Conical second-harmonic generation via cooperation of Bragg diffraction and birefringent phase matching

The generation of conical beams is a significant nonlinear phenomenon that arises from noncollinear phase-matching configuration. However, previous studies have primarily concentrated on the generation of such beams within crystals with modulated second-order nonlinear coefficients. In this work, we experimentally observed even-order conical second-harmonic generation (SHG) within a single lithium niobate crystal with the spatial refractive index modulated by femtosecond laser writing (FLW). These conical SHG were attributed to the cooperation of linear Bragg diffraction and birefringent phase matching (BPM), facilitated by the scattering of fundamental waves within the nonlinear photonic crystal. Furthermore, overlapping of adjacent even-order conical rings could be used to enhance the SHG at odd-order diffraction, attributed to the noncollinear BPM scheme. Lastly, we verified the positively correlation between the power of conical SHG and the corresponding fundamental diffraction by altering the FLW energy. Our results unveil a new method to generate multiple short-wavelength conical beams, which serve as an effective tool for light scattering studies.