In this section, we provide a brief overview of linear and non-linear spectroscopy using the Liouville pathways that contribute to the response signals. We then briefly review how the PLDM approach computes response functions for any operator dynamics. We further use Lindbald dynamics to describe the effect of cavity loss and develop a new trajectory-based approach to combine Lindbald dynamics with the PLDM approach, in order to provide a systematic way to incorporate cavity loss in polariton dynamics simulations for calculating linear and non-linear spectra.