Second harmonic generation in glass-based metasurfaces using tailored surface lattice resonances

3.2.1 Linear optical properties

Figure 3(a) shows the change in the experimental transmission spectrum when we fix the lattice period P and vary the particle size S = 2r = P − G by the process of successive dewetting, where r is defined as the radius of the particle. The total deposited thicknesses represented in the graph (40, 50, and 60 nm) dictate the size of the particles and therefore also their spacing. The initial broad dip for 40 nm thickness decouples into two dips, which redshift as the thickness (and hence the size of the particles) increases, indicative of a change in the coupling regime as the particles resonance shift, as illustrated in Figure 1. Before investigating and exploiting this effect, we experimentally study the effect of changing the lattice period P, while keeping the same deposition conditions (60 nm film thickness). As shown in Figure 3(b), it reveals the appearance of a strong asymmetric resonance, which increases when P is varied from 360 to 400 nm. A further increase of the period to 450 nm leads to spectral reshaping from one asymmetric Fano-type resonance to two symmetric resonances, indicative of a change in the coupling strength in the system [21]. From these experimental results, we identify a sharp resonance of FWHM of approximately 4 nm in the air for a lattice period of 400 and 60 nm total thickness.

Figure 3:

Experimental transmission spectra illustrating the gap and the lattice effect.

(a) Transmission spectra were obtained for successive dewetting steps corresponding to an increased equivalent thickness T, maintaining the pressure during the nanoimprint at 0.1 MPa. The transmission spectrum is observed to split from a single broad resonance (at 40 nm) to two resonances (50 and 60 nm). (b) Transmission spectra for a 60 nm deposited film obtained as the pressure during the imprinting process are varied from 0.1 to 0.2 MPa. As the nanoimprinted pressure is increased, the asymmetric resonance becomes sharper (0.15 MPa) corresponding to an increase in lattice periodicity to 400 nm. Further increases of the pressure lead to the disappearance of Fano resonance and give rise to two broad symmetric dips (period 450 nm).

To unveil the origin of the different resonances and their coupling, FDTD simulations were performed using the commercially available Lumerical software. The effect on the transmission spectrum of decreasing the inter-particle gap upon successive dewetting is first illustrated in Figure 4(a), keeping a fixed period p = 400 nm. The inter-particle gap distance was varied from 50 to 10 nm. The simulated transmission spectra (Figure 4(a)) show a sharp asymmetric dip that red-shifts on decreasing the inter-particle gap, which corresponds to experimental observations. Figure 4(b) and (c) relate the respective spectral evolution of the electric field amplitude in the interparticle gap and the magnetic field amplitude at the particle center. The interparticle electric field maximum both decreases and red-shifts with a reduced interparticle gap (Figure 4(b) and (d)). This electric field maximum is attributed to the interference of the electric dipole (ED) mode and the diffraction order due to the lattice (LR) as observed from the electric field maps (ED-LR, Figure S.I.6). The evolution in Figure 4(b) corroborates the trend observed for maximal electric field intensity at resonance in the metasurface’s symmetry plane (Figure 4(d)), which strongly decreases as the gap is reduced from 50 to 10 nm. This effect contrasts with the appearance of hot spots at a lower gap in plasmonic metasurfaces [41, 42]. As shown in Figure 4(c), the magnetic field monitor (at the particle center) indicates a broad magnetic resonance (MD) associated with the particle, which overlaps with another sharper magnetic peak, located at the exact position of the ED-LR. The origin of the MD mode is associated with Mie-type modes due to the ensemble (periodic arrays) macroscopic resonant response which is excited with a circular flow of the displacement current (Figure S.I.6). The spectral position of such MDs can be tuned by changing the size as well as their arrangement of particles employed for meta-atoms [1], [2], [3]. Depending on the particle diameter (and thus the gap G) the two modes change spectral shape – from a Fano-type resonance (particle gap 50 nm) to a more symmetric resonance (particle gap 10 nm). Such spectral tuning directly relates with the critical and strongly coupled regime as we explain schematically in Figure 1. Figure 4 shows that both the particle as well as the lattice modes varies with the change in the particle size (G) or lattice constant (P). This behavior is expected as schematically shown in Figure S.I.7, for one specific value of G and P, a particular lattice and particle mode (Figure S.I.7(a)). A change in G leads to a change in the particle mode (particle mode 2 Figure S.I.7(b)) and hence a change in the interaction, thus leading to a change in the entire spectrum. A similar effect arises when the lattice is varied while the particle size is fixed as suggested in Figure S.I.7(c) and visible in Figure 4.

Figure 4:

Effect of the periodicity and gap on the mode properties.

(a)–(d) Effect of gap/particle size for a period of 400 nm. (a) Simulated transmission spectra, (b) simulated electric field magnitude in the interparticle region, and (c) simulated magnetic field magnitude at particle center as a function of wavelength with a reduction of the interparticle gap from 50 to 10 nm. (d) Simulated maximal electric field intensity along the unit period’s symmetry plane. (e)–(h) Effect of periodicity for a fixed particle diameter of 350 nm. (e) Simulated transmission spectra, (f) simulated electric field magnitude in the interparticle region, and (g) simulated magnetic field magnitude at particle center as a function of wavelength with an increase in the period from 370 to 400 nm. (h) Simulated maximal electric field intensity along the unit period’s symmetry plane. (i) Simulated field distribution in increasing lattice constant.

Our simulations clearly suggest that MD and ED-LR modes interfere with the considered range of interparticle gaps.

We now turn toward the influence of the array periodicity on the optical spectrum, keeping a fixed particle size S = P − G = 350 nm. Structures with varying lattice periods (from 370 to 450 nm, see Figures 4(e)–(g)) are illuminated with a polarized plane wave at normal incidence. The sharp asymmetric resonance apparent in the transmission spectrum (Figure 4(e)) for an initial small period increases in strength and then transforms to a symmetric dip for the highest periodicities considered in this work (450 nm). As the period increases to 600 nm (Figure S.I.8), the two resonances merge, leading to a single resonance, which disappears upon increasing the period to 800 nm. The asymmetric resonance observed in the experimental (Figure 3(a)) and simulated (Figure 4(e)) transmission spectra for a small period, is mainly attributed to the ED-LR (Figure S.I.6). Figure 4(f) and (g) show the electric and magnetic field amplitude at the interparticle gap and particle center, respectively, as the array period is varied from 370 to 450 nm. The interparticle electric field maximum (associated with the ED-LR as shown in Figure 4(f)) first increases with an increase in the period from 370 to 410 nm and decreases when the period is further expanded beyond 410 nm. This is in line with the trend observed for maximal electric field intensity at resonance, based on the electric intensity profile distribution in the metasurface’s symmetry plane (Figure 4(h) and (i)), which reaches a maximal value at around 400 nm. For decreasing periods below 400 nm, the ED-LR and MD modes couple critically giving rise to a sharp Fano resonance, with the highest QF of 175. On increasing the array period, we observe the modes to shift toward the red and the Fano resonance becomes more symmetric with an observed increase of the FWHM and lower QF. This appearance of symmetric modes is an indication of a strong coupling regime (Figure 1) between ED-LR and MD modes as suggested in Figure 4(e)–(g). This symmetric mode with a lower QF leads to a sharp drop in the field enhancement [20, 42] above a period of 430 nm (Figure 4(g)).

Thus, to obtain a high QF it is essential to engineer the mode coupling through the fine tuning of the lattice period and particle size allowed by our process. For this specific substrate, texture, and dielectric material, we find that the optimal resonance overlap occurs at λ = 700 nm for a lattice period of 400 nm and a Se particle size of 350 nm. This architecture leads to sharp resonant modes with a strong field enhancement and a high experimental QF of 175 at λ = 700 nm.

3.2.2 Second harmonic generation

To demonstrate the potential of our metasurfaces design capabilities, we used the previously demonstrated nano-photonic structures with optimized light–matter interactions for resonantly enhanced SHG. Simulated linear transmission spectrum (Figure 5(a), wine-red curve) for a nanoparticle size of 350 nm and a period of 400 nm reveals a dip associated with the lattice resonance excitation. The experimental linear measurement is in line with simulation predictions, showing a corresponding dip in transmission at λ = 700 nm (Figure 5(b), wine-red curve). This resonance leads to an enhancement of the electric field intensity by two orders of magnitude (∼90×) in comparison with off-resonance spectral regions (Figure 5(b), light red markers).

Figure 5:

Resonantly Enhanced Second Harmonic Generation in critically and strongly coupled conditions.

(a)–(c) Fixed period of 400 nm and particle size of 350 nm, providing critical coupling conditions. (a) Simulated linear transmission spectrum (wine-red) and electric field intensity evaluated at the Se nanoparticle center (light red). (b) Experimental transmission spectrum (wine-red curve) and normalized second harmonic signal (with respect to the incident power, in light red dots) showing a ∼90× signal enhancement. (c) Distribution of the electric field intensity enhancement in a plane perpendicular to the metasurface for an incident wavelength λ = 700 nm. (d)–(f) Fixed period of 470 nm and particle size of 350 nm, yielding a strongly coupled regime. (d) Simulated linear transmission spectrum (wine-red) and electric field intensity evaluated at the Se nanoparticle center (light red). (e) Experimental transmission spectrum (wine-red curve) and normalized second harmonic signal (with respect to the incident power, in light red dots) showing a ∼38× signal enhancement. (f) Distribution of the electric field intensity in a plane perpendicular to the metasurface for an incident wavelength λ = 750 nm.

SHG measurements were performed in reflection using a previously reported setup [43]. From each of the obtained scanned images, the SH intensity at a particular wavelength was calculated from the mean value of those images as shown in Figure 5(c) (light red dots) when the pump wavelength is tuned between λ = 680 and 780 nm. The conversion efficiency η is defined as:

where P p h o t o n S H and P p h o t o n F u n d a m e n t a l are the power of the generated SH and the fundamental incident signal, respectively. The intensity I is related to the power P according to the following equation:

where A is the area of illumination (defined by the LASER beamwidth of 20 μm). We proceed to measure the re-emitted SH intensity P S H over a fixed integration time (10 s), as well as the power of the fundamental P F u n d a m e n t a l reflected from a gold mirror surface over a reduced integration time to avoid saturation (1 s).

We proceed to measure the re-emitted SH intensity I SH over a fixed integration time (10 s), as well as the intensity of the fundamental I Fundamental reflected from a gold mirror surface over a reduced integration time to avoid saturation (1 s). All measurements are done under normal incidence. Normalizing these powers with time and combining relations (ii) and (iii) finally provide the conversion efficiency, which is evaluated here at 10⁻⁸ at λ = 800 nm (off-resonance). The normalized SHG power shows a peak at the asymmetric electric resonance (λ = 700 nm) due to the electromagnetic field enhancement (Figure 5(a)). When exciting at the resonant wavelength of λ = 700 nm (i.e. maximal field enhancement), the SH signal normalized with the incident power exhibits a 100 times enhancement with respect to the nonresonant region (λ = 800 nm), and almost four orders of magnitude enhancement as compared to the nonpatterned Se dewetted film of comparable thickness in the nonresonant region (λ = 800 nm) (Figure S.I.9). The SH enhancement is thus attributed mainly to the electric-dipole lattice resonance (EDLR) mode, while a lower SH signal was obtained at MD mode. From the field simulation (Figure S.I.6) it is apparent that the MD enhancement is located within the particle as compared to the surface located EDLR mode. This field localization at MD resonance within such amorphous structures leads to significant low SH enhancement clearly demonstrating the surface effect of SH enhancement in such amorphous Se-based metasurface.

Moreover, our meta-structures do not show a clear influence of incident light polarization on the conversion efficiency. Rotating the incident light polarization by 90° changes the emission efficiency at λ = 350 nm from 90× to about 60× as compared to the nonresonant region (Figure S.I.11), which is mainly attributed to the small asymmetry in the nanoimprinted structure (Figure S.I.1). This leads to a reduction in the coupling strength and hence a reduction in the field enhancement.

Figure 5(d)–(c) reproduce the study done for Figure 5(a)–(c) for an increased period of 470 nm with the same particle size of 350 nm. Based on the transmission spectrum, this situation is akin to the strong coupling illustrated in Figure 1 and demonstrates comparatively broader symmetric resonances with lower QF and field enhancement and SHG emission as compared with the critically coupled case of Figure 5(a)–(c).

The dependence of the field intensity enhancement ( I ω = | E | 2 ) on the lattice period ( P ) for these structures follows a quadratic law defined by:

where A _o is determined by the nature of meta-atoms and metasurface design (see S.I. Figure S.I.12(a)). It is worth noting that a similar quadratic dependency on critical coupling has been observed for asymmetric structures [44]. Furthermore, the FWHM is also observed to scale quadratically with the lattice period based on numerical simulations (S.I. Figure S.I.12(b)):

where B _o is a constant governed by the metasurface structure and P _c is the critical period, which leads to critical coupling of the radiative dipole and the in-plane diffractive modes. To illustrate the SHG efficiency as a function of the period, we plotted the maximum SH signal for different periodicities (Figure S.I.13). It is observed that below and above the critical period ( P _c ), the SH intensity scales as the 4th power of the period ( P ). This can be rationalized from our previous numerical analogy where the fundamental intensity ( I ω ) scales quadratically ( P − 2 ) above P _c . In a first approximation [45], the observed SH intensity is expected to scale quadratically with the fundamental field enhancement, thus demonstrating a quadratic dependency on the period ( I 2 ω α   I ω 2 → I 2 ω α   P − 4 ) . From the simulation, it appears that the SH signal should be at least 8100 times. The discrepancy seen between the numerical simulation and experimental data (Figure 4) can have different origins. The total scattered SH far-field intensity is proportional to the perpendicular component of the electric field intensity ( E z ( r , ω ) ) . To further analyze the perpendicular ( E z ( r , ω ) ) and parallel components ( E y ( r , ω ) ) of the electric field, we plotted the mode profiles as shown in Figure S.I.14. From such mode profile plots, the electric field appears to be significantly enhanced in the substrate plane (reaching an amplitude of 100), while the enhancement for the field amplitude normal to the substrate plane reaches about 12. It is difficult to separate the contributions of the in-plane and normal fields on the overall SH enhancement. In planar media, it is usually the normal field component that is assumed to play the dominant role in the nonlinear conversion mechanism [46], and the amplitude enhancement of about 10 observed in Figure S.I.14 could explain the measured 100× SH enhancement. The system under study is however far from a planar geometry and it is likely that the overall SH signal stems from a combination of in-plane and normal field components. Elucidating these mechanisms in detail would require polarization- and angle-resolved measurements, that are beyond the scope of this publication, which primary aim is to demonstrate a facile large area fabrication technique with full geometrical control. In the same experimental context, the detection of the SH signal in reflection mode might also be another cause for the discrepancy, since a non-negligible part of the SH wave can propagate in the forward direction and escape detection. In any case, the experimental results clearly show the ability of our fabrication technique to produce efficient metasurfaces that yield both high SHG and tunable QF with a low FWHM.