Fig. 1. (a) and (b) The ideal and simplified 3D nonlinear photonic structures for collinear generation of a second harmonic vortex beam (l_c = 1) from a fundamental Gaussian wave. (c) and (d) The phase profiles of the second harmonics generated in the ideal and simplified four-grating structures, respectively. (e) and (f) The corresponding far-field second harmonic profiles.

Fig. 2. (a) The phase delay of π/2 is introduced between the neighboring segment of grating structures, for the first-order QPM SHG. (b) The corresponding second harmonic far-field intensity profile of the first-order SHG. (c) The phase delay and (d) far-field second harmonic intensity profile for the second-order QPM interaction. (e) The phase delay and (f) far-field second harmonic intensity profile for the third-order interaction.

Fig. 3. The Čerenkov second harmonic microscopic image of the fabricated 4 grating structures. (a) 3D image of the fabricated structure. (b) Amplified view of the 2D images of two gratings showing clearly the grating period and the lateral replacement between them.

Fig. 4. (a) The wavelength tuning response of second harmonic generation in the 4 grating structures, showing the 1st- and 3rd-order QPM resonances at a fundamental wavelength of 1.4 and 1.14 µm, respectively. (b) The part of the wavelength tuning curve zoomed in to show the resonant wavelength of the second-order SHG at fundamental wavelength of 1.01 µm. (c)–(e) The experimentally recorded second harmonic far-field profiles at the 1st, 2nd, and 3rd QPM orders, respectively.

Fig. 5. (a) The powers of the second harmonic versus the power of the fundamental beam for the 1st, 2nd, and 3rd order QPMs. (b) The amplified view of the second-order SHG for more details.