Key Points:
- While circular and square cross section nanoposts are common, offering more straightforward fabrication and polarization insensitivity, more complex meta-atoms can offer additional functionality
- Multi-scatterer meta-atoms and multi-layer designs, exploiting asymmetries and effects such as Pancharatnam-Berry phase, enable unique functionalities in terms of polarization, frequency, and wavevector control
- While more complicated scatterer designs offer potential performance enhancements, this must be balanced with impacts on fabrication ease, reliability, and yield
Introduction
In metasurface design, the grating structure used (i.e., the scatterer type or “meta-atom”), can take on a variety of different shapes and orientations. In a given unit cell, a meta-atom can be treated as a permittivity function (for the most part we assume here that the material is non-magnetic, so permeability is constant). A typical permittivity function for a metasurface would consist of a square or circular slab of constant permittivity located at the center of the cell that is higher than and distinct from a uniform background material, often just treated as vacuum; however, a designer is not always limited to such a simple permittivity function.
In some cases, more complex shapes can be used, or multiple isolated “islands” of material can be located in a single cell (e.g., cases where multiple “meta-atoms” comprise a single cell). It is also possible to consider permittivity functions with multiple layers (i.e., that vary with height in a layer-by-layer manner). Ultimately, the permittivity function will determine the function of the metasurface. In practice, a designer cannot utilize an arbitrary unit cell design because of both physical limitations and fabrication constraints. In this article, we discuss some of the typical cases and their applications. We conclude with a discussion on some of the practical considerations in selecting scatterer designs.
Simple Geometries
A typical, simple scatterer design is a square or circular cross section nanopost. This design has the nanopost material surrounded by a uniform background index. This design is often the standard choice for metalens designers, as it’s one of the most straightforward and reliable to make. These cross sections, in particular, circular cross sections are a good match for many lithography and etch-based processes that often induce rounding during multiple process steps. In being based on a single meta-atom per unit cell, they tend to exhibit larger features compared to more complicated shapes or multi-scatterer designs. With their symmetry, for normal incidence, these scatterers offer polarization-insensitive behavior.
With the addition of a reflective layer beneath the scatterer with a spacer layer, this simple design can begin offering more complex functionalities, with the spacer gap enabling adjustments in the resonant behavior of the design. This can be useful when trying to design multi-wavelength elements where more rich resonant characteristics are often required to reach the necessary performance. This configuration requires operation in reflection.
Asymmetry
More interesting behaviors become feasible once you start to change the scatterer design beyond simple symmetric cross sections. With asymmetry in the unit cell design, the transmission or reflection coefficient begins to look different for different polarization states. Even with as small a change as converting to a rectangular cross section nanopost rather than a square, the long axis and short axis will respond differently to horizontal and vertical polarizations. On the one hand, this could be considered a limitation as often the incident polarization in imaging applications is unknown; however, because the scatterer responds distinctly to different polarizations states, it offers the ability to engineer multiplexing surfaces.
Under a change polarization, the functionality of a surface can be altered. From this perspective, it enhances the degrees of freedom and control that an optical component can exhibit. Traditionally, this type of behavior would require separate paths with a beamsplitter, but with a meta-optic and appropriately designed asymmetric scatterers, distinct functions (e.g., lensing, hologram generation, beam deflection, etc.) can be encoded onto each polarization state without requiring any additional optics.
One prominent example of an asymmetric scatterer design are ones exploiting Pancharatnam-Berry (PB) phase. In this approach, an asymmetric scatterer (e.g., a rectangular rod-shaped scatterer) does not change in shape but instead the orientation is altered in order to alter its response. PB phase elements depend on circularly polarized illumination and by rotating the phase element by some angle, the induced phase shift will be equal to 2 times the change in orientation angle, the sign of which changes depending on the helicity of the incident light (i.e., if it’s right or left circularly polarized). The physical mechanism for this method is quite fascinating and also manifests in a number of other wave phenomena in which the phase and amplitude are slowly (adiabatically) varied. In practice, this approach is beneficial because the phase shift with rotation tends to be more “broadband” compared to a simple nanopost that does not exploit PB phase, and often the scatterer thickness can be reduced compared to propagation phase-based unit cell designs. The requirement of circular polarization, however, prevents this approach from working with ambient light without including additional polarization optics that would reduce overall efficiency and increase form factor.
Multi-scatterer Meta-atoms
In the discussion thus far, we have limited ourselves to considering unit cells that comprise a single nanostructure; however, designs are possible in which there are multiple nanostructures per unit cell. These include different pillar shapes placed in close proximity, wherein both the shape, orientation, and gap between individual elements are additional degrees of freedom available to the designer. By adjusting the shapes of elements and the gaps between them, researchers have previously demonstrated achromatic functionality at several discrete wavelengths. This approach can also enable additional control over polarization or wavevector. Compared to a single nanostructure, the additional degrees of freedom offers greater flexibility to engineer desired resonant phenomena. One prominent example of this is in dispersion engineering, in which the goal is to utilize the unit cell designs to match not only the phase at a desired wavelength but also the group delay and group delay dispersion, in effect matching the Tayler expansion of the phase over a continuous band of frequencies. This usually exploits a PB phase element coupled with another non-rotating element per unit cell.
Bilayer or Multi-layer Designs
While most metasurface designs are based on a single layer of nanostructures, there have been some demonstrations of multi-layer meta-optics. This requires a fabrication process in which repeated lithography stages enable different patterns that are effectively stacked on top of one another. Thematically there is some overlap here with multi-scatterer meta-atom design, except this is along the z or height axis of the unit cell, rather than laterally. Additional degrees of freedom along the height axis again can enable more rich resonant behavior, with some early demonstrations of bilayer designs showing more fine control over angular behavior as compared to a single layer of meta-atoms.
Practical Considerations and Tradeoffs
In practice, more complex designs often require more complex fabrication as the associated feature sizes are reduced. The unit cell size is often driven by the desire to suppress higher diffraction orders for a given wavelength and incidence angle. As such, the pitch often will remain the same, but by introducing additional elements per unit cell, the critical dimension requirement will decrease. Features that require sharp corners are often rounded during processing and so resonant designs that require these features are often not practical when needing high yield.
With multi-layer scatterer designs, there are a number of challenges with layer-to-layer alignment and ensuring each subsequent layer is planarized and amenable to subsequent deposition and lithography steps. As with any nanofabrication process, each step has an associated probability of success and as the number of steps increases, the yield is likely to reduce.
These challenges are not necessarily prohibitive but are additional considerations when evaluating the overall cost and complexity of a metasurface-based solution.
Additional References
Arbabi, Amir, et al. “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays.” Nature communications 6.1 (2015): 7069.
Lin, Dianmin, et al. “Dielectric gradient metasurface optical elements.” science 345.6194 (2014): 298-302.
Bomzon, Ze’ev, Vladimir Kleiner, and Erez Hasman. “Pancharatnam–Berry phase in space-variant polarization-state manipulations with subwavelength gratings.” Optics letters 26.18 (2001): 1424-1426.
Wang, Shuming, et al. “Broadband achromatic optical metasurface devices.” Nature communications 8.1 (2017): 187.
Zhou, You, et al. “Multifunctional metaoptics based on bilayer metasurfaces.” Light: Science & Applications 8.1 (2019): 80.
Smith, David R., John B. Pendry, and Mike CK Wiltshire. “Metamaterials and negative refractive index.” science 305.5685 (2004): 788-792.
Aieta, Francesco, et al. “Multiwavelength achromatic metasurfaces by dispersive phase compensation.” Science 347.6228 (2015): 1342-1345.