Lecture1 CEM SH Final
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Transcript of Lecture1 CEM SH Final
1
Computational Methods for Electromagnetics (and Photonics)
E-mail: [email protected]: 08-7908465
Sailing HeDivision of Electromagnetic Engineering(also with Photonics Lab in Kista, KTH-ZJU Joint Research Centre of Photonics)
2
Course introduction• Twelve LecturesMy part of lectures:Lecture 1: Introduction to CEM…. Lecture 9: Detailed application examples of CEM, from Stealth to
Cloaking, from RF antennas to optical nano-antennas, Computational project on waveguides.
Lecture 10: Application examples of FDTD for resonators, etc., Lecture 11: CEM for planar lightwave circuits, photonics, etc. • ….• Four Lab Works
• TA: Ning Zhu, [email protected] , tel. 790 4266 (Kista)
3
Lecture 1. Introduction to Computational Electromagnetics
I. Brief introduction to Computational Electromagnetics (CEM);
II. Classification of Computational Methods;
III. Some Applications
IV. Challenging Problems
4
I. Brief introduction to CEM
• The Stage of Closed-Form Solutions(paper and pen)
• The Stage of Approximate Solutions(calculator, computer)
• The Stage of Numerical Solutions(computer, super computer)
Three Stages of EM Simulations
5
The Stage of Closed-Form Solutions
• After the Maxwell’s equations were published in 1864, and in the beginning of 1900s, many closed-form solutions have been obtained:
Mie, ca. 1900: Mie series solution of scattering by a sphere (separation of variables)
Lord Rayleigh, 1897: Guided-wave solution in a hollow waveguide (separation of variables)
Lord Rayleigh: Rayleigh scattering by small particles
……
6
The Stage of Approximate Methods
• High-Frequency MethodsGeometrical Optics (GO)Geometrical Theory of Diffraction (GTD)Uniform Theory of Diffraction (UTD)Physical Optics (PO)Physical Theory of Diffraction (PTD)Shooting and Bouncing Ray (SBR): XPATCH
combination of High-Frequency and Numerical Methods.
High-frequency methods are ray-based methods, which require information of shadow region and illuminated region.
7
The Stage of Numerical MethodsAge of numerical methods: MOM, FDTD, FEM
Yee, 1966; Harrington, 1968; Silvester, 1972; Rao, Wilton & Glisson, 1982; Mittra, 1980+; Taflove, 1980+.
Differential Equation Solvers (FDTD, FEM)Integral Equation Solvers (MoM, BIM)
VIZ =⋅
Many numerical methods started in the electromagnetic community, and later spread to other communities and become popular…
The radiation condition at infinity is emulated by the use of absorbing boundary conditions (ABC), such as Perfect Matched Layer (PML)
8
EMEMSIMULATIONSSIMULATIONSWireless
Comm. &Propagation
Physics BasedSignal Processing & Imaging
ComputerChip Design& Circuits
Lasers &Optoelectronics
MEMS &MicrowaveEngineering
RCS Analysis,Design, ATR& StealthTechnology
AntennaAnalysis &Design
EMC/EMIAnalysis
RemoteSensing &SubsurfaceSensing & NDE
BiomedicalEngineering& BioTech
Nano-phootnics
Education
New Materials (metamaterials)
Impact of EM simulations
9
Computational electromagnetics (CEM) refers to the process of modeling the interaction of electromagnetic fields with physical objects and the environment, in which computationally efficient approximations to Maxwell's Equations are typically used.
What’s the CEM?
10
Solving a Complex Problem Needs …• Electromagnetic Physics:
A correct and efficient problem definitionA good physical insight within calculationsA good physical model can reduce complexity
• MathematicsA correct and efficient mathematical descriptionMathematical analysis: convergence, stability, conditioning, error analysis, error control
• Computer ScienceEfficient algorithms for the math problemEfficient memory arrangement: shared memory and local memoryParallelization of computers and interprocessorcommunications
11
Basic Theory in Electromagnetics
+t
0
0
t
t
ρ
ρ
με
∂∇ × = −
∂∂
∇ × =∂
∇ • =∇ • =
∂∇ ⋅ + =
∂==
BE
DH J
DB
J
B HD E
Faraday’s Law
Ampere’s Law
Gauss’s LawNo magnetic charge
James Clerk Maxwell (1831-1879)
Current Continuity
Constitute Relation
The most elegant equations in the universe.
12
1 1 2 2
1 1 2 2
1 1 2 2
1 1 2 2
s
s
s
ms
ρρ
× + × =⎧⎪ × + × =⎪⎨ ⋅ + ⋅ =⎪⎪ ⋅ + ⋅ =⎩
n H n H JE n E n Mn D n Dn B n B
1ε1μ
2ε2μ
1n̂
2n̂
…with Boundary Conditions
13
Solving Maxwell’s Equations
Time Domain Frequency Domain
Fourier transform
14
Time vs. Frequency Domain
Broadband simulation/frequency sweepNonlinear material modelingTransient phenomena
Time domain:
Frequency domain:Multiple excitation/angular sweepDispersive material modelingSteady state phenomena
15
II. The Classification of CEM• Analytical methods• Numerical Methods
– Finite Difference Time Domain (FDTD);– Finite Element Method (FEM); – Method of Moments (MoM); – Beam Propagation Method (BPM) -- Lecture 11;– Transmission-line modeling;– Monte Carlo method;
– …• Hybrid Methods
16
CEM Overview
17
Numerical Methods(Labs 2 and 4 with commercial softwares)
• Method of moments (Harrington, 1960s)– Integral equation based– Versatile geometry handling– Small number of unknowns
• Finite Difference Time Domain Method (Yee, 1960s)– Differential equation based– Simplicity– Large number of unknowns– Sparse matrix system
18
(1). Method of Moments (MoM)MoM for EM Problems
Derive integral equation (IE)
Convert the IE into a matrix equation using basis functions and weighting functions
Evaluate matrix elements
Solve the matrix equation and obtain the poarameters of interest
19
Conducting Cylinders, TM caseConsider a perfectly conducting cylinder excited by an impressed electric field Ez
i
PP ′
PP ′−nld
φφ ′
C
The impressed field induces surface currents Jz on the conducting cylinder, which produce a scattered field Ez
s.
x
y
o
20
Conducting Cylinders, TM caseThe field due to Jz is given by
∫ ′′−′−=C
zsz ldkHJkE )()(
4)( )2(
0 ρρρηρ
On the cylinder surface C, the boundary condition is
C on ,0=+= sz
izz EEE
C on ,)()(4
)(
C on 0)()(4
)(
)2(0
)2(0
ρρρρηρ
ρρρρηρ
∫
∫
′′−′=⇒
=′′−′−⇒
Cz
iz
Cz
iz
ldkHJkE
ldkHJkE
where )(ρizE is known and zJ is the unknown to be determined.
21
Method of Moments
gLf =Consider inhomogeneous equation
L: operator g: excitation (source) (known function) f: field or response (unknown function to be determined)
n
N
nnuaf ∑
=
=1
~functions (basis) expansion:
constant:
n
n
ua
For exact solutions the summation is usually infinite and un form a complete set of basis functions
For approximate solutions the summation is usually finite.
(*)
(**)
22
Method of Moments
gLua nn
n =∑Substitude (**) in (*) and use the linearity of L
Now define a set of weighting functions or testing functions, w1,w2, w3 ,... İn the range of L, take the inner product with each wm.
,...3,2,1,,, ==∑ mgwLuwa mnmn
n
This set of equations can be written in matrix form:
[ ]⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
.........
...,,
...,,
2212
2111
LuwLuwLuwLuw
lmn [ ]⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡= 2
1
aa
an [ ]⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡= gw
gwgm ,
,
2
1
[ ][ ] [ ]mnmn gal =
23
More About MoM• MOM is an old topic, which was proposed by Harrington in 1966.
However, new bloods have been put in MOM in the past decades.• For Basis Function (for PEC, for example):
Rao-Wilton-Glisson (RWG) basis , triangular patch (1982)High-order basis, triangular patch or quadr. patchHigh-order basis, curvelinear triangular patchWire-surface junctionSurface-surface junctionNew physics-based basis functions
Fewer Unknowns,ComplicatedEvaluation
24
Download software Feko-lite: http://www.feko.info/sales
25
CADFeko
26
Basic steps• Establish the model in CADFEKO
– Create CAD geometry using canonical structures and perform boolean operations on these.
– Add the properties, e.g. dielectric constant, coating, conductivity
• Add the excitation– Set solution parameters (e.g. frequency, loads).– Set excitations (e.g. frequency, loads).
• Add the request for results – e.g. far-fields, near-fields, S-parameters, SAR analysis
• Mesh and Calculation– Create mesh (surface and volume meshes) from CAD geometries.
Once the model preparation is complete (geometry, mesh, excitations and calculation requests), the Solution is obtained by running the solver FEKO.
27
Lab 2. Design a rectangle patch antenna of a given size (10cmx7.8cm) working at 915MHz on a substrate withThe patch is located at the middle of the substrate (20cmx15cm). Find the best feeding point (i.e., |S11| is minimal and at least less than -10dB when the input port impedance is 50Ω ). Show the far field radiation and S-parameters of the antenna
4.4, 1.55r h mmε = =
28
(2). FDTD Method
• The acronym of FDTD stands for Finite Difference Time Domain.
• first developed by Kane S. Yee in 1966.
• A method to simulate electromagnetic wave propagation in any kind of materials (including metals with dispersion).
• Very useful tool for simulating waves in subwavelength scale object (e.g. near-field optics).
29
Electromagnetic waveH Et
E Ht
μ
ε
∂= −∇×
∂∂
= ∇×∂ finite-
difference approximation
( ) ( )x
xxFxxFxF
ΔΔ−−Δ+
=∂∂ 2/2/
Finite difference scheme (discretization)
30
electric field points are spatially half-grid offset from the magnetic field points.
Yee’s mesh1 cell
( , , , ) ( , , , )
( , , )n
F x y z t F i x j y k z n t
F i j k
= Δ Δ Δ Δ
=
In 1966, K. S. Yee in the first time presented the finite difference approximation of Maxwell’s equations. These formulas are called Yee’s formulas. This method is called Finite Difference Time Domain now.
31
FDTD method
( ) ( )⎭⎬⎫
⎩⎨⎧
⎟⎠⎞
⎜⎝⎛ −−⎟
⎠⎞
⎜⎝⎛ +−= −−−
21
21
21
211 kHkHCkEkE n
ynyEXLZ
nx
nx
( ) ( ){ }1121
21
21
21
−−+−⎟⎠⎞
⎜⎝⎛ +=⎟
⎠⎞
⎜⎝⎛ + −+ kEkECkHkH n
xnxHYLZ
ny
ny
εztCEXLZ Δ
Δ=
μztCHYLZ Δ
Δ=
• Maxwell equation for plane wave traveling in the positive z direction (in one dimension):
• time-stepping in the discretized form:zE
tH
zH
tE
∂∂
=∂∂
∂∂
=∂∂ με ,
32
This flow chart often called ‘Leap-flog Algorithm’
Algorithm
33
FDTD Resultswhat will you see with FDTD?
a “movie” of the field propagating in or being scattered by the object.
34
Cell phone interaction with the human head.Digested from: Recom Inc. Website:
http://www.recomic.com/html/index.html.
FDTD simulation: Cell phone interaction with a human head
35
A commercial software for FDTD simulation: OptiFDTD
OptiFDTD is a powerful, highly integrated, and user friendly CADenvironment that enables the design and simulation of advanced passive and non-linear photonic components.
Some applications:
• Waveguide-based planar light circuits such as
splitters, couplers and resonators
• Photonic band gap materials and devices
• Surface plasmon devices
• Nonlinear materials and dispersive materials
36
Main components of OptiFDTD
• DesignerCreates a layout of devices on a wafer.
• SimulatorProcesses data in designer files,
monitors the progress and stores the results.
• AnalyzerLoads and analyzes the result files by simulator.
37
Designer
• Very user-friendly CAD interface, in which you can easily draw your structures.
• Conveniently switching between different views.
38
Simulator and Analyzer
• You can edit any simulation parameters in simulator.
• In simulation, an animation of what is happening makes you intuitively understand the phenomenon.
• Analyzer offers you convenient tools for dealing with the data provided by the simulator.
Edit parameters
Simulating Data analyzing
39
Lab 4. 2D ring resonator
• You are required to design a ring resonator in 2D case based on the provided materials, which acts like a filter for specific resonant wavelengths.
• You need to optimize the structure parameters, such as the radius of the ring, distance between the waveguides, etc.
• You can use the commercial software for the simulation and test your own design. schematic diagram
for a ring resonator
40
Commercial FDTD Codes are found on the Web:• APLAC http://www.aplac.hut.fi/aplac/general.html• Apollo Photonics http://www.apollophoton.com/• Applied Simulation Technology http://www.apsimtech.com/• CFD Research http://www.cfdrc.com/datab/software/maxwell/maxwell.html• Cray http://lc.cray.com/• Empire http://www.empire.de/• EMS Plus http://www.ems-plus.com/ezfdtd.html• ETH
http://www.iis.ee.ethz.ch/research/bioemc/em_simulation_platform.en.html• Optima Research http://www.optima-
research.com/Software/Waveguide/fullwave.htm• Optiwave http://www.optiwave.com/• Quick Wave http://www.ire.pw.edu.pl/ztm/pmpwtm/qw3d/• Remcom http://www.remcominc.com/html/index.html• RSoft http://www.rsoftinc.com/fullwave_info.htm• Schmid http://www.semcad.com/solver_performance.html• Vector Fields http://www.vectorfields.com/concerto.htm• Virtual Science http://www.virtual-
science.co.uk/celia/Celia_code/celia_home.htm• Zeland Software http://www.zeland.com/fidelity.html
41
References:• Yee, K. S., “Numerical solution of initial
boundary value problems involving Maxwell’s equations in isotropic media,”IEEE Trans. Antennas Propagat., vol. 14, 1966, pp. 302-307.
• A. Taflove, Computational Electrodynamics-The Finite Difference Time-Domain Method, Norwood: ArtechHouse, 2005.
42
III. Some Applications
43
1. Applications in Microwave AntennaDipoles--the Simplest Antennas
base stationReal-time evolution of the electric
field of an oscillating electric dipole
Pictures form http://en.wikipedia.org/wiki/
III. Some Applications
44
CST Microwave Studio™
HFSS Finite Element Method (FEM)
FEKO Method of Moments (MoM)
XFDTD Finite Difference time-domain Methods (FDTD)
Common Commercial Softwares for Antenna Simulation
Finite-Volume Time-Domain (FVTD) method
45
Reflector Antennas
National Radio Astronomy Observatory in U.S
46
Patch Antenna
FR4 substratemicrostrip fed
air substratecoaxial line fed
PIFA (Planar Inverted-F Antenna)
feeding probe
shorted patch
ground plane
47
VSWR
Antenna Structure Animated Current Distribution
Example I : UWB (Ultra-Wide Band) Antenna (using HFSS software)
Bandwidth: VSWR < 1.5
48
0
30
60
90
120
150
180
210
240
270
300
330
-100
-80
-60
-40
-20
0
-100
-80
-60
-40
-20
0
3GHz 10GHz
0
30
60
90
120
150
180
210
240
270
300
330
-100
-80
-60
-40
-20
0
-100
-80
-60
-40
-20
0
Radiation Patterns (H plane)
49
Example II: E Shaped Patch Antenna (using CST)
Antenna Structure Model in CST
50
Broad band formed by 3 resonances
f1=2.252GHz
f2=2.422GHz
f3=2.553GHz
Return Loss
51
f1=2.252GHz
Animate Current Distribution
E field and surface current
3D pattern
52
f1=2.422GHz
Animate Current Distribution
E field and surface current
3D pattern
53
f1=2.553GHz
Animate Current Distribution
E field and surface current
3D pattern
54
Array Applicationsarray antenna
on F22 combat aircraft
reflector antenna arraymicrostrip fed planar phase array
55
2. Radar Applications
RCS (Radar cross section) is the unit of measure of how detectable an object is with a radar. For example, a stealth aircraft (which is designed to be undetectable) will have design features that give it a low RCS, as opposed to a passenger airliner that will have a high RCS.
In particular, an article on stealth provides an overview of various methods used in designing aircraft so that they are more difficult to detect.
A USAF B-2 Spirit in flight
56
Concept of pulse radar
http://www.aerospaceweb.org/question/electronics/q0168.shtml
57
1. The power transmitted in the direction of the target 2. The amount of power that impacts the target and is reflected back in
the direction of the radar 3. The amount of reflected power that is intercepted by the radar antenna 4. The length of time in which the radar is pointed at the target
Factors that determine the energy returned by a target
58
T-33 jet trainer
T-33 radar cross section
T-33 medianized radar cross section
Typical RCS diagram
Website: http://www.cst.com/
5959
Invisible (transparent) cloaking with metamaterials (n=0)
60
Obtain macroscopic (effective) material parameters from an
artificial structure of microscopicelements through CEM
6161
Our world (refractive index n>0)
Positive refraction
slab: defocusing
n>0
>0.5 λ
6262
3 decades ago,Veselagopredicted theoretically:
Metamaterials with negative refractive index
refractive
index n<0permeabilityμ<0
permittivityε<0
slab: focusing
n<0
V.G. Veselago, Sov. Phys. Usp. 10, 509, 1968
6363SCIENCE VOL 292 6 APRIL 2001
lattice of split ring resonators
First experiment for metamaterial with n<0
---- at microwave frequencies
6464
Negative permeability at 100 THz(metal’s permittivity is already negative at optical
frequencies)
Retrieved real part of Effective Permeability
M. Wegener et al., Science 306, 1351 (2004)
Au
65
•Can be applied to both simple and complicated structures
66
67
Cloaking, realized with SRRs
First experimental demonstration of cloaking at 8.5GHz
68
Cloak OFF Cloak ON
Non-magnetic cloak @ 632.8nm with silver wires in silica
69
3. Circuit design(1). Microwave circuits.Waveguide based on Split Ring Resonators (SRRs) (with CST STUDIO SUITE)
Dual band-rejection filterOverall size: 15mm*10mmRejection bands: 2.47~2.7GHz, 4.7~5.3GHz
70
Current distribution
f = 2.5GHz
f = 5GHz
71
(2). Electronic integrated circuits(with CST STUDIO SUITE)
System-in-Package model with material definitions
Applications in EMC Transient Simulation of a System-in-Package (SiP), shown in figure 1 and imported from the CDS Cad design System, consists of copper (lossy metal), polyimide and Silicon with bond wires and through vias.
72Definition of the discrete ports in the SiP model
Figure 2 shows the discrete port assignment for the power suppy pin (1) and the signal pins (2,3,4,5).
73
Surface currents in the SiP at 10 GHz for Port 1 excitation - some materials have been hidden for clarity
Figure 4 shows an animated field plot of the surface currents at 10GHz as a function of phase.
Pictures from http://www.cst.com
74
a bad design may result in:
Breakdown
75
(3). Photonic Integrated CircuitsOptical Coupler. Waveguide ports have been defined at the waveguide feeds. The ring and feed lines are defined with a dielectric constant of 9. The frequency range simulated was between 170 THz and 250 THz.
Geometry of the Optical Coupler with Waveguide Ports
76
frequency dependent behaviour of the field. Ports 3 and 4 are isolated at 211.6 THz whereas ports 1 and 2 are isolated at 250 THz.
E-Field Plot at 211.6 THz
E-Field Plot at 250 THz
Website: http://www.cst.com/
77
Ultra-compact resonator filterHere is an ultra-compact thermally-tunable microring resonator filter with a submicron heater on silicon nanowires.
pad
pad
metal SiO2 Si
Input
Through
Output
metal
Si core SiO2 up-cladding
SiO2 insulator layer
The 3D view of schematic configuration of the present tunable MRR filter
J. Lightwave Technol. 26(6): 704-709, 2008.
78
the designed mask and the details of the structure
Heater Pad
Heater Pad Lmid
wT
Ltp Ltp
wtp
R wg
100μm
100μ
m
Inpu
t Th
roug
h
Dro
p
T-junction
79
TE
Ltp=1μm
Lmid=0.4μm wT=0.2μm
(a)
TM
Ltp=1μm
Lmid=0.4μm wT=0.2μm
(b)
The 2D-FDTD simulated light propagation in an optimally designed T-junction for (a) TE polarization; (b) TM polarization.
80
Thermal characteristics
T(x,y) @ P=5mW:Below heater: 350ºC Core: 152ºC~155ºC
x (μm)
y (μ
m)
SiO2 insulator
Si core
cladding Unit:ºC
2.44
2.46
2.48
2.5
2.52
2.54
0 1 2 3 4 5 6Power(mW)
Loss
(dB
/cm
)
TETM
P (mW)
n eff
numerically solve the Laplacian Equation with appropriate boundary conditions.
Δneff/ΔP: ~0.00644 mW-1
P=5mW Δneff=0.0322,Δλ ~ 20nm from Δλ=(Δneff/neff)λ
81
The spectral response (TE) as power increases
• Power: 0mW 5mW, 1551.7nm 1571.8nm, Δλ: ~20nm;
• IL: ~0.25dB; Extinction ratio: >20dB;
• Q(=λ/Δλ): ~1000;
1550 1560 1570 1580-30
-20
-10
0
1550 1560 1570 1580-30
-20
-10
0
1550 1560 1570 1580-30
-20
-10
0
1550 1560 1570 1580-30
-20
-10
0
1550 1560 1570 1580-30
-20
-10
0
1550 1560 1570 1580-30
-20
-10
0
wavelength (nm)
spec
trum
(dB
)
λres:1551.7nm λres:1555.3nm
λres:1559.1nm λres:1563.1nm
λres:1567.35nm λres:1571.8nm
(a) 0mW (b) 1mW
(c) 2mW (d) 3mW
(e) 4mW (f) 5mW
• Higher Q: decrease the coupling by increasing the gap width. E.g., Q~104 when Gap=200nm.
1
3
2
4
2’
4’
1’
3’
l44’
l22’
Gap
82
IV. Challenging Problems
Scattering by an airplane
Current distribution
83
Faster solver for a very large object
• Currents are induced on a PEC scatterer illuminated by a source.
• The induced currents adjust themselves to cancel the incident field.
• Hence, every current element needs to talk to the other elements.
Js Einc
PECPEC
Example: Fast Multipole Method
84
Fast Multipole Method
• all current elements talk directly to each other. The number of “links” is proportional to N 2 , where N is the number of current elements. => large matrix
OneOne--Level AlgorithmLevel Algorithm
• “hubs” are established to reduce the number of direct “links” between the current elements.
TwoTwo--Level AlgorithmLevel Algorithm
85
Fast Multipole Method (cont’d)
• A tree structure showing the procedure to form a multilevel algorithm. (N log N)
MultiMulti--Level AlgorithmLevel Algorithm
"Efficient MLFMA, RPFMA and FAFFA Algorithms for EM Scattering by Very Large Structures,“IEEE Transactions on Antennas Propagation, vol. 52, no. 3, pp. 759-770, March 2004.
86
an airplane hit by lightning:(with CST STUDIO SUITE)
The lightning strike, modelled by the shown double exponential waveform, is applied to the nose of the aircraft using a discrete current port. A 300 Ohm load from the tail to the electric boundary forms the discharge channel.
Lightning strikes most commonly occur in clouds: either inter- or intra-cloud or cloud-to-ground. The simulation of indirect lightning effects on structures with metallic shells
87
The surface current magnitude on the aircraft due to the lightning strike is shown as it varies in time.
Pictures from http://www.cst.com
88
CEM for a tank
On the ground
89
Car communications
90
91
Homework:
Derive the boundary conditions on page 12 from Maxwell’s equations(on page 11).