# How do I calculate the wavenumbers for a Broadband CARS system?

I had the question when I was reading a paper by Camp (High-Speed Coherent Raman Fingerprint Imaging of Biological Tissues), and I've been researching how to calculate wavenumbers from the 4 wave mixing. I have compiled a matlab script that attempts to answer this question:

clear
clc
close all
%%in nm/s
c = 2.998e+17
%%in nm
bandwidth = 1:1000;
wprobe = 780

%%in 1/s
deltaomega = c./bandwidth;
probe = c./wprobe;
%%in 1/s
was = deltaomega + probe;
%%in nm
lambdaas = c./was;
%% in inverse cm
vhat = 1e+7./lambdaas;
plot(bandwidth,(vhat));
vhat(end)


From literature, I can see that 3-color BCARS is was=wpump-wstokes+wprobe, which I do by converting the nm wavelengths to frequency. Since it's only the difference between pump and stokes that really matters, I have replaced it with a bandwidth term. I then convert back to wavelength and subsequently to relative wavenumber which I then plot as a function of bandwidth. However, the values I am getting are much bigger than expected (15,000 cm^-1) and the values only descend below 1e4 when the bandwidth is very large, which is not something that can be achieved with photonic crystal fibers. Any help would be very useful!

Classic mistake! $\Delta f\ne \frac{c}{\Delta\lambda}$. Rather, $\Delta f = \frac{c}{\lambda_1} - \frac{c}{\lambda_2}$.