Ray Optics MinicourseCOMSOL Tokyo Conference 2014

What is the Ray Optics Module?• Add-on to COMSOL Multiphysics

• Can be combined with any other COMSOL Multiphysics Module

• Includes one physics interface, the Geometrical Optics interface

What are the Key Applications?• Building science• Cameras• Coatings• Imaging• Interferometers• Lasers• Lens systems• Optical Components• Monochromators• Ray heating• Solar energy harvesting• Spectrometers Ray Trajectories in an assembly of a beam splitter with two adjustable

mirrors, used in a Michelson interferometer.

What effects are considered within domains?• Ray propagation is computed in uniform & graded

refractive index materials• Reflection and refraction at material interfaces

What effects can be modeled at boundaries?

Transparent andPerfect Absorption

SpecularReflection

DiffuseReflection

Mixed: Specular & Diffuse

Or completely User-Defined Reflection

Thin dielectric films

Arbitrary number of different layers of material

m = -1 m = 0

m = +1

Gratings

Arbitrary number of diffraction orders

What effects can be modeled at boundaries?

• Linear Polarizer• Linear Wave Retarder• Circular Wave Retarder• Ideal Depolarizer• User-defined Mueller Matrices

What effects can be modeled at boundaries?

How can ray release be modeled?

Plane Wave Spherical Hemispherical Conical

α

All are available in 2D and 3D

How can far-away sources be modeled?

• Release reflected or refracted rays when a surface is illuminated by a plane wave, point source, or by solar radiation.

• Includes corrections for finite source diameter, surface roughness, and solar limb darkening

Comparison of a grid-based release with a Bounce wall condition (left) to the Illuminated Surface BC (right).

How to compute ambient solar radiation?

• Release from Grid feature that computes direction based on solar position

• Can compute solar position based on latitude and longitude or by selecting a city

How to model Frequency-Dependent Refractive Indices?

• Frequency-dependent refractive indices option

• Rays can be released with a distribution of frequencies

• Refractive index can be a function of frequency or wavelength, for example:

A polychromatic beam enters a dispersive medium and splits into monochromatic rays moving in different directions.

n = 1.13-gop.nu/5E15[Hz]

Different frequency variable for each ray

What properties can be tracked, and postprocessed, along the path of the ray?

Phase & Interference PatternsMichelson interferometer

What properties can be tracked, and modified, along the path of the ray?

PolarizationPolarized, Partially Coherent, and Incoherent sources can be modeled

IntensityRadius of curvature is computed

What Intensity Computations Options Exist?

• None – Intensity is not computed.

• Using Principal Curvatures –Stores information about ray intensity and polarization.

• Using Principal Curvatures and Ray Power – Select this when rays are used to generate heat sources for other physics interfaces.

Principal radius of curvature (left) and the log of intensity (right) for a bundle of rays crossing a material discontinuity.

What is the underlying mathematical framework?

• Define first-order ordinary differential equations (ODEs) for ray position q and wave vector k

• Equations are solved in the time-domain

• Additional first-order ODEs can be solved for each ray. The variables being solved for in these ODEs are called auxiliary dependent variables.

• Calculation of many other quantities can be activated via the settings window for the physics interface.

Ray trajectories in the graded medium of a Luneburg lens.

What solver settings are available?• 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.

How fine a mesh is needed?

Within uniform domains, the solution does not depend at all upon mesh refinement

Within graded media, the mesh must be fine enough to resolve the material variations

At boundaries, a minimum of three elements per 90° circular arc are recommended

What effects are not considered?Full-wave Electromagnetics formulation (using either RF or Wave Optics Module) is needed to model diffraction at edges and small gaps

Geometrical Optics assumes wavelengths are much smaller that the object size, there is no diffraction at edges and holes

• 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 be exported to a file

Caustic surfaces generatedBy rays .

What post-processing options exist?

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

against each other at selected timesteps– When plotting over time, data series operations 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 grating as the number of dielectric layers is increased.

What post-processing options exist?

What post-processing options exist?• Interference Pattern Plot

– Plot the interference fringes resulting from the intersection of coherent rays with a cut 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).

What post-processing options exist?• Deposited Power on Surfaces• Absorbed Power in Domains

Reflected Solar Flux

Absorbed Power in a Lens

Model Library Examples

More examples will become available at: http://www.comsol.com/models/ray-optics-module

Example Highlight: Caustic surfaces at the Vdara® Hotel in Las Vegas • At certain times of the year, the Vdara® hotel in Las Vegas, Nevada would reflect solar

radiation so that its intensity became extremely high at ground level.• This model uses the Illuminated Surface feature to compute the trajectories and

intensity of rays reflected by the curved surface of the hotel.

Intensity of solar radiation reflected by the Vdara® hotel (left) and the intersection of the caustic surface with the ground (right).

Example Highlight: Thermal Lensing• Bidirectional coupling between a heat transfer model and a ray tracing

model is possible, accounting for thermal expansion.• Temperature and ray trajectories are computed using an iterative

process until a self-consistent solution is obtained.

Rays are focused by a lens system. Due to thermal deformation of the lenses, the focal point is shifted.

Example Highlight: Solar Dish Receiver• Solar radiation is reflected

by a parabolic dish and focused at a small collector, generating large heat fluxes.

• The effects of finite solar diameter and surface roughness are included.

• The resulting heat flux agrees with published values.

Reflected rays converging on a small reflector. For clarity, some rays have been hidden from view using a Filter node.

Heat flux on the surface of the collector.

Example Highlight: Linear Wave Retarder• A series of optical components, such as polarizers and wave retarders, can

be used to manipulate ray intensity and polarization.• The Geometrical Optics interface includes built-in boundary conditions for

several common optical components.• A combination of two linear polarizers and a linear wave retarder can

create varying states of elliptical polarization by changing the retardance.

A quarter-wave retarder can be used to convert linearly polarized radiation to circularly polarized radiation.

Other Model Library Examples• Graded Media

– Gravitational lensing– Luneburg lens

• Industrial Models– Michelson interferometer– Solar dish receiver– Thermal lensing

• Polychromatic Light– Czerny-turner

monochromator

Other Model Library Examples• Tutorial Models

– Antireflective coating multilayer

– Corner cube retroreflector

– Diffraction grating– Distributed bragg

reflector– Linear wave retarder– Newtonian telescope

Summary of the Ray Optics Module• Flexible ray tracing tool with a

wide variety of settings, release features, and boundary conditions

• Built-in variables for many frequently used ray properties

• One-way or two-way coupling to other physics interfaces

Ray trajectories in a Czerny-Turner monochromator