Fano lineshapes and Rabi splittings: Can they be artificially generated or obscured by the numerical aperture?

TL;DR

This study demonstrates that high numerical aperture objectives can artificially produce or hide Fano lineshapes and Rabi splittings in optical spectra, leading to potential misinterpretations of coherent coupling in nanophotonics.

Contribution

The paper reveals that numerical aperture effects can create spectral artefacts mimicking true Fano resonances and Rabi splittings, providing guidelines to distinguish genuine phenomena from artefacts.

Findings

High NA objectives can generate false Fano and Rabi features.

Modest NA values can obscure true strong coupling signatures.

Transfer matrix calculations confirm artefacts arise from incoherent intensity sums.

Abstract

Fano resonances and Rabi splittings are routinely reported in the scientific literature. Asymmetric resonance lineshapes are usually associated with Fano resonances, and two split peaks in the spectrum are often attributed to a Rabi splitting. True Fano resonances and Rabi splittings are unequivocal signatures of coherent coupling between subsystems. However, can the same spectral lineshapes characterizing Fano resonances and Rabi splittings arise from a purely incoherent sum of intensities? Here we answer this question through experiments with a tunable Fabry-P\'erot cavity containing a CsPbBr\textsubscript{3} perovskite crystal. By measuring the transmission and photoluminescence of this system using microscope objectives with different numerical aperture ($NA$), we find that even a modest $NA=0.4$ can artificially generate Fano resonances and Rabi splittings. We furthermore show that this modest $NA$ can obscure the anti-crossing of a bona fide strongly coupled light-matter system. Through transfer matrix calculations we confirm that these spectral artefacts are due to the incoherent sum of transmitted intensities at different angles captured by the $NA$. Our results are relevant to the wide nanophotonics community, characterizing dispersive optical systems with high numerical aperture microscope objectives. We conclude with general guidelines to avoid pitfalls in the characterization of such optical systems.