An optic to replace space and its application towards ultra-thin imaging systems

The quest for better imaging has driven centuries of progress in lens design and combination. Nanotechnology has introduced metalenses—engineered surfaces—as a promising path towards miniaturization of imaging systems. However, a critical, often overlooked component, is the significant space between lenses, which is essential for image formation but considerably increases the overall size of the system. This paper addresses this issue by proposing and experimentally validating an optical element called a 'spaceplate'. The spaceplate aims to reduce this inter-lens space, enabling significantly thinner imaging systems and other applications. The concept is analogous to the field compression achieved in some metamaterials based on transformation optics, but specifically targets the minimization of imaging system size. Many optical devices implicitly use imaging or spatially manipulate light through propagation (e.g., spectrometers, solar concentrators, integrated optical components). The spaceplate promises to miniaturize these systems, offering significant advantages. The paper details the theory, design, and experimental demonstration of several spaceplate types, highlighting the potential for ultra-thin monolithic cameras and similar advancements across various optical technologies.

The paper reviews existing research on metasurfaces and their applications in flat optical components and miniaturized imaging systems. It highlights the lack of focus on minimizing the space between lenses, which is a major contributor to the size of imaging devices. Previous work on metamaterials and transformation optics implicitly compresses electromagnetic fields, but this hasn't been explicitly targeted for miniaturizing imaging systems. The paper acknowledges related work in nonlocal responses used for angular pass-filtering, image processing, and analog computing, but points out that these approaches typically only affect the magnitude of Fourier components, not the phase as the spaceplate is designed to do.

The paper uses Fourier optics to analyze spaceplate operation, describing how free propagation transforms plane-wave components of an incident field and highlighting the key role of phase shift. The ideal spaceplate's transfer function is defined, emphasizing its momentum-dependent phase profile and its difference from a lens's position-dependent response. The paper explores two main spaceplate designs: a multilayer thin-film stack and homogeneous media. The multilayer design employs an optimization-based method (genetic algorithm) to create a 25-layer structure using silica and silicon, aiming for a specific numerical aperture (NA). Full-wave simulations validate the performance of this design, showing polarization insensitivity and focus advancement. The homogeneous media approach considers uniaxial crystals (calcite) and low-index media (air) as spaceplates. Experiments using a calcite crystal and linseed oil demonstrate the spaceplate's ability to advance a beam's focus in a broadband visible imaging system. Measurements of beam displacement are compared with theoretical predictions to validate the operation of uniaxial spaceplates. The paper details experimental setups, including light sources, field relay systems (4f systems), and image acquisition methods, noting the use of monochromatic and color cameras for different experiments. The experimental setup for beam measurements includes laser sources, filters, waveplates, and polarization control elements, while the setup for imaging measurements involves a white-light source, lenses, a tank for the background medium, and a CCD camera. Precise specifications for lens focal lengths, beam waists, and spatial filtering elements are also provided. The design process for the multilayer spaceplate includes the use of a genetic algorithm and transfer matrix formalism for calculating the transmission amplitude.

The paper's key findings include the successful experimental demonstration of spaceplates, which effectively propagates light over a distance significantly larger than its physical thickness. A multilayer spaceplate design (25 layers of silica and silicon) achieved a compression factor (R) of approximately 5, meaning 10 μm of the spaceplate replaced 50 μm of vacuum propagation. Simulations showed polarization insensitivity and a broadband (30 nm) operation of this metamaterial. Experiments using a uniaxial calcite crystal as a spaceplate in linseed oil and glycerol demonstrated broadband operation and a high numerical aperture (NA = 0.85 in oil). The calcite spaceplate also showed an image advance of -3.4 mm in a visible light imaging system, without altering magnification. The results confirmed that a spaceplate's compression factor is not limited by the ratio of indices of its constituent materials and can exceed unity. The study also investigated the feasibility of homogeneous media (uniaxial and low-index) as spaceplates, providing insights into the operating mechanisms. The findings demonstrate that spaceplates can be broadband, achromatic, high NA, highly transmissive, and polarization-independent (though not necessarily all simultaneously in one design).

The successful experimental realization of spaceplates using both multilayer metamaterials and homogeneous uniaxial crystals validates the concept and theoretical predictions. The demonstrated properties—broadband operation, high NA, polarization insensitivity, and significant compression factors—highlight the potential for substantial miniaturization of imaging systems and other optical devices. The work's significance lies in addressing the often-overlooked space between lenses and offering a new direction in nonlocal metamaterial research. The ability to manipulate the phase of transverse Fourier components directly opens up opportunities for more compact and efficient optical systems. The achievement of a high compression factor (R ≈ 5) exceeding the ratio of refractive indices suggests there are no fundamental physical limitations.

This paper introduces the concept and experimental validation of the optical spaceplate, a device that significantly reduces the physical space required for light propagation. The study demonstrates successful fabrication and testing of spaceplates using both multilayer metamaterial and homogeneous uniaxial crystal approaches, showing promise for miniaturization of optical systems. Future work should focus on combining the various demonstrated properties (broadband operation, high NA, polarization insensitivity, high compression factor) into a single device with a sufficiently large compression factor for practical applications. This will likely involve further optimization of multilayer designs, exploring alternative homogeneous materials and investigating potential trade-offs between the spaceplate's different performance parameters.

The current designs demonstrated in the paper have limitations in terms of the compression factor and the simultaneous achievement of all desired properties (high compression factor, broadband operation, high NA, polarization insensitivity). The multilayer design showed a high compression factor but over a limited bandwidth and NA, while the uniaxial crystal demonstrated broadband operation and high NA but with a modest compression factor. Further research is necessary to optimize designs that can simultaneously achieve these goals. The surface quality of the calcite crystal used in the experiments also impacted results, indicating the need for improved fabrication techniques. The study focused mainly on linear optical responses, leaving nonlinear effects for future investigation.