# Wide-Band Lorentzian FDTD Algorithm

I want to convert a simulated gain/absorption of a material, which can be understood as a discreet (dispersive?) function $$g_i(f_i)$$ ($$f$$ is for frequency) or $$g_i(\lambda_i)$$, into $$\tilde g(t)$$ for Finite-Discrete Time-Domain simulations. My title is actually almost the title of this paper where you can find the (mainly theoretical) details.

I know that a wide-band lorentzian algorithm can do the job and that I probably have to do a parameter extraction (based on an analytical solution of a corresponding system of non-linear equation) or somehing like this, but I don't know where to get or how to write the (complete) algorithm. I have MatLab and I can also code a bit Python and a bit C++.

• Is there in MatLab a toolbox for this, can i use/how to use FIR/IIR-Filter or other Convolutional Coding?

• I don't really got the theory! Fit multispectral lorenz curves to my $$g(f)$$-data and do some magic Fourier-Transformation with filters, kernels and/or recursive convolution to get $$g(t)$$?

• Does the Kramers–Kronig relations also play a role to convert the absorption/gain function to real refractive index, to fit over the complex refractive index function ?

I also read a lot of buzzwords but cannot connect them properly: convolutional coding, (linear) recursive convolution procedure, FIR-Filter, (multispectral-lorentzian fit, kernel function etc...)

• I have absolutely no background in FTDT simuation, but where I'm from "convolutional coding" is a technique for adding redundancy to data so errors can be corrected at a receiver. I don't think this comes up in your papers at all. Convolution itself is a very basic math operation, and coding is an extremely specific application of that. If you haven't, I'd recommend reading up on what convolution is (it's way easier than you seem to think and you probably already know it) – Marcus Müller Feb 1 at 13:48
• Thx for clarification and editing my text, I will do that. – Tom Key Feb 1 at 15:32