Figure 4

Cascade nonlinear excitation of SW leaky modes. (a) Scheme of nonlinear cascade process explaining the excitation of edge and plane SW in the system with an incident SW beam of frequency \(f=45\) GHz propagating under angle \(\theta =30^{\circ }\). The SW modes are symbolized with ovals whose colors indicate the modes of the same characteristics. The proposed cascade process is divided into four phases connected by SSP and two CPs. (b) Dispersion relation of the system with the marked modes shown in (a) (the color of the dots corresponds to the colors of the ovals). (c) Amplitude \(|m_z|\) of the edge mode I (red, solid line) at the layer edge in the vicinity of the incidence spot of the incident SW beam. The black, dashed line is the extrapolation of the antenna-excited edge mode I behind the incident beam spot, i.e., for \(x>-3~\mathrm{\upmu m}\). (d–g) Space distributions of \(|m_z|\) at frequencies \(\nu =14\) GHz, \(f-\nu =31\) GHz, \(f=45\) GHz, \(f+\nu =59\) GHz, respectively. The dots indicate spots where SW modes amplitudes, A indicated in (a), were taken. (h–k) Results of the two-dimensional Fourier transform from the space to wavevector domain of SW amplitude distribution are shown in (d–g). Figures (j,k) additionally contain isofrequency contours that correspond to frequencies of SWs presented in these pictures. (l) Investigated system’s dispersion relation with marked frequencies for which excitation of SW plane waves occurs at different angles of incidence (this picture shares the colorbar with Fig.1b).