论文和技术资料

Introduction: Flat lenses require precise control of a phase gradient across an interface, which is enabled through the application of engineered surfaces, such as Metasurfaces [1]. Periodic arrays of plasmonic antennas have been utilized to generate this desired phase gradient, which dictates the angle of “anomalous” refraction of the cross-polarized field scattered from a normal-incidence beam. However, the designs utilized to-date have been simple geometries, due to the challenges of numerical modeling more complex forms, and as a result scattering efficiencies have been unacceptable for real-world application. Therefore, an optimization effort is necessary to improve the performance. In order to establish confidence before proceeding with complex designs, COMSOL Multiphysics® software was used to generate several simple plasmonics-based flat lens designs, which were then fabricated and measured for validation of the simulated results. These lenses were assessed for characterization of their depth-of-field under a changing focal ratio (f/#) in the long-wave infrared (LWIR) regime.

Use of COMSOL® software:
Controlling the phase gradient requires understanding of the phase and amplitude profile of the field scattered from the plasmonic antenna. Mimicking the original numerical model of a v-antenna [2], COMSOL Multiphysics® software was used to produce these profiles as a function of the antenna geometries: dipole length and the relative angle of separation of the dipoles. These profiles were used to select which N elements will form the basis of the lens design. These elements must meet the two constraints of having phase separation 2π/N apart while also maintaining equal field amplitudes:

∆φ=φ(i+1)-φi=2π/N |Ei^(x-pol) |=|E(i+1)^(x-pol) |

Following the “Scatterer on a Substrate” model library, the Wave Optics Module of the COMSOL® software is used to sequentially calculate an input field based on the full-field results of the substrate-only model. The N antenna elements were each isolated within perfectly matched layer (PML) boundaries and illuminated with this input field, with the phase and amplitude of the scattered cross-polarized field extracted at the ports. These elements are aligned in a “supercell” and again illuminated with the input field to validate the overall anomalous refraction. This supercell was then expanded into a rectangular lens architecture spanning several 2π phase periods and output to a file suitable for e-beam lithographic mask production.

Results: The scattered field phase and amplitude profiles were sufficiently recreated from the original work to generate basis elements for the flat lens designs (Fig.1). Fig.2 shows a supercell design and the phase broadside generated by the metasurface, giving rise to an anomalous refraction. The measured depth-of-field and the numerical calculations and compare favorably (Fig.3), validating the design process.

Conclusion: The COMSOL Multiphysics® simulations demonstrated how novel metasurfaces can be confidently generated in the early stages of flat lens designs to focus infrared light across a single, flat interface. By validating the design of a simple numerical model (v-antenna), the computational tool can now be used by optical engineers to explore a vast parameter space of metasurface inclusions and materials which would be inaccessible using simplified numerical models alone.