**4. Conclusions**

It has been shown that a long-range coupling within a gold nanodisc array affects significantly the SERS intensity of a molecular probe (4-mercaptobenzoic acid). This type of coupling corresponds to the emergence of a new radiative order in the substrate plane. This interaction is maximum for a critical grating constant Λ*<sup>c</sup>*, when the plasmon mode wavelength is close to the Rayleigh anomaly position. As a consequence, the REF is strongly dependent on the grating constant. The maximum of REF is not obtained for a grating constant corresponding to a maximum of local electric field intensity, but systematically obtained for smaller grating constants regardless the environment. Experimental and theoretical values of the REF display that one needs to consider a symmetric environment, in order to optimize the REF. More importantly, it is demonstrated that the Raman gain of molecular probes can be improved with one order of magnitude in a symmetric medium (in oil) compared to SERS experiments in air, by considering the appropriate grating constant.

**Author Contributions:** Investigation, I.R., M.B. and A.B.; formal analysis, S.L.-T.; resources, A.R.; data curation, S.K.; methodology, P.-M.A.; software, A.C.-B.; writing—original draft preparation, G.L. and J.A.; writing—review and editing, L.B.-L. and supervision, N.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the LabEx SEAM (Science and Engineering for Advanced Materials and devices) of Sorbonne Paris Cité in the frame of the project HOTSPOT.

**Conflicts of Interest:** The authors declare no conflict of interest.
