Fig. 3

Comparison between surface Dyakonov–Cherenkov radiation and surface-polariton Cherenkov radiation. a The contour plot of the power flow density in the cross section formed by the surface normal \(\hat{y}\) and the power flow direction \(\overline{P}_{{{\text{sw}}}}\) of DSWs. b The contour plot of the power flow density in the cross section formed by the surface normal \(\hat{y}\) and the power flow direction \(\overline{P}_{{{\text{sw}}}}\) of conventional SPPs. In a, b, \(y_{0} = 0.09\delta\), which is the penetration depth in the superstrate \(\delta = 2.2\) µm (\(\delta = 0.1\) µm) for DSWs (SPPs) at \(\lambda = 0.641\) µm. The insets of a, b highlight the orientations of studied cross sections (as marked in cyan) to the particle velocity. c The Poynting power \(\overline{P}_{sw}\) integrated along the y-direction versus the propagation distance l, when y₀ = 0.9δ, 0.09δ and 0.009δ, respectively. In our comparison, we choose Si₃N₄–YVO₄ and Al₂O₃–Au as the platforms to excite DSWs and SPPs, respectively, such that the corresponding DSWs and SPPs have an identical effective mode index \(n_{{{\text{eff}}}} = 2.0309\) at \(\lambda = 0.641\) µm. The particle velocity is \(v = 0.5c\) for both configurations. As a result, DSWs/SPPs propagate in a direction with \(14.02^\circ\)/\(11.21^\circ\) to the particle trajectory (see insets of a, b)