![]() ![]() To maximize the focusing intensity ∣ E ~ ( ω 0 ) ∣ 2 at a single frequency ω 0, the desired phase profile within each zone should be hyperbolic, i.e., ∅ i ( ω 0, r ) = ω 0 c ( F ( ω 0 ) − F ( ω 0 ) 2 + r 2 ), where F(ω 0) is the focal length at frequency ω 0 in addition, the phase discontinuities at the zone boundaries should be zero, ∆∅ i(ω 0) = 0. The electric field E ~ ( ω ) at the focal spot is determined by the interference of electric field within each zone and the interference of the electric fields from N different zones ( Fig. (1)where N is the number of zones, and r i is the radial coordinate of each zone boundary ( r 0 = 0) t(ω, r) characterizes the amplitude of the scattered electric field by meta-atoms at a frequency of ω ∅ i(ω, r) is the designed phase profile within the ith zone and ∆∅ i(ω) is the phase discontinuity at the boundary between ( i − 1)th and ith zone. In recent works, researchers have demonstrated metalenses working in the visible based on new material platforms ( 10, 11) and by complementary metal-oxide semiconductor (CMOS)–compatible fabrication techniques ( 12) that are feasible for mass production of large-diameter metalenses. ![]() Fundamentally different from traditional lenses, metalenses are optically thin and light and can be designed to correct monochromatic and chromatic aberrations without requiring the complexity of refractive optics by controlling the phase, amplitude, and polarization state of the transmitted light with subwavelength resolution high numerical aperture (NA) is easy to achieve in metalenses ( 9). Metalenses, in particular, have been widely studied to address the challenges of conventional optics and show considerable potential for practical applications ( 6– 8). They are arrays of nanostructures assembled on a subwavelength scale, which can mold electromagnetic wavefronts at will. Metasurfaces have emerged as a platform for novel flat optics in recent years ( 4, 5). Achromatic lenses, such as camera objectives, have a large form factor due to their composite nature, which imposes a bottleneck to next-generation optical systems such as wearable display in terms of footprint, imaging quality, complexity, and cost. Fresnel lenses have a reshaped compact form yet suffer from poor imaging quality due to their strong chromatic aberrations ( 2) and other limitations. Moreover, multilens sets, such as doublets and triplets, are required to correct chromatic aberrations. Light focusing by a refractive lens relies on accumulation of propagation phase, and thus, lens thickness scales up as diameter ( 3). Unlike electronics that has rapidly evolved and shrunk in size following the Moore’s law over the past decades, the appearance and the underlying physics of today’s optical lenses are similar to the Nimrud lens dating back to ~3000 years ago ( 1, 2). They are being widely used in electronic devices such as smart phones. Optical lenses are in demand more than ever before. ![]()
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