Nonlinear Meta Surface (THG)¶

Third-harmonic generation (THG) is a nonlinear optical process in which waves are generated at a frequency three times that of the fundamental (incident) wave. In this tutorial example, we compute the THG response of a gold/amorphous silicon meta surface following the study by Y.Li et al. [1]. The meta surface is illuminated from the front side with a normally incident $x-$ polarized plane-wave with frequency $\omega$ , generating third-harmonic waves oscillating at frequency $3\omega$ . According to the manuscript [1], the length and width of the gold meta-atoms are set to $l = 168\mathrm{nm}$ and $w = 80\mathrm{nm}$ , respectively. The thicknesses of the gold meta-atoms, the amorphous silicon spacer and the gold mirror are taken to be $30\mathrm{nm}$ , $83\mathrm{nm}$ and $120\mathrm{nm}$ , respectively. We analyze THG process in the undepleted pump approximation, which assumes no back-coupling between the fundamental and third-harmonic fields, i.e., the down-conversion process is disregarded. Therefore, we use two-step procedure: in the first step the linear response of the meta surface at the fundamental (pump) frequency is computed. In the second step, the computed linear electric fields within the domains of interest are used to construct the third-order NonLinearPolarization $\TField{p}^{(3)}$ , which acts as a source term for the third-harmonic signal. Finite-element simulations are then repeated at the third-harmonic frequency using this nonlinear source.

The figure below presents the intensities of the $-x$ and $-y$ components of the third-harmonic signal as functions of the incident fundamental wavelength. The meta surface periodicity is fixed at $p = 500\mathrm{nm}$ . The script data_analysis/run_wavelength_scan.py aims to reproduce Fig.4(b) from the referenced publication [1].

Intensities of $-x$ and $-y$ components of the third-harmonic signal as functions of the incident fundamental wavelength¶

Next, we display the TH intensity for the case of an incident wave with fundamental wavelength of $\lambda=1380\mathrm{\nm}$ . The displayed plot is extracted from the fieldbag generated by TH calculations, and can be reproduced by running the script run_project.py.

Third-harmonic field intensity at the interface of gold meta-atom and the amorphous silicon spacer¶

[1]	(1, 2, 3) Li, G. Zhang, Y. Tang, X. Zhang, W. Cai, Y. Liu, T. Cao, and G. Li. “Third harmonic generation from the gold/amorphous silicon hybrid meta surface.” In Nanophotonics, vol. 11, p. 2245-51, 2022.