Fourier transform analysis of multi-cavity random laser spectra: Applicability and limits

Derivative analysis in spectroscopy is widely used. It is possible to use spectral derivative techniques to analyze the emission spectra of laser action. In conjunction with Fourier's analysis, they enable a broader description of the physics of the phenomenon, especially for multi-resonator lasing emission as is often the case of random lasing. We have developed a numerical algorithm that mimics the lasing action coming from multi-resonator system. In this work, we propose an analytical protocol enhancing the accuracy of the analysis using n-th derivatives of the laser emission spectra with respect to the wave-vector in conjunction with the Fourier transforms. We evaluate the proposed method by applying it to model systems of numerically simulated optical resonators of randomly chosen sizes and Q-factors. The proposed analytical methodology helps retrieving the size of the resonators and recovering their Q-factor values.