Design Parameters of Free-Form Meta-Color Routers for Sub-Micron-Pixel Image Sensors

<br/>Meta color routers are emerging as a next generation color filter for complementary metal-oxide-semiconductor (CMOS) image sensors. In a classical image sensor, a micro-lens and a color filter is placed on top of a silicon photodetector. The micro-lens focuses the light into the photodiode area and the color filter absorbs or reflects the light of unwanted wavelength. Until now, the classical image sensor configuration has dominated the visible image sensor market, but the reduction in pixel size to sub-micron range is limiting its performance. The geometric-optics based configuration is no longer valid and reduction of pixel area leads to a smaller number of photons reaching the photodiode.<br/>As most of the light incident on the image sensor is blocked by the color filter, the optical efficiency of the classical image sensor is limited to 25% for red/blue lights and 50% for green lights. The meta color routers break this limit by directing all the incident light into the corresponding subpixel area.<br/>A typical meta color router is configured by allocating dielectrics of different refractive indices inside the design region, thus involves freeform optimization of high degrees of freedom (DoF). Due to the advantages that can be brought by the meta color router, optimization of the meta color router has been widely investigated, both theoretically [1, 2] and experimentally [3, 4]. However, those studies lack the investigation on the selection of design parameters. The design parameters of a meta color router are the parameters that define the geometry and the design space of the device, and have critical effects on final device performance.<br/>In this work, we investigate how the optical efficiency of a meta device is affected by the choice of each design parameters. We classify the design parameter into two different types: physical parameters, and spatial resolution parameters. Design parameters such as pixel size, device thicknesses, and refractive indices are the physical parameters. Spatial resolution parameters are parameters that determine how the design area is gridded. Through parameter tuning, we report the existence of optical thickness of the device and optimal choice of dielectrics. Also, we report how the subpixel resolution parameters affect the optical efficiency.<br/>[1] Philip Camayd-Muñoz, Conner Ballew, Gregory Roberts, and Andrei Faraon, "Multifunctional volumetric meta-optics for color and polarization image sensors," Optica 7, 280-283 (2020)<br/>[2] Catrysse, Peter B., Zhao, Nathan, Jin, Weiliang and Fan, Shanhui. "Subwavelength Bayer RGB color routers with perfect optical efficiency" Nanophotonics, vol. 11, no. 10, 2022, pp. 2381-2387. https://doi.org/10.1515/nanoph-2022-0069<br/>[3] Zhao, N., Catrysse, P.B. and Fan, S. (2021), Perfect RGB-IR Color Routers for Sub-Wavelength Size CMOS Image Sensor Pixels. Adv. Photonics Res., 2: 2000048. https://doi.org/10.1002/adpr.202000048<br/>[4] Masashi Miyata, Naru Nemoto, Kota Shikama, Fumihide Kobayashi, and Toshikazu Hashimoto, "Full-color-sorting metalenses for high-sensitivity image sensors," Optica 8, 1596-1604 (2021)