Rigorous analysis of general 2D and 3D gratings with VirtualLab 4
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1 Webinar, November 15, 2010 Rigorous analysis of general 2D and 3D gratings with VirtualLab 4 Hagen Schweitzer, LightTrans GmbH Hagen.Schweitzer@lighttrans.com
2 Grating Toolbox - Introduction
3 Introduction Simulation of diffraction at gratings by: Starter Toolbox Grating Toolbox Starter Toolbox: scalar simulation of 2D and 3D surface gratings Grating Toolbox: Rigorous electromagnetic analysis of general 2D and 3D gratings. Rigorous simulation for gratings with features smaller than approximately 5 wavelengths.
4 Introduction Typical grating structures that can be modeled by Grating toolbox: Surface gratings Volume gratings Photonic crystals Sub-wavelengths gratings Combinations of different gratings (e.q. surface + volume grating)
5 Introduction 2D Grating Arbitrary non periodic modulation in z-direction constant in y-direction Periodic in x-direction 3D Grating Arbitrary non periodic modulation in z-direction Periodic in y-direction Periodic in x-direction
6 Introduction Typical applications Polarizers Anti-reflection structures Laser beam splitting Spectroscopy Coupling of light in wave guides Artificial media Grating Toolbox enables: Analysis of optical performance Optimization of grating parameters by Parameter Run Tolerance simulation
7 Modeling of 2D and 3D Gratings as a sequence of surfaces and media
8 General 2D/3D Grating A base block (substrate) of a homogeneous medium Can have a stack of surfaces and media on left and right side.
9 General 2D/3D Grating A base block (substrate) of a homogeneous medium Can have a stack of surfaces and media on left and right side.
10 General 2D/3D Grating A stack is modeled as a sequence of surfaces and media. Homogeneous and inhomogeneous media can be between the optical interfaces.
11 General 2D/3D Grating Media and surfaces can be loaded from catalog. Stacks can be so stored to and loaded from catalog.
12 General 2D/3D Grating Any surface of VirtualLab can be switch in periodic mode. Periods of different surfaces can be different Surfaces and media share a common stack period
13 Customized surfaces profiles and media
14 Customized Surfaces in VirtualLab A lot of different definitions of grating surfaces are used in optics software and literature. Definitions are typically optimized for specific application. VirtualLab supports three different surface types that enable the modeling of customized grating surface: Programmable interface Sampled interface Combined interface
15 Programmable Interface h(x,y) The programmable interface allows to specify the height profile of one or multiple surface periods by a formula. Global parameters can be defined that can be varied by Parameter Run.
16 Programmable Interface Height profile and gradient are specified by snippet. User defines an equation that describes the height profile depending on x,y position. Visit LightTrans web site for snippets.
17 Example Programmable Interface Height profile: sin(x/1mm)*y/5 Source code editor allows to enter a formula. Global parameters can be defined that can be varied in the parameter run.
18 Sampled Interface h(x i,y j ) h(x,y) The sampled interface allows to define a height profile by discrete data points and a interpolation method.
19 Sampled Interface Height profile specified by equidistant sample discrete data points. Allows to simulate Pixelated surfaces Fresnel type surfaces Smooth surfaces with low or high spatial frequencies Data points can be imported from ASCII or bitmap files.
20 Example Sampled Interface Height profile sampled data can be imported from ASCII or bitmap file. Sampled data can be also the result of the optimization of a diffractive optical element.
21 Combined Interface h 2 (x,y) h(x,y) + h 1 (x,y) Defines a new surface as a sum of the height of two elementary optical interfaces
22 Combined Interface The combined interface allows to select to elementary optical interfaces of VirtualLab. The height profiles of these interfaces are added.
23 Example Combined Interface Hybrid surface: sum of aspherical and Fresnel surface. Aspherical surface radius 25 mm and conical constant 1. Fresnel surface radius 25 mm.
24 Combined Optical Interface Single lens surface of lens arrays with sinusoidal grating modeled by combined interface.
25 Programmable Medium The programmable medium allows to define a formula that describes the refractive index depending on x,y,z position. Global parameters can be defined that can be varied in the parameter run.
26 Programmable Medium The programmable medium allows to define a formula that describes the refractive index depending on x,y,z position. Global parameters can be defined that can be varied in the parameter run.
27 Simulation of coated gratings
28 Coatings at Grating Surfaces Coatings must be added to a stack as a sequence of surfaces and media in order to perform an exact rigorous modeling of the light propagation. The function Stack Tool Insert Coating allows to add a coating from the catalog to a surface profile.
29 Coatings at Grating Surfaces It is assumed that the coating is generated by a particle source on the optical axis in infinite distance. Coating thickness depends on surface normal vector. This will result in thinner coating layers for surfaces regions with strong inclination.
30 Scenario : Rigorous Simulation of Light Diffraction at Coated Sinusoidal Grating This example demonstrates the rigorous simulation of a coated sinusoidal grating and the illustrates the effect of the coating on the diffraction efficiency of the ±1 st orders. Keywords: rigorous, FMM, sinusoidal grating, coating Required Toolboxes: Grating Toolbox Related Tutorials:
31 Modeling Task 532 nm Fused Silica 1 µm 1 µm Air Rigorous simulation of efficiency of diffraction orders. 532 nm Fused Silica 1 µm 1 µm Air Rigorous simulation of efficiency of diffraction orders. Antireflection coating:bbcoat3_ nm
32 Simulation Results The antireflection coating increases the transmitted power from 90% to 95%. The antireflection coating does not significant increase the amount of energy of the zero diffraction order. The efficiencies of the ±1 st diffraction orders are increased by the coating.
33 Conclusion The rigorous simulation of coated gratings requires to specify the coating layers as a sequence of surfaces. The Grating Toolbox allows to take into account the effect of coatings and to use coatings of the VirtualLab coating catalog. VirtualLab can take into account the reduction of the layer thickness depending on the normal vector as it often appears during the fabrication process.
34 Modeling of Anti-Reflection Structures
35 Anti-Reflection Structures Sub-Wavelength dielectric structures can be used to reduce the reflection of light. Dielectric of metallic sub-wavelength structures can be applied for modification of polarization of light. Metal Glas/ Plastic
36 Pillar-Type Gratings Homogeneous Medium: Air h Pillar Substrate
37 Pillar-Type Gratings s y Medium Parameters a y d y x a x d x Origin of Medium CS
38 Pyramid-Type Gratings Modeling of sub-wavelength antireflection structures (i.e. moth-eyes structure) require often cone-,pyramid-, pillar-type gratings. Pillar-type gratings are supported by pillar medium. Pyramid-type gratings are introduced programmable interface and snippet SN.016. Pyramids are defined by: x-/y-base diameter x-/y- top diameter Height Height factor (scales profile and allows inversion)
39 Cone-Type Gratings Cone-type gratings are introduced programmable interface and snippet SN.015. Cones are defined by: Base diameter Top diameter Height Height factor (scales profile and allows inversion)
40 Scenario : Rigorous Analysis and Optimization of pillar-type antireflection structure. The optimization and analysis of a pillar-type sub-wavelengths antireflection grating by rigorous Fourier Modal Method is demonstrated in this example. The optimization of the grating parameters is done by the parameter run of VirtualLab. Keywords: pillar, antireflection, grating, rigorous, FMM, sub-wavelength Required Toolboxes: Grating Toolbox Related Tutorials:
41 Modeling Task Air Fused Silica Plane Wave Incident angle: 0 Wavelength: 532 nm Linear polarized in x-direction 3D Pillar Grating
42 Modeling Task Homogeneous Medium: Air h Pillar Fused Silica
43 Modeling Task s y Medium Parameters a y d y x a x d x Origin of Medium CS
44 Modeling Task Optimization of grating parameters so that no reflection will appear for perpendicular incident light with 532nm wavelength. Most critical parameters are pillar diameter and layer thickness. Optimization can be done by varying all free parameters after each other by the parameter run.
45 Optimization of Depth Reflectance vs. Depth (TM Polarization) Minimum reflectance for 110 nm depth. Parameter run see Scenario_190.01_Pillar_Grating_2.run
46 Optimization of Pillar Diameter Reflectance vs. Pillar Diameter (TM Polarization) Minimum reflectance for 140 nm pillar diameter. Parameter run see Scenario_190.01_Pillar_Grating_3.run
47 Optimization Results Homogeneous Medium: Air 110 nm Pillar Fused Silica
48 Rigorous Analysis of Pillar-Type Gratings 125 nm y Medium Parameters x 125 nm 140nm 250 nm Origin of Medium CS 140 nm Reflectance: 0% Transmittance: 100%
49 Analysis of Angular Dependency Reflectance vs. Angle (TM Polarization) Reflectance antireflection structure Reflectance plane surface Parameter run see Scenario_190.01_Pillar_Grating_4.run
50 Analysis of Wavelength Dependency Reflectance vs. Wavelength (TM Polarization) Reflectance antireflection structure Reflectance plane surface Parameter run see Scenario_190.01_Pillar_Grating_5.run
51 Conclusion Grating Toolbox of VirtualLab enables rigorous analysis of 3D gratings by Fourier Modal Method. Optimization of grating of sub-wavelengths gratings can be done by parameter run. Analysis of angular and wavelengths dependency of gratings by parameter run.
52 Rigorous Simulation of Lens Arrays
53 Definition of Lens Arrays Only one period (a single) lens is defined in the grating toolbox. For lens definition the following surfaces are helpful: Conical interface Aspherical interface Cylindrical interface Fresnel and cylindrical Fresnel interface Programmable Interface Sampled Interface Combined Interface
54 Definition of Lens Arrays Left image shows stack with conical interface. Stack contains single lens (one period).
55 Discretization of Lens Structure Fourier Modal Method (FMM) requires the discretization of the structure in layers and transition points A sufficient large number of layers must be used for an accurate representation of a lens array
56 Numerical Accuracy of FMM A sufficient large number of evanescent orders must be used in order to reduce numerical orders. The number of orders must be increased until the simulation results converge to the final result.
57 Scenario : Rigorous Analysis high-na cylindrical lens array High-NA lens arrays with small periods should be analyzed by rigorous methods to accurately predict wave front and Point Spread Function. The analysis of a lens arrays with a NA=0.46 is demonstrated in this example. Keywords: lens arrays, cylindrical array, rigorous, PSF, wavefront Required Toolboxes: Grating Toolbox Related Tutorials:
58 Modeling Task R = 12 µm NA = 0.46 ~19 µm 20 µm Fused Silica
59 Modeling Task Lens array illuminated by plane wave. Focus is inside of substrate. Analysis of wave front aberrations and PSF.
60 Simulation Results Left upper image: wave front aberrations after cylindrical interface of single lens of array. Left lower image: Intensity after single lens of array. Spherical phase (best fit) 18.9 µm.
61 Simulation Results Points Spread Function in a distance of 18.9 µm from cylindrical lens surface. Propagation from lens to focal plane by Spectrum of Plane Waves (SPW) (Menu item Propagation Rigorous SPW Operator).
62 Summary Rigorous analysis of 2D and 3D lens arrays by Grating Toolbox. Analysis of wave front and points spread function behind single or multiple lenses. Simulation includes diffraction, interference, aberrations, polarization.
63 Lens array with anti-reflection cones
64 Lens Array with Anti-Reflection Structure Structures modeled by cones, pyramids and pillars can help to reduce lens reflection. Anti-reflection structures must be analyzed together with a high-na lens to find out the effect on wave front and PSF.
65 Lens Array with Anti-Reflection Structure Combined interface can be used to add a micro structure to a lens surface. Programmable interface and snippets on LightTrans webpage help to introduce cones and pyramids.
66 Grating Toolbox Advanced Version
67 Advanced Version Parallel Parameter Run Parallel rigorous computation in Grating Toolbox Grating Toolbox can use more than 2GB RAM memory
68 Parallel Computing Parameter Run is using the number of CPU cores selected in the globals dialog. The rigorous analysis is using always all CPU cores. A selection of the number of cores is currently not possible. Typical acceleration with 8 cores factor 3-5.
69 Grating Toolbox Memory Improvements RAM usage increased to ~11GB (2D gratings) and ~ 15GB (3D gratings). Approximately 5 times more orders and up to 5 times larger periods (2D gratings ) than in Standard version. Maximum grating period ~500 λ (2D gratings) and ~20 λ x 20 λ (3D gratings). Maximum number of orders 5800 (2D gratings) and 75 x 75 (3D gratings).
70 Summary Description of general 2D and 3D gratings by sequence of surfaces and media. Customization of surfaces and media by programmable interface/medium, sampled and combined interface. Grating Toolbox enables rigorous analysis of antireflection structures and lens arrays. Analysis of hybrid period structures as for example lens array with anti-reflection structure. Calculation memory and time consuming Advanced version.
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