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)




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




None, press 【創建(Create)】 button




Checked out the simulation geometries, and then press 【輸出 Output】button to output the geometries files

Data_Materials.csv // (simulation index of structures)



1. Set the Spectrum Analysis & Wavelength range

2. Check out the source




1. Set the simulation time setp

2. Save parameters

3. Calculation



★(Result Analysis):

頻譜 (Spectrum) : Analysis the spectrum




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

1. Set the simulation time setp

2. Save parameters

3. Calculation

★(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



Temporary fields analysis




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