Optical Applications
with CST Microwave Studio®
Dr. Frank Demming-Janssen
1
Outline
• What’s so special on optical simulations?
– optics for beginners
– materials
• Solver overview for optical simulation
• Application examples
2
2n
dO
na
nd
k
l
3r
dOr
de
rn
on
am
Be
Gradien
t Index
ss
au
G
TF
F
S
/
u
c
l
Ca
n
o
i
at
rd
er
an
d
Fiber/O
ar
ma
ter
Fresnel equations
ptics
m
s
a
Pl
3
lin
e
on
ial
s
n and k
are called the refractive index and extinction coefficient
)
*
n = n + i ⋅ k = n ⋅ (1 + iκ )
ε re = n − k
ε im = 2nk
2
2
optical user will ALWAYS use these parameters
* sometimes:
4
)
n = n + i ⋅κ
Calculate Drude Parameter Macro
5
Optical WG Modes with CST MWS
a
n = 1.16
n = 1.45
a = 500 nm
Freq: 330 THz -> 909 nm wavelength
6
optical_wg_sweep.zip
www.cst.com
Theoretical Dispersion Plot
With:
7
b=
β / ko − n2
n1 − n2
(
V = ko ⋅ a ⋅ n1 − n2
2
)
1
2 2
*G.P. Agrawal: Fiber Optics Communication Systems, Wiley Series in Microwave and Optical Engineering, pp 34
www.cst.com
Modes
HE11
HE12
8
www.cst.com
Modedispersion Mode 1
Error calculation: Because of the use of the normalized propagation const. b the
error in this curve seems larger then it is! An error of less the 1% in the β might
show up as a error of more then 5% in b!
9
www.cst.com
Modedispersion Higher Order modes
10
www.cst.com
Plasmon
11
Materials
• For metals the real part of eps is NOT negligible and is negative and dispersive!
12
CST MICROWAVE STUDIO®
Solver Overview Optical Applications
Transient
Frequency
Domain
Eigenmode
13
• Large Problems
– Memory efficient algorithm
– Hardware Accelerator, Cluster Computing
• Perfect Boundary approximation
– eliminates staircase error at dielectric/dielectric and
dielectric/PEC interface
• Broadband Solution
– Broadband Farfield Monitor
• periodic structures with Floquet port modes
– unit cells surface plasmons
• TET mesh
– accurate field solutions at dielectric/Drude metal interface
• periodic boundaries (unit cells)
– Dispersion diagrams
Transient Solver
- advantages • Memory efficient algorithm
– solves electrical large problems
14
Transient Solver
- advantages • Memory efficient algorithm
• Perfect Boundary Approximation
– eliminates staircase error at dielectric/dielectric and dielectric/PEC
interface
15
Transient Solver
- advantages • Memory efficient algorithm
• Perfect Boundary Approximation
• Calculates Broadband Solution
Coated Silica Sphere
16
Transient Solver
- some weaknesses -
• Local Field Error (Drude Material)
MWS
FDTD from publication
• PBA works only “perfect” on normal dielectric materials.
• On Drude materials with a sign change of real par of ε at
interface PBA has no effect – only affect local field values
17
Frequency Domain Solver
- advantages • TET and HEX mesh
– TET mesh resolves material interfaces: Accurate local field
information for Drude Materials
HEX
18
TET
Frequency Domain Solver
- advantages -
• TET and HEX mesh
– TET mesh resolves material interfaces: Accurate local field
information for Drude Materials
HEX
19
TET
Fields along line across material interface
Example: Nanometric Optical Tweezers
E
metal tip
P
dielectric Sphere:
5 nm radius
20
Reference: Lukas Novotny, Randy X.
Bian, and X. Sunney Xie,
Physical Review Letters, Volume 79,
No. 4, 28 July 1997
Acrobat-Dokument
Field enhancement
Incident field
λ = 810 nm
Polarization of the incident E-field
aligned with tip axis:
enhancement factor 75
P
E
Polarization of the incident E-field
perpendicular to the tip axis:
no enhancement
E
21
P
Trapping a particle underneath the tip
Incident field
λ = 810 nm
Trapped dielectric particle
Trapped metallic particle
22
Frequency Domain Solver
- advantages • TET and HEX mesh
• Periodic and Unit cell calculation
– Allows arbitrary angle of incidents for plane waves
23
Example: Frustrated Total Reflection
Transmission vs. Gap Width
Power Flow vs. Gap Width
24
Example: Surface Plasmon Generation
ε = 1.69
metal sheet
50 nm
ε = -15.99 + 0.8i
P
E
Incident field phi > phi critical
25
ε = 2.56
Example: Surface Plasmon Generation
26
Example: Plasmon Scattering
Grating distance
P
E
27
Example: Plasmon scattering by grading
scattered field
P
E
28
Example: Plasmon excitation by grading
E
P
Surface Plasmon
Grating distance
29
Example: Plasmon excitation by grading
- structure setup -
• 2 D Solution
– setup only 1 mesh cell in
height
• Periodic Boundaries
• Ports at both ends
30
Example: Plasmon excitation by grading
- structure setup -
• record “balance”: Energy absorb by system
31
Example: Plasmon excitation by grading
TD Simulation
grating
450 THz
550 THz
32
Frequency Domain Solver
- advantages • TET and HEX mesh
• Periodic and Unit cell calculation
• Arbitrary material dispersion
For FD Solver ignore warning concerning material fit
33
Example: Scattering on a coated sphere
Test vehicle: nano shell - silver
coated silica
34
Results: Extinction Cross Section
Published results
35
MWS: different solvers
Thank you
36