# Approximations used in the analysis of signals in pump-probe spectroscopy

## TL;DR

This paper evaluates the validity of common approximations in pump-probe spectroscopy, especially optical pump-THz probe, revealing they are only accurate in extreme optical thickness cases.

## Contribution

It introduces a general transfer matrix method to assess when typical approximations in pump-probe spectroscopy are valid.

## Key findings

- Approximations are valid only in extreme optical thickness regimes.
- The transfer matrix approach provides a systematic evaluation.
- Most common approximations are not generally applicable.

## Abstract

In pump-probe spectroscopy, one often needs to analyse the transmission or reflection of electromagnetic waves through optically pumped media. Here, it is common practice to approximate the analysis in order to extract non-equilibrium values for the optical constants of the media. Concentrating on optical pump-THz probe spectroscopy, and using the transfer matrix approach, we present a general method for evaluating the applicability of the most common approximations. Somewhat surprisingly, we find that these approximations are truly valid only in extreme cases where the optical thickness of the sample is several orders of magnitude smaller or larger than the probe wavelength.