When plotting dielectric function from a tabulated n and k, why do I need to interpolate with another material?

Why do I need to interpolate TiO2 with Ge before plotting dielectric function of TiO2? Is there away I can plot the dielectrics function directly without interpolation? Since real(epsilon)=n^2-k^2 and Imag(epsilon)=2nk. Below is the part of the code

Thanks

e_TiO2 = dlmread('e_TiO2.txt');

w_Ge = e_TiO2(:,1);

[w_Ge uidx] = unique(w_Ge);

e_TiO2 = e_TiO2(:,2) + 1i*e_TiO2(:,3);

e_TiO2 = e_TiO2(uidx);

e_TiO2_interp = interp1(w_Ge, e_TiO2, w);

dielectric_function = e_TiO2_interp;

frequency = w(:,1);

Answer 1

[Hari]

Hi Ambali Odebowale,

I understand that you have tabulated data for the refractive index (n) and extinction coefficient (k) of TiO2 and want to plot the dielectric function without interpolating with another material, such as germanium (Ge).

In the context of your specific problem, if you only have data for TiO2 and do not need to match it with data from Ge or another material, and if your data points for TiO2 cover the required frequency or wavelength range adequately, you should be able to plot the dielectric function directly without interpolation.

Interpolation is needed when aligning TiO2 data points with specific frequencies or wavelengths, smoothing noisy data, combining datasets from different sources, achieving high-resolution plots, or estimating the dielectric function outside the measured range (extrapolation).

Assumptions:

1. Data points for TiO2 cover the required frequency or wavelength range adequately
2. First column of your data file is the frequency or wavelength,
3. Second column is the refractive index 'n',
4. Third column is the extinction coefficient 'k'.

Here's an example of how you could calculate and plot the real and imaginary parts of the dielectric function directly:

% Read the data for TiO2
e_TiO2 = dlmread('e_TiO2.txt');
frequency = e_TiO2(:,1);
n = e_TiO2(:,2); % Assuming column 2 is the refractive index n
k = e_TiO2(:,3); % Assuming column 3 is the extinction coefficient k

% Calculate the real and imaginary parts of the dielectric function
real_epsilon = n.^2 - k.^2;
imag_epsilon = 2.*n.*k;

% Plot the real and imaginary parts of the dielectric function
figure;
plot(frequency, real_epsilon, 'DisplayName', 'Real(ε)');
hold on;
plot(frequency, imag_epsilon, 'DisplayName', 'Imag(ε)');
xlabel('Frequency (or wavelength)');
ylabel('Dielectric Function');
title('Dielectric Function of TiO2');
legend('show');

Also, the real and imaginary parts of the dielectric function are calculated using the provided formulas and then plotted against the frequency or wavelength.

For more information on reading data from text files, refer to the documentation of "dlmread" https://www.mathworks.com/help/matlab/ref/dlmread.html

To understand how to plot data in MATLAB, you can look at the documentation for the "plot" https://www.mathworks.com/help/matlab/ref/plot.html

Hope this helps!