# Second Harmonic Generation from Phase-Engineered Metasurfaces of Nanoprisms

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## Abstract

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## 1. Introduction

_{2}-Si structure allows controlled SHG enhancement. We fabricate and characterise metasurfaces made of plasmonic nanoparticles with a controlled-thickness SiO

_{2}spacer layer on top of a Si substrate. Numerical modeling by finite difference time domain (FDTD) was carried out to reveal characteristics of light field enhancement.

## 2. Experimental

#### 2.1. Fabrication of Metasurfaces

_{2}. The oxidation was performed under a water-vapor atmosphere at 1000 ${}^{\circ}\mathrm{C}$ with thickness determined by the hold time at temperature.

#### 2.2. Characterisation of Metasurfaces

#### 2.3. Numerical Modeling

_{2}, and Au were taken from the database included within the software. Periodic boundary conditions were used for the triangular lattice pattern under auto-optimised mesh size (Figure 2a,b).

_{2}or SiO

_{2}-on-Si showed strong scattering around 800 nm wavelength which was used in this study for SHG from such metasurfaces. At this nanoprism size, the scattering is stronger than absorbance which is also important for efficient SHG. Only a SiO

_{2}spacer thickness of $w=180$ nm is shown in Figure 2c to illustrate the effect of markedly increased scattering. Nanoprisms on Si had red-shifted resonance and is outside the scope of this study. It is noteworthy, that light E-field enhancement is even stronger at the Au-Si interface as compared with Au-SiO

_{2}and can be useful for sensor applications in the IR spectral range. These numerical estimates of light absorption and scattering by single nanoprisms was encouragement to embark on fabrication of arrays with different sized nanoprisms on reflective Si substrates with different SiO

_{2}spacer thicknesses.

## 3. Results and Discussion

#### 3.1. Au Triangular Nanoprisms on Glass

#### 3.2. Au Triangular Nanoprisms on Si with SiO${}_{2}$ Spacer

_{2}spacer conferred anti-reflective properties to the surface (R smaller as compared with bare Si). The reflectivity of a metasurface with Au nanoprisms is defined by the geometry: period and size of nanoparticles. At peak reflectivity of the fundamental wavelength, the strongest SHG was observed.

_{2}-Au interface. It is noteworthy that the absolute values of enhancement obtained by FDTD should not be considered due to ideal geometrical structures and interfaces being different due to fabrication tolerances [30,31,32]. The difference in SHG emission for the ${E}_{x}$ and ${E}_{y}$ (Figure 3b) followed the scaling of the field enhancement at the Au-SiO

_{2}interface: the $2\omega $ emission was stronger under ${E}_{y}$ excitation as compared with that at ${E}_{x}$.

_{2}(between air and Si) which contributes to light enhancement at neighbouring nanoprisms.

_{2}-air-Au point (note, the lateral cross sections are shown at 15 nm above the interface at the middle thickness of Au nanoparticle). These locations of largest E-field locatization at the interface are locations for SHG. From the side-view image it is also clear that some light was deposited into the SiO

_{2}spacer which also facilitates field enhancement at the neighbouring nanoparticles.

_{2}, which showed SHG from monolayered flakes [40]. Also, photo and thermally induced material re-organisation can be used for breaking usually random orientation and symmetry of polymers to make them active for SHG [41]. Use of anisotropic bio-polymers such as silk [42], nanocellulose [43] and their polymer composites is another way to make host materials anisotropic for the light-matter interaction required for efficient SHG. Light localisation on nano-structured surfaces provides strong light gradients required for optical trapping/binding [44,45,46], which is useful for surface assisted light enhancement in sensing and fabrication [34,47,48,49,50], while generation of second harmonic at the nanoscale features could be explored for their contribution to the biocidal conditions [51,52,53].

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Reflection and SHG Spectra for w = 200 nm SiO_{2} on Si

_{2}-reflected and Si-reflected rays. Each of them experience $\pi $ phase shift due to reflectance from the medium with a higher refractive index. The Si-reflected ray has additional propagation phase traversing the SiO

_{2}spacer twice. When the spacer is close to the $\lambda /4$ condition, a constructive E-field addition takes place on the air-SiO

_{2}surface (where Au nanoprisms are positioned). The actual field values depend on the Fresnel coefficients, which are, in turn, incidence angle dependent. This interference and phase matching is the physical reason for the increased SHG efficiency with the optimised thickness of SiO

_{2}spacer around $w=300$ m [18]. Such description is strictly valid for the optical far-field representation of reflection and the actual near-field conditions where diffraction from the Au nanoprisms is taking place is accounted for in the FDTD simulations. More systematic studies are required for the dependence of SHG from the spacer thickness w. Here, only two thicknesses $w=200$ nm and 300 nm were tested at normal incidence. Angle dependent SHG has to be measured and more information on the light trapped in the waveguiding mode could be obtained.

**Figure A1.**Plots showing experimentally measured SHG excitation spectra from metasurfaces (cyan dots, left-axis) of Au triangular nanoparticles on a SiO

_{2}/Si substrate with triangle side-lengths, $L=120$ nm to 220 nm. Reflectivity spectra $R\left(\lambda \right)$ (right-axis) are shown for bare Si (red), Si with SiO

_{2}(dark blue), and the metasurface for different size L nano-prisms (color coded). The SiO

_{2}spacer width was the same $w=200$ nm. Polarisation of the incident field was horizontal ${E}_{x}$.

**Figure A2.**FDTD simulations for the $L=220$ nm $w=200$ nm case. (

**a**) E-field enhancement at $\lambda =825$ nm (see Figure 2b for comparison) and 871 nm which are close-to-maximum. (

**b**) Top- and side views of E-field enhancement for a linearly polarised plane wave. Refractive index cross-section is shown on right-side to distinguish the lateral cross-sections. Note, the cross-section A-A’ is made though the center of triangle and not at the largest intensity vertexes. Incident light has ${E}_{x}$ polarisation. Inset “ray-box” shows schematically the phase change upon reflection from interfaces for the incident, transmitted and reflected E-fields ${E}_{i,t,r}$ in ray optics presentation [18]. In addition to the Fresnel coefficient defined phase changes, a propagation phase is adding up and amounts to $\pi $ for traversing a $\lambda /4$ thickness twice upon back-reflection from Si.

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**Figure 1.**(

**a**) Schematic of the sample (top) and an SEM image of the triangular Au nanoparticles (bottom). The spacer of SiO

_{2}with width $w=200,300$ nm was deposited on the Si substrate to control the E-field enhancement at the plasmonic Au triangular nanoparticles. The pattern was triangular with period $\Lambda =L+s$ where separation between nanoparticles was $s=300$ nm and the side-length of the triangle was $L=(120-220)$ nm changed in steps of 20 nm. Thickness of Au nanoparticles made by electron beam lithography (EBL) and lift-off was $d=30$ nm. (

**b**) Setup to detect second harmonic generation (SHG) from the metasurfaces under the linearly and circularly polarised excitation. The second harmonic light was analysed at $\approx {1}^{\circ}$ reflection to the normal. This setup was used to maximise collection of the second harmonic. The excitation light source was Ti:sapphire fs-laser with the wavelength tunable from 730 to 920 nm.

**Figure 2.**(

**a**) 3D finite difference time domain (FDTD) setting for calculations under linearly polarised (along x-axis) E-field; plane wave illumination. Refractive index cross section (A-A’). (

**b**) E-field $E/{E}_{0}$ cross section at the middle-plane of 30-nm-thick Au nano-particles (15 nm above SiO

_{2}). The incident field $|{E}_{0}|=1$. The maximum field cross section shown is at $\lambda =825$ nm as in the experiment, see text for discussion. (

**c**) Absorption, scattering and extinction cross sections ${\sigma}_{ext}={\sigma}_{abs}+{\sigma}_{sc}$ for the $L=180$ nm nanoprism on SiO${}_{2}$ (solid lines; refractive index $n=1.4$), Si (dashed-lines), and SiO${}_{2}$ ($w=180$ nm)-on-Si; optical properties of Si were taken from the material database of Lumerical. The FDTD calculations were carried out using total-field scattered-field (TFSF) light source. Geometrical cross-section corresponds to the footprint area of the nanoprism ${S}_{Au}=\frac{\sqrt{3}}{4}{L}^{2}\approx 0.1403\times {10}^{5}$ nm${}^{2}$.

**Figure 3.**(

**a**) Scattering spectrum of Au nanoprisms on glass for two polarisations in back-scattering geometry. The sizes of the nanoprism were: $L=150$ nm base of the equilateral triangle, 30 nm thickness, corner-to-corner separation was 250 nm. The prisms arranged two-dimensionally in a trigonal lattice (see SEM image in inset). (

**b**) Polarisation-resolved SHG ($2\omega $) at 800 nm ($\omega $) excitation for different linear and the circular (left- and right-hand) polarisations of excitation in back-scattering/reflection geometry. SHG was y-polarised for different angles of orientation of the incident linearly polarised light ($\omega $). SHG was linearly polarised at $\pm {45}^{\circ}$ from y-axis for the LHC and RHC excitation ($\omega $); see Figure 1b.

**Figure 4.**Plots showing experimentally measured SHG excitation spectra from metasurfaces (cyan dots, left-axis) of Au triangular nanoparticles on a SiO

_{2}/Si substrate with triangle side-lengths, $L=120$ nm to 220 nm. Reflectivity spectra $R\left(\lambda \right)$ (right-axis) are shown for bare Si (red), Si with SiO

_{2}(dark blue), and the metasurface for different size L nano-prisms (color coded). The SiO

_{2}spacer width was the same $w=300$ nm (see Figure A1 for $w=200$ nm). Polarisation of the incident field was horizontal ${E}_{x}$. The insets show $lg\left(E\right)$ maps of the calculation cell at the wavelength of maximum enhancement, which was at 824 nm for $L=160,180$ nm and at 871 nm for $L=200$ nm (see text for details).

**Figure 5.**(

**a**) Top view FDTD calculations at the maximum E-field enhancement for $L=180$ nm and $w=300$ nm (see Figure 4) for both ${E}_{y}$ and ${E}_{x}$ polarisations. The top-view monitor is at the air-SiO

_{2}interface and the side-view monitor crosses the side of triangle and vertexes with the highest field enhancement. The E-field scale bars are linear; polarisation of incident field was horizontal ${E}_{x}$. Larger enhancement for ${E}_{y}$ orientation as compared with ${E}_{x}$ is manifested in corresponding scaling of SHG (See Figure 3). Calculations for the two ${E}_{x,y}\left(\omega \right)$ fields were carried out for the same unit cell. (

**b**) Side view cross section for the ${E}_{x}$ excitation.

**Figure 6.**Experimental (Exp; red) and calculated (FDTD; dashed) reflectivity spectra of Au nanoprisms with $L=180$ nm side length. The thicknesses of the SiO

_{2}spacer were (

**a**) $w=200$ nm and (

**b**) 300 nm.

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**MDPI and ACS Style**

Mochizuki, K.; Sugiura, M.; Yogo, H.; Lundgaard, S.; Hu, J.; Ng, S.H.; Nishijima, Y.; Juodkazis, S.; Sugita, A. Second Harmonic Generation from Phase-Engineered Metasurfaces of Nanoprisms. *Micromachines* **2020**, *11*, 848.
https://doi.org/10.3390/mi11090848

**AMA Style**

Mochizuki K, Sugiura M, Yogo H, Lundgaard S, Hu J, Ng SH, Nishijima Y, Juodkazis S, Sugita A. Second Harmonic Generation from Phase-Engineered Metasurfaces of Nanoprisms. *Micromachines*. 2020; 11(9):848.
https://doi.org/10.3390/mi11090848

**Chicago/Turabian Style**

Mochizuki, Kanta, Mako Sugiura, Hirofumi Yogo, Stefan Lundgaard, Jingwen Hu, Soon Hock Ng, Yoshiaki Nishijima, Saulius Juodkazis, and Atsushi Sugita. 2020. "Second Harmonic Generation from Phase-Engineered Metasurfaces of Nanoprisms" *Micromachines* 11, no. 9: 848.
https://doi.org/10.3390/mi11090848