Dielectric Nonlocal Metasurfaces for Fully Solid-State Ultrathin Optical Systems

Abstract

Most optical systems involve a combination of lenses separated by free-space regions where light acquires the required angle-dependent phase delay for a certain functionality. Very recently, flat-optics structures have been proposed to compress these large free-space volumes and miniaturize the overall optical system. However, these early designs can only replace freespace volumes of limited length, or operate in a very narrow angular range, or require a high-index background. These issues raise questions about the applicability of these devices in practical scenarios. Here, we first derive a fundamental trade-off between the length of compressed free space and the operating angular range, which explains some of the limitations of earlier designs, and we then propose a solution to relax this trade-off using nonlocal metasurface structures composed of suitably coupled resonant layers. This strategy, inspired by coupled-resonator-based band-pass microwave filters, allows replacing free-space volumes of arbitrary length over wide angular ranges, and with very high transmittance. Finally, we theoretically demonstrate, for the first time, the potential of combining local and nonlocal metasurfaces to realize compact, fully solid-state, planar structures for focusing, imaging, and magnification, in which the focal length of the lens (and, hence, its magnifying power) does not dictate the actual distance at which focusing is achieved. Our findings are expected to extend the reach of the field of metasurfaces and open new unexplored opportunities.

To What Extent Can Space Be Compressed? Bandwidth Limits of Spaceplates

“…[17], where the authors observed a distinct tradeoff between compression ratio and NA in monochromatic multi-layered spaceplates designed using inverse design techniques, confirming earlier theoretical predictions by Chen and Monticone in Ref. [18]. Within this context, in this paper we first elucidate the basic physical mechanisms at the origin of generic space-compression effects, and we then derive physical bounds and tradeoffs on the performance of spaceplates, with a particular focus on the issue of bandwidth, which has not yet been addressed in the literature despite its relevance for some of the main potential applications of spaceplates, particularly for imaging systems.…”

“…In addition, we note that, even at a single frequency, these resonator-based designs are constrained by other fundamental tradeoffs between the numerical aperture and the length of compressed space, as demonstrated in Ref. [18].…”

“…Instead, the device should be transversely homogeneous, not adding any focusing power, but simply implementing the transfer function of free space over a shorter distance. As mentioned in the Introduction, while this effect can be achieved with homogeneous media in a higher-index background, a promising way to realize space compression in free space is by using a suitable nonlocal structure, namely, a structure with an angle-dependent (i.e., transverse-momentum dependent) but position-independent response, which can be implemented, for instance, in the form of a multilayer thinfilm structure [15,[18][19][20] (this property is also known as spatial dispersion, the spatial analogue of the concept of frequency dispersion).…”

“…[16] or the spaceplates based on a single Fabry-Perot cavity in Refs. [18] and [23]. In this case, assuming that only one resonance is used (as done in [16], [23], and the first part of [18]), we can apply the delay-bandwidth product for a single-mode resonator, κ = 2 (valid for any individual single-mode resonator, reciprocal or nonreciprocal [24]) to calculate the maximum achievable fractional bandwidth from Eq.…”

“…Miller's limit, however, was derived for one-dimensional structures, while spaceplates are clearly not one-dimensional devices. We circumvent this problem by noting that most spaceplate designs reported in the literature are transversely invariant, such as the homogeneous or multilayered structures in [15,17,18]. In this case, the problem is formally equivalent to a one-dimensional one, as the transverse wavenumber k x is invariant in such a structure and, for transverse-electric (TE) or transversemagnetic (TM) incident plane waves, a one-dimensional effective wave equation can be derived that does not depend on the transverse direction (see, e.g., [26,27]).…”