Optical Applications with CST Microwave Studio Optical Applications with CST Microwave Studio ® Dr. Frank Demming-Janssen 2 Outline • What’s so special on optical simulations?

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Optical Applicationswith CST Microwave Studio ®

Dr. Frank Demming-Janssen

22

Outline

• What’s so special on optical simulations?– optics for beginners

– materials

• Solver overview for optical simulation• Application examples

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Gradient Index Fiber/Optics

TF/SF Calculatio

n

2nd-Order and 3rd-Order nonlinear materials

Plasmon

Gauss Beam

n and k

Fresnel equations

44

n and k

are called the refractive index and extinction coefficient

nk

kn

inkinn

im

re

2

)1(22

=−=

+⋅=⋅+=

εε

κ)

optical user will ALWAYS use these parameters

κ⋅+= inn)

*

* sometimes:

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Calculate Drude Parameter Macro

66 www.cst.com

Optical WG Modes with CST MWS

n = 1.45n = 1.16

a = 500 nm

Freq: 330 THz -> 909 nm wavelength

a

optical_wg_sweep.zip

77 www.cst.com

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2/

nn

nkb o

−−= β ( )2

12

22

1 nnakV o −⋅⋅=

Theoretical Dispersion Plot

*G.P. Agrawal: Fiber Optics Communication Systems, Wiley Series in Microwave and Optical Engineering, pp 34

With:

88 www.cst.com

Modes

HE11

HE12

99 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 ββββ might show up as a error of more then 5% in b!

1010 www.cst.com

Modedispersion Higher Order modes

1111

Plasmon

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Materials

• For metals the real part of eps is NOT negligible and is negative and dispersive!

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CST MICROWAVE STUDIO®

• periodic boundaries (unit cells)– Dispersion diagramsEigenmode

• periodic structures with Floquet port modes – unit cells surface plasmons

• TET mesh– accurate field solutions at dielectric/Drude metal interface

Frequency Domain

• 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

Transient

Solver Overview Optical Applications

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Transient Solver- advantages -

• Memory efficient algorithm– solves electrical large problems

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Transient Solver- advantages -

• Memory efficient algorithm• Perfect Boundary Approximation

– eliminates staircase error at dielectric/dielectric and dielectric/PEC interface

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Transient Solver- advantages -

• Memory efficient algorithm• Perfect Boundary Approximation• Calculates Broadband Solution

Coated Silica Sphere

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Transient Solver- some weaknesses -

• Local Field Error (Drude Material)

• 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

MWS FDTD from publication

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Frequency Domain Solver- advantages -

• TET and HEX mesh– TET mesh resolves material interfaces: Accurate local field

information for Drude Materials

HEX TET

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Frequency Domain Solver- advantages -

• TET and HEX mesh– TET mesh resolves material interfaces: Accurate local field

information for Drude Materials

Fields along line across material interface

HEX TET

2020

Example: Nanometric Optical Tweezers

EP

metal tip

dielectric Sphere: 5 nm radius

Reference: Lukas Novotny, Randy X. Bian, and X. Sunney Xie,

Physical Review Letters, Volume 79, No. 4, 28 July 1997

Acrobat-Dokument

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Field enhancement

E

P

EP

Polarization of the incident E-field aligned with tip axis : enhancement factor 75

Polarization of the incident E-fieldperpendicular to the tip axis :

no enhancement

Incident fieldλ = 810 nm

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Trapping a particle underneath the tip

Trapped dielectric particle

Trapped metallic particle

Incident fieldλ = 810 nm

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Frequency Domain Solver- advantages -

• TET and HEX mesh• Periodic and Unit cell calculation

– Allows arbitrary angle of incidents for plane waves

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Example: Frustrated Total Reflection

Power Flow vs. Gap Width

Transmission vs. Gap Width

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Example: Surface Plasmon Generation

EP

metal sheet50 nm

Incident field phi > phi critical

ε = 2.56

ε = 1.69

ε = -15.99 + 0.8i

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Example: Surface Plasmon Generation

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Example: Plasmon Scattering

EP

Grating distance

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Example: Plasmon scattering by gradingscattered field

EP

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Example: Plasmon excitation by grading

EP

Grating distance

Surface Plasmon

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Example: Plasmon excitation by grading- structure setup -

• 2 D Solution– setup only 1 mesh cell in

height

• Periodic Boundaries• Ports at both ends

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Example: Plasmon excitation by grading- structure setup -

• record “balance”: Energy absorb by system

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Example: Plasmon excitation by gradingTD Simulation

grating

550 THz

450 THz

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Frequency Domain Solver- advantages -

• TET and HEX mesh• Periodic and Unit cell calculation• Arbitrary material dispersion

For FD Solver ignore warning concerning material fit

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Example: Scattering on a coated sphere

Test vehicle: nano shell - silver coated silica

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Results: Extinction Cross Section

MWS: different solversPublished results

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Thank you