Plotting the Electric field of a SPR sensor

Hello everyone,

I want to plot the Electric field for a SPR sensor under Kretschmann configuration to get something that looks like the image

It doesn't have to be the same configuration as in the image above, just a simple (BK7/Ag) configuration.

Answer 1

[William Rose]

@Mohamed,

Do you have the data, and you want to know how to make a plot? If so, see here.

If you are looking for a formula for the electric field as a function of distance from the prism interface, you may want to look here or here or here or here, and follow the citation chains.

[Mohamed]

I only have the configuration of the sensor, I need a code that calculates the data and plots it as in the figure, I tried to look at the papers but no code was available

[William Rose]

@Mohamed,

Do you have the equaitons for the electric field intensity as a function of perpendicular distance from the interface? The figure you posted appears to be Figure 6 in Salahuddin et al., 2022. In th future, please cite the source of your data, so that othercs can assist you more effectively.

Perhaps equations 4 through 7 in Salahuddin et al. will allow you to reproduce the results in Figure 6. If not, check Salahuddin's references 6, 39, 40. Or email the authors.

The "Ag layer" and "sensing medium" in your figure are called the metal layer and the dielectric layer, respectively, in other sources.

Homola, Surface Plasma Resonance Bsed Sensors (Springer, 2006) says (p.12) that the E-field decays exponentially into the metal layer and into the dielectric layer. The characteristic decay distances are given by equation 49 in Homola. The decay length formula here looks different , but the formulas may be the same, rearranged - you can check.

Salahuddin et al. show exponential decay in the dielectric (sensing) layer, but the decay in the metal layer is more complex than a simple decaying exponential. I assume this difference is due to the mutiple thin layers between the metal and the dielectric, in Salhuddin. Again, for the formula, check Salhuddin and the articles they cite, or email the authors.

Once you have a formula, try to implement it in Matlab. Come back to this discussion if you think your Matlab implementaiton is not working. And when you do, include the formula you are trying to implement.

[Mohamed]

Here is my code, The result is just a straight line..

% Constants
lambda = 633e-9; % Wavelength in meters
n_BK7 = 1.515; % Refractive index of BK7
n_Ag = 0.059+4.243*i; % Refractive index of Silver
n_BP = 3.5+0.01*i; % Refractive index of BP
n_water = 1.315; % Refractive index of sensing medium
d_Ag = 45e-9; % Thickness of Silver layer in meters
d_BP = 6 * 0.53e-6; % Thickness of BP layer in meters

% Wave vector in vacuum
k0 = 2 * pi / lambda;

% Calculate wave vectors in each layer
k_BK7 = k0 * n_BK7;
k_Ag = k0 * n_Ag;
k_BP = k0 * n_BP;
k_water = k0 * n_water;

% Distance from the prism interface
z = linspace(0, 5e-6, 1000); % From 0 to 5 micrometers

% Electric field calculation
E_field = zeros(size(z));
for i = 1:length(z)
    if z(i) < d_Ag
        E_field(i) = exp(1i * k_Ag * z(i)); % In Silver
    elseif z(i) < d_Ag + d_BP
        E_field(i) = exp(1i * k_Ag * d_Ag) * exp(1i * k_BP * (z(i) - d_Ag)); % In BP
    else
        E_field(i) = exp(1i * k_Ag * d_Ag) * exp(1i * k_BP * d_BP) * exp(1i * k_water * (z(i) - d_Ag - d_BP)); % In Water
    end
end

% Plotting the electric field
figure;
plot(z * 1e6, abs(E_field)); % Convert z to micrometers for plotting
xlabel('Distance from Prism Interface (µm)');
ylabel('Electric Field Amplitude');
title('Electric Field as a Function of Distance from Prism Interface');
grid on;