When light transitions from one medium to another, differences in refractive indices cause partial reflection which reduces the intensity of the transmitted light. Partial reflection is common to all types of waves and in the optical regime can significantly degrade the performance of optical devices such as lenses, solar panels, displays, and even eyeglasses. Thus, anti-reflection (AR) techniques have become ubiquitous and are employed in numerous applications.
Approaches for reflection suppression have been developed since the 19th century following the pioneering works of Raleigh and Fraunhofer1,2 on utilizing graded index layer for AR purposes. Approaches such as thin-film AR coating3,4,5, adiabatic graded index layers6,7,8,9,10,11, metamaterials12, and resonant nanostructures13,14 have been proposed and demonstrated. The growing interest in spatiotemporal shaping of optical beams15,16,17 poses significant challenges to AR structures design as such beams are characterized by broadband spectral and spatial profiles. Recent developments in graded index layers and three-dimensional configurations have been shown to support polarization-insensitive and broadband reflection suppression18,19. Particularly, moth-eye-inspired20 nanostructures mimicking biological AR have drawn significant interest. More recently, a broadband reflection suppression approach utilizing white light cavities and exceptional points has been suggested and demonstrated in RF21,22.
Many of the more advanced AR techniques exhibit excellent performances in terms of bandwidth (spectral and spatial), particularly those employing gradient index profiles or 3D nanostructures. Such approaches can indeed cope with the challenges associated with beams exhibiting complex spatiotemporal shapes. However, the practical realization of such AR structures is quite complex, requiring extreme control capabilities over fabrication processes, and is often not very repetitive. Moth-eye-like AR structures, for example, rely on continuously varying surface profiles with very fine features that are difficult to optimize and to fabricate accurately or in a repetitive manner. To date, the commonly used AR approach in optics is based on thin films. The basic AR coating employs a single layer placed between one medium (e.g., air) and another (e.g., glass). By choosing the layer thickness to be a quarter wavelength and its refractive index to be the geometric mean of the indices of the two media, it is possible to cancel completely the reflectivity at a specific wavelength. Employing multilayer coatings can yield broadband AR. However, achieving this in practice is challenging due to the difficulty in obtaining transparent materials with specific refractive indices that do not necessarily exist23. Nevertheless, optimal performances can be traded for realizability by employing intensive numerical optimization procedures based on existing materials.
Despite the practical success of thin-films AR coating, there are applications for which a monolithic approach (i.e. the AR coating consists of a single material) is advantageous24. For example, practical AR for high-power applications25,26 is difficult to attain, mainly because of the different thermal expansion coefficients associated with different materials. Consequently, thin-film AR coatings are susceptible to thermal damage under high-power illumination conditions27.
In this paper, we present a hybrid broadband (spectral and spatial) AR scheme, utilizing nanostructure arrays in a multi-layer metasurface configuration with periodicity in the order of a wavelength (see Fig. 1). This scheme offers a rigorous design and fabrication approach, allowing for a quick realization flow with good control over the spectral reflectivity. It also allows for optimizing the geometry and obtain more repetitive realization (in terms of obtaining as specific design) than that of moth-eye-like approaches. In parallel, the monolithic, single-material, nature of structure supports high-power applications as well as operation at very high temperature conditions. Furthermore, such AR structures can also be realized using additive manufacturing techniques such as 3D printing and Nano-Imprint Lithography.
Figure 1 depicts a schematic of the proposed AR scheme, comprising a periodic array with several layers of dielectric metasurface composed of the same material as the substrate. For practical realization purposes, the dimensions of the nanostructures in each layer are smaller than those in the lower layers (S2 < S1).
The rest of the paper is arranged as follows: In Sect. 2, we present the design concept and optimization approach. In Sect. 3, we present various broadband AR structures for telecom wavelengths and discuss the impact of the nanostructures geometry and arrangement, as well as the impact of the array periodicity and the illumination angle. In Sect. 4, we study the sensitivity of the AR performances to fabrication errors, in Sect. 5, we present optimized design for wide angle incidence, and in Sect. 6, we summarize and conclude.
Fig. 1
Dimensions definition for the two-layer case. h1 and h2 are the height of the first and second layer respectively, S1 and S2 are the widths of the layers. In the case of circularly shaped nanostructures, S1, and S2 correspond to their diameters. \(\:{\Lambda\:}\) is the periodicity of the array.