# Angle-Resolved Fluorescence of a Dye Coupled to a Plasmonic Nanohole Array
## 1 Introduction  
Metal-based metastructures are ordered systems made of highly efficient electromagnetic scatterers. By changing their size, shape, and composition, their optical response can be tuned as desired, from ultraviolet through visible to near-infrared regions. This peculiar optical response is driven by coherent collective oscillations of conduction electrons in metal, a phenomenon known as surface plasmon resonance. At the plasmon resonant wavelength, the scatterers act as tiny antennas, increasing the local electromagnetic field intensity near the metastructure surface. Interestingly, these enhanced near fields associated with the surface plasmon resonances can interact with molecules close to the metastructure surface, granting a better interaction between light and matter at the nanoscale and enabling the detection of a very small amount of molecules through surface field-enhanced spectroscopy techniques. The most popular configuration for performing field-enhanced spectroscopy is Surface-Enhanced Raman Spectroscopy (SERS) [1, 2]. Moreover, Surface-Enhanced Fluorescence (SEF), i.e., the study of fluorescence and its dependence on the local environment, has been investigated for a long time [3, 4]. Above all, the deposition of a dye on a generic surface and its interaction with the surroundings has been theoretically and experimentally investigated, especially for metallic surfaces [5; 6]. This topic gathers a huge interest [7], in particular, thanks to the field enhancement effects [8], which are crucial for technologically relevant applications such as (bio)molecule sensing. In this framework, the concept of critical distance between the dye and the metal surface needs to be introduced: for small distances, the Forster quenching process prevails, suppressing the fluorescence signal, whereas, for large separation distances, the enhancement is reduced until it is lost [8]. Nevertheless, in several studies dealing with different metallic platforms, such a constraint has been discussed and relaxed [9; 10; 11; 12]. The key point is the plasmonic near-field capability to strongly interact with the dye and the consequent establishment of an energy exchange between the two. In this scenario, the transduction of such an interaction in terms of suppression or enhancement of the far field emission depends on the specific coupling established with the far field radiation mechanism of the plasmon itself. In the case of bulk metals, where the plasmonic modes are non-radiative, suppression prevails. For localized resonances, such as in metallic nanoparticles where plasmonic dipolar modes are supported or nanostructured films, where additional coupling schemes can be supported, emission enhancement can be observed. As a result, beyond the near-field enhancement provided by the metal and acting on the dye pumping and/or emission processes, the energy exchange efficiency depends mostly on the specific coupling mechanism established between the plasmonic modes and the far-field radiation. In this regard, a wide amount of studies and applications concerning plasmon-enhanced fluorescence (PEF) have been performed using metallic nanoparticles, likely because plasmonic localized resonances (LSPR) can be easily optically excited and detected [13; 14; 15; 16; 17]. Instead, the use of metallic surfaces poses many constraints regarding the specific optical configuration to be used for exploiting the plasmonic resonances: in the case of thin layers, a prism must be used; for corrugated surfaces or gratings, the diffraction must be considered [7; 18; 19; 20; 21]. Nevertheless, several applications have been developed using gold nanohole arrays (GNAs), exploiting the capability of this particular kind of metal-based metastructure to tailor the pumping and/or emission features of a dye laid on its surface [22; 23; 24; 25].