Talk.017 BNL Optical Modeling Beyond Ray Tracing

8/12/2019 Talk.017 BNL Optical Modeling Beyond Ray Tracing

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Optical Modeling Task

Light distribution insource plane is given.

Light distribution intarget/detector plane is demanded.

Light distribution is to beanalyzed to allow evaluating theoptical function of the system.


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Optical Modeling Challenges: Source Modeling

Source modeling :Dependent on type of source,light in source plane must be

represented in a suitable way.


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Optical Modeling Challenges: Propagation

Source modeling Light propagation:Initial light distribution must bepropagated through the system in

order to obtain distribution in targetplane (or any other region of the system).


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Optical Modeling Challenges: Detection

Source modeling Propagation

Light detection:

Light in target plane must berepresented in a way, which enablesanalysis of any merit function of concern.


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Representation and Propagation of Light

Source modeling Propagation Detection

The ways to represent and propagatelight are the TWO essential decisions to bemade in optical modeling and design.


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Ray tracing

Light representation: Ray bundles Light propagation: Geometrical optics


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Rigorous electromagnetic modeling

Light representation: Electromagnetic field


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Electromagnetic Field Representation

Harmonic electromagnetic fields are completelydescribed by its six electric and magnetic field

components:

Just two of them are independent inhomogeneous and isotropic media.

Typically the x - and y-components of the electricfield are selected to be independet of the others. The other four components follow from them.


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Field Tracing with VirtualLab: Experiment B.00


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Rigorous electromagnetic modeling

Light representation: Electromagnetic field Light propagation: Rigorous solution ofMaxwells equations by, e.g., FEM, FMM, andFDTD.


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What are the demands on light

representation and propagationto tackle current and future challenges inoptical modeling and design?


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What are the demands on light

representation and propagationto tackle current and future challenges inoptical modeling and design?


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Tendencies: Sources

Increasing number of different types of light sourcesranging from: Spatially coherent to incoherent Unpolarized to polarized Cw/stationary to fs pulses Small to large bandwidth X-ray to IR

Light representation Ray bundles allow to handle some of the

situations. Electromagnetic f ields allow to handle all

situations.


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What are the demands on light representation and propagationto tackle current and future challenges inoptical modeling and design?


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Tendencies: Detectors

Innovative optical design often requires accurateaccess (merit function) to e.g. Amplitude and phase Polarization, e.g. Stokes or Jones vector Degree of polarization and coherence Poynting vector, energy flow Pulse duration, chirp,

Light representation Ray bundles allow to handle some of the

situations. Electromagnetic f ields allow to handle all

situations.


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Tendencies in Optical Science and Technology

Enormous variety of different types of opticalsurfaces: Smooth freeform surfaces


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Enormous variety of different types of opticalsurfaces: Smooth freeform surfaces Microstructured surfaces


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Enormous variety of different types of opticalsurfaces: Smooth freeform surfaces Microstructured surfaces Multilevel surfaces


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Enormous variety of different types of opticalsurfaces: Smooth freeform surfaces Microstructured surfaces Multilevel surfaces Miniaturized components

Surfaces with different feature sizes are combinedin optical systems.

One modeling technique for all of that?


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DetectorLight

Source

System Modeling by Ray Tracing

Ray tracing?


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DetectorLight

Source

Rigorous System Modeling (FEM, FTDT,..)

Rigorous electromagneticsolution of Maxwells

equations?


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Rigorous Modeling of Entire Optical Systems?

With todays PCtechnology: Rigorous

modeling restricted tosystem size of aboutV = (100 )3 = (100 m) 3

A rigorous modelingof entire systems isnot practical!

A complete rigoroussystem modeling isnot needed!


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DetectorLight

Source



equations?


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DetectorLight

Source



equations?


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DetectorLight

Source

Unified Optical Modeling

Different modeling techniquesincluding Geometrical Optics Physical/Computational Optics


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Field Representation for Unified Modeling

The combination of any kind of modelingtechniques requires:

Otherwise it is impossible to use rigorouspropagation methods in parts of the system.

Light representation by electromagnetic fields


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Field Representation for Unified Modeling

The combination of any kind of modelingtechniques requires:

Otherwise it is impossible to use rigorouspropagation methods in parts of the system.

Light representation by electromagnetic fields


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Combining Modeling Techniques

Geometrical Optics Finite differene timedomain (FDTD)

Finite elementmethod (FEM)

Fourier modal

method (FMM)

Fresnel integralSpectrum of plane

waves (SPW)Beam propagationmethod (BPM)

Thin elementapproximation (TEA)

Rigorous coupled waveapproach (RCWA)

Layer matrices

more

Unified Modeling


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Combining Modeling Techniques

Geometrical Optics Finite differene timedomain (FDTD)

Finite elementmethod (FEM)

Fourier modal

method (FMM)

Fresnel integralSpectrum of planewaves (SPW)Beam propagationmethod (BPM)

Thin elementapproximation (TEA)

Rigorous coupled waveapproach (RCWA)

Layer matrices

more

Unified Modeling


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Field Tracing

Light representation: Electromagnetic field Light propagation: Combination of rigorousand approximate solutions of Maxwellsequations in different regions of the system


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Modeling with Field Tracing

Instead of ray bundles,are traced

through the system.


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Typical Questions about Field Tracing

What is the role of geometrical optics in thisapproach?

What is the difference to rigorous electromagneticmodeling?

How does field tracing work in practice? How are general electromagnetic fields modeled? What is the difference between sequential and

non-sequential field tracing?


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Geometrical Optics in Field Tracing


Ray tracing Light representation: Ray bundles Light propagation: Geometrical optics


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Geometrical optics field tracing technique Light representation: Ray bundles Light propagation: Geometrical optics


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Geometrical optics field tracing technique Light representation: Ray bundles Light propagation: Geometrical optics


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Geometrical optics field tracing technique Light representation: Electromagnetic field Light propagation: Geometrical optics


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Basic Concept of Geometrical Optics Operator

Rays

Tube

Interface

2d shape of tube: triangle


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Basic Concept of Geometrical Optics Operator

Rays

Tube

Field per tube describes parabasalelectromagnetic subfield, which ispropagated by geometrical optics.

Interface

2d shape of tube: triangle


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Modeling Task

?

Aspherical lens Focal plane

f = 1.73 mm

Laser beam

5 mm

Focusing

NA=0.68

Quality of this lens?


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Modeling Task

Polarization: linearly polarizedin x-direction

Laser diameter (1/e 2): 2 mm Wavelength: 600 nm


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Modeling by Ray Tracing

?

f = 1.73 mm5 mm

Ray Tracing


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Result by Ray Tracing


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Result by Ray Tracing


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Modeling by Field Tracing

?

f = 1.73 mm5 mm

GeometricalOpitcs

PhysicalOptics


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Phase Aberration behind Lens

Intensity

h b b h d


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Phase Aberration behind Lens

Intensity

B I i i F l Pl


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Beam Intensity in Focal Plane

El i Fi ld i F l R i A li d


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Electric Field in Focal Region: Amplitudes

x-component y-component z-component

1 1/85 1/3.8

Fi ld T i ith Vi t lL b E i t F 02


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Field Tracing with VirtualLab: Experiment.F.02

Ray TracingOptions 2D, 3D

Source tabField Tracing

LoggingDetectors

Parameter run

T i l Q ti b t Fi ld T i g


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Field Tracing vs Rigorous Modeling


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Field Tracing vs. Rigorous Modeling

Field Tracing Light representation: Electromagnetic field Light propagation: Combination of rigorous

and approximate solutions of Maxwellsequations in different regions of the system

Rigorous electromagnetic modeling Light representation: Electromagnetic field Light propagation: Rigorous solution of

Maxwells equations by, e.g., FEM, FMM, andFDTD.

Field Tracing vs Rigorous Modeling: Example


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Field Tracing vs. Rigorous Modeling: Example

f = 100 mm

100 mm 100 mm

Super Gaussian Ideal Lens Screen

Rigorous modeling:

Spectrum of plane waves integral(SPW)

r = 5 mm



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f = 100 mm

100 mm 100 mm


r = 5 mm



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f = 100 mm

100 mm 100 mm


r = 5 mm



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f = 100 mm

100 mm 100 mm


r = 5 mm



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f = 100 mm

100 mm 80 mm


r = 5 mm

Field Tracing vs Rigorous Modeling


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Field Tracing vs. Rigorous Modeling

We combine different models in order tominimize both, the physical error and thecomputational effort.

Field Tracing Light representation: Electromagnetic field

Light propagation: Combination of rigorousand approximate solutions of Maxwellsequations in different regions of the system

Field Tracing with VirtualLab: Experiment.F.01


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Field Tracing with VirtualLab : Experiment.F.01

Gaussian Field

SPW: Default, 1 mAutomatic operatorExperiment

F.010, 100 m, 3 mm, 10 mm



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?

f = 1.73 mm5 mm

GeometricalOpitcs

InverseFar Field

Grating(period 1 m)

FEM

Field Tracing Result


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g

Real part of the electric field

(2D FEM by NGSolve)



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yp Q g







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yp Q g







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p p g g






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Current Field Tracing Techniques in VirtualLab


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Free-space propagation Spectrum of plane wave integral (SPW)

Fresnel integral Far field integral Geometrical optics propagation Automatic selection operator

Geometrical optics propagation (GeOp) Thin element approximation (TEA)

Beam propagation method (BPM) Fourier modal method (FMM) Finite Element Method (FEM) (programmable)

Current Field Tracing Techniques in VirtualLab


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Free-space propagation Spectrum of plane wave integral (SPW)

Fresnel integral Far field integral Geometrical optics propagation Automatic selection operator

Geometrical optics propagation (GeOp) Thin element approximation (TEA)

Beam propagation method (BPM) Fourier modal method (FMM) Finite Element Method (FEM) (programmable)

User Defined Modeling by Field Tracing


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VirtualLab comes with a wide variety ofcomponents and associated modeling techniques.

Field tracing allows inclusion of any componentwith any associated modeling technique.

In order to take maximum benefit of this fieldtracing capability, VirtualLab provides aprogrammable component which can be usedtogether with all other components.

Programming languages: C# with the full VirtualLab programming library MATLAB code can be used in VirtualLab

User Defined Modeling by Field Tracing


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Different modeling techniques

DetectorLight

Source

Field Tracing Gives Full Flexibility in Modeling


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DetectorLight

Source

Any kind ofmodeling technique

Any kind ofdetector function

Any kind ofsource model



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From Harmonic to General Fields


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Harmonic Field

Set ofHarmonic

Fields

Harmonic field setsorted by the triplet

(u,s,n) allow modelingof any type of partiallycoherent field.

u

s nJani Tervo

General Source Modeling


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Stationary sources: Color

Spectroscopy


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Chromatic Coating Effects


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Chromatic Aberrations


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RGB Light Interferometry


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Stationary sources: Color Stationary sources: Temporal coherence

Skip demo


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Temporal Coherence: Double Slit Experiment


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Propagation of light of Hg-lamp through doubleslit

Light distribution on screen



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Glas plate (n=1.5)6 mm thick plate

must avoid interference

LightSource Component Screen

Double Slit + 2f-setup



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Propagation of light of Hg-lamp through doubleslit

Light distribution on screen



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Spatially partially coherent sources: Multimode laser,excimer laser, VCSEL, LED

Skip demo

Modeling Partially Spatial Coherence


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Quasi homogeneouspartial coherent

source model: Light describe by set oflaterally shiftedidentically muttualyuncorelated modes.

Far field of sourcedefines mode.

Near field describeslocal weight of modes.

x

I(x)

Modeling Partially Spatial Coherence


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Source plane z = 1 mm z = 10 mm

Modeling Task


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Partial coherentsource

Double Slit Target Plane

Fourier Lensf=100 mm

100 mm100 mm

Simulation of the interference pattern in the target plane depending onthe slit distance.

Simulation Results


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Intensity of interference pattern incase of a slit distance of 30 m.

Intensity of interference pattern incase of a slit distance of 150 m.



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Spatially partially coherent sources: Multimode laser,excimer laser, VCSEL, LED Non-stationary sources: Ultrashort pulses

Skip demo

10 fs Pulse at 800 nm


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Same experiment as for stationary HG lamp Now glass plate about 40 m thick to avoid

interference

Effect in the frequency as wll as timedomain?

Without Glass Plate

F D i Ti D i


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Frequency Domain Time Domain

With 40 m Glass Plate

F D i Ti D i


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Frequency Domain Time Domain



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What is the difference to rigorous electromagneticmodeling? How does field tracing work in practice?

How are general electromagnetic fields modeled? What is the difference between sequential and




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Non-Sequential Field Tracing

detector


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Formally a system is subdivided into subdomains. Input: source field on the source boundary. Output: resulting field on the detector boundary.

We look for a formulation that represents the Maxwellproblem in R for the unknown boundary fields.

sourceboundary

detectorboundary

sequential

non-sequential

Example: Field Tracing Through a System


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In field tracing all the steps (arrows) areassociated with fields, not just rays. We have developed efficient tree algorithm.

Source DetectorComponent Component

Simulation Task: Modeling of Newtons Rings


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?Field in

reflection.

2.4 mm

Non-sequentialField Tracing

2 m

air air

n=2

Wavelength: 632 nmr=100 mm

Resulting Reflected Intensity


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Field in z-y Plane inside plate (amplitude)


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Sequential Result Non-Sequential Result

Result for RGB Light


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What is the role of geometrical optics in this


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Modeling of Reflection

The Modelling Task

Single plane wave


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Single plane wave

Incident plane wave

Fresnel equations

The Modelling Task

General beam


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General beam

Incidentbeam

Propagation operator

Tilt operatorInterface operator

The Modelling Task

An illustrative example


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An illustrative example polarized Gaussian input;

Propagated field (SPW); Propagated field on interface (tilt);

P h

a s e

The Modelling Task

An illustrative example


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An illustrative example Reflection at the interface;

Rotation of reflected field; Propagation of rotated field (SPW);

P h

a s e

Examples

Brewster angle ( 1 , 2 )


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Brewster angle ( , ) At 63.43 incidence;

Input: 45 - polarized Gaussian ; Reflection; Transmission.

PhasePhase of Phase of

Field Tracing with VirtualLab: Experiment.B.01


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Gaussian FieldComponentsPolarization

Donut modeCatalogue

Scattering experimentB.01

Field Tracing with VirtualLab: Experiment I.01


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Conclusion

Field tracing gives maximum flexibility in


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Field tracing gives maximum flexibility inoptical modeling and design.

Conclusion



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g g yoptical modeling and design.

This is enabled by anelectromagnetic field representation

throughout the modeling.

Conclusion



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g g yoptical modeling and design.

Todays PC technology developmentenables field tracing in practice better andbetter.

Field tracing seems to be a consequent andpowerful approach to solve challenges in

optical modeling and design.

Field Tracing with VirtualLab


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ByVirtualLabweimplement andprovide the FieldTracing approach.


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Thank You for Your Attention!

Talk.017 BNL Optical Modeling Beyond Ray Tracing

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