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CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com
Optical Applications with CST Microwave Studio®
Dr. Frank Demming-Janssen CST AG
Gothic stained gwindow of Notre-Da
http://en.wikipedialasmon
Yuehe Ge
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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
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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
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Terminology: TranslationHowever, translation is simple:
λεε
κ
/2
)1(22
cfnk
kninkinn
==′′
−=′
+⋅=⋅+=)
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Plasmonic?!Solver Choice for Optical ApplicationsOptical Tutorial
Overview
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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.
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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
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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
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Why is plasmonic still “hot”
Channel plasmon-polariton
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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
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Memory efficient algorithmsolves electrical large problems
Solver Choice: Transient Solver
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Memory efficient algorithmPerfect Boundary Approximation
reduces staircase error at dielectric/dielectric and dielectric/PEC interface
Solver Choice: Transient Solver
PBA Staircase
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Memory efficient algorithmPerfect Boundary ApproximationCalculates Broadband Solution
Solver Choice: Transient Solver
Silver coated silica sphere
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Possibly faster for electrically small modelsTET mesh more accurate at metallic material interfaces -> plasmons
Solver Choice: Frequency Domain
HEX TET
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Possibly faster for electrically small modelsTET mesh more accurate at metallic material interfaces -> plasmonsUnit Cells with Flouquet Ports
Solver Choice: Frequency Domain
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Installation of Optical ToolkitExamples
Plasmon grating optical scatterer & antennas
Tutorial Content
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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
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Extract Material Library file
Extract *.mtd files into \\CST STUDIO SUITE
2012\Library\Materials
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Extract Project Template fileExtract all Optical Application*.* files into \\CST STUDIO SUITE 2012\Library\
\\STUDIO SUITE 2012\Library\New Project Templates
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Extract Optical Nano Emitter MacroExtract the Optical Nano Emitter.mcs files into \\ C:\Program Files (x86)\CST
STUDIO SUITE 2012\Library\Macros\Solver\Sources
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After Extraction
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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
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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
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Online Example…
Start with optical application template to set the units to THz and nm
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Online Example…
Specify background material and frequency range
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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.
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Create Al2O3 Material
Create Al2O3 material with a ε = n2 of 1.732
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Create Substrate
Define Brick and align WCS as shown
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Create Grove
Define cylinder and cut away
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Blend Edges
Select edges and blend with 20 nm
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Create Silver Layer
Create 5 nm Silver layer by performing a transform/copy. Do NOT yet perform a boolean operation
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Create Al2O3 Layer
Create 14 nm Al2O3layer by performing a transform/copy of the silver layer. Do NOT yet perform a Boolean operation
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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
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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
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Rename Layer
final geometry
rename the layers with proper names “Silver Layer, Dielectric Layer, Gold Layer”
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Specify Boundary and Excitation Condition
Specify boundary conditions, scan angle and floquetport boundaries
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Define Field Monitors
Define e-field monitor
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Specify Mesh and Solver Parameteres
Specify curved mesh and solver settings and start solver
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Field Results
Results: Plasmon is generated in dielectric layer if polarization of the field is in parallel to the plane of incident
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Define Parameter
Define Parameter for grating width and angle of incident
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Define Parameter Sweep
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Define Result Templates
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Sweep Result
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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
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Geometry Details: Silver coated Silica Shell
Ø 96 nm
Ø 78 nm
Silver: (drude material)
Silica: ε = 2.08
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Online Example…
Start with optical application template to set the units to THz and nm
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Define silica sphere
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Define Silver sphere
use „DrudeDispersion Model“.
Factor 1.602 is used, because in
the reference paper, the drudeparameters are
given in terms of “eV”
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Specify background and frequency range
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Perform Boolean Operation
final geometry
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Specify Boundary and Symmetry Condition
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Specify Excitation
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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
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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.
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Define Field Monitors of Interest
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Setup Result Template to extract field along line
+
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Define 0D Results for Mesh Adaptation
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Specify Solver Settings and Start Solver
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Specify Solver Settings and Start Solver
Max Field strength along line should not vary by more then 1% for two
checks in a row
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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.
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Add dummy spheres on vacuum silver interface
Add Dummy spheres with 1 nm radius at both sides
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Add dummy spheres on silver silica interface
Add two dummy spheres with 1 nm radius on silver silica interface
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Mesh View with/ without dummy spheres
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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.
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Field Results
Field inside and outside the sphere are out of phase
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Setup Extinction Cross Section Simulation
Define broadband monitors
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Change mesh adaptation settings and start solver
Without any active goal, the maximum numbers of passes is
performed
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Scattering and absorption cross section
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Extract extinction cross section vs. wavelength
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Extract extinction cross section vs. wavelength
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Extract extinction cross section vs. wavelength
Rename and create wavelength plot and evaluate all
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Scattering and absorption cross section
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Comparison vs. publication
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Tutorial Example IIIExcitation of a Surface Plasmon
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Geometry/Unit Cell Details
Vacumm
250 nm Flint Glass
50 nm Au λ= 720 nm -> 416 THztheta = variable
100 nm
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Define Template
Start with optical application template to set the units to THz and nm
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Load Materials form Library
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.
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Create Flint Glass Material
Create Flint Glassmaterial with a ε = n2
of 1.622
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Specify background material
Specify background material
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Specify frequency range
Specify frequency range
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Create substrate
Define Brick
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Create gold layer by extruding top face
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Create vacuum top by extruding top face
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Specify boundary and excitation condition
Specify boundary conditions and scan angle
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Define excitation port
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Define excitation port
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Define Field Monitors
Define e-field monitor
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Specify Solver Parameteres
Specify solver settings and start solver
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First Results
Only weak Plasmon is at this time. large Reflection of the incident wave. The S-Parameter (magnitude linear) are close to 1
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Setup Parameter Sweep for excitation angle
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Setup Parameter Watch
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Start Sweep
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Sweep Results
Best angle = 39.5
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Plasmon at 39.5 deg
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Tutorial Example IVBright and Dark Plasmon Excitation of a Nanorod
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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”
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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
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First Step
Start with optical application template to set the units to THz and nm
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Background material and Frequency Range
Specify background material and frequency range
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Define Nano Rod
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Blend Edges
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Create Nano Emitter
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Create Gap
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Create Nano Emitter
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Create Nano Emitter Port
Create Port Sheet by using pick points
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Create Nano Emitter Port
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Move Emitter
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Define Probe
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Define Broadband Monitors
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Define Integration Face for Monitor
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Define Intgration Face for Monitor
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Define Intgration Face for Monitor
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Define Intgration Face for Monitor
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Mesh Setup
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Symmetry Setup
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Solver Setup + Start
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Post Processing - Probes
E-Field probe shows two distinct resonance peaks -> 2 plasmons
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Post Processing - Farfield
Radiated Power shows only one distinct resonance peaks -> Only one Plasmon can decay by radiation
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Post Processing - PowerFlow
Choose proper name
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Post Processing - PowerFlow
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
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Post Processing – Add. Templates
for comparison, add templates from the farfield results …
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Post Processing – Add. Templates
.. and S-Parameter balance
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Post Processing – calc. accepted power
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Post Processing – Evaluate
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Post Processing – Results: Abs. Power
Power absorbed by the Rod. Is negative because I have a net power flow into the surface
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Post Processing – Results: Port Power
Power leaving the port. Should be similar to the power from the S-Parameter balance.
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Post Processing – Results: Port Power
Comparison port power and balance
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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
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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
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Enhancement and Quenching of Single-Molecule Fluorescence
Pascal Anger, Palash Bharadwaj, and Lukas Novotny; PHYSICAL REVIEW LETTERS 96, 113002 2006
Tutorial Example V
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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.
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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)
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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.
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Model 1: Select Template
Start with optical application template to set the units to THz and nm
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Online Example…
Specify background material and frequency range
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Load Materials form Library
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.
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Define gold sphere
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Define line to extract field strength
move WCS
Define line
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Define mesh dummy
Toggle WCS Off
Create two copies of curve
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Define mesh dummy
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Define local mesh
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Specify Boundary and Symmetry Condition
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Specify Excitation
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Define Field Monitors
Define e-field monitor
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Mesh Setup
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Solver Setup + Start
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Field Results
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Add Template Evaluate Field on Curve
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Field Results along curve
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Model 2:
Save Model 1 under a different name. Delete the wires and result templates
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Create Nano Emitter
Check if WCS is still located on the top of the sphere. Move WCS by a new parameter “gap”
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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
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Specify Boundary and Symmetry Condition
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Define Field Monitors
Define power flow monitor
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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.
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Mesh Setup
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Solver Setup + Start
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Post Processing - PowerFlow
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.
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Post Processing – calculate Qeff
The quantum efficiency is the ratio for the two power flow integrations
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Define Parameter Sweep
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Results of Parameter Sweep
published MWS
Comparison of published results and CST MWS Results for a 80 nm diameter gold sphere
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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.
CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com
Set up simulation tasks
CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com
Set up simulation tasks
CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com
Define Global Parameter in DS
Assign global parameters to the local block parameters
CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com
Setup Post Processing
Load “field along line”
CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com
Setup Post Processing
Get Field at Position “gap”
CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com
Setup Post Processing
Load “Qeff”
CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com
Setup Post Processing
Calculate “Fluorescence enhancement”
CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com
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
CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com
First DS Results
CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com
Setup nested sweep
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Setup nested sweep
CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com
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.
CST – COMPUTER SIMULATION TECHNOLOGY | www.cst.com
Final Results
MWS/DS Results Published Results
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