Ray Optics Minicourse
COMSOL 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?
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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 and
Perfect Absorption
Specular
Reflection
Diffuse
Reflection
Mixed:
Specular & Diffuse
Or completely User-Defined Reflection
What effects can be modeled at boundaries?
m = -1
m=0
m = +1
Thin dielectric films
Gratings
Arbitrary number of
different layers of material
Arbitrary number of
diffraction orders
What effects can be modeled at boundaries?
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Linear Polarizer
Linear Wave Retarder
Circular Wave Retarder
Ideal Depolarizer
User-defined Mueller Matrices
How can ray release be modeled?
α
Plane Wave
Spherical
Hemispherical
All are available in 2D and 3D
Conical
How can far-away sources be modeled?
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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?
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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:
n = 1.13-gop.nu/5E15[Hz]
A polychromatic beam enters a dispersive
medium and splits into monochromatic rays
moving in different directions.
Different frequency
variable for each ray
What properties can be tracked, and
postprocessed, along the path of the ray?
Michelson
interferometer
Phase & Interference Patterns
What properties can be tracked, and
modified, along the path of the ray?
Polarization
Intensity
Polarized, Partially Coherent, and
Incoherent sources can be modeled
Radius of curvature is computed
What Intensity Computations Options Exist?
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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?
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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
What post-processing options exist?
• 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
generated
By 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:
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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?
• 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
Absorbed Power in a Lens
Reflected Solar Flux
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
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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
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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
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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
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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