Optical Applications with CST Microwave Studio® · Optical Applications with CST Microwave Studio...

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Optical Applications with CST Microwave Studio®

Dr. Frank Demming-Janssen CST AG

Gothic stained gwindow of Notre-Da

http://en.wikipedialasmon

Yuehe Ge


All solvers solve Maxwell’s EquationsQuantum effects are not considered, so:

Objects should be at least a few Ǻ in sizeA statistically large number of photons should be considered

Both solvers(Time Domain with FIT and Frequency Domain with FEM) have no inherent spatial or frequency limitationElectrically large structures may require large amounts of memory

Validity and Limitations


Terminology: Differences

Optical Engineer:

- n and k

- wavelength [380 … 750 nm]

- Transmission &Reflection coeff.

Electrical Engineer:

- ε’ and ε’’

- frequency[400 … 790 THz]

- S-parameters


Terminology: TranslationHowever, translation is simple:

λεε

κ

/2

)1(22

cfnk

kninkinn

==′′

−=′

+⋅=⋅+=)


Plasmonic?!Solver Choice for Optical ApplicationsOptical Tutorial

Overview


What is a Plasmon?From Wikipedia: (..) Plasmons are collective oscillations of the free electron gas density, for example, at optical frequencies (….) Since plasmons are the quantization of classical plasma oscillations, most of their properties can be derived directly from Maxwell's equations.


What is a Plasmon?

Gothic stained glass rose window of Notre-Dame de Paris. The colors were achieved by colloids of gold nano-particles. Window was created by Jean de Chelles on the 13th century

http://en.wikipedia.org/wiki/Plasmon


Why is plasmonic still “hot”Light focusing & enhancement

In classical optical systems the field “concentration” is limited by the wavelength. Focal spots of lens systems or optical fibers have about the diameter of λ/2Plasmons generate concentrated field distribution and are hot candidates for light transmission thru sub-λ devices and for sub-λ light focusing

“optical computers”, sub-λ optical lithography


Why is plasmonic still “hot”

Channel plasmon-polariton


General purpose solver 3D-volume

Transientlarge problemsbroadbandarbitrary time signals

Frequency Domain

narrow band / single frequencysmall problemsperiodic structures with Floquet port modes

Special solver 3D-volume: closed resonant structures

Eigenmode strongly resonant structures, narrow bandcavities

Special solver 3D-surface: large open metallic structures

Integral Equation (based on MLFMM)

large structuresdominated by metal

Asymptotic Solver extremely large structures

3D EM Solver Overview


Memory efficient algorithmsolves electrical large problems

Solver Choice: Transient Solver


Memory efficient algorithmPerfect Boundary Approximation

reduces staircase error at dielectric/dielectric and dielectric/PEC interface


PBA Staircase


Memory efficient algorithmPerfect Boundary ApproximationCalculates Broadband Solution


Silver coated silica sphere


Possibly faster for electrically small modelsTET mesh more accurate at metallic material interfaces -> plasmons

Solver Choice: Frequency Domain

HEX TET


Possibly faster for electrically small modelsTET mesh more accurate at metallic material interfaces -> plasmonsUnit Cells with Flouquet Ports

Solver Choice: Frequency Domain


Installation of Optical ToolkitExamples

Plasmon grating optical scatterer & antennas

Tutorial Content


Installation of optical toolkit

The supplied ZIP file contains material files for metals at

optical frequencies as well as a project template file for optical applications. These files need to be extracted into the proper directory


Extract Material Library file

Extract *.mtd files into \\CST STUDIO SUITE

2012\Library\Materials


Extract Project Template fileExtract all Optical Application*.* files into \\CST STUDIO SUITE 2012\Library\

\\STUDIO SUITE 2012\Library\New Project Templates


Extract Optical Nano Emitter MacroExtract the Optical Nano Emitter.mcs files into \\ C:\Program Files (x86)\CST

STUDIO SUITE 2012\Library\Macros\Solver\Sources


After Extraction


Efficient optical coupling into metal-insulator-metal plasmon modes with subwavelength diffraction gratings

Michael J. Preiner, Ken T. Shimizu, Justin S. White, and Nicholas A. Melosha. APPLIED PHYSICS LETTERS 92, 113109 2008

Tutorial Example I


Geometry/Unit Cell Details

5 nm Ag

14 nm Al2O3

10 nm Au

Au

λ= 720 nm -> 416 THztheta = 53 deg

20 nm

135 nm Au


Online Example…

Start with optical application template to set the units to THz and nm


Online Example…

Specify background material and frequency range


Load Materials form Library

Load optical material properties for Gold and Silver form the library. Hint: You might want to use the filter “*optical” to only display the materials for the optical frequency range.


Create Al2O3 Material

Create Al2O3 material with a ε = n2 of 1.732


Create Substrate

Define Brick and align WCS as shown


Create Grove

Define cylinder and cut away


Blend Edges

Select edges and blend with 20 nm


Create Silver Layer

Create 5 nm Silver layer by performing a transform/copy. Do NOT yet perform a boolean operation


Create Al2O3 Layer

Create 14 nm Al2O3layer by performing a transform/copy of the silver layer. Do NOT yet perform a Boolean operation


Create top Gold LayerCreate top 12 nm Gold layer by performing a transform/ copy of the Al2O3 layer.

Perform several “Trim highlighted

shape” so that only the top layer of Gold

remains


Boolean Operations

Perform a Intersection check on the Al2O3 and Silver layer (in this order) as well and select “trim” so that the layer structure is created


Rename Layer

final geometry

rename the layers with proper names “Silver Layer, Dielectric Layer, Gold Layer”


Specify Boundary and Excitation Condition

Specify boundary conditions, scan angle and floquetport boundaries


Define Field Monitors

Define e-field monitor


Specify Mesh and Solver Parameteres

Specify curved mesh and solver settings and start solver


Field Results

Results: Plasmon is generated in dielectric layer if polarization of the field is in parallel to the plane of incident


Define Parameter

Define Parameter for grating width and angle of incident


Define Parameter Sweep


Define Result Templates


Sweep Result


Optical Properties of MetallodielectricNanostructures Calculated using Finite Difference Time Domain Method

Chris Oubre, Peter Nordlander, The Journal of Physical Chemistry B (2004), Vol. 108, pp. 17740-17747

Tutorial Example II


Geometry Details: Silver coated Silica Shell

Ø 96 nm

Ø 78 nm

Silver: (drude material)

Silica: ε = 2.08


Online Example…



Define silica sphere


Define Silver sphere

use „DrudeDispersion Model“.

Factor 1.602 is used, because in

the reference paper, the drudeparameters are

given in terms of “eV”


Specify background and frequency range


Perform Boolean Operation

final geometry


Specify Boundary and Symmetry Condition


Specify Excitation


For plasmonic applications the following quantities might be of interest:

E and H Fields – possible along lines and surfacesabsorption, scattering and extinction cross section.

The following slides shows, how to extract those results

Results


Define Mesh Adaption GoalTo compare the results with the published paper, the following results should be extracted:

• E-Field at 553.5 THz along a line thru the sphere• Extinction cross section vs. wavelength

Since the FD Solver calculates one frequency point at a time, we will check mesh convergence with respect to the field along the line.


Define Field Monitors of Interest


Setup Result Template to extract field along line

+


Define 0D Results for Mesh Adaptation


Specify Solver Settings and Start Solver


Specify Solver Settings and Start Solver

Max Field strength along line should not vary by more then 1% for two

checks in a row


Results

Field strength along line for the first 6 passes. Results are reasonable close together. Zooming in at the material interface between silver

and vacuum shows a “slope” instead of a “jump” in the field strength. To get better results, increase mesh density at observation

point by using dummy objects.


Add dummy spheres on vacuum silver interface

Add Dummy spheres with 1 nm radius at both sides


Add dummy spheres on silver silica interface

Add two dummy spheres with 1 nm radius on silver silica interface


Mesh View with/ without dummy spheres


Results

Field strength along converged after three passes. Zooming in at the material interface between silver and vacuum shows a poper jump“in

the field strength.


Field Results

Field inside and outside the sphere are out of phase


Setup Extinction Cross Section Simulation

Define broadband monitors


Change mesh adaptation settings and start solver

Without any active goal, the maximum numbers of passes is

performed


Scattering and absorption cross section


Extract extinction cross section vs. wavelength


Extract extinction cross section vs. wavelength

Rename and create wavelength plot and evaluate all


Scattering and absorption cross section


Comparison vs. publication


Tutorial Example IIIExcitation of a Surface Plasmon


Geometry/Unit Cell Details

Vacumm

250 nm Flint Glass

50 nm Au λ= 720 nm -> 416 THztheta = variable

100 nm


Define Template




Load optical material properties for Gold form the library. Hint: You might want to use the filter “*optical” to only display the materials for the optical frequency range.


Create Flint Glass Material

Create Flint Glassmaterial with a ε = n2

of 1.622


Specify background material

Specify background material


Specify frequency range

Specify frequency range


Create substrate

Define Brick


Create gold layer by extruding top face


Create vacuum top by extruding top face


Specify boundary and excitation condition

Specify boundary conditions and scan angle


Define excitation port


Specify Solver Parameteres

Specify solver settings and start solver


First Results

Only weak Plasmon is at this time. large Reflection of the incident wave. The S-Parameter (magnitude linear) are close to 1


Setup Parameter Sweep for excitation angle


Setup Parameter Watch


Start Sweep


Sweep Results

Best angle = 39.5


Plasmon at 39.5 deg


Tutorial Example IVBright and Dark Plasmon Excitation of a Nanorod


Model InfoIn Tutorial II we showed already, how a Plasmon can be excited in a nano particle by a plane wave. Due to symmetry reasons, only dipole and quadruple (e.g. odd) Plasmon modes can couple to a plane wave. Those plasmons are call “bright” since they can observed by light scattering. Plasmons, which will not couple to radiating field are called “dark” plasmons.

external field internal field

“bright” “bright” “dark”


Geometry Details: Nanorod with NanoemitterDark Plasmon might be excited by localized sources near the apex of the rod. In this test model, we will use a small physical dipole of 3 nm length. The 0.25 nm gap is driven by a high impedance port

100 nm

Ø 10 nm gold

Ø 0.25 nm3 nm0.25 nm

Frequency range: 200 – 650 THz

0.25 nm


First Step



Background material and Frequency Range



Define Nano Rod


Blend Edges


Create Nano Emitter


Create Gap


Create Nano Emitter


Create Nano Emitter Port

Create Port Sheet by using pick points


Create Nano Emitter Port


Move Emitter


Define Probe


Define Broadband Monitors


Define Integration Face for Monitor


Define Intgration Face for Monitor


Mesh Setup


Symmetry Setup


Solver Setup + Start


Post Processing - Probes

E-Field probe shows two distinct resonance peaks -> 2 plasmons


Post Processing - Farfield

Radiated Power shows only one distinct resonance peaks -> Only one Plasmon can decay by radiation


Post Processing - PowerFlow

Choose proper name



The power flow integrated over the rod surface gives the total absorb power! Two more templates for the power flowing out of the port (accepted power) and power flowing away from the device (radiated power) give use the complete power balance of radiated and absorbed power


Post Processing – Add. Templates

for comparison, add templates from the farfield results …


Post Processing – Add. Templates

.. and S-Parameter balance


Post Processing – calc. accepted power


Post Processing – Evaluate


Post Processing – Results: Abs. Power

Power absorbed by the Rod. Is negative because I have a net power flow into the surface


Post Processing – Results: Port Power

Power leaving the port. Should be similar to the power from the S-Parameter balance.


Post Processing – Results: Port Power

Comparison port power and balance


Post Processing – Results: Rad. Power

Radiated Power from Power Flow. This is a peak value and should be twice as the radiated power from farfield (RMS) value


Post Processing – Results: Rad. Power

Comparison for Radiated power from Powerflow and Farfield. Farfieldresults have been scaled by a factor of 2 to have peak values


Enhancement and Quenching of Single-Molecule Fluorescence

Pascal Anger, Palash Bharadwaj, and Lukas Novotny; PHYSICAL REVIEW LETTERS 96, 113002 2006

Tutorial Example V


Model InfoThe lifetime of an excited atomic state is not only a function of the atom but also of its environment. In the mentioned paper, the fluorescence rate of a single molecule as a function of its separation from a laser irradiated, spherical gold nanoparticle is investigated for the case of weak excitation (no saturation). The fluorescence process can be separate into to states. First the single molecule is excited by the incident radiation. The excitation rate scales with |p E|2 where p is the intrinsic transition dipole moment of the molecule and E is the local E Field at the position of the molecule. The E-Field and therefore the excitation rate will be enhanced closed to the particle surface. The decay of the excited state can be divided into a radiative (fluorescence) an non radiative (ohmic losses/heat generation) path. The closer the nano emitter to the surface of gold particle the larger the relative amount of energy lost to ohmic effects. As is shown in the reference paper, there is a certain gap width, where the combined effects lead to an overall increased fluorescence. The field enhancement is strong enough to out weight energy losses to the absorption by the gold sphere.


Geometry Details

gap

To find the optimum particle radius “r” and gap distance “gap” , two separate simulations are required. First, we need to know the field strength at the positions of the molecule due to the presence of the gold nano particle. Secondly we need simulate the quantum yield for the molecule which is the ratio of radiated to total emitted energy. The emitting molecule is modeled as electrical small dipole. The simulation is performed for a wavelength of 650 nm (461.5 THz)


Setup DetailsTo fully automate the simulation of the enhancement we use simulation flow control mechanism of Design Studio. We will setup up two independent CST MWS Models. The first model calculates the field enhancement in the near field of the nano particle. The second model calculates the quantum efficiency of a nano emitter. Both models are then uploaded into the Design Studio and linked with global parameters. A nested parameter sweep then allows to calculate the enhancement factor in a single simulation setup.


Model 1: Select Template



Online Example…




Load optical material properties for Gold form the library. Hint: You might want to use the filter “*optical” to only display the materials for the optical frequency range.


Define gold sphere


Define line to extract field strength

move WCS

Define line


Define mesh dummy

Toggle WCS Off

Create two copies of curve


Define mesh dummy


Define local mesh


Specify Excitation


Mesh Setup


Field Results


Add Template Evaluate Field on Curve


Field Results along curve


Model 2:

Save Model 1 under a different name. Delete the wires and result templates


Create Nano Emitter

Check if WCS is still located on the top of the sphere. Move WCS by a new parameter “gap”


Create Nano Emitter

Run the Macro “Create optical Nano Emitter.”This macro will create an electrical small dipole (1 nm length) in direction of the “w”. The dipole will be driven by a high impedance Port. Furthermore, a closed face is create to be used for integration of a Powerflowmonitor to watch the total emitted power. For badly matched ports, this is more accurate then the power balance of the port itself



Define power flow monitor


Define Integration Face for Powerflow

Pick gold sphere surface and create a face including the emitter and the sphere. An offset of “gap + 5” will included the emitter.


Mesh Setup



Define two „Evaluate field of face“ monitors. One for the „Source“ – this gives us the power emitted from the source only. And one for the „radiation“ which returns the power which is radiated into free space. Please use proper names for the monitors.


Post Processing – calculate Qeff

The quantum efficiency is the ratio for the two power flow integrations


Define Parameter Sweep


Results of Parameter Sweep

published MWS

Comparison of published results and CST MWS Results for a 80 nm diameter gold sphere


Calculate Fluorescence Rate in DS

Load the two CST MWS models to calculate the field along the line (E-Fields) and the quantum efficiency (Qeff) into a DS Project. These blocks will have the local parameter assigned.


Set up simulation tasks


Define Global Parameter in DS

Assign global parameters to the local block parameters


Setup Post Processing

Load “field along line”



Get Field at Position “gap”



Load “Qeff”



Calculate “Fluorescence enhancement”


Run SimulationDS will now • start a simulation for the block

with the plane wave excitation with the a gold sphere of radius “radi”

• extract the field along the line• start a simulation with the

nano emitter at the position “gap” with the a gold sphere of radius “radi”

• extract the Qeff• and finally calculates the

fluorescence enhancement


First DS Results


Setup nested sweep


Define Full workflowWith „Drag and Drop“ and „move up/down“ you can sort the workflow. For each „radi“, the E-Field is extracted along the line in one simulation. Then the nanoemitter is swept along the position “gap” to calculate the Qeff. The field strength at the position of the emitter is extracted from the first simulation in the post processing inside the “gap” sweep.


Final Results

MWS/DS Results Published Results

Optical Applications with CST Microwave Studio® · Optical Applications with CST Microwave Studio...

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