Fig. 1. (a) Illustrating the femtosecond laser writing of periodic fork-shaped χ⁽²⁾ gratings in a z-cut CBN crystal; (b) 3D image of the fabricated periodic fork domain structures, obtained using Čerenkov SH microscopy^[28]; (c) Čerenkov microscopic image of a single layer of the structure.

Fig. 2. (a) Wavelength tuning response of the SHG in periodic fork-shaped grating at normal incidence; (b) recorded SH images at resonant wavelengths of 1270, 1160, and 1070 nm in the far field. They correspond to QPM interactions involving different orders of longitudinal reciprocal lattice vectors. (c) The phase-matching diagrams at these resonance wavelengths; the transverse phase-matching conditions are the same for these three wavelengths, but the longitudinal conditions are different. From left to right (1070 to 1270 nm), the corresponding reciprocal lattice vectors in the longitudinal direction are G_0,0,4, G_0,0,3, G_0,0,2, i.e., m = 4, 3, 2, respectively.

Fig. 3. (a) and (b) Quasi-phase-matching diagrams of SHGs using reciprocal lattice vectors G_0,1,2 and G_0,-1,2 at oblique incidence of the fundamental wave, respectively. These two conditions are usually fulfilled at different wavelengths.

Fig. 4. (a) and (b) Experimental wavelength tuning responses of the SHs using G_0,-1,2 and G_0,1,2, respectively; (c) and (d) recorded SH images at fundamental wavelengths of 1260 and 1275 nm, respectively.

Fig. 5. (a) Ferroelectric domain structure for conversion of a fundamental Gaussian beam into an SH Bessel beam; (b) Fourier transform spectrum of this structure; (c) phase-matching conditions are different along the azimuthal directions at normal incidence of the fundamental Gaussian beam. Here an extreme case is given where phase-matching conditions are obtained only on the left edge of the ring-shaped reciprocal vectors. (d) Calculated SHs at normal incidence; (e) the phase-matching conditions become the same for all the azimuthal angles by employing an obliquely incident fundamental beam. (f) Calculated SH Bessel beams at the oblique incidence.