The Second Harmonic Generation in the ABC-type Metamaterials

The metamaterials in the form of amorphous heterostructures are fabricated by superlattices of three oxides grown by atomic layer deposition. Their centrosymmetry is broken, which is a necessary condition for the second-order nonlinear processes to happen [1], [2]. We systematically study the changes in the behaviour of bulk second-order susceptibility by varying the thickness of the three oxides: SiO<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> (A), TiO<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>(B), and Al<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>O<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> (C), from tens of nanometers down to the atomic scale. Interface boundaries inherently lack inversion symmetry, leading to an interface second-order electric susceptibility. Increasing the number of interfaces per unit of thickness in ABC-type nanolaminates enhances this interface nonlinear effect, thereby boosting second harmonic generation. Furthermore, our research demonstrates that strengthening nonlinear optical properties is closely linked to the transition between anisotropic and isotropic forms of matter, i.e., if the nanometer-thick layers are still physically separated or the constituent layers are intermixed due to their atomic thickness. Astonishingly, a significant nonlinear response is observed in these heterostructures despite all constituents not possessing inherent bulk second-order nonlinearity and while being amorphous. We determine <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\chi^{(2)}$</tex> tensor values [3] for each morphological composition, and we report the highest achieved nonlinearity of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\chi_{z z z}^{(2)}=2.0 \pm 0.2 \mathrm{pm} / \mathrm{V}$</tex> for optimized amorphous ABC-type nanolaminates.