Multi-height metasurface for wavefront manipulation fabricated by direct laser writing lithography

2.1 Polarization-dependent metasurface

Dielectric metasurfaces composed of silicon nanoparticles provide ranges of functionalities due to the low absorption loss. Nonetheless, the application of those based on single localized mode is restricted in reflection geometry due to the sharp increase in reflectance at the resonance wavelength [32]. Therefore, optimizing the size (height, width, length, and pitch) of individual nanopillar is crucial to control the excitation of electric and magnetic dipolar resonances simultaneously, realizing reflectionless behavior at the targeted wavelength. To calculate the accumulated phase shift φ (neglecting Fabry–Perot effects) as light passes through the nanopillar, the following equations are used [33]:

where n_eff is the effective refractive index, H, W, L denote the height, width, and length of the nanopillar, and P is the pitch between adjacent nanopillars. By these formulae, we can see that phase shift φ can be modified by adjusting H, W and L. In order to achieve the wavefront control through a multi-height metasurface around the telecommunication, geometry parameters optimization was performed using commercially available software CST MICROWAVE STUDIO.

As schematically demonstrated in Figure 1(a), structure of single unit with rectangular nanopillars, composed of resin (n _r = 1.53), standing on 700-μm silica fused substrate (n _s = 1.444). As illustrated in Figure 1(b) and (c), when H and P are fixed in 5.56 and 2.5 μm, the phase shift φ _x and φ _y under the x- and y-polarized incidence at 1550 nm are recorded respectively as we gradually varied the W and L. The phase shifts φ _x and φ _y cover 0 to 2π as W and L ranges from 1.0 to 2.4 μm. The phase shift of the incidence at different frequency from 185 to 205 THz is shown in Figure 1(d). The result reveals a large amount of Mie-type scattering resonances resulting from both induced electric and magnetic dipoles as designed within the range [11, 34], which explains the dramatic changes in phase shifts φ with slight variation in W and L under both polarizations. On the other hand, the tuning ranges still approach 2π at 185 and 205 THz, details can be looked up in Supplementary Material, suggesting the free phase modulation can be achieve in broadband from 185 to 205 THz, corresponding to 1460.1–1618.0 nm.

Figure 1:

Schematic and simulation results of structure. (a) Schematic of a rectangular nanopillar. Phase shift with varying width and length under (b) x-polarized, (c) y-polarized, (d) in range of 185 ∼ 205 THz. Transmission amplitude with width and length under (e) x-polarized, (f) y-polarized. (g) Phase shift and transmission amplitude with varying height. (h) Farfield when monitor is 500 μm away from the metasurface. All results are under incidence at 1550 nm.

The transmission amplitude, represented by the square root of the intensity transmittance, is defined by t=ts/ns [9], where t _s denotes the simulated transmission coefficient of the interface from the silica fused substrate across the resin to the air. The transmission amplitudes t _x and t _y under x- and y-polarized are plotted in Figure 1(e) and (f). It can be observed that both the phase shifts and transmission amplitudes are polarization-dependent but have symmetry about the line W = L due to the anisotropic rectangular-shaped elements. It is worth mentioning that the transmission amplitude is basically above 77 % across the entire range, indicating that full phase modulation can be achieved while ensuring considerably high transmission. Nevertheless, modulating the phase by varying W and L has a fundamental flaw – the phase shift φ can change drastically with small fabrication errors. By contrast, as shown in Figure 1(g), when W and L is set to be 1.4 and 2.0 μm, measured under x-polarized at 1550 nm, the phase shift decreases linearly with the height within one cycle (such as 5.68–6.96 μm) of change while the transmission can drop to 39 % in some specific height. Hereby, it is more reliable to modulate phase through the optimized height and then improve further by altering W and L. In addition, although we know the propagation phase is wavelength-dependent, such height tuning of phase shift is also effective for a fixed wavelength. According to simulation results, we specified the respective sizes of 9 areas, and the parameters are listed in Table 1. H of nanopillars varies between 4.36 and 7.76 μm, W and L are from 1.0 to 2.4 μm in Regions I ∼ IX. In this way, the φ _x in adjacent regions are set at an approximately 45° interval and maintain t _x at a relatively high level even at resonance. For the φ _y and t _y under y-polarized, they are all different from but relatively close to those which are under x-polarized except for the transmission amplitudes t _y of Region IV (∼46.20 %). Figure 1(h) depicts the simulated far-field of Region IX when placing the monitor 500 μm away from the metasurface. Most of intensity gathers in the center, which is the component transmitting directly through the metasurface. There is also a slight distribution at a deflection angle of θ = 59°, attributed to the first-order diffraction.

2.2 Polarization-independent metasurface

Various functionalities, such as resonant forward scattering, broad-band reflector and spontaneous emission control, have also been demonstrated with isotropic cylindrical-shaped metasurfaces. Similarly, Periodic structures composed of nanodisks, also known as Huygens’ metasurfaces [34–36], have been wildly utilized due to their extremely high transmittance. In line with these purposes, the metasurface consisting of different-sized nanodisks in 3 × 3 regions has also been thoroughly studied, and the effective refractive index can be expressed as:

where R denotes the radius of nanodisks. Figure 2(a) demonstrates the structure of single unit with cylindrical nanodisk, made of resin polymer, standing on silica fused substrate. As shown in Figure 2(b), when H and P are fixed at 5.60 and 2.5 μm, respectively, the phase shift φ and transmission amplitude t are both recorded. By altering radius R, we achieve 0 to 2π phase shift when radius is above 0.7 μm, however, the transmission amplitude is low at some points within this range. Moreover, the phase shift changes linearly only in small ranges, such as 1.08–1.16 μm, making it difficult to fabricate the optimized radii with precision. Figure 2(c) demonstrates that, when the radius is 1.1 μm, the phase shift decreases linearly between 4.32–5.52 and 5.56–6.84 μm, and the transmission amplitude is mostly above 80 % except for a few points. Transmission amplitude with respect to height for a wider range of incident light frequencies (180 ∼ 300 THz) is illustrated in Figure 2(d). The transmission amplitude is above 70 % between 180–280 THz when height in the range of 4.20–7.20 μm, indicating its broad-band availability. At the same time, results of the phase shift and transmission amplitude are independent of the polarization of the incidence. Since the transmittance is high enough, we only varied the heights of nanodisks between 4.28–6.52 μm with the same radius of 1.1 μm in 9 areas, and the parameters are listed in Table 2. At arbitrary polarization, the phase shift φ interval is roughly 45° between the adjacent. The average transmission amplitude t is higher than that of the polarization-dependent metasurface. Especially for Regions B, C, F, G, and H, the amplitudes approach 100 %, which proves reflectionless thanks to electromagnetically dual-symmetric behavior.

Figure 2:

Schematic and simulation results of structure. (a) Schematic of a cylindrical nanopillar. Phase shift and transmission amplitude with varying (b) radius and (c) height, under an incidence light at 1550 nm. (d) Transmission amplitude with height in range of 180–300 THz.

2.3 Fabrication

Two gradient height metasurfaces were achieved by using the commercial prototyping instrument (Nanoscribe Photonic Professional GT) based on 2 PP in a tightly focused femtosecond laser beam [37, 38], as shown in Figure 3(a). The nanopillars with 9 different sizes were fabricated within separated 3 × 3 areas throughout the entire metasurfaces. The polymer based metasurfaces were built on a fused silica substrate with IP-Dip2 resist on. For exposure, high numerical aperture (NA1.4) objective (Zeiss Plan-Apochromat 63×) was applied in immersion configuration. The laser beam was working on Galvo scanning mode, and to fit various sizes of pillars, optimized scan speed 10,000 μm s⁻¹, laser power of 32.5 and 45 mW for rectangular-shaped and cylindrical-shaped were chosen, respectively. Small slicing and hatching (laser movement step in longitudinal and transverse direction were set to be 0.04 and 0.1 μm to enable high aspect ratios and maintain mechanical strength of the polymer nanopillars simultaneously. Afterwards, the exposed samples were developed in propylene glycol monomethyl ether acetate (PGMEA) for 15 min and then immersed in isopropanol for 5 min. Eventually, the fabricated polymer sample would be dried in nitrogen for 2 min. The two fabricated samples both contain 9 square areas with same size of 125 × 125 μm, 25 μm spacing between adjacent square regions, and the size of entire metasurfaces are 425 × 425 μm, as exhibited in Figure 3(b), which is photo of polarization-dependent metasurface taken by the optical microscope. Figure 3(c) is the SEM top view of Region I after deposited a layer of Au to enable conductivity for the photo purpose. The resolution along the height direction is the same as the small slicing of 0.04 μm. The SEM side views of Regions A, I, IX, and V are, respectively, depicted in Figure 3(d)–(g), which indicates the shape and height variation in two metasurfaces, and the precision of fabrication through 2 PP as well.

Figure 3:

Details of fabricated metasurfaces. (a) Schematic of 2 PP fabrication technology. (b) Microscope photo of the polarization-dependent metasurface. (c) SEM image of Region I in polarization-independent metasureface (top view). (d), (e), (f), (g) SEM images of Regions A, I, IX, V in polarization-independent and -dependent metasurefaces, respectively (side view).