P&S COMSOL Design Tool Week 3: Simulation Concept
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1 P&S COMSOL Design Tool Week 3: Simulation Concept Nikola Dordevic, Yannick Salamin Yannick Salamin
2 Content Simulation concept - Homework Matlab examples Intro to Comsol Software environment First examples: Point source Young slit Homework Young double slit Yannick Salamin yannick.salamin@ief.ee.ethz.ch
3 Maxwell s quations Formulation Differential form B t D H J t D 4. B 0 Faraday s Law of Induction Ampere s Circuital Law Gauss lectric Law Gauss Magnetic Law Yannick Salamin yannick.salamin@ief.ee.ethz.ch
4 Maxwell s quations Formulation We can write them only with and H D B H H t H J t H 0 Free space no source H 0 t H 0 t 0 H 0 Yannick Salamin yannick.salamin@ief.ee.ethz.ch
5 Wave equation Wave propagation limited to one dimension - x H z x y x y z 0 0 x 0 x y z x H 0 t z y 0 x y z x z 0 y z x y x z x y x y H x H 0; y 0 t t y x H 0 t z Yannick Salamin yannick.salamin@ief.ee.ethz.ch
6 Wave equation Wave propagation limited to one dimension - x H z x y H 0 t H H z y x H 0 0 x y z t H x H z y H y 0 z x t H y H x z H 0 0 z x y t H z y 0 x t y x 0 t H 0 t y H x z z 2 1 y H z 2 0 x xt t 2 y 0 2 H z xt 2 2 y 1 y x c t c Yannick Salamin yannick.salamin@ief.ee.ethz.ch
7 Materials Relations In order to analyze an M problem we need to define the material properties involved. Material defined by its resistance to an electric and magnetic field Permittivity ε Permeability µ e - e - (t) Yannick Salamin yannick.salamin@ief.ee.ethz.ch
8 Material Relations Material Polarizability Polarizability D = ε 0 + P P = ε 0 χ e D = ε 0 + ε 0 χ e D = ε 0 ε r ε r = 1 + χ e Yannick Salamin yannick.salamin@ief.ee.ethz.ch
9 Materials Relations Dielectric Function What is it? It s a relation of the optical properties of a material with respect to (λ/f/). D = ε lectrical Displacement Why is it important? It helps us relate the effect of electrical and magnetic fields on used material. What form does it have? Its equation is given by: ε = ε 1 (λ) + ε 2 (λ)i Dispersion Relation with the refractive index n = με n = ε Optical Frequency Range Yannick Salamin yannick.salamin@ief.ee.ethz.ch
10 Boundary Conditions Maxwell s Laws Purpose of boundary conditions 4 general categories: Present structure boundaries as ideal (metals/dielectrics). Limit simulation Reduce resources/time. Reduce scattering/reflected waves. Introduce symmetry (periodic structures). Yannick Salamin yannick.salamin@ief.ee.ethz.ch
11 Boundary Conditions Maxwell s Laws Maxwell s Boundary Conditions Boundary Conditions t,1 t,2 1 n,1 2 n,2 t,1 t,2 0 H H J H H 1 n,1 1 n,2 0 Yannick Salamin yannick.salamin@ief.ee.ethz.ch
12 Boundary Conditions Domain 1 (Air) AIR Incident Wave: Reflected Wave: 1 t,1 n,1 1 t,1 n,1 n t MATRIAL k Domain 2 (Material) Refracted Wave: 2 t,2 n,2 If charge are absent t,1 t,1 t,2 1 1 n,1 n,1 2 n,2 (Tangential) (Normal) If no reflection t,2 t,1 1 n,2 n,1 2 Yannick Salamin yannick.salamin@ief.ee.ethz.ch
13 Boundary Conditions Software conditions Software applications Apply a variety of boundary conditions. Some of the most commonly used are: Perfect lectric Conductor (PC). Perfect Magnetic Conductor (PMC). Perfectly Matched Layers (PML). Periodic Boundaries (PBC). Yannick Salamin yannick.salamin@ief.ee.ethz.ch
14 Boundary Conditions Perfect lectric Conductor Perfect lectric Conductor (PC) Properties xhibits infinite electric conductivity. Used for phenomenon when resistance is negligible with respect to our value of interest. Tangential component of electric field is zero. t = 0 lectric field is located on the surface of the conductor/material. xamples of PC Microwave planar structures. Metallic substrates. Yannick Salamin yannick.salamin@ief.ee.ethz.ch
15 Boundary Conditions Perfect Magnetic Conductor Perfect Magnetic Conductor (PMC) Properties Infinite magnetic conductivity. Tangential component of magnetic field is zero. H t = 0 Magnetic field is located on the surface of the magnetic conductor/material. xactly the reciprocal of a PC. xamples of PMC Interface between a dielectric and air. Open circuit interface. Yannick Salamin yannick.salamin@ief.ee.ethz.ch
16 PML Boundary Conditions Absorbing Boundary Perfectly Matched Layer (PML) Scattering Boundary Properties Absorbing boundary. Truncates M space in numerical simulations. Possible to simulate open boundary problems. Reduce scattered/reflected waves. PML PML xamples Antennas Reflectors Absorbing structures Metamaterials Real life absorber Yannick Salamin yannick.salamin@ief.ee.ethz.ch
17 Boundary Conditions Periodic Boundaries Periodic Boundary Condition (PBC) Properties Use a unit cell for the analysis. Reduces size of structure by introducing symmetry. Simulates systems expanding infinitely in 1D/2D. Mapping between successive cells. xamples Grating structures Periodic structures in 1D/2D Large structures showing symmetry Infinite approximated structures Metamaterials Yannick Salamin yannick.salamin@ief.ee.ethz.ch
18 Simulation concept Matlab xample Define Domain Mesh (discretization) Source (point source) Plot electric field e ikr () r 0 r domain x domain y 2 k 2 2 r x x y y 0 0 mesh cell Yannick Salamin yannick.salamin@ief.ee.ethz.ch
19 Introduction to COMSOL Yannick Salamin
20 Introduction to COMSOL Yannick Salamin
21 Introduction to COMSOL Yannick Salamin
22 Source Point Field Yannick Salamin
23 Source Point Field Results Z component of field Yannick Salamin yannick.salamin@ief.ee.ethz.ch
24 Young Slit xperiment Yannick Salamin
25 Young Slit xperiment - COMSOL Yannick Salamin yannick.salamin@ief.ee.ethz.ch
26 Young Slit xperiment Yannick Salamin
27 Young Slit xperiment Yannick Salamin
28 Young Slit xperiment Results Yannick Salamin
29 Homework Young slit experiments Double Slit w slit wfringe 2 z d Parameters: wavelength = 1550nm = z = 10um w slit = 4 d = 5um z Prediction: 1550 nm wfringe z 10um 3.1um d 5 um Yannick Salamin yannick.salamin@ief.ee.ethz.ch
30 xpected Results z 2 Yannick Salamin yannick.salamin@ief.ee.ethz.ch
31 Next lesson Wave-guiding Mode Analysis QUSTIONS??? Yannick Salamin
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