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.

We observed conical second-harmonic generation in a one-dimension anomalous-dispersion-like medium, which manifests itself as scattering-assisted nonlinear interaction via quasi-phasematching sum frequency process. The parameters for the ring-shaped second harmonic beam are analyzed experimentally and theoretically, which disclose the structure information of the nonlinear photonic crystal and imply potential applications as characterization methods. Furthermore, by varying the angles of incident beam, the conical beam can be significantly enhanced owing to collinear nonlinear coupling between the input beam and the scattering light.

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