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.

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