Super-localisation of a point-like emitter in a resonant environment: Correction of the mirage effect

Abstract

<p style='text-indent:20px;'>In this paper, we show that it is possible to overcome one of the fundamental limitations of super-resolution microscopy: the necessity to be in an <i>optically homogeneous</i> environment. Using recent modal approximation results from [<xref ref-type="bibr" rid="b10">10</xref>, <xref ref-type="bibr" rid="b7">7</xref>], we show, as a proof of concept, that it is possible to recover the position of a single point-like emitter in a <i>known resonant environment</i> from far-field measurements, with a precision two orders of magnitude below the classical Rayleigh limit. The procedure does not involve solving any partial differential equation, is computationally light (optimisation in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^d $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M2">\begin{document}$ d $\end{document}</tex-math></inline-formula> of the order of <inline-formula><tex-math id="M3">\begin{document}$ 10 $\end{document}</tex-math></inline-formula>) and is therefore suited for the recovery of a very large number of single emitters.</p>