what is the matlab code for ploting dispersion against wavelength (for chromatic dispersion)?

D=(-lamda*3*10^8)*(d^2(neff)/d(lamda)^2)

[Hiro Yoshino]

whad does "d" stand for? Is neff the refractive index?

[Ahmed]

Yes neff the refractive index

The second derivative

Answer 1

[Star Strider]

Try this —

syms c lambda n_eff(lambda)
D_T = -(lambda/c) * diff(n_eff,2)

D_T(lambda) = 

See MATLAB Onramp

.

[Ahmed]

Thank you

[Ahmed]

Lambda=[0.8 0.9 1 1.2 1.3 1.4 1.5 1.55 1.6 1.7];

neff=[1.4338 1.4275 1.4211 1.4073 1.4 1.3924 1.3845 1.3804 1.3763 1.3678 1.3650];

D=(-Lambda/3*10^8)*((diff(diff(neff)))/(diff(Lambda).^2));

plot(Lambda,(D));

This way, is it correct?

[Star Strider]

As always, my pleasure!

For numeric data, I would do something like this —

Lambda=[0.8 0.9 1 1.2 1.3 1.4 1.5 1.55 1.6 1.7];
n_eff=[1.4338 1.4275 1.4211 1.4073 1.4 1.3924 1.3845 1.3804 1.3763 1.3678 1.3650];

% dn_effdlambda = gradient(n_eff) ./ gradient(Lambda)
dn_effdlambda = gradient(n_eff(1:end-1)) ./ gradient(Lambda);

D = (-Lambda/3*10^8) .* dn_effdlambda.^2;

figure
plot(Lambda,D)
grid
xlabel('\lambda')
ylabel('D')

There appears to be a missing λ value, so I shortened by one element to calculate the derivative.

See the documentation on the gradient function for details.

.

[Ahmed]

Thank you Dr

[Star Strider]

As always, my pleasure!

Answer 2

[Hiro Yoshino]

You can use gradient to calculate this problem numerically.

Let me use SiO2 as an example.

data = readtable("SiO2.txt");

Warning: Column headers from the file were modified to make them valid MATLAB identifiers before creating variable names for the table. The original column headers are saved in the VariableDescriptions property.
Set 'VariableNamingRule' to 'preserve' to use the original column headers as table variable names.

lambda = data.Wavelength_nm_;
n = data.n;
c = 3e8;

plot(lambda,n);
xlabel("\lambda (nm)");

Here is how to visualize D for you:

dn_dlambda = gradient(n,5); % 1st order
d2n_dlambda2 = gradient(dn_dlambda,5); % 2nd order

D = -lambda/c.*d2n_dlambda2; % your D
plot(lambda,D)

[Ahmed]

Thank you