In the following scritp I continue to get errors about the material assignemnt.
clear; close all; clc;
% ===== PHYSICAL PARAMETERS =====
lambda = 785e-9; % Wavelength [m]
omega = 2*pi*3e8/lambda; % Angular frequency [rad/s]
eps0 = 8.8541878128e-12; % Vacuum permittivity [F/m]
% ===== MATERIAL PROPERTIES =====
eps_au = (-24.051 + 1.3i) + 25; % Gold permittivity (shifted to Re(ε)>0)
eps_sio2 = 2.25; % SiO2 relative permittivity
% ===== CREATE MODEL =====
model = createpde(‘electromagnetic’,’harmonic’);
model.VacuumPermittivity = eps0;
% ===== GEOMETRY DEFINITION =====
% SiO2 substrate (500nm x 100nm)
rect_sio2 = [3;4; 0;500e-9;500e-9;0; 0;0;100e-9;100e-9];
% Air gap (500nm x 5nm, starting at y=100nm)
gap_y_start = 100e-9;
gap_height = 5e-9;
rect_air = [3;4; 0;500e-9;500e-9;0; …
gap_y_start+1e-12; gap_y_start+1e-12; … % Slightly offset to avoid overlap
gap_y_start+gap_height-1e-12; gap_y_start+gap_height-1e-12];
% Gold nanoparticle (radius 50nm at x=250nm, y=149nm)
circ = [1;250e-9;149e-9;50e-9; zeros(6,1)];
% Combine geometry with constructive solid geometry
gd = [rect_sio2, rect_air, circ];
ns = char(‘sio2′,’airgap’,’gold’)’;
sf = ‘(sio2 + airgap) + gold’; % Proper CSG formula
dl = decsg(gd,sf,ns);
geometryFromEdges(model, dl);
% ===== VISUALIZE FACE LABELS (CRUCIAL STEP) =====
figure;
pdegplot(model,’FaceLabels’,’on’,’EdgeLabels’,’on’);
title(‘Geometry Face Labels’);
axis equal;
% ===== MATERIAL ASSIGNMENT =====
% Assign properties based on face numbers from plot
% NOTE: Face numbers may differ – adjust based on pdegplot output!
electromagneticProperties(model,’Face’,1,’RelativePermittivity’,eps_sio2,…
‘RelativePermeability’,1,’Conductivity’,0); % SiO2
electromagneticProperties(model,’Face’,2,’RelativePermittivity’,1,…
‘RelativePermeability’,1,’Conductivity’,0); % Air
electromagneticProperties(model,’Face’,3,’RelativePermittivity’,eps_au,…
‘RelativePermeability’,1,’Conductivity’,0); % Gold
% ===== BOUNDARY CONDITIONS =====
k_spp = 2*pi/lambda * sqrt(eps_au/(1 + eps_au));
jsFun = @(location,~) exp(1i * k_spp * location.x);
electromagneticBC(model,’Edge’,1,’SurfaceCurrentDensity’,jsFun); % SPP excitation
electromagneticBC(model,’Edge’,[2,4],’FarField’,’absorbing’,…
‘Thickness’,lambda/4); % Absorbing BCs
% ===== MESH GENERATION =====
generateMesh(model,…
‘Hmax’,lambda/20, …
‘Hmin’,gap_height/2, …
‘Hgrad’,1.3, …
‘GeometricOrder’,’linear’);
figure;
pdemesh(model);
title(‘Mesh’);
axis equal;
% ===== SOLVE & VISUALIZE =====
result = solve(model,’Frequency’,omega);
E = result.ElectricField;
Emag = sqrt(abs(E.Ex).^2 + abs(E.Ey).^2 + abs(E.Ez).^2);
figure;
pdeplot(model,’XYData’,Emag,’ColorMap’,’jet’,’Mesh’,’off’);
title(‘Electric Field Magnitude |E|’);
colorbar;
axis equal;In the following scritp I continue to get errors about the material assignemnt.
clear; close all; clc;
% ===== PHYSICAL PARAMETERS =====
lambda = 785e-9; % Wavelength [m]
omega = 2*pi*3e8/lambda; % Angular frequency [rad/s]
eps0 = 8.8541878128e-12; % Vacuum permittivity [F/m]
% ===== MATERIAL PROPERTIES =====
eps_au = (-24.051 + 1.3i) + 25; % Gold permittivity (shifted to Re(ε)>0)
eps_sio2 = 2.25; % SiO2 relative permittivity
% ===== CREATE MODEL =====
model = createpde(‘electromagnetic’,’harmonic’);
model.VacuumPermittivity = eps0;
% ===== GEOMETRY DEFINITION =====
% SiO2 substrate (500nm x 100nm)
rect_sio2 = [3;4; 0;500e-9;500e-9;0; 0;0;100e-9;100e-9];
% Air gap (500nm x 5nm, starting at y=100nm)
gap_y_start = 100e-9;
gap_height = 5e-9;
rect_air = [3;4; 0;500e-9;500e-9;0; …
gap_y_start+1e-12; gap_y_start+1e-12; … % Slightly offset to avoid overlap
gap_y_start+gap_height-1e-12; gap_y_start+gap_height-1e-12];
% Gold nanoparticle (radius 50nm at x=250nm, y=149nm)
circ = [1;250e-9;149e-9;50e-9; zeros(6,1)];
% Combine geometry with constructive solid geometry
gd = [rect_sio2, rect_air, circ];
ns = char(‘sio2′,’airgap’,’gold’)’;
sf = ‘(sio2 + airgap) + gold’; % Proper CSG formula
dl = decsg(gd,sf,ns);
geometryFromEdges(model, dl);
% ===== VISUALIZE FACE LABELS (CRUCIAL STEP) =====
figure;
pdegplot(model,’FaceLabels’,’on’,’EdgeLabels’,’on’);
title(‘Geometry Face Labels’);
axis equal;
% ===== MATERIAL ASSIGNMENT =====
% Assign properties based on face numbers from plot
% NOTE: Face numbers may differ – adjust based on pdegplot output!
electromagneticProperties(model,’Face’,1,’RelativePermittivity’,eps_sio2,…
‘RelativePermeability’,1,’Conductivity’,0); % SiO2
electromagneticProperties(model,’Face’,2,’RelativePermittivity’,1,…
‘RelativePermeability’,1,’Conductivity’,0); % Air
electromagneticProperties(model,’Face’,3,’RelativePermittivity’,eps_au,…
‘RelativePermeability’,1,’Conductivity’,0); % Gold
% ===== BOUNDARY CONDITIONS =====
k_spp = 2*pi/lambda * sqrt(eps_au/(1 + eps_au));
jsFun = @(location,~) exp(1i * k_spp * location.x);
electromagneticBC(model,’Edge’,1,’SurfaceCurrentDensity’,jsFun); % SPP excitation
electromagneticBC(model,’Edge’,[2,4],’FarField’,’absorbing’,…
‘Thickness’,lambda/4); % Absorbing BCs
% ===== MESH GENERATION =====
generateMesh(model,…
‘Hmax’,lambda/20, …
‘Hmin’,gap_height/2, …
‘Hgrad’,1.3, …
‘GeometricOrder’,’linear’);
figure;
pdemesh(model);
title(‘Mesh’);
axis equal;
% ===== SOLVE & VISUALIZE =====
result = solve(model,’Frequency’,omega);
E = result.ElectricField;
Emag = sqrt(abs(E.Ex).^2 + abs(E.Ey).^2 + abs(E.Ez).^2);
figure;
pdeplot(model,’XYData’,Emag,’ColorMap’,’jet’,’Mesh’,’off’);
title(‘Electric Field Magnitude |E|’);
colorbar;
axis equal; In the following scritp I continue to get errors about the material assignemnt.
clear; close all; clc;
% ===== PHYSICAL PARAMETERS =====
lambda = 785e-9; % Wavelength [m]
omega = 2*pi*3e8/lambda; % Angular frequency [rad/s]
eps0 = 8.8541878128e-12; % Vacuum permittivity [F/m]
% ===== MATERIAL PROPERTIES =====
eps_au = (-24.051 + 1.3i) + 25; % Gold permittivity (shifted to Re(ε)>0)
eps_sio2 = 2.25; % SiO2 relative permittivity
% ===== CREATE MODEL =====
model = createpde(‘electromagnetic’,’harmonic’);
model.VacuumPermittivity = eps0;
% ===== GEOMETRY DEFINITION =====
% SiO2 substrate (500nm x 100nm)
rect_sio2 = [3;4; 0;500e-9;500e-9;0; 0;0;100e-9;100e-9];
% Air gap (500nm x 5nm, starting at y=100nm)
gap_y_start = 100e-9;
gap_height = 5e-9;
rect_air = [3;4; 0;500e-9;500e-9;0; …
gap_y_start+1e-12; gap_y_start+1e-12; … % Slightly offset to avoid overlap
gap_y_start+gap_height-1e-12; gap_y_start+gap_height-1e-12];
% Gold nanoparticle (radius 50nm at x=250nm, y=149nm)
circ = [1;250e-9;149e-9;50e-9; zeros(6,1)];
% Combine geometry with constructive solid geometry
gd = [rect_sio2, rect_air, circ];
ns = char(‘sio2′,’airgap’,’gold’)’;
sf = ‘(sio2 + airgap) + gold’; % Proper CSG formula
dl = decsg(gd,sf,ns);
geometryFromEdges(model, dl);
% ===== VISUALIZE FACE LABELS (CRUCIAL STEP) =====
figure;
pdegplot(model,’FaceLabels’,’on’,’EdgeLabels’,’on’);
title(‘Geometry Face Labels’);
axis equal;
% ===== MATERIAL ASSIGNMENT =====
% Assign properties based on face numbers from plot
% NOTE: Face numbers may differ – adjust based on pdegplot output!
electromagneticProperties(model,’Face’,1,’RelativePermittivity’,eps_sio2,…
‘RelativePermeability’,1,’Conductivity’,0); % SiO2
electromagneticProperties(model,’Face’,2,’RelativePermittivity’,1,…
‘RelativePermeability’,1,’Conductivity’,0); % Air
electromagneticProperties(model,’Face’,3,’RelativePermittivity’,eps_au,…
‘RelativePermeability’,1,’Conductivity’,0); % Gold
% ===== BOUNDARY CONDITIONS =====
k_spp = 2*pi/lambda * sqrt(eps_au/(1 + eps_au));
jsFun = @(location,~) exp(1i * k_spp * location.x);
electromagneticBC(model,’Edge’,1,’SurfaceCurrentDensity’,jsFun); % SPP excitation
electromagneticBC(model,’Edge’,[2,4],’FarField’,’absorbing’,…
‘Thickness’,lambda/4); % Absorbing BCs
% ===== MESH GENERATION =====
generateMesh(model,…
‘Hmax’,lambda/20, …
‘Hmin’,gap_height/2, …
‘Hgrad’,1.3, …
‘GeometricOrder’,’linear’);
figure;
pdemesh(model);
title(‘Mesh’);
axis equal;
% ===== SOLVE & VISUALIZE =====
result = solve(model,’Frequency’,omega);
E = result.ElectricField;
Emag = sqrt(abs(E.Ex).^2 + abs(E.Ey).^2 + abs(E.Ez).^2);
figure;
pdeplot(model,’XYData’,Emag,’ColorMap’,’jet’,’Mesh’,’off’);
title(‘Electric Field Magnitude |E|’);
colorbar;
axis equal; pde, electromagnetic model, properties MATLAB Answers — New Questions

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