Ray Optics Minicourse COMSOL Tokyo Conference 2014

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1 Ray Optics Minicourse COMSOL Tokyo Conference 2014

2 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

3 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.

4 What effects are considered within domains? Ray propagation is computed in uniform & graded refractive index materials Reflection and refraction at material interfaces

5 What effects can be modeled at boundaries? Transparent and Perfect Absorption Specular Reflection Diffuse Reflection Mixed: Specular & Diffuse Or completely User-Defined Reflection

6 What effects can be modeled at boundaries? m = -1 m = 0 m = +1 Thin dielectric films Arbitrary number of different layers of material Gratings Arbitrary number of diffraction orders

7 What effects can be modeled at boundaries? Linear Polarizer Linear Wave Retarder Circular Wave Retarder Ideal Depolarizer User-defined Mueller Matrices

8 How can ray release be modeled? α Plane Wave Spherical Hemispherical Conical All are available in 2D and 3D

9 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).

10 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

11 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: n = 1.13-gop.nu/5E15[Hz] Different frequency variable for each ray A polychromatic beam enters a dispersive medium and splits into monochromatic rays moving in different directions.

12 What properties can be tracked, and postprocessed, along the path of the ray? Michelson interferometer Phase & Interference Patterns

13 What properties can be tracked, and modified, along the path of the ray? Polarization Polarized, Partially Coherent, and Incoherent sources can be modeled Intensity Radius of curvature is computed

14 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.

15 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.

16 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.

17 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

18 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

19 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.

20 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.

21 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).

22 What post-processing options exist? Deposited Power on Surfaces Absorbed Power in Domains Absorbed Power in a Lens Reflected Solar Flux

23 Model Library Examples More examples will become available at:

24 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).

25 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.

26 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. Heat flux on the surface of the collector. Reflected rays converging on a small reflector. For clarity, some rays have been hidden from view using a Filter node.

27 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.

28 Other Model Library Examples Graded Media Gravitational lensing Luneburg lens Industrial Models Michelson interferometer Solar dish receiver Thermal lensing Polychromatic Light Czerny-turner monochromator

29 Other Model Library Examples Tutorial Models Antireflective coating multilayer Corner cube retroreflector Diffraction grating Distributed bragg reflector Linear wave retarder Newtonian telescope

30 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

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