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A breakthrough in optical technology, metalenses are thin, flat surfaces that can augment traditional lenses for a wide range of applications. However, metalens development is challenging because of the complexity of the design workflow. A metalens typically consists of millions of subwavelength unit-cells called meta-atoms. A Maxwell equation solver is needed to simulate the optical properties of the meta-atoms, but it is difficult to do this on a millimeter-scale surface without approximations. Synopsys offers design tools to streamline this design workflow accurately and efficiently.
In this article, we demonstrate how to solve metalens design challenges by combining a ray-based automatic design tool in CODE V with a wave-based inverse design tool—MetaOptic Designer—to design an ultra-wide angle metalens imaging system.
Calculate Meta-Atom Optical Properties
A metalens is an optical element that uses nanostructures to modify the wavefront. These nanostructures are often referred to as meta-atoms. The meta-atoms are arranged on the metasurface with subwavelength spacing to eliminate high-order diffraction from the nanostructures. The meta-atoms modify the phase and transmission of an incident field. This modification to the optical properties depends on factors such as the material, shape, and orientation of the meta-atoms. Using design tools, we can vary the meta-atom design parameters spatially varying wavefront control.
Figure 1. Illustration of a metalens and various meta-atoms.
The meta-atom optical property that is relevant to a metalens design can be described with a bidirectional scattering distribution function (BSDF) database. Synopsys offers tools for calculating the meta-atom database, such as RSoft DiffractMOD RCWA or FullWAVE FDTD. This database can be used in both the ray-based design approach in CODE V and the wave-based inverse design tool, MetaOptic Designer.
In the example that follows, we use a hexagonal arrangement of nano-pillars on an SiO2 substrate as our meta-atom. We vary the pillar diameter to obtain the phase delay. It is easy to use the RSoft BSDF Generation Utility to calculate the optical property of the meta-atoms.
Designing a Metalens with CODE V
To generate a starting point for the metalens design, we use the CODE V MetaOptic Design feature, which is available in CODE V version 2024.03.
We represent the meta-atom design parameter distribution on the metalens surface with a polynomial function. By accessing the BSDF database, CODE V considers the angular and wavelength dependence of the meta-atom transfer function.
The ray-based method in CODE V treats the metalens similarly to a diffractive optical element. Instead of designing for an optimum phase, CODE V directly designs the distribution of the meta-atom design parameters. As shown in the example in Figure 2, we varied the coefficients of the polynomial that represent the design parameters to optimize the optical performance. A second step of the ray-based design flow in CODE V involves optimizing the transmission by varying the maximum and minimum design parameter on the metalens. In the end, a GDS file for manufacturing can be generated in CODE V.
Figure 2: The meta-atoms used for the design (left). Side view of the 170-degree field of view ultra-wide-angle metalens designed in CODE V with MetaOptic Module (right).
Further Optimization with MetaOptic Designer
The ray-based design in CODE V can be easily imported into MetaOptic Designer for analysis and further optimization, as shown in Figure 3.
Figure 3: CODE V design imported into MetaOptic Designer for analysis
In MetaOptic Designer, which uses an inverse design capability, the meta-atom design parameter distribution function on the surface is allowed to vary freely. This design freedom allows us to further optimize the metalens. After optimization in MetaOptic Designer, the MTF and focusing efficiency are both improved. The final design, exported as a GDS data file, is shown in Figure 4. The GDS file provides mask information based on the optimized design parameters and is generated on the hexagonal arrangement.
Figure 4: GDS layout of the 1-mm metalens
Validation with FDTD
To test the effects introduced by using locally periodic approximations assumed in both CODE V MetaOptic Module and MetaOptic Designer, we then validate the design using the RSoft FullWave FDTD tool, which is a rigorous finite-difference time-domain solver. The results are shown in Figure 5. FullWAVE FDTD validates the optimization performed with CODE V MetaOptic Design and MetaOptic Designer by demonstrating the well-defined image plane of the field for different angles of incidence (here 0°,45° and 60° are evaluated)
Figure 5: FDTD validation of the final design
Conclusion
We have shown an example of how to design an ultra-wide-angle metalens using Synopsys tools. Synopsys offers complete solutions to calculate the meta-atom database and streamline the overall design workflow. Our tools are developed by experts in ray optics, nanophotonics, and lithography to help designers effectively navigate the metalens design process. By bringing manufacturing awareness to optical design and streamlining the design workflow, we hope to facilitate wider adoption of metalenses in optical system design.