Download Concepts for the simulation of volume and surface scattering based

Concepts for the simulation of volume and
surface scattering based on field tracing
Dr. Michael Kuhn
Dr. Hagen Schweitzer
LightTrans VirtualLab UG
Introduction
Introduction
• Presentation will show concepts for
physical optics modeling of scattering
effects.
• Discussion of:
– Surface scattering
– Volume scattering
Surface Scattering
• Surface scattering caused by:
– Roughness
– Scratches
– Fabrication tolerances
• Roughness  statistical variation
Surface Scattering
Rough surface of plate.
Surface Scattering
• Surface scattering caused by:
– Roughness
– Scratches
– Fabrication tolerances
• Roughness  statistical variation
• Scratches and fabrication tolerances  often
regular variations of the surface.
Surface Scattering
Surface deviation of aspherical lens manufactured by CNC technic.
Regular surface deviations are visible.
Volume Scattering
• There exists several different scattering effects.
• Scattering caused by particles, schlieres/reams,
mechanical stress.
• Size of scattering structures ranges from atomic
size to large extensions.
• We will discuss scattering at volume structures
with dimension of several 10 nm to Millimeters.
• Scattering models have to include diffraction and
interference effects.
Volume Scattering
Spherical particles
Modeling
Modeling of Scattering
• Measurement of intensity of scattered light
distribution and usage of measured data for
simulations:
 No phase and coherence information. Can’t be
used for accurate physical optics modeling.
• Analytical models for surface and volume
scattering:
 Modeling of specific scattering setups only. No
general solution.
• Numerical simulation of scattering required!
Modeling of Scattering: System
Light
Source
Detector
Modeling of Scattering: Sources
Increasing number of different types of light sources
ranging from:
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Spatially coherent to incoherent
Unpolarized to polarized
Cw/stationary to fs pulses
Small to large bandwidth
X-ray to IR
Light representation
• Electromagnetic f ield representation required.
Modeling of Scattering: Detectors
Innovative optical design often requires accurate
access (merit function) to e.g.
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Amplitude and phase
Polarization, e.g. Stokes or Jones vector
Degree of polarization and coherence
Poynting vector, energy flow
Pulse duration, chirp, …
Light representation
• Electromagnetic f ield representation required.
Modeling of Scattering: Structures
• Enormous variety of different types of optical
surfaces:
– Smooth freeform surfaces
Modeling of Scattering: Structures
• Enormous variety of different types of optical
surfaces:
– Smooth freeform surfaces
– Microstructured surfaces
Modeling of Scattering: Structures
• Enormous variety of different types of optical
surfaces:
– Smooth freeform surfaces
– Microstructured surfaces
– Multilevel surfaces
Modeling of Scattering: Structures
• Enormous variety of different types of optical
surfaces:
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–
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–
Smooth freeform surfaces
Microstructured surfaces
Multilevel surfaces
Miniaturized components
• Surfaces with different feature sizes are combined
in optical systems.
• One modeling technique for all of that?
Modeling of Scattering: Propagation
Light
Source
Detector
Ray tracing?
Rigorous System Modeling
Light
Source
(FEM, FTDT,..…)
Detector
Rigorous electromagnetic
solution of Maxwell‘s
equations?
Modeling of Scattering: Propagation
Light
Source
Detector
Different modeling techniques
including
• Geometrical Optics
• Physical/Computational Optics
• Local semi-analytical methods
Combining Modeling Techniques
Unif ied Modeling
Geometrical Optics
Thin element
approximation (TEA)
Finite differene time
domain (FDTD)
Layer matrices
Fresnel integral
Finite element
method (FEM)
Spectrum of plane
waves (SPW)
Beam propagation
method (BPM)
Rigorous coupled wave
approach (RCWA)
Fourier modal
method (FMM)
… more …
Combining Modeling Techniques
Unif ied Modeling
Geometrical Optics
Thin element
approximation (TEA)
Finite differene time
domain (FDTD)
Layer matrices
Fresnel integral
Finite element
method (FEM)
Spectrum of plane
waves (SPW)
Beam propagation
method (BPM)
Rigorous coupled wave
approach (RCWA)
Fourier modal
method (FMM)
… more …
Modeling with Field Tracing
Instead of ray bundles,
are traced
through the system.
Field Tracing
Applications
Surface Scattering
• Light propagation through surface profiles:
– Requires a model or measurement data of scattering
surface.
– Rigorous or approximate light propagation depending on
feature size and required simulation accuracy.
• Approximate light propagation:
– Thin element approximation
– Geometrical optics
• Rigorous light propagation:
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–
–
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RCWA/FMM
Integral method
FEM
FDTD
Surface Scattering
200 mm
23 mm
?
Focusing
Laser beam
Refractive
beam shaper
Target plane
Surface Scattering
• Polarization: linear polarized in
x-direction
• Laser Diameter (1/e2): 8 mm
• Wavelength: 632 nm
Surface Scattering
Intensity of Top Hat
generated by perfect
lens.
Surface Scattering
• Measured height error of
aspherical surface of beam
shaper.
• Measurement by Zygo
interferometer.
• Corresponds to phase
modulation of 0.3λ.
• Feature size: 25 µm – 3 mm
Surface Scattering
Measured intensity
Simulated intensity
(simulation combines
geometrical and physical optics)
Volume Scattering
• Analytical scattering models for example by MieScattering:
– Only spherical particles.
– For coherent monochromatic light and plane wave
only.
– Volume scattering only  No interaction between
volume scattering and surfaces.
• Numerical rigorous simulation:
– Not limited to specific particles
– For arbitrary coherent or partially coherent light
– Modeling of interaction between volume scattering and
surfaces.
Volume Scattering
• Typically rigorous electromagnetic simulation
• Rigorous light propagation by:
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–
–
–
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RCWA/FMM
Integral method
FEM
FDTD
….
Volume Scattering
PMMA with gold particles
100 nm - 200 nm size
1016 particles per m3
Grating surface
40 µm
Plane wave
λ=532nm
Polarization: Ex
Incident angle: 0°
50 µm
Volume Scattering
Grating Surface
1 µm
645 nm
Volume Scattering
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Analysis by Fourier Modal Method (FMM)
Efficiency of transmitted orders
±1st orders of grating have not equal efficiency.
Stray light appearys
Transmitted light: 20.4%
Reflected light: 7.3 %
Absorbed light: 72.3%
Outlook, Summary
User Defined Modeling by Field Tracing
• Simulation have been done with LightTrans
VirtualLab™ which comes with a wide variety of
components and associated modeling techniques.
• Field tracing allows inclusion of any component with
any associated modeling technique.
• In order to take maximum benefit of this field tracing
capability, VirtualLab™ provides a programmable
component which can be used together with all other
components.
• Programming languages:
– C# with the full VirtualLab™ programming library
– User defined MATLAB® code can be used in VirtualLab™
User Defined Modeling by Field Tracing
Light
Source
Detector
Different modeling techniques
Summary
• Physical optical simulation of surface and volume
scattering requires modeling of diffraction and
interference effects.
• Numerical simulation enables high flexibility of
scattering simulations for various surface and
particle shapes.
• Field Tracing enables analysis of micro and macro
structured components, different light sources
and detectors.
• Rigorous and approximate analysis is possible.
Thank You!
www.lighttrans.com
[email protected]