Fig. 2
Energy loss of a swift charged particle emitting Dyakonov surface wave. A power spectral density \(G_{{{\text{DSW}}}}\) (owing to the excitation of DSWs) as a function of the normalized particle velocity \(v/c\) and the angle \(\theta_{q}\) (corresponding to the orientation of the particle trajectory). \(G_{{{\text{DSW}}}}\) acquires a nonzero value only when \(v\) and \(\theta_{q}\) satisfy the phase matching condition given by Eq. (1). b The total power spectral density \(G_{{{\text{DSW}}}} + G_{{{\text{ph}}}}\) (where \(G_{{{\text{ph}}}}\) refers to the radiation loss of free-space Cherenkov photons) versus the normalized particle velocity \(v/c\) for angle \(\theta_{q} = 40.9^\circ\), \(64.8^\circ\), \(75.1^\circ\) and \(81.8^\circ\), respectively. c The total power spectral density \(G_{{{\text{DSW}}}} + G_{{{\text{ph}}}}\) versus the angle \(\theta_{q}\) for particle velocity \(v = 0.5c\), \(0.6c\), \(0.7c\) and \(0.8c\), respectively. θq,max (θq at the maximum energy loss) is marked for each velocity in c. In particular, we denote \(G_{{{\text{ph}}}}\) as the straight dashed line b, c. d The maximum achievable photon number \(N_{{{\text{DSW}}}} \left( {\theta_{{q,{\text{max}}}} } \right)\) of DSW generated per unit length of the particle path at each particle velocity. For comparison, we also plot the photon number \(N_{{{\text{ph}}}}\) of free-space Cherenkov radiation as a function of particle velocity. The studied wavelength is 0.635 µm