Ray Optics Simulations with COMSOL Multiphysics®

Christopher Boucher

Developer

COMSOL

© Copyright 2015 COMSOL. COMSOL, COMSOL Multiphysics, Capture the Concept, 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

Jennifer Segui

Technical Marketing Engineer

COMSOL

Agenda

• Why Simulate?

– Simulating with COMSOL Multiphysics®

• The Multiphysics Approach

• Live Demo

– Thermally Induced Focal Shift

• Q&A Session

• How To

– Try COMSOL Multiphysics

– Contact Us

Ray Tracing in a Newtonian telescope

Why Simulate?

• Conception and understanding – Enables innovation

• Design and optimization – Achieve the highest possible

performance

• Testing and verification – Virtual testing is much faster than

testing physical prototypes

Homogenization of an LED source by total internal reflection within a bent light pipe.

Simulating with COMSOL Multiphysics®

• Electrical, mechanical, fluid, and chemical simulations

• Multiphysics – include and couple all relevant physical effects

• Single physics in one integrated environment

• Cross-disciplinary product development

All Industries Benefit from Multiphysics Simulation

Metamaterials Make Physics Seem Like Magic

Extract from COMSOL News 2012 © 2012 COMSOL. All rights reserved.

• Metamaterials have complex structures that are able to ‘shield’ objects from wave phenomena with countless applications and design obstacles

• COMSOL’s tools enable creative and quick testing of new ideas that would be much more difficult, time-consuming, and expensive to test in the lab

• COMSOL News 2012: J. Wilson, NASA Glen Research Center, Cleveland, OH, USA

G. Karunasiri & F. Alves, Naval Postgraduate School, Monterey, CA

D. Smith & Y. Urzhumov, Duke University, Durham, NC

Aporous metamaterial shell that eliminates a wake in subsurface flow

Unidirectional acoustic cloak based on quasi-conformal transformation optics

Extract from IEEE Spectrum Multiphysics Simulation Insert 2014 © 2014 COMSOL. All rights reserved.

Nanoresonators Get New Tools for their Characterization

• Investigate the electromagnetic properties of nanoresonators and predict the interactions between a resonator and its environment

• Simulate excitation modes, and use results to determine physical properties such as scattering, absorption, and radiation parameters

• IEEE Spectrum Multiphysics Simulation Insert 2014 : Jianji Yang1, Matthias Perrin2, and Philippe Lalanne1, National Centre for Scientific Research, Paris, France

1 Laboratoire Photonique, Numérique et Nanosciences 2 National Centre for Scientific Research

COMSOL simulation showing the electric field radiated by a nanoresonator.

Simulation results showing the intensity of the electric field and flux around a silver sphere of radius 20nm.

Poll Question #1 • How many software tools do you currently

use for ray tracing simulations? – None

– One

– Two

– Three or more

Model Builder Provides instant access to any of the model settings • CAD/Geometry • Materials • Physics • Mesh • Solve • Results

A Complete Simulation Environment

Graphics Window Ultrafast graphic presentation, stunning visualization

COMSOL Desktop® Straightforward to use, the Desktop gives insight and full control over the modeling process

Product Suite – COMSOL® 5.0

Application Design Tools

Simulation Application Any COMSOL model can be turned into an app with its own interface using the tools provided in the Application Builder

Application Builder Provides all the tools needed to build and run simulation apps • Form Editor • Method Editor

Run Applications

Simulation Apps They can be run in a COMSOL® Client for Windows® and major web browsers

COMSOL Server™ It’s the engine for running COMSOL apps and the hub for controlling their deployment, distribution, and use

Microsoft and Windows are either registered trademarks or trademarks of Microsoft Corporation in the United States and/or other countries.

Electrical Simulations • AC/DC current and field distribution • Electromechanical machinery and electrical

circuits • RF and microwave components • Wave propagation in optical media

Magnetic field in a Helmholtz coil Microstrip patch antenna array

Electrical Simulations

• MEMS devices and sensors

• Low temperature plasma reactors

• Semiconductor devices

• Ray tracing in optically large systems

Inductively coupled plasma reactor Prestressed micromirror

The Ray Optics Module For Ray Tracing Simulations in

Optically Large Systems

Overview of Ray Optics Simulation

• Ray optics vs wave optics

• Ray properties

• Boundary conditions

• Ray release features

• Dedicated multiphysics functionality

• Results and visualization Solar radiation is reflected by a parabolic mirror.

The incident flux on a small receiver is computed.

Electromagnetic Wave Simulation • Electromagnetic Waves, Frequency

Domain – RF or Wave Optics Module – Mesh must resolve wavelength – Full-wave solution: Solves Maxwell’s

Equations

• Electromagnetic Waves, Beam Envelopes – Wave Optics Module – Mesh need not resolve wavelength – Must know direction of propagation – For modelling waveguides or fibers

• Geometrical Optics – Ray Optics Module – Approximate method for small wavelengths – Mesh need not resolve wavelength – Direction of propagation not required

Shortening Wavelength Fixed Mesh

Failure to Resolve Waves

Geometrical Optics • Geometrical optics can be used to model electromagnetic

wave propagation in optically large structures. • Electromagnetic waves are treated as rays. • Advantages:

– Mesh can be very large compared to wavelength. – Wave propagation can be modeled over extremely long

distances. – Support for frequency distributions and varying degrees of

polarization.

• Requirements: – Wavelength must be much smaller than the smallest detail in the

geometry. – Diffraction at sharp edges and corners is negligible.

Ray Optics vs RF/Wave Optics • RF or Wave Optics

– Full-wave formulation is required to model propagation around small objects.

• Ray Optics – Ray paths are not

strictly solutions to a wave equation.

– Diffraction is not included.

Key Application Areas • Building science

• Imaging

– Cameras, telescopes, microscopes

• Laser systems

• Solar power

• Spectrometers Ray trajectories in an assembly of a beam splitter with two

adjustable mirrors, used in a Michelson interferometer.

Key Features • Ray tracing in homogeneous and graded

media. • Analysis of ray intensity and polarization. • Variety of features for releasing rays and

controlling interaction with boundaries. • Dedicated boundary conditions to

manipulate ray polarization. • Multiphysics couplings to model thermal

effects. • Dedicated study step and postprocessing

tools.

Ray Tracing with the Geometrical Optics Interface

• Solves for: – Ray position q – Wave vector k

• Can trace rays in homogeneous or graded media.

• Additional equations can be defined and solved for each ray.

• Built-in calculation of ray intensity, curvature, optical path length, etc.

Ray trajectories in the graded medium of a Luneburg lens.

Intensity Computation • Rays are treated as

wavefronts that converge or diverge.

• Wavefront radii of curvature are computed for each ray.

• Intensity can be computed accurately regardless of the number of rays used. Pictoral representation of the two principal radii of curvature

of an advancing wavefront (top). Sign conventions for

wavefront radii of curvature (bottom).

Intensity Variables • Stokes parameters

are used to store information about ray polarization.

• At boundaries: – Stokes parameters

are reset based on polarization of the incident ray.

– Radii of curvature are reinitialized based on surface curvature.

Principal radius of curvature (left) and the log of intensity (right) for a

bundle of rays crossing a material discontinuity.

Frequency Distributions • It is possible to assign a

unique frequency value for each ray, allowing polychromatic light to be modeled.

• Built-in options to sample frequency from a normal, log-normal, or uniform distribution

• A list of numerical values can be entered directly.

• Rays can be separated using dispersive media or diffraction gratings.

A prism with a frequency-dependent refractive index separates

polychromatic light into distinct colors.

More Built-in Variables

• Phase calculation – Instantaneous electric field

can be plotted for polarized rays.

– Can be used to view interference patterns.

• Optical path length calculation – Defines a variable for the

optical path length of each ray.

Ray trajectories in a corner cube retroreflector.

The color indicates the optical path length.

Poll Question #2 • Are you primarily interested in modeling:

– Thermal applications (Laser heating, solar power, etc.)

– Imaging applications (cameras, spectrometers, etc.)

– Other

Wall Conditions • Three settings for

absorption of rays at a boundary: – Freeze: retain position q and

wave vector k. – Stick: retain q only. – Disappear: retain nothing.

• Pass through – For transparent boundaries.

• General reflection – Reflection in a user-defined

direction.

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Wall Conditions, Continued • Specular reflection – Uses the curvature

of the surface to update the curvature of the wavefront.

• Diffuse scattering – Reflect in a random direction using Lambert’s cosine law.

• Mixed diffuse and specular reflection – Assign a probability of specular reflection.

Material Discontinuity • Default interior

boundary condition. • Creates reflected and

refracted rays based on Snell’s Law.

• Updates wavefront curvature based on the shape of the surface.

• Updates intensity using the Fresnel Equations.

Caustic surfaces generated by rays passing through the

material discontinuities on either side of a lens.

Coatings on Material Discontinuities

• Thin dielectric layers can be added to material discontinuities.

• Single-layer and multilayer films are supported.

• Use these layers to model: – Anti-reflective coatings – Distributed Bragg

reflectors – Beam splitters

Analysis of a multilayer antireflective coating. The reflectance of two

different coatings is plotted over a range of vacuum wavelengths.

Diffraction Gratings • Release transmitted

and reflected rays of diffraction order 0.

• Option to add any number of higher diffraction orders.

• Transmittance and reflectance of each diffraction order can be set separately.

Analysis of polychromatic light by two mirrors and a grating in

a crossed Czerny-Turner configuration.

Other Boundary Conditions

• Optical devices

– Linear polarizers

– Linear wave retarders

– Circular wave retarders

– Ideal depolarizers

– User-defined Mueller matrices for custom optical devices

Effects of the Linear Polarizer (top) and Circular Wave

Retarder (bottom) boundary conditions on ray polarization.

Releasing Rays • Domain-based release

– Based on mesh elements or user-defined density.

• Release from boundaries

– Rays can inherit the wavefront curvature of the surface.

• Release from a grid of

points – Initial direction can be

based on solar position. Grid-based release

Boundary-based release

Mesh-based release

Illuminated Surfaces • Rays can be directly released

from an illuminated surface.

• Options for specifying incident ray direction: – Plane wave

– Point source

– Based on solar position

• No shadowing effects.

• Corrections for finite source diameter, surface roughness, and solar limb darkening.

Comparison of a grid-based release with a Specular reflection

wall condition (left) to the Illuminated Surface (right).

Initial Intensity and Polarization • Rays can be assigned a degree of polarization. • Rays can be linearly, circularly, or elliptically polarized.

Propagation of a circularly polarized ray through a series of linear wave retarders.

Accumulators • It is possible to communicate information from rays to the

domains they pass through or the boundaries they hit. • Features called Accumulators define variables that can be affected

by rays. • Dedicated accumulators are available for generating heat source

terms on domains and boundaries.

Accumulated

variables on

domains (left)

and boundaries

(right).

Using Accumulators

• Each Accumulator creates one degree of freedom per mesh element.

• Accumulation can occur at the end point of the ray or along its entire path.

• Built-in option to create density terms by dividing by the mesh element volume or area.

Propagation of rays (top) and the

corresponding change in an accumulated

variable defined on the domain (bottom).

Ray Optics with Heat Transfer • It is possible for rays to

generate a heat source term as they pass through absorbing media.

• Energy lost by the rays is dissipated as heat.

• Unidirectional or “one-way” coupling between rays and temperature field.

Ray Optics Coupling: Ray

Power Attenuation Heat Transfer

A ray passes through a slab of an absorbing

material and raises its temperature.

Bidirectional Couplings • The heat source from ray attenuation can affect ray trajectories via:

– Temperature dependence of the refractive index. – Strain dependence of the refractive index. – Physical deformation of the geometry.

• When we consider these effects, the rays change the temperature, which in turn perturbs the rays.

• We speak of a bidirectional or “two-way” coupling.

Geometrical Optics Attenuation Heat Transfer

Temperature-dependent refractive indices

Solid Mechanics Thermal Stress Deformation

Ray Tracing Study Step

• Ray Trajectories are computed in the time domain.

• With the Ray Tracing study step, the range of times can either be specified directly or in terms of maximum optical path length.

• Built-in stop conditions can end the study early if all rays are no longer active.

Ray Trajectories Plot

• Plot ray trajectories as lines or tubes.

• Plot current ray positions using points, arrows, or comet tails.

• Apply deformations or color expressions to the ray trajectories.

• Use filters to view only a subset of rays.

• Plot data can easily be exported to a file. Caustic surfaces generated by rays .

Ray Plot • Plot a ray property versus time for all rays, or plot two ray properties against each

other at selected time steps. • When plotting over time, use data series operations to compute the following

quantities over all rays: – Average – Sum – RMS – Maximum – Minimum – Standard deviation – Variance

The ray plot is used to visualize the

reflectance of a distributed Bragg reflector as

the number of dielectric layers is increased.

Interference Patterns

• Plot the interference fringes resulting from the intersection of coherent rays with a plane.

• The solid angles subtended by the wavefronts are assumed to be small.

Interference fringes from two spherical waves with different radii of curvature

(left) and from two plane waves with different angles of incidence (right).

Ray Evaluation • Create data tables that can be plotted or exported to files.

Other Visualization Tools

• Poincaré maps

• Phase portraits A Poincaré map (right) is created

when ray trajectories intersect a

cut plane after passing through a

lens (bottom).

Demo: Thermally Induced Focal Shift

• A high-powered laser is focused onto a target by two convex lenses.

• Due to thermal effects, the focus changes position as the power of the laser system increases.

• This example includes temperature-dependence of the refractive index and deformation of the lenses.

Further Resources • Introduction to COMSOL Multiphysics

– The COMSOL Desktop® – Step-by-Step Tutorials

• Structural Analysis of a Wrench – includes mesh convergence analysis • The Busbar – A Multiphysics Model

– Advanced Topics • Parameters, functions, variables, and couplings • Material properties and the Material Library • Adding meshes, physics, and parametric sweeps • High-performance computing

– Building a Geometry – Keyboard and Mouse Shortcuts http://www.comsol.com/shared/downloads/IntroductionToCOMSOLMultiphysics.pdf

Q&A Session

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