Time Domain Equation . 151 Vector Elements . 153 Eigenfrequency Calculations. 153 Gaussian Beams as Background Fields . 153 Theory for the Electromagnetic Waves, Time Explicit 6 | CONTENTS Interface 156 The Equations . 156 In-plane E Field or In-plane H Field . 160 Fluxes as Dirichlet Boundary Conditions . 161 Absorbing Layers. 162 Chapter 4: Heat Transfer Interfaces The Laser Heating Interface 166 Chapter 5: Glossary Glossary of Terms 172 CONTENTS | 7 8 | CONTENTS 1 Introduction This guide describes the Wave Optics Module, an optional add-on package for COMSOL Multiphysics® designed to assist you to set up and solve electromagnetic wave problems at optical frequencies. This chapter introduces you to the capabilities of this module. A summary of the physics interfaces and where you can find documentation and model examples is also included. The last section is a brief overview with links to each chapter in this guide. In this chapter: • About the Wave Optics Module • Overview of the User’s Guide 9 About the Wave Optics Module These topics are included in this section: • About the Wave Optics Module • What Problems Can You Solve? • The Wave Optics Module Physics Interface Guide • Common Physics Interface and Feature Settings and Nodes • Selecting the Study Type • The Wave Optics Module Modeling Process • Where Do I Access the Documentation and Application Libraries? Building a COMSOL Multiphysics Model in the COMSOL Multiphysics Reference Manual About the Wave Optics Module The Wave Optics Module extends the functionality of the physics interfaces of the base package for COMSOL Multiphysics. The details of the physics interfaces and study types for the Wave Optics Module are listed in the table in The Wave Optics Module Physics Interface Guide. The functionality of the COMSOL Multiphysics base package is given in the COMSOL Multiphysics Reference Manual. The Wave Optics Module solves problems in the field of electromagnetic waves at optical frequencies (corresponding to wavelengths in the nano- to micrometer range). The underlying equations for electromagnetics are automatically available in all of the physics interfaces — a feature unique to COMSOL Multiphysics. This also makes nonstandard modeling easily accessible. The module is useful for simulations and design of optical applications in virtually all areas where you find electromagnetic waves, such as: • Optical fibers • Photonic waveguides • Photonic crystals • Nonlinear optics 10 | CHAPTER 1: INTRODUCTION • Laser resonator design • Active devices in photonics The physics interfaces cover the following types of electromagnetics field simulations and handle time-harmonic, time-dependent, and eigenfrequency/eigenmode problems: • In-plane, axisymmetric, and full 3D electromagnetic wave propagation • Full vector mode analysis in 2D and 3D Material properties include inhomogeneous and fully anisotropic materials, media with gains or losses, and complex-valued material properties. In addition to the standard postprocessing features, the module supports direct computation of S-parameters and far-field radiation patterns. You can add ports with a wave excitation with specified power level and mode type, and add PMLs (perfectly matched layers) to simulate electromagnetic waves that propagate into an unbounded domain. For time-harmonic simulations, you can use the scattered wave or the total wave. Using the multiphysics capabilities of COMSOL Multiphysics you can couple simulations with heat transfer, structural mechanics, fluid flow formulations, and other physical phenomena. What Problems Can You Solve? The Wave Optics Module allows you to make high-frequency electromagnetic wave simulations. It distinguishes itself from the AC/DC Module, in that the AC/DC Module targets quasi-static simulations, where the size of the computational domain is small compared to the wavelength.