in a quasi-adiabatic change in geometrical size of
MBBs across the interface. Plasmonic MBBs can
easily fulfill this criterion because they can be
closely packed, owing to the deep-subwavelength
confinement of plasmonic modes. High-index
dielectrics can also satisfy these conditions by
enhancing light confinement and reducing near-field coupling, thus allowing a smaller U.
Due to their large refractive index and mature
fabrication technology, silicon-based metasurfa-
ces are a promising platform for realizing metal-
enses, particularly in the NIR region (51, 56–60),
the transparency window of silicon. Reflective di-
electric planar lenses were theoretically (56) and
experimentally (57) reported using one-dimensional
amorphous silicon (aSi) gratings for which the
period and the FF of the grating elements were
gradually altered from the center of the lens to-
ward the edge (Fig. 2A). Because of the asym-
metric cross section of the grating elements, the
performance of these lenses depends on polar-
ization. A transmissive lens was also demonstra-
ted in aSi using the PB phase (Fig. 2B). The lens is
designed at l = 550 nm and has NA = 0.43 (51). In
the visible region, especially at shorter wave-
lengths, the optical loss of silicon substantially
degrades the lenses’ efficiency. This can be par-
tially overcome by changing the material to a
dielectric with transparency in the visible region;
examples include silicon nitride (61) and tita-
nium dioxide (21). However, the refractive index
of these materials (n 2) is lower than that of
silicon (n 3.5). In general, to achieve full 0-to-
2p phase coverage using these materials, one
needs to compensate for the smaller index with
higher DW height (Eq. 2). As a result, high-AR
structures are required, which poses major challenges for conventional fabrication techniques
such as dry-etching (21, 61) and liftoff (62). The
latter substantially limits the maximum attainable height of DWs, and the former does not provide adequate control over the geometry of DWs.
One prevailing problem is the angled sidewall,
which introduces an error in the resultant phase
(63). A recently developed process based on atomic
layer deposition (ALD) of titanium dioxide (64)
has successfully circumvented these issues. DWs
are defined only by the patterned resist in this
liftoff-like process, which can then be extended
to a wide range of dielectrics supported by the
ALD technique. With the use of this approach,
large NA = 0.8 lenses with efficiency as high 86%
were demonstrated (52, 65) across the visible
spectrum (Fig. 2C).
To realize polarization-independent lenses,
one can utilize the propagation phase using DWs
with circular or fourfold-symmetric cross sections.
By using arrays of circular silicon posts, Vo et al.
(66) demonstrated polarization-independent transmissive lenses with 70% efficiency. The lens focuses
the incident light (l = 850 nm) into a spot of ~10l
size. The lens’s BB was a hexagonal array of posts
(Fig. 3A). This BB configuration reduces the maximum achievable spatial phase gradient due to the
increased U and thus limits the maximum obtain-able NA. Later, Arbabi et al. (58) showed that one
silicon post can serve as an efficient BB (Fig. 3B).
This BB provides full phase coverage with sub-wavelength spatial resolution while maintaining
high transmission, thus enabling highly efficient
metalenses with large NAs. Lenses with efficiencies higher than 42% and focal spots as small as
0.57l at l = 1550 nm were reported. Owing to
their high refractive indices, these posts are weakly
coupled to each other, which prevents deviation
from the designed phase due to near-field coupling.
High-performance metalenses in the visible spectrum were demonstrated by Khorasaninejad et al.
(63). These polarization-independent lenses were
fabricated by using ALD-prepared titanium dioxide circular posts and have NAs as high as 0.85.
At this NA, metalenses designed at wavelengths
of 532 and 660 nm provide diffraction-limited
focusing with efficiency larger than 60% (Fig. 3C).
For the metalenses designed at a shorter wavelength (405 nm), the efficiency drops to 33% due
to stringent fabrication tolerances because the
posts’ radii scale proportionally with wavelength.
In addition, when the NA was reduced to 0.6,
focusing efficiency as high as 90% was achieved
at a design wavelength of 660 nm.
Imaging by metalenses
Theoretically, the imaging resolution of a lens
is set by the diffraction limit, but in practice,
various aberrations such as spherical and coma
reduce it. Spherical aberration is a common issue
in refractive lenses (particularly high-NA objectives) and is typically corrected by cascading several lenses, which not only increases the size of
imaging systems but also adds cost. Metalenses
can be free of spherical aberrations because their
phases can be tailored at the designer’s will.
Figure 4A shows images formed by a high-NA
(0.81) flat lens designed at l = 532 nm. This lens
resolves micrometer-size features over a large area
of 250 mm × 250 mm. The same lens also resolves
the details of an object with subwavelength resolution; however, its field of view (FOV) is very
limited. The latter is a manifestation of other
remaining monochromatic aberrations, mainly
coma. These aberrations can be reduced by adding a correcting layer (67, 68) to a flat lens
Khorasaninejad and Capasso, Science 358, eaam8100 (2017) 1 December 2017 5 of 8
Fig. 4. Imaging with monochromatic all-dielectric metalenses. (A) Images formed by a metalens
of the 1951 U.S. Air Force resolution test chart (left) and of a customized target object (right) with
a minimum gap size of ~800 nm (right top) and ~450 nm (right bottom) (52). Illumination was
provided by a tunable laser with a 530-nm center wavelength and a bandwidth of 5 nm. (B) (Right)
Image taken with a doublet lens made of silicon posts operating at a wavelength of 850 nm. Scale
bar, 100 mm. (Left) Zoomed-in views of the images at the regions indicated by the rectangles.
Scale bars, 10 mm. The illumination source was an LED paired with a 10-nm bandpass filter centered
at 850 nm. [Reproduced from (67)] (C) Two images of a beetle, Chrysina gloriosa, formed by
a chiral lens in the same field of view of a camera (73). This chiral lens simultaneously forms two
spatially separated images (with opposite handedness) of the beetle, revealing its natural circular
dichroism. The chiral lens has diameter D = 3 mm and a focal length of ~3 cm at its 530-nm
design wavelength. Green LEDs paired with a 10-nm bandpass filter centered at 532 nm were used
as illumination sources. (D) (Top) Images of metallic stripes formed by confocal imaging with an
oil immersion lens used for illumination (69). (Bottom) Mean peak-to-peak values of 400 nm (left)
and 593 nm (right) with less than 10% SD. This metalens is made of titanium dioxide nanofins and
has NA = 1.1 at its 532-nm design wavelength.