## 3 Experimental Results and Discussion
For the former, we have an exponential decrease with the characteristic length \(l_{ext}=\frac{\lambda}{4\pi\sqrt{\rho^{2}-1}}\cong 180\) nm, that is much larger than the thickness of the ZnS layer adjacent to the silver nanofilm. Inside the Photonic Crystal, we have a standing wave with an exponentially decreasing envelope \(e^{Kz}\). The value of \(K\) can be found applying e.g., Formulae (2) of [8]. An easy calculation gives \(e^{K\Lambda}=1.163\) which corresponds, for the PC period \(\Lambda=231\) nm, to the characteristic decay length of \(l_{PC}\cong 1.53\) um. (Actually, the same value can be obtained calculating the transmission coefficient for one period of PC, see Section 2.4 of [27]). The precise field distribution inside a metal layer and, correspondingly, inside the dielectric layers immediately adjacent to it, is  
Figure 2: Schematic of an experimental equipment (**1**–**5**), color photograph of the reflected light spot (**6**) and intensity profile (7) measured at a distance of 405 cm. 1- He-Ne laser, 2-polarizer, 3-lens, 4-investigated structure SiO\({}_{2}\)/(HL)\({}^{19}\)/Al\({}_{2}\)O\({}_{3}\)/ZnS(I)/Ag/ZnS(2)/air glued to silica prism via a droplet of phase-matching oil, 5-CMOS (complementary metal-oxide semiconductor) camera. quite sensitive to the exact thickness of metal layer and its refraction index which define the location of the minimum of an electric field inside the nanofilm, see a detailed discussion in [8,27]. This question is not relevant for the present work and has not been specially studied. Discussing the obtained results, we first want to note that the observed LRSPP propagation length in our silver nanofilm-based structures is quite comparable to the value of 160 microns reported in [8] for LRSPP supported by a specially designed PC and ca. 5 nm--thick gold film at the wavelength of 710 nm. This is not surprising given the quite comparable \"plasmonic qualities\" of gold and silver at the (different) wavelengths at question: according to [PERSON]'s book [29], at 710 nm we have \(\varepsilon_{Au}=-15.723+1.3413i\) which gives \(\text{Im}(\sqrt{\frac{\varepsilon_{Au}}{\varepsilon_{Au}+1}})=0.0030i\) for the quantity describing the dissipation for SPP propagating along the interface air--infinitely thick gold layer [28]. For our case, using the experimentally measured (by our group) value of the silver refraction index for a given wavelength, \(n_{Ag}=0.1345+3.986i\), that is \(\varepsilon_{Ag}=-15.8701+1.0722i\), we have \(\text{Im}(\sqrt{\frac{\varepsilon_{Ag}}{\varepsilon_{Ag}+1}})=0.0023i\). However, one should also note more than two times smaller value of the metal layer thickness, ca. 5 nm, in experiments reported in [8]: a very important factor, given the inverse quadratic dependence of the LRSPP dissipation on this same thickness [1, 2, 3]. All this, again, should be considered as the demonstration of truly high-quality silver nanofilm in our case. Indeed, comparable LRSPP propagation lengths have been observed also in experiments with Pd [10] and Co [12] nanofilms deposited onto the properly designed PC. The common characteristic feature here is that in all of these cases, the experimentally measured values, although are impressively large enough and much exceed the propagation lengths for simple metal--dielectric interfaces, turn out to be substantially smaller than those which could be achieved according to the theoretical predictions. The latter can be estimated approximating the real system by a \"symmetrical sandwich structure composed by an infinite medium with the refraction index \(n_{\textit{eff}}\)--thin, with the thickness \(d_{m}\), metal layer with the refraction index \(n_{m}\)--an infinite medium with the refraction index \(n_{\textit{eff}}\)\", using the value \(n_{\textit{eff}}=1.03\) described above (varying of this value contributes to the result quite slightly).