High‑Efficiency All‑Dielectric Phase‑Gradient Metasurface for Near‑Infrared Anomalous Transmission

Introduction

Phase‑gradient metasurfaces have revolutionised wavefront engineering, offering flexible control over amplitude, phase, and polarization of light without bulky optics. Unlike conventional diffractive elements, these two‑dimensional metamaterials can be integrated into photonic chips, enabling applications ranging from beam steering to holography. However, most metal‑based designs suffer from intrinsic ohmic losses, limiting efficiency. All‑dielectric metasurfaces—using low‑loss silicon or other high‑index dielectrics—have emerged as a promising alternative, yet achieving simultaneously high anomalous transmission efficiency and large refraction angles remains challenging. Recent studies have reported efficiencies up to 83 % with refraction angles around 30°, but larger angles typically come at the cost of reduced transmission. In this work, we overcome these limitations by designing a regular‑hexagon silicon nanorod array that delivers both >96 % transmission and refraction angles up to 69° in the near‑infrared band.

Design and Methods

The metasurface comprises 2‑µm‑long hexagonal silicon nanorods (height H1, side length w) on a 7050 nm silica substrate (H2). We employ 2‑dimensional periodic boundary conditions along x and y, and perfectly matched layers along z, to model a normally incident transverse‑electric (TE) wave in the 1400–1600 nm band. Silicon and silica refractive indices are taken from Palik’s database. Fabrication would involve LPCVD of a 1200 nm silicon film, e‑beam lithography of the hexagonal pattern, and a PEC‑corrected dose to avoid proximity‑induced rounding.

We first analyse the phase response of a single unit cell. By varying H1 (800–1200 nm) and w (100–220 nm) we obtain a full 2π phase swing at 1529 nm, while maintaining transmission >90 % for H1 = 1200 nm. The Fabry‑Pérot‑type resonance of the nanorod dominates the phase shift, as confirmed by eigenmode analysis and multipole expansion. The metasurface phase gradient is discretised into five phase steps (0, 2π/5, 4π/5, 6π/5, 8π/5) using six distinct nanorod sizes, forming a complete period of Px = 3000 nm (Ny = 500 nm). Generalised Snell’s law predicts an anomalous refraction angle θr = λ0/Px; by reducing Px or increasing the number of elements per period we can tune θr from 19.35° to 68.58°.

a Phase shift of the metasurface across 1400–1600 nm. b Phase profile at 1529 nm. c Transmitted and reflected intensities.

Results and Discussion

The simulated phase map (Fig. 4a) confirms a smooth 2π sweep over the entire band. Total transmission exceeds 60 % across 1400–1600 nm, peaking at 96.5 % (λ = 1529 nm). Reflection is below 3 % at the design wavelength, and absorption remains <0.1 % due to silicon’s low imaginary index in this band.

Calculated anomalous transmission efficiency (Fig. 5a) surpasses 80 % between 1527–1545 nm and 1591–1600 nm. At 1529 nm, the efficiency reaches 96.2 % and the far‑field power concentrates at θr = 30.64°, as predicted by Eq. (3). By increasing the number of elements per period (from nine to three), we can achieve anomalous refraction angles up to 68.58° while maintaining >70 % efficiency at 1536 nm (Fig. 7f, 8f). The metasurface tolerates ±10 nm deviations in w with only a 2 % drop in efficiency, demonstrating robust fabrication prospects.

a Total transmission vs. substrate thickness. b Anomalous transmission vs. thickness. c Polarisation dependence. d Size‑tolerance curves.

Conclusions

We have designed an all‑dielectric phase‑gradient metasurface that delivers >96 % anomalous transmission efficiency at 1529 nm and refraction angles up to 68.58°. By varying the period and element count, the device supports a wide range of angles (19.35°–68.58°) while preserving high efficiency (>80 % for angles <46.68°). These performance metrics surpass most reported dielectric metasurfaces and position the design as a strong candidate for compact wavefront‑control components in integrated photonics.

Availability of data and materials

The datasets supporting this study are available from the corresponding author upon reasonable request.

Abbreviations

FDTD

Finite‑difference time‑domain

TE

Transverse‑electric

LPCVD

Low‑pressure chemical‑vapor deposition

EBL

Electron‑beam lithography

PEC

Proximity‑effect correction

EME

Electromagnetic‑multipole expansion

SCSs

Scattering cross sections

ED

Electric dipole

MD

Magnetic dipole

EQ

Electric quadrupole

MQ

Magnetic quadrupole