Meta-Deflectors Made of Dielectric Nanohole Arrays with Anti-Damage Potential

Abstract

In intense-light systems, the traditional discrete optical components lead to high complexity and high cost. Metasurfaces, which have received increasing attention due to the ability to locally manipulate the amplitude, phase, and polarization of light, are promising for addressing this issue. In the study, a metasurface-based reflective deflector is investigated which is composed of silicon nanohole arrays that confine the strongest electric field in the air zone. Subsequently, the in-air electric field does not interact with the silicon material directly, attenuating the optothermal effect that causes laser damage. The highest reflectance of nanoholes can be above 99% while the strongest electric fields are tuned into the air zone. One presentative deflector is designed based on these nanoholes with in-air-hole field confinement and anti-damage potential. The 1st order of the meta-deflector has the highest reflectance of 55.74%, and the reflectance sum of all the orders of the meta-deflector is 92.38%. The optothermal simulations show that the meta-deflector can theoretically handle a maximum laser density of 0.24 W/µm². The study provides an approach to improving the anti-damage property of the reflective phase-control metasurfaces for intense-light systems, which can be exploited in many applications, such as laser scalpels, laser cutting devices, etc.

1. Introduction

With the dramatic development of intense-light systems, the complexity of optical systems has risen sharply due to the intrinsic limitations of the traditional discrete components, leading to a very high cost of construction, operation, and maintenance. Therefore, the integratable flat optical components with high damage thresholds are very desirable for the miniaturization and integration of complex intense-light systems. Previous research has shown that the optical damage mainly comes from precursors induced by strong electric fields [1,2,3]. To improve the damage threshold of traditional components, dielectric films were deposited to tune the electric field intensity distribution [2,4]. Meanwhile, anti-reflection nanotextures were also designed and fabricated on fused silica optics to manipulate the local field into the air zone for high damage thresholds [5,6]. However, there are still no reports on the phase-control flat components with manipulation of the electric field distribution for high damage thresholds, which could be one important part of integrated intense-light systems.

Optical metasurfaces, 2D artificial metamaterials with thicknesses smaller than the working wavelength, have attracted much attention due to many peculiar properties that do not exist in nature [7,8,9,10,11]. They are made of two-dimensional arrays of subwavelength nanostructures and can locally control the amplitude [12,13,14,15], phase [15,16,17,18], polarization [19,20], and non-linear effect [21,22,23] of light. In particular, the all-dielectric metasurfaces have the advantages of low-loss, thermal stability, magnetic effect, etc., [8,10], which is a promising candidate for the miniaturization and integration of complex intense-light systems [24,25]. Although all-dielectric metasurfaces have realized lenses [26,27,28], gratings [29,30], deflectors [31], perfect absorbers [32,33,34,35], etc., the metasurfaces for intense-light applications are less reported in the literature. Some phase-control metasurfaces made of refractory materials such as HfO₂ are reported with the application potential in the high-power systems [31]. Except for refractory materials, the method of tuning the electric field distribution provides a new approach to improve the anti-damage property of the phase-control metasurfaces of general materials.

In this study, we proposed a reflective meta-deflector composed of silicon nanohole arrays with anti-damage potential. Unlike the nanoholes for enhanced absorption in photovoltaics [36,37], by tuning the electric-field energy into the air zone, the in-air electric field does not interact with the silicon material directly, attenuating the optothermal effect that causes laser damage. The rules of tuning the reflectance, phase, and field distribution through the geometrical parameters are investigated numerically. One deflector is designed based on the nanoholes with in-air-hole field confinement and anti-damage potential. Finally, the maximum laser intensity that the meta-deflector can handle is estimated quantitatively. The study provides an approach to improve the anti-damage property of the phase-control metasurfaces for intense-light systems.

2. Materials and Methods

The studied meta-deflectors are composed of silicon (Si) nanoholes within a square lattice on SiO₂ substrates, as shown in Figure 1. The nanohole is rectangular with length L, width W, and height H. The lattice period of unit-cells is constant P = 600 nm. The operating wavelength 1064 nm is chosen because silicon has a very weak absorption (k = 8.26 × 10⁻⁵) at 1064 nm. It is also one of the usually-used laser wavelengths in intense-light systems. In the study, the height is kept as H = 200 nm, and the length L and width W are the variables to tune the reflectance, phase, and field distribution of the reflected light. The x-polarized incidence is injected from the bottom of nanoholes and propagates along the z-axis direction.

In the study, the optical simulations are based on the finite-difference time-domain (FDTD) algorithm with the commercial software package FDTD solutions provided by Lumerical Solutions, Inc., and the thermal simulations are based on the finite element method with the software Device from the same company. In optical simulations, the x-/y-axis boundaries of the unit-cell (in Figure 1) are periodic boundary conditions, and the top and bottom boundaries (z-axis) were perfectly matched layer boundary conditions. The source, all objects, and monitors were limited in the simulation region. In thermal simulations, the x-/y-axis boundaries were set as “closed”, and the z-axis boundaries were set as “shell”. All the optical and thermal parameters of the materials came directly from the software’s database.

3. Results and Discussion

The unit-cells of nanostructures with the phase coverage of 0–2π are the fundament of designing the phase-control metasurfaces. By tailing the parameters (length L and width W) of nanoholes, the rules of tuning silicon nanoholes’ reflectance and phase are obtained via numerical simulations. As the height H of the Si film is 200 nm and the lattice constant P is 600 nm, the corresponding reflectance and phase of reflected light are reported in Figure 2. It is seen in Figure 2a that a near-100% reflectance can be obtained by choosing suitable values of L and W. There are several high-reflection strips in Figure 2a, which come from the electromagnetic resonances of the nanoholes. According to the electromagnetic distributions, the resonances can be divided into two groups: electric dipoles and magnetic dipoles, as indicated by the arrows. The electromagnetic behavior of nanoholes comes from the coupling between the electric/magnetic dipoles of the nanoholes in the lattice with photonic crystal radiation [38]. More details of the electromagnetic modes will be further analyzed when discussing the eight selected nanoholes (marked by the stars *) with the 0–2π phase coverage. Figure 2b shows that the 0–2π phase coverage can be achieved by tuning the nanohole size. For intense-light applications, except for the reflectance and phase coverage, the electric field distribution in the unit-cells that compose the reflective metasurfaces is also very important.

The 0-2π phase coverage is discretized into 8 segments with an interval of π/4. At each of the phase points of 0, π/4, …, 7π/4, the unit-cell of nanoholes with in-air-hole field confinement and high reflectance are chosen from Figure 2 (marked by the asterisks *), as shown in

Table 1. Unit-cells selected for designing meta-deflectors. The 0-2π phase range is discretized into eight segments with an interval of π/4.

Phase Point	0	π/4	π/2	3π/4	π	5π/4	3π/2	7π/4
Phase offset	0.012	0.059	0.052	0.055	0.07	0.207	0.183	0.072
Reflectance	0.995	0.949	0.945	0.733	0.38	0.796	0.992	0.994
W(nm)	425	500	355	270	485	460	430	425
L(nm)	365	260	555	555	550	520	525	425

. When selecting the 8 unit-cells of nanoholes, the principle is that the maximum value of the electric field in air zones has to be bigger than that in silicon zones. The term “phase offset” describes the difference between the desirable phase points and the phase values of the 8 selected unit-cells. It is found that, on the ground of the in-air-hole field confinement, there is no high reflectance at some phase points (3π/4, π, 5π/4). To illustrate the physical relationship between the field distribution, reflectance, and phase, the electric field distributions of the 8 selected unit-cells are shown in Figure 3. It can be seen that the strongest electric field is confined in the air nanoholes while the strong reflection appears at the phase points (0, π/4, 3π/2, 7π/4). The field distributions have a dipole-like feature in the nanoholes. The in-air electric field does not interact with the silicon directly.

To further demonstrate the electromagnetic modes, the effective electric polarizability ${\mathsf{\alpha }}_{\mathrm{e}}^{\mathrm{eff}}$ and the effective magnetic polarizability ${\mathsf{\alpha }}_{\mathrm{m}}^{\mathrm{eff}}$ of the 8 selected unit-cells are calculated according to the equations $j\omega {\alpha }_e^{eff}=2\left(1-t-r\right)/\left. [\sqrt{\mu /\epsilon }\left(1+t+r\right)\right]$ and $j\omega {\alpha }_m^{eff}=2\sqrt{\mu /\epsilon }\left(1-t+r\right)/\left(1+t-r\right)$ [39]. Here, t and r are the transmission and reflection coefficients, respectively. By tuning the resonances, i.e., ${\alpha }_e^{eff}$ and ${\alpha }_m^{eff}$, of the electric and magnetic dipoles in nanoholes, near-100% reflection (Huygens sources, t = 0 and r = 1e^i(φ+π)) can be achieved [40]. In Figure 4, the red solid curves are the real part of the ideal effective electromagnetic polarizabilities of the reflective Huygens sources while the blue one is the imaginary part. It can be seen that the effective electric polarizabilities of the 8 unit-cells are close to the solid curves, but the effective magnetic polarizabilities of some phase points are far from the solid curves. At the phase points (0, π/4, 3π/2, 7π/4), the effective magnetic polarizabilities are close to the value of 0 while the electric polarizabilities are far from the 0 value. Thus, the strong reflection at these points should come from the electric dipole. It also agrees with the dipole-like electric field distribution in the air nanoholes in Figure 3. At the phase points (π/2, 3π/4, π, 5π/4), the magnetic modes dominate and the electric polarizabilities are close to the 0 value. The effective magnetic polarizabilities of the phase points (π, 5π/4) are smaller than the values of the ideal Huygens source. Because the electric field of a strong magnetic resonance mainly concentrates in the silicon zone, the nanoholes with smaller magnetic polarizabilities are chosen to decrease the in-silicon-energy intensity.

Beam steering is one typical applications of phase engineering. Based on the 8 selected unit-cells with the 0-2π phase coverage, a presentative deflector is designed based on these nanoholes with in-air-hole field confinement. The minimum linewidth of the meta-deflector’s structure is 90 nm, which can be fabricated by the e-beam lithography and dry etching. As shown in Figure 5a, the strongest electric field concentrates in the air nanoholes. The deflection can be seen obviously from the oblique wavefront. The reflectance of the different diffraction orders of the meta-reflector is shown in Figure 5b. The 1st order of the meta-deflector has the highest reflectance of 55.74% and the steering angle is 8.8°. The steering angles of all the orders (from −6 to +6) are −66.7°, −49.9°, −37.8°, −27.3°, −17.8°, −8.8°, 0°, 8.8°, 17.8°, 27.3°, 37.8°, 49.9°, and 66.7° respectively. The reflectance sum of all the orders of the meta-deflector is 92.38%. Although the 3 unit-cells at the phase points (3π/4, π, 5π/4) do not have high reflectance, a high reflectance sum of the deflector is still obtained.

The electric field distribution only shows the anti-damage potential of the meta-deflector qualitatively. For quantitative analysis, some optothermal simulations are conducted to estimate the maximum laser intensity that the meta-reflector can handle. Figure 6a shows the temperature distribution in the unit element (its structure is presented as an inset image, which is composed of the 8 selected unit-cells in Table 1, area: 0.6 µm × 4.8 µm = 2.88 µm²) of the meta-deflector illustrated by a plane-wave laser with power 0.53 W. The unit-cells have similar temperature values from 1160 K to 1320 K. Under the illumination of different incident powers, the maximum temperature values in the 3D volume made of the unit element are reported in Figure 6b; 1683 K is the melting point of silicon. It is shown that the meta-deflector can handle the maximum laser power (0.68 W per 2.88 µm²), i.e., the laser density of 0.24 W/µm².

4. Conclusions

In the study, meta-deflectors made of dielectric nanohole arrays are investigated to achieve anti-damage potential via tuning the distribution of the electric field. The rules of tuning the reflectance, phase, and electric field distribution through the geometrical parameters are investigated. The highest reflectance of nanoholes can be above 99% while the strongest electric fields can be tuned into the air zone. The in-air electric field does not interact with the silicon material directly, attenuating the optothermal effect that causes laser damage. One presentative meta-deflector is designed based on these nanoholes with in-air-hole field confinement. The 1st order of the meta-deflector has the highest reflectance of 55.74% and the steering angle is 8.8°. The reflectance sum of all the orders of the meta-deflector is 92.38%. The optothermal simulations show that the meta-deflector can theoretically handle a maximum laser density of 0.24 W/µm². The study provides an approach to improve the anti-damage property of the reflective phase-control metasurfaces for the intense-light optical systems, which can be exploited in many applications, such as laser scalpel, laser cutting devices, etc.