Inverse design of microcavities for fluorescent excitation and collection using Lorentz reciprocity and topology optimisation

We present a theoretical and computational framework for the inverse design of photonic structures aimed at enhancing fluorescence excitation and collection from incoherent emitters, particularly nitrogen-vacancy centres in diamond. By integrating Lorentz reciprocity with topology optimisation, we formulate an objective function based on electromagnetic field intensities at both excitation and emission wavelengths. This approach enables the simultaneous optimisation of structure for both input excitation and output collection. We demonstrate the method through three two-dimensional design cases. Our results reveal fluorescence signal enhancements of up to six orders of magnitude compared to bulk diamond, attributed to the formation of resonant cavities for both excitation and emission frequencies. This framework shall be broadly applicable to fluorescent-based sensing, quantum photonics, and microcavity laser design.