Efficient second harmonic generation using nonlinear substrates patterned by nano-antenna arrays

We study theoretically various design considerations for efficient generation of second harmonic using a nonlinear substrate patterned with nano-antennas. The analysis is focused on a gap Bowtie nano-antenna array recessed in LiNbO₃ which is shown to be preferable over on surface structures due to field enhancement, field profile and linear and non-linear polarization considerations. In addition, we develop the nano-antenna counterpart of the Boyd-Klienmann model in order to analyze the impact of a Gaussian shaped fundamental beam on the generated second harmonic. Finally, we show that the dielectric properties of the substrate lead to preferable directions for the incident fundamental harmonic and the emission of the second harmonic. Our analyses lead to several design rules which can enhance second and high harmonic generation from nanoantennas arrays by several orders of magnitude.