Diffraction is the core working principle of a large amount of photonic devices and represents a remarkable effect of light-matter interaction. The speed of light in a medium depends on its refractive index; as such, a plane wave impinging on a medium whose refractive index is periodically modulated undergoes a wavefront distortion. For instance, light propagating through a phase diffraction grating results into a far-field light pattern made of areas illuminated at specific angles. The Fourier space representation of this phenomenon is reported in Figure 1. The vector equation governing the diffraction into a specific order *m* can be written as

Figure 1: Typical Fourier space geometries in phase diffraction gratings. (A) Bragg incidence, (B) Bragg-mismatched incidence, and (C) evanescent (nonradiative) condition of a diffracted order.

$${k}_{i}+mq={k}_{d}+\Delta \text{,}$$(1)

where *k*_{i}=*n*_{inc}2*π*/*λ* and *k*_{d}=*n*_{dif}2*π*/*λ*, respectively, are the moduli of the wave vectors of the light impinging on the grating and diffracted by it; *q*=2*π*/Λ is the modulus of the vector associated with the grating and Λ its period; *n*_{inc} and *n*_{dif} are respectively the refractive indices of the media where the light is coming from (before diffraction) and propagating to (after diffraction). Finally, the vector Δ is usually indicated as wave-mismatch and distinguishes the case of Bragg-matched (Δ=0; Figure 1A) and mismatched (Δ≠0; Figure 1B) incidence [1].

In Figure 1C, the case when diffraction results in non-radiative or evanescent orders is instead depicted. This happens when

$$\left|mq\right|\ge {k}_{i,x}+{k}_{d}.$$(2)

In the previous equation, the equality sign corresponds to the cut-off between radiative and evanescent diffracted orders. This limit has been first identified by Wood [2] and then explained by Rayleigh [3]. For this reason, Eq. (2) (with equality sign) is indicated as Rayleigh anomaly and commonly written as

$$m{\lambda}_{\text{RA}}=\Lambda \mathrm{(}{n}_{\text{inc}}sin{\theta}_{inc}+{n}_{\text{dif}}\mathrm{)}.$$(3)

Noteworthy, the Rayleigh wavelength *λ*_{RA} depends on *n*_{inc}, *n*_{dif}, the angle *θ*_{inc}, formed by the beam incoming on the grating with its normal, and the considered diffracted order (*m*). Once previous parameters are fixed, the grating behaves in subwavelength (SW) regime for all wavelength values *λ*>*λ*_{RA}.

The behavior of the grating is peculiar when the diffracted order is evanescent. If the first order (*m*=+1) is considered, the electric field, associated with the diffracted wave, remains confined in proximity of the grating interface (with air, in this case) and can be written as

$${E}_{\text{dif}}=A\text{exp}\mathrm{(}i\omega t\mathrm{)}\text{exp}\mathrm{(}\text{-}ik\alpha x\mathrm{)}\mathrm{exp}\mathrm{(}\text{-}k\beta \left|z\right|\mathrm{)},$$(4)

which is the expression of a progressive wave propagating in the direction parallel to the grating (along *x*) with an amplitude term exponentially decaying in the direction orthogonal to the grating (along *z*) [4]. In the previous equation, *k=*(2*π*/*λ)n*_{dif}, while

$$\{\begin{array}{l}\alpha =\text{sin}{\theta}_{\text{dif}}=\left|\frac{1}{{n}_{\text{dif}}}\mathrm{(}\frac{m\lambda}{\Lambda}\text{-sin}{\theta}_{\text{inc}}\mathrm{)}\right|>1\\ \beta =\sqrt{{\alpha}^{2}\text{-}1}=\sqrt{{\left[\frac{1}{{n}_{\text{dif}}}\mathrm{(}\frac{m\lambda}{\Lambda}\text{-sin}{\theta}_{\text{inc}}\mathrm{)}\right]}^{2}\text{-}1}\end{array}.$$(5)

*θ*_{dif} is the angle made by the considered diffracted beam with the grating normal. When the condition in Eq. (2) is verified for a specific diffracted order, the grating behaves in SW regime [5]. Many applications of SW gratings made of dielectric materials are reported in the literature. Even if made of isotropic materials, these gratings show a form of birefringence, thus an anisotropic response when illuminated by light of different polarization. This property has been exploited in several applications and mainly as antireflection layers [6], waveplates [7], for polarization control [8], and metamaterials [9]. Different is the situation when a grating is made of metallic stripes or arrays of metal nanoparticles (NPs). Actually, the lineshape features of the localized surface plasmon resonance (LSPR) of a single plasmon subunit are strongly influenced by the regular arrangement of the subunits. As suggested by Eq. (4), if the NP array is illuminated with a wavelength close to *λ*_{RA}, the considered diffracted order is evanescent and propagates along the sample substrate. The evanescent electric field associated with this order is localized in the substrate and can couple with the plasmon fields scattered by the particles, thus inducing a collective resonance (CR) mode [10]. Indeed, theoretical studies have demonstrated that this near-field coupling is much more efficient when the LSPR wavelength of the isolated metal NP (*λ*_{LSP}) is close in value to the Rayleigh wavelength (*λ*_{LSP}~*λ*_{RA}) [11], [12], [13]. This choice is functional to maximize the energy transfer between the evanescent waves, propagating in proximity of the substrate, and the NP plasmon modes. The evident consequence of this energy transfer is the modification and extreme narrowing of the LSPR lineshape. Schatz et al. [11], [12] have first suggested that these narrow resonances are possible in regular arrays of NPs, while Markel has elaborated the theory [13]. Several experimental verifications have also been provided [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], and considering the very narrow linewidth achievable (few nanometers), results hold promises for many applications in lasing, sensing, and metamaterials [24].

An interesting possibility is to study the coupling between diffractive and plasmon modes in the condition *λ*_{RA}*<λ*_{LSP}. In this paper, a short-pitch 2D array of Au nano-cylinders (designed and fabricated to the scope) produces purely evanescent orders for impinging wavelengths in the close vicinity of *λ*_{LSP}. The plasmonic properties of the array have been experimentally characterized by performing angular resolved extinction measurements. Depending on the incidence angle and polarization of the exciting light, it is possible to continuously follow the evolution of a grating-induced plasmon mode and the appearance of higher-order modes, including a vertical mode. Numerical simulations, performed on both isolated particles and arrays, allow the complete analysis of spectral position and origin of these modes.

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