Researchers at Cornell University have proposed a definition for the fundamental and practical limits of spaceplates, a technology developed to support the miniaturization of optical systems. According to the researchers, their attempt marks the first time spaceplate bounds have been identified. In optical systems, the free-space volume between the detector and the lens (or between lenses) allows light to acquire the distance- and angle-dependent phase necessary for the system to focus. Free-space volumes can increase the length and weight of a system, thwarting the miniaturization of optical setups. To replace some or all of the free space in optical systems, a thin, transparent device — a spaceplate — was developed. The flat-optic devices can implement the optical response of a free-space volume over a smaller length, effectively “compressing space” for light propagation. In the research, the Cornell team defined the limits of a spaceplate’s ability to maximize three optical parameters: compression ratio, numerical aperture, and bandwidth. “It’s very complicated to meet these three goals at the same time,” professor Francesco Monticone said. “Having maximal compression ratio and, at the same time, also maximizing numerical aperture and bandwidth. In this paper we try to clarify the general physical mechanism behind any space compression effect, regardless of how you implement the spaceplate.” Cornell researchers previously used computer simulations to design scalable spaceplates and demonstrate their role in an optical system. The researchers derived the general, fundamental bounds on the maximum achievable bandwidth of spaceplates as a function of their compression ratio and numerical aperture. With these theoretical results, they assessed different spaceplate designs and how to improve them, how the bandwidth limits of spaceplates and metalenses compare, and how high the maximum compression ratio can be for a spaceplate targeting the entire visible range. “There’s a lot of interest in knowing whether spaceplates would work for the entire visible spectrum of light and in free space, and nobody was sure we could do that,” researcher Kunal Shastri said. “So we really wanted to see if there were any physical bounds that would prevent spaceplates from working for real cameras for the entire visible bandwidth.” Shastri said that the boundaries defined by the team will inform engineers working in the field how far or how close they are to the global fundamental limits of the spaceplate devices that they’re designing. Researchers at Cornell defined the fundamental and practical limits of spaceplates — flat-optic devices that implement the optical response of a free-space volume over a smaller length to enable light propagation. The spaceplate reduces the distance at which light is focused over a broad range of wavelengths. Courtesy of the Monticone Research Group. Spaceplates can be made with the same materials that are used to make conventional imaging systems; as long as the spaceplate is highly transmissive, it can be made from layers of glass and other transparent materials with different refractive indexes, or a patterned surface, or a photonic crystal slab. High transmissiveness is key, since to work, the spaceplate cannot absorb light. “In the simplest possible implementation, a spaceplate could be fabricated as a stack of layers, and the layers would have at least two different refractive indexes,” Monticone said. “By optimizing the thickness and the spacing, you can optimize the optical response.” Previous research into spaceplate technology yielded impractical designs that worked for a single color or a small range of angles, or needed to be immersed in a material with a high refractive index, such as oil. These devices, while functional, could not be used to miniaturize typical optical systems. The researchers believe that their findings will help guide the design of new spaceplates with better performance. The team is looking forward to moving beyond computer models and designing physical experiments with manufactured spaceplates. “The next step will be the experimental demonstration of a spaceplate working in free space at optical frequencies,” Monticone said. “Using computational design methods, we will look to optimize spaceplates to work as close as possible to our fundamental limits. Perhaps we’ll be able to combine a flat lens and a spaceplate within a single device, realizing ultrathin, monolithic, planar optical systems for a variety of applications.” Additionally, spaceplates could be used to miniaturize projectors, telescopes, and even antennas that engage a wide range of frequencies. The research was published in Optica (www.doi.org/10.1364/OPTICA.455680).