Nonlinear Cherenkov Radiation in an Anomalous Dispersive Medium

By using ultrathin nonlinear media, the phase velocity of nonlinear polarization waves can be continuously adjusted. We realized nonlinear Cherenkov radiation (NCR) in an anomalous dispersion medium experimentally, which breaks the minimum speed limit of NCR. This modified nonlinear Cherenkov radiation has two new special states with respect to its prior, i.e., the degenerate state and extreme state. Also, periodically arranged ultrathin nonlinear media can enhance NCR and realize the nonlinear Smith-Purcell effect.

Figure 1

Red along the incident arrow denotes the fundamental wave, the yellow arrow along the ultrathin plane denotes the polarization wave, and the green arrow in (b) and (c) denotes the harmonic wave. (a) Modulating of polarization wave velocity by the ultrathin nonlinear plane; (b) The fundamental wave cannot exceed the harmonics phase velocity in an anomalous dispersion medium; (c) Modulation of the polarization wave breaks the velocity threshold.

Figure 2

(a) Theoretical refractive index in 5 mol% $\mathrm{MgO}\mathrm{\text{:}}\mathrm{LiNb}{\mathrm{O}}_3$ crystal; (b) SEM image of domain wall in the sample

Figure 3

(a) NCR pattern of $e$-polarized and $o$-polarized incident light in single-domain crystal; (b) NCR pattern of $o$-polarized incident light at single wall, the incident angle is marked on the right; (c) Relationship between NCR angle and incidence angle in single domain wall experiment.

Figure 4

Potential 3-D cases in an ultrathin column anomalously dispersive nonlinear material.

Figure 5

(a) The incident angle satisfied the condition of the nonlinear Smith-Purcell effect in corresponding to different fundamental wavelength, the leftmost yellow line denotes the degenerated NCR; the inset is experimental results using continuous laser of 1064 nm. (b) Nonlinear Smith-Purcell effect achieved in different dispersion area, by adjusting the temperature. Sample: 5 mol% MgO:PPLN.