cients (see, e.g., [8]). These resonance anomalies can result in the complete suppression of the reflectivity by a proper choice of parameters. Here we consider the excitation of high- frequency SJPWs (Ω ≫ 1) by a wave incident from a dielectric prism with permittivity ε$_{p}$ onto a layered superconductor separated from the prism by a vacuum gap of thickness δ (the so-called “attenuated-total-reflection” method for producing surface waves, see Fig. 3). The suppression of the specular reflectivity | R | 2 = | H $^{r}$/H$^{i}$| 2 due to the resonant excitation of the surface waves can be observed by changing the incident angle at a given frequency or by changing the frequency at a given incident angle, as demonstrated in Fig. 4 (a, b). Here H i and H r are the magnetic field amplitudes of the incident and reflected waves, respectively. Figure 4 (c) shows the sharp decrease of the reflectivity in the ( θ, Ω) plane. Conclusions .— Here we predict the existence of a new branch of SJPWs in layered su- perconductors for the frequency range higher than the Josephson plasma frequency, which is a very unusual phenomenon for plasma-like media. It is important that a NRI can only be observed for frequencies within the gap in the spectrum of the SJPWs. Thus, some kind of complementarity between NRI and surface waves is established in this paper. We have also described the excitation of these SJPWs by means of the attenuated-total-reflection method. We gratefully acknowledge partial support from the NSA, LPS, ARO, and NSF grant No. 0726909. [1] M. Ricci et al. , Appl. Phys. Lett. 87 , 034102 (2005); C. Du et al. , Phys. Rev. B 74 , 113105 (2006); B. Wood et al. , J. Phys.: Condens. Matter 19 , 076208 (2007); F. Magnus et al. , Nature Materials 7 , 295 (2008); E. Narimanov, ibid. 7 , 273 (2008); M.B. Romanowsky et al. , Phys. Rev. A 78 , 041110 (2008); K.Y. Bliokh et al. , Rev. Mod. Phys. 80 , 1201 (2008). [2] A.L. Rakhmanov et al. , arXiv:0907.3564 (2009). [3] V.A. Podolskiy and E. E. Narimanov, Phys. Rev. B 71 , 201101 (2005); J.B. Pendry, Science 306 , 1353 (2004); A. Alu et al. , J. Opt. Soc. Am. B 23 , 571 (2006); O.V. Ivanov et al. , Crystallogr. Rep. 45 , 487 (2000). [4] R. Kleiner et al. , Phys. Rev. Lett. 68 , 2394 (1992); R. Kleiner and P. Muller, Phys. Rev. B 49 , 1327 (1994). [5] S. Savel’ev et al. , arXiv:0903.2969; Rep. Prog. Phys. (to be published). 8