Metallic Nano Sphere
中文/English
To simulate single metallic silver sphere , radius = 200 nm (diameter=400nm) and then observe the scattering-absorption spectrum
Dipole
(Wavelength) = 1095 nm
Localized Surface Plasmon Resonance
Quadrupole
(Wavelength) = 625 nm
Localized Surface Plasmon Resonance
Example results and CAD download
Sphere_Mie_diameter400nm_metal.zip
https://drive.google.com/open?id=15m0DXK2uKcpYmsZJEdFhIf5WDoU47Sw3
Analytical Solution download :
bhmie_analytical.zip
https://drive.google.com/open?id=1TdyHFRQGLTOWf20DCmPLQbdFijPZmb3x
Theoretical Solution refer to these web
http://scatterlib.wikidot.com/mie
http://juluribk.com/2013/01/22/electric-field-at-localized-plasmon-resonance-using-meep/
Field pattern analysis examples download:
Sphere_Mie_diameter400nm_metal_1095.zip
https://drive.google.com/open?id=1Rpq971Boki000_BefQF4mu8IJOHxOGY5
Sphere_Mie_diameter400nm_metal_625.zip
https://drive.google.com/open?id=1i-Ro2IgD1dr_zx8dzbTmcmYjN-d6rVyW
Sphere_Mie_diameter400nm_metal_300.zip
https://drive.google.com/open?id=10jZ1VEmXmdH6e499n4AFMbJd69ojlZII
*.FCstd is the save file of FreeCAD
Add the boundary of the CAD files (FreeCAD)
Reference : 3D-CAD Simulation & Examples
Define Parameters
1. Selected the simulation dimension.
2. Define total x, y, z length that equal to CAD, and then set a appropriate resolution.
3. Import CAD files.
4. Define the material of each CAD.
5. Press【建立網格 Cad to Grids (Create)】button to create simulation grids.
Due to FreeCAD default unit is mm, and in this case the sphere unit is nm. If use nm unit in FreeCAD, the resolution of output STL file will not enough. So, at here express
"the unit can directly transform between any unit, nm <=> um <=> mm "
setup the dielectric constant of metal gold (using Electrical Model 1)
instruction webpage : Electric & Magnetic Models
A. Define the boundary conditions
B. Press the【創建 (Create)】button => Create the total grid size (Include the boundary condition & add space)
To simulate the Scattering-Absorption spectrum, select the (TFSF-RCS) radar cross section source
Checked out the simulation geometries, and then press 【輸出 Output】button to output the geometries files
Data_Materials.csv // (simulation index of structures)
Theoretical Solution refer to this web
bhmie_analytical.zip
https://drive.google.com/open?id=1TdyHFRQGLTOWf20DCmPLQbdFijPZmb3x
Theoretical Solution refer to these web
http://scatterlib.wikidot.com/mie
http://juluribk.com/2013/01/22/electric-field-at-localized-plasmon-resonance-using-meep/
Code :
clear all
a=100 ; %The normalization unit used in the simulation
rad=2; % radius of the sphere in normalized units, If a=100 then radius =2*100 nm
resl=10 ; % Normalized Resolution of the simulation domain if resl = 10 and a=100 then the actual resolution in nm is a/resl=100 nm/10=10 nm
fcen=0.3 ; % Central frequency of the source in normalized units if fcen =0.3 then the actual central wavelength is a/fcen =100/0.3=333 nm
df=0.3 ; % Frequency span of the source in normalized units
nfreq=60; % Number of wavelengths in the wavelenth spectrum to calculate the electric field, extinction
sample=10; %
decayby=1e-8 ; % This determines the accuracy. Smaller this value, longer the simation time, but more accurate calculations.
mpirun_bool=1 ; % controls whether computation is on parallel (uses multiple processors on a computer) or serial.
rad=a*rad; % Should be in nanometers.
lam=[200:2:2000]; % Should be in nanometers
[epsr,epsi,N]=LD(lam*1e-9,'Ag','LD');
for k=1:1:length(lam)
x=2*pi*rad/lam(k);
[s1,s2,qext,qsca,qback,gsca]=mie(x,N(k),2);
temp(:,k)=[qsca,qext,qext-qsca];
end
temp=temp';
plot(lam,temp)
xlabel('Wavelength (nm)')
ylabel('Efficiencies')
legend('Scattering','Extinction','Absorption')
temp2=[lam',temp(:,1),temp(:,2),temp(:,3)];
save('analytical.dat','temp2','-ascii')
print('silver_analytical.png','-dpng','-r100')
Field pattern analysis
The simulation results show the first order resonance is at about wavelength 1095 nm,
the second order resonance wavelength at about 625nm,
the maximum absorption peak at about 300 nm
Method 1, Using the 【Geometries Sweep】function to sweep the frequencies
refer to the instruction web-page:
Method 2, press 【saveas project】, and use the continue wave input
1. Set the Spectrum Analysis & Wavelength range
2. Check out the source
(Wavelength) = 1095 nm
★(Result Analysis):
頻譜 (Spectrum) : Analysis the Field pattern
(Wavelength) = 1095 nm
Localized Surface Plasmon Resonance - Dipole
the same can obtain
(Wavelength) = 625 nm
Localized Surface Plasmon Resonance - Quadrupole
(Wavelength) = 300 nm for Absorption
Dipole
(Wavelength) = 1095 nm
Localized Surface Plasmon Resonance
Quadrupole
(Wavelength) = 625 nm
Localized Surface Plasmon Resonance
Recommend paper and simulation reference
Localized Surface Plasmon Resonance Spectroscopy and Sensing, Katherine A. Willets and Richard P. Van Duyne
https://pdfs.semanticscholar.org/8101/b9e4d794020a8924ef7fec815f3628c47290.pdf
Lumerical FDTD Solution:
Methodology - Fluorescence Enhancement
https://kb.lumerical.com/en/sp_methodology_fluorescence_enhancement.html
Mie Scattering 3D (FDTD)
https://kb.lumerical.com/en/particle_scattering_mie_3d.html