Nelly: A User-Friendly and Open-Source Implementation of Tree-Based Complex Refractive Index Analysis for Terahertz Spectroscopy

Terahertz
(THz) spectroscopy is a powerful tool for unambiguously
extracting complex-valued material properties (e.g., refractive index,
conductivity, etc.) from a wide range of samples, with applications
ranging from materials science to biology. However, extracting complex
refractive indices from THz time-domain spectroscopy data can prove
challenging, especially for multilayer samples. These challenges arise
from the large number of transmission-reflection paths the THz pulse
can take through the sample layers, leading to unwieldy strings of
Fresnel coefficients. This issue has often been addressed using various
approximations. However, these approximations are only applicable
to specific classes of samples and can give erroneous results when
misapplied. An alternative to this approach is to programmatically
model all possible paths through the sample. The many paths through
the sample layers can be modeled as a tree that branches at every
point where the paths diverge, i.e., whenever the pulse can either
be transmitted or reflected. This tree can then be used to generate
expressions relating the unknown refractive index to the observed
time domain data. Here, we provide a freely available open-source
package implementing this method as both a MATLAB library and a corresponding
graphical user interface, which can also be run without a MATLAB license
(https://github.com/YaleTHz/nelly). We have
tested this method for a range of samples and compared the results
to commonly used approximations to demonstrate its accuracy and wide
applicability. Our method consistently gives better agreement than
common approximations.