CC BY
0Numerical simulation of the single silicon pillar scattering modes
for second harmonic generation
M.A. Anikina1'2*, A. Kuznetsov1'2, A.D. Bolshakov1'2
1-Moscow Institute of Physics and Technology, Dolgoprudny, Russia 2- Alferov University, Saint Petersburg, Russia
* mari.a.nikina@yandex.ru
It is well-known that bulk single-crystal silicon does not exhibit second order nonlinear optical effects because of the presence of the inversion symmetry center. However, there are ways to break this symmetry, and as a result, the second harmonic generation (SHG) can be observed on silicon nanostructures [1,2]. Optical circuit engineering requires standardized design of components, and the initial step of such design is a numerical simulation of the individual structures.
This study reports numerical simulations of scattering spectra from a single silicon nanopillar. The calculations were provided by the finite-difference time-domain method (FDTD) according to Yee algorithm in Ansys Lumerical software. Single pillars were represented as cylinders of heights and radii standing on the Si substrate. The main goal is to match scattering peaks with pump and SHG wavelengths. The SHG at 550 nm is assumed for the considered structures. In Fig. 1 (a, b), the scattering spectra intensity maps in 500-1300 nm range are demonstrated for different diameters and heights of 0.45 and 1.8 ^m.
In Fig. 1 (c), the change in mode composition of the spectrum at successive changes of the height and radius of the structure is presented, which allows us to precisely control the number of resonant modes and their spectral positions. Thus, a nanopillar with a radius of 112.5 nm and a height of 0.45 ^m provides the perfect match of two scattered modes with pump and SHG spectral lines. The case of larger structures higher than 1 ^m and thicker than 300 nm, which should be easier to fabricate, has also been considered. The numerical calculation of such structures shows that the scattering intensity increases significantly, but the number of modes visibly increases with the increase in pillar height. Additional longitudinal modes can affect the energy redistribution between them, which can lead to undesirable consequences such as a decrease the SHG response.
This work was supported by the Russian Science Foundation (grant 24-12-00225).
Fig. 1. Scattering spectra intensity maps of the single Si pillars of different radii a) 0.45 ^m and b) 1.8 ^m tall; c) scattering spectra of the single Si pillars with specific dimensions.
[1] S.V. Makarov, et al, Efficient second-harmonic generation in nanocrystalline silicon nanoparticles, Nano letters, 17(5), pp. 3047-3053, (2017).
[2] M. Cazzanelli, et al, Second-harmonic generation in silicon waveguides strained by silicon nitride, Nature materials, 11(2), pp. 148-154, (2012).
