Broadband Achromatic Metalens in the Midinfrared Range

Abstract

Midinfrared devices based on metalenses are of great utility for numerous applications, including free-space communication, imaging, and molecule sensing. However, because of the intrinsic dispersion of their building bricks, metalenses significantly suffer from large chromatic aberration. In this paper, we propose an achromatic metalens that can operate over a broad band of wavelengths in the infrared region from 3.7 to 4.5 μm for circularly polarized incidences. The Pancharatnam-Berry phase and the propagation phase are used to control the wavefront of light and eliminate the chromatic aberration, respectively. As a proof-of-principle demonstration, we numerically study two devices: an achromatic focusing lens and a beam deflector. The simulation results demonstrate the devices have a focusing efficiency of about 20.7% in the infrared region from 3.7 to 4.5 μm. Our proposed approach may pave the way toward practical application of midinfrared devices.

Full text

PHYSICAL REVIEW APPLIED 11, 024066 (2019)
Broadband Achromatic Metalens in the Midinfrared Range
Hongping Zhou, Lei Chen, Fei Shen, Kai Guo, and Zhongyi Guo*
School of Computer and Information, Hefei University of Technology, Hefei, 230009, China
(Received 24 August 2018; revised manuscript received 2 December 2018; published 26 February 2019)
Midinfrared devices based on metalenses are of great utility for numerous applications, including free-
space communication, imaging, and molecule sensing. However, because of the intrinsic dispersion of
their building bricks, metalenses significantly suffer from large chromatic aberration. In this paper, we
propose an achromatic metalens that can operate over a broad band of wavelengths in the infrared region
from 3.7 to 4.5 μm for circularly polarized incidences. The Pancharatnam-Berry phase and the propagation
phase are used to control the wavefront of light and eliminate the chromatic aberration, respectively. As
a proof-of-principle demonstration, we numerically study two devices: an achromatic focusing lens and a
beam deflector. The simulation results demonstrate the devices have a focusing efficiency of about 20.7%
in the infrared region from 3.7 to 4.5 μm. Our proposed approach may pave the way toward practical
application of midinfrared devices.
DOI: 10.1103/PhysRevApplied.11.024066
I. INTRODUCTION
The unique ability of metasurfaces lies in their capa-
bility to control the amplitude, phase, and polarization
of incident light via artificially varying nanostructures. A
variety of functional optical devices based on metasur-
faces have been realized covering a wide range of the
spectrum from the visible region [1–3], the near-infrared
region [4–6], and the midinfrared region [7–9] to the
terahertz region [10–12]. In particular, the midinfrared
region is of great interest for practical applications, such
as free-space communication, imaging, and molecule sens-
ing. Recently, there various midinfrared metasurface-based
devices have been repoted, including metalenses [13],
polarization controllers [14], modulators [15,16], perfect
absorbers [17–20], vortex-beam generators [21], thermal
emitters [22], nonlinear converters [23], and infrared sen-
sors [24]. Among them, the devices based on metallic
nanostructures are restricted to the reflective scheme due
to the large intrinsic Ohmic loss in the midinfrared region.
Therefore, dielectric metasurfaces are introduced to over-
come this shortcoming [25–27], and transmissive dielectric
metaoptics provide several well-established advantages
in optical system design, including increased alignment
tolerance and simplified on-axis configuration [25].
Almost all imaging systems suffer from chromatic aber-
rations, which means that light of different incident wave-
lengths generates focal spots at different spatial locations
[28]. For metasurface devices, their chromatic aberra-
tion mainly stems from the diffractive elements, whose
chromatic aberration comes mainly from the geometric
*guozhongyi@hfut.edu.cn
arrangement of the device [29,30]. Such chromatic aber-
ration is a serious problem in imaging system, causing
degradation of imaging quality. Conventionally, chromatic
aberration is eliminated by integration of several differ-
ent materials with opposite dependence of the refrac-
tive index on wavelength. In contrast, metamaterials and
metasurfaces provide a new paradigm for elimination of
chromatic aberration by manipulating the phase, ampli-
tude, and polarization of incident light [28,31–33]. So far,
several studies have suggested the achievement of achro-
matic metalenses, ranging from the visible region to the
near-infrared region [28,32–38]. Recently, the achromatic
effect was also studied in the midinfrared region, such
as reducing chromatic aberration by 55% via compensa-
tion between structure and material dispersion [39], where
the peak transmissivity was 65% for 4.7–4.9 μm, and a
10 ×10 metalens array was used to achieve achromatic
behavior at 3.2–4.1 μm with NA of 0.35 [40]. In the
simulation [40], the average focusing efficiency was 70%
over a wavelength range from 3 to 5 μm and the max-
imum focusing efficiency was 80%. However, the depth
of focus of the metalens is too great compared with the
wavelength. Nevertheless, it is still a great challenge to
design an achromatic metalens that is able to eliminate the
chromatic effect over a broad band of wavelengths in the
midinfrared region.
In this paper, we propose a broadband achromatic met-
alens (BAML) in a transmission scheme with NA of 0.82
that eliminates the chromatic aberration over a continuous
range of wavelengths from 3.7 to 4.5 μm. Our designs
are based on silicon nanobricks, which stand on a CaF2
(n=1.4) substrate. We vary the length and width of the Si
nanobricks to introduce the required phase compensation
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HONGPING ZHOU et al. PHYS. REV. APPLIED 11, 024066 (2019)
between λmin and λmax. In theory, this bandwidth from
λmin to λmax can be engineered by design of the geometric
parameters, and here we choose a bandwidth with a range
of 3.7–4.5 μm. As a proof-of-principle demonstration, we
numerically study two devices: an achromatic focusing
lens and a beam deflector. The simulation results demon-
strate that the devices have an efficiency of about 20.7% at
4.5 μm.
II. THEORY, RESULTS, AND DISCUSSION
We describe the design principles for a BAML, which is
schematically shown in Fig. 1(a), focusing different inci-
dent wavelengths to the same spot. A left-handed circularly
polarized (LCP) beam is incident from the bottom of the
substrate. The arrows with different colors indicate various
incident wavelengths. Passing through the metasurfaces,
the light is transformed to a right-handed circularly polar-
ized (RCP) beam and focused at the same spot. In general,
the required phase profile to achieve a focusing effect for
collimated incident light is
ϕ(R,λ)=−
2π
λR2+f2−f,(1)
where R=x2
0+y2
0is the distance from an arbitrary posi-
tion (x0,y0) on the metalens to the center (assuming the
metalens is located in the plane of z=0), λis the incident
wavelength, and fis the focal length. However, because of
the chromatic dispersion of metasurface lenses stemming
mainly from the phase-wrapping discontinuities [29], the
metalens is designed to focus light of λmax [Fig. 1(b)], and
does not focus light of wavelength λ(λmin <λ<λ
max)to
the same focal length. Therefore, we need to modify the
phase profile ϕ(R,λ)to focus light with different wave-
lengths at the same position. To show the concept, the
required phase profile for a BAML is schematically plotted
in Fig. 1(b), where a phase difference ϕ (R,λ)is needed
for a wide range of wavelengths. λmin and λmax are the
minimum and maximum wavelengths in the band of inter-
est, respectively. Thus, the phase profile in Eq. (1) can be
rewritten as follows: [38]:
ϕlens (R,λ)=ϕ(R,λmax)+ϕ (R,λ),(2)
with a compensation phase
ϕ (R,λ)=−2πR2+f2−f1
λ−1
λmax .
(3)
Equation (2) indicates that to achieve achromatic focus-
ing within a given bandwidth of λ =λmax −λmin, the
required phase profile provided by an optical element can
be divided into two components. The first part ϕ(R,λmax)
(a) (b)
FIG. 1. (a) An achromatic metalens. The focal length is
unchanged as the incident wavelength is switched, resulting in
a single spot at the designed focal point for a BAML with opti-
mized phase compensation. (b) Phase profile for a BAML at a
bandwidth of λ =λmax −λmin.
is regarded as a basic phase profile and is related to λmax.
The second part ϕ (R,λ)is a function of the working
wavelength and is linearly related to 1/λ, which is con-
sidered as the phase difference between λand λmax.Itis
important to keep in mind that ϕ (R,λ)is the key to
achieve achromatic function.
To obtain the corresponding phase profile of ϕLens (R,λ),
each unit element of the metalens should be artificially
selected. The first term (basic phase) in Eq. (2) can be
obtained by our adopting the Pancharatnam-Berry phase
(PB phase). Hereafter, we introduce the design of the basic
phase distribution ϕ(R,λmax). As shown in Fig. 1(a), when
a LCP beam passes through the nanobrick, the transmitted
light can be expressed by the Jones vector [33,41]:
t=tL+tS
21
i+tL−tS
2ei2α1
−i,(4)
where tLand tSare complex transmission coefficients when
the incident light is polarized along the long and short
axes of the nanobrick, and αis the rotation angle. The first
and second terms in Eq. (4) represent the copolarized and
cross-polarized transmission, respectively. An additional
PB phase of 2αis ϕ(R,λmax)that is independent of the
frequency and equal to twice the rotation angle. To acquire
the phase profile of ϕ(R,λmax), we use the geometric phase
(PB phase) as the phase modulation in each metalens unit
element. This means that we should rotate the unit ele-
ments in metasurfaces under the condition of normal LCP
incidence [42].
In addition, we use the propagation phase to achieve
the second term; that is, compensation-phase profile
ϕ (R,λ). In general, the propagation phase allows inde-
pendent and arbitrary manipulation of phase profiles for
each of two orthogonal, linear polarizations, mainly by
change of the geometric parameters of the nanostructure
to obtain the abrupt phase [43]. Here it is used to compen-
sate for the required phase difference due to the dispersion
of materials, as shown in Fig. 1(b). This design princi-
ple of combining the propagation phase and the PB phase
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BROADBAND ACHROMATIC METALENS... PHYS. REV. APPLIED 11, 024066 (2019)
provides an opportunity to eliminate the chromatic aberra-
tion, achieving a BAML. Ideally, this principle is universal
and the working bandwidth can be engineered by design
of the composite materials and geometric parameters. In
practice, the bandwidth will be restricted to a finite value
due to limited computational ability and manufacturing
difficulties.
Figure 2(a) shows the structural configuration and
defines the geometric parameters. To operate efficiently
in the midinfrared region, two aspects should be consid-
ered in the design of a BAML. First, a high contrast in
the refractive index between the nanoscatters and their sur-
roundings is essential for realization of enhanced manip-
ulation of the incidence. To achieve a BAML, we use
(a)
(c)
(f) (g) (h)
(d) (e)
(b)
FIG. 2. A metalens element. (a) The element consists of one Si nanobrick of differing dimensions but equal height h=4μm evenly
spaced by a distance p=1.8 μm. The length L, width w, and rotation angle αare shown. The nanobrick is rotated with respect to
the center of the square (1.8 ×1.8 μm2). (b) The effective refractive index neff simulated by finite-element simulations of different
dimensions for a Si nanobrick. LCP-to-RCP conversion efficiency (c) and phase profile (d) of two examples used in a metalens with
L=1.2 μmandw=0.3 μm (blue curve) and L=1.3 μmandw=0.7 μm (green curve). (e) Phase profile as a function of frequency
for different rotation angles of the nanobrick with L=1.2 μmandw=0.3 μm. The slopes of the three lines are the same; that is, the
phase difference remains constant when the rotation angle changes within a given bandwidth (3.7–4.5 μm). Simulated magnetic field
distribution in the y-zplane (f) and in corresponding rotated cross sections (g) at the numbers I, II, III, IV, V, and VI in (c) and (e),
respectively. (u,v) represents the coordinate axis in corresponding rotated cross sections. (h) Simulated magnetic field distribution in
the y-zplane at efficiency peaks (green curve) between solid black lines in (c).
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HONGPING ZHOU et al. PHYS. REV. APPLIED 11, 024066 (2019)
silicon nanobricks since they have a high refractive index
(n=3.429) and negligible loss in the midinfrared region.
Moreover, because of the high refractive index compared
with the surrounding material, electromagnetic waves will
be highly concentrated in the Si nanobricks and the cou-
pling between neighboring nanobricks can be negligible.
Therefore, we may obtain a phase difference of πbetween
the transmission with polarization along the long and short
axes of the nanobricks under the optimal conversion condi-
tion [35]. Second, materials with a low refractive index and
low mid-IR absorption should be used as the substrate [7]
to avoid affecting the metasurface structure. Here we chose
calcium fluoride (CaF2) for its low refractive index (n=
1.4) and low absorption. The Si nanobrick with height
of 4 μm stands on a CaF2substrate with a fixed thick-
ness of 3 μm[44]. The length and width of the nanobrick
are optimized to achieve various degrees of phase com-
pensation between λmax and λmin. The devices based on
the Si-on-CaF2wafer can be experimentally fabricated by
photolithography followed by reactive-ion etching [45].
We briefly describe the working principle of our pro-
posed BAML. To eliminate chromatic aberration, we
choose 14 types of element structures (summarized in
Table I) satisfying the condition that the propagation phase
is a linear function of 1/λ. To demonstrate this, we calcu-
late the optical property of elements 3 and 13 for wave-
lengths from 3.2 to 5 μm by using the finite-element
method. Periodic boundary conditions are used in the xand
ydirections to save calculation memory and time. Perfectly
matched layers are applied on boundaries in the zdirection.
Figure 2(c) presents the LCP-to-RCP conversion efficiency
for element 3 (blue curve) and element 13 (green curve),
presenting multiple resonances that are the origin of the
compensation phase. Figure 2(d) shows the linear rela-
tionship between phase and frequency (1/λ) in the design
wavelength range (the gray region). In addition, a required
phase-compensation value can be calculated by ϕ (R,λ)
TABLE I. Types of unit elements.
Element no. Phase compensation (deg) L(μm) w(μm)
0 340 1.00 0.20
1 350 1.20 0.20
2 370 1.00 0.30
3 390 1.20 0.30
4 410 1.00 0.40
5 440 0.90 0.50
6 470 1.50 0.60
7 510 1.70 0.60
8 540 0.80 0.70
9 550 0.90 0.70
10 570 1.00 0.70
11 600 1.12 0.70
12 630 1.26 0.70
13 660 1.30 0.70
between λmax and λmin. If one needs to compensate a
phase difference that equals the phase difference from 3.7
to 4.5 μm in Fig. 2(d), then either element 3 or element
13 could be used. The phase compensations achieved by
the two nanobricks are 390◦(blue line) and 660◦(green
line). Figure 2(e) shows the dependence of the propagation
phase on the PB phase (i.e., rotation angle α) for the former
nanobrick for different incident wavelengths. The slopes
are linear and independent of the rotation angle within a
given bandwidth. This means that the phase compensation
implemented by the nanobrick is unchanged for different
rotation angles. This property is another key to design a
BAML that can operate over a large bandwidth [33].
For analysis, we calculate the near-field distribution,
as shown in Figs. 2(f) and 2(g). The wavelengths cho-
sen correspond to I–VI in Figs. 2(c) and 2(e), indicating
that waveguidelike cavity resonances are supported in each
Si nanobrick [37]. From Fig. 2(g), it can be seen that
the resonance mode is almost invariable, which explains
the physical origin of the unchanged phase compensa-
tion for different rotation angles. It is worth noting that
we choose relatively high nanobricks with a height of
h=4μm (the working wavelength is 3.7–4.5 μm). There-
fore, multiple resonances could have been excited inside
the Si nanobricks to obtain a large phase compensation.
A higher height is required to satisfy larger phase com-
pensation, which causes great difficulties for experimental
manufacturing. For verification, we calculate the near-field
distribution of the Si nanobrick with L=1.3 μmandw=
0.7 μm, as shown in Fig. 2(h), where the wavelengths cho-
sen correspond to the efficiency peaks (green curve) in Fig.
2(c). From these results, compared with Figs. 2(f) and 2(g),
we can see more clearly the origin of the large compensa-
tion phase comes from the multiple resonances excited in
the nanobrick.
The propagation phase at a given coordinate Ris
φ(R,λ) =2π/λneffh, where neff and hrepresent the effec-
tive refractive index and the height of the nanobrick,
respectively. Thus, the underlying physical mechanism to
obtain a large phase compensation is manipulation of neff,
and neff can be expressed as neff =kvλ/2π(kvis the axial
propagation constant in Si) [46], which is closely related
to the length and width of the nanobricks [46,47]. Now we
describe the manipulation of neff quantitatively by repro-
ducing the propagation constant in a Si nanobrick. In our
design, the incident light is LCP light that can be decom-
posed into two orthogonal waveguide modes. To demon-
strate this, Fig. 2(b) quantitatively shows that neff of the
fundamental resonance mode increases as the dimensions
of the nanobrick increase, which agrees well with waveg-
uide theory [46]. The geometry size ranges are consistent
with those used in our design and the working wavelength
is 4.5 μm. Owing to the geometric symmetry, we investi-
gate only the resonance mode where the main electric field
component is parallel to the xaxis. From the discussion
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above, it is demonstrated that our approach has significant
ability to eliminate chromatic aberration over a broadband
range in the midinfrared region.
III. ACHROMATIC FOCUSING
As a proof of concept, a broadband achromatic con-
verging metalens in the midinfrared region is designed
and demonstrated. The designed BAML has a diame-
ter of 77.4 μm with NA of 0.82. Figure 3(a) shows the
simulated light-intensity profiles of the BAML in the x-
zplane for incident wavelengths of 3.7, 3.9, 4.1, 4.3,
and 4.5 μm. As predicted theoretically, the focal length
remains almost unchanged at f=26 μm (the dashed
white line) within the bandwidth of interest, indicating suc-
cess of the designed BAML. The inset curves represent
the normalized intensity profile (divided by the maxi-
mum value in each image) along the white dashed lines
at each incident wavelength. Because of the elimination of
chromatic aberration, the BAML maintains its focal-spot
profile for the entire spectrum from 3.7 to 4.5 μm. For
comparison, the chromatic metalens has the same size as
the achromatic metalens. Figure 3(b) shows the simulated
light-intensity profiles of the common diffractive metalens
in the x-zplane for incident wavelengths of 3.7, 3.9, 4.1,
4.3, and 4.5 μm. It is clear that the focus moves toward
the common metalens with increasing wavelength. In addi-
tion, without the elimination of chromatic aberration, the
normalized intensity profile along the dashed white line
exhibits significant defocusing property. The shorter wave-
lengths in Fig. 3(a) show darker focal spots, since the
transmission efficiency of the unit elements used is lower
at short wavelengths than at long wavelengths.
Figure 3(c) shows the dependence of the focal length
on the incident wavelength for the achromatic case (green
circles) and the chromatic case (blue circles). As pre-
dicted, all focal lengths for the achromatic case remain
almost unchanged when the incident wavelength varies
over the bandwidth from 3.7 to 4.5 μm. In contrast to
the BAML, the focal length of the chromatic metalens
designed by use of the PB phase undoubtedly depends on
the incident wavelength. Within the bandwidth of interest,
with increasing wavelength, obvious chromatic aberration
can be observed as evidenced by focal-length reduction.
These results clearly demonstrate again that the BAML
can eliminate the chromatic aberration effect very well. In
addition, the chromatic aberration of a conventional met-
alens is identical to that of a diffractive lens, which can be
described as [48]
f=fλ
λ,(5)
where λand fare the nominal (central) wavelength and
focal length of the imaging system, respectively, λ is
the wavelength band over which the system operates, and
fis the corresponding change in focal length. Substitut-
ing the corresponding parameters of the designed BAML
(a)
(b)
(c)
(d)
FIG. 3. Simulation results for the BAML and the chromatic metalens. Simulated intensity profiles of the focal spot in the x-zplane
of (a) the designed BAML and (b) the common diffractive metalens at incident wavelengths (3.7, 3.9, 4.1, 4.3, and 4.5 μm). The
inset curves show the normalized intensity profile along the dashed white line. The metalenses are designed at a basic wavelength
λ=4.5 μm with focal length f=27 μm. (c) Focal lengths of the designed BAML and the chromatic metalens as a function of the
incident wavelength. The dashed black line is for f=27 μm. (d) The dependences of the FWHM and focusing efficiency of the
designed BAML on the incident wavelength.
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HONGPING ZHOU et al. PHYS. REV. APPLIED 11, 024066 (2019)
into Eq. (5), we can obtain f=4.8 μm. In contrast, the
simulation results for the BAML show give f≤0.5 μm,
which further demonstrates the BAML can eliminate the
chromatic aberration effect very well.
To further investigate the focusing performance of the
designed BAML [as plotted in Fig. 3(d)], the full width
at half maximum (FWHM) and the focusing efficiency are
calculated at wavelengths of 3.7, 3.9, 4.1, 4.3, and 4.5 μm.
The FWHM is calculated by our fitting the simulated light
intensity along the focal line with a Gaussian function [38].
All calculated FWHM are in the range from 0.9λ–1.2λ.A
maximum focusing efficiency (ratio of energy at the focus
to incident energy) of 20.7% is achieved at λ=4.5 μm,
while the efficiency decreases as the wavelength decreases.
This results from the low polarization-conversion effi-
ciency of the unit elements at short wavelength. The focus-
ing efficiency could be further increased by optimization of
the structural configuration [38].
IV. ACHROMATIC DEFLECTION
The second example we present here to demonstrate
achromatic wavefront control using our proposed struc-
tures is achromatic deflection over a broadband width in
the mid-IR region. The designed achromatic deflection
metasurface has the ability to deflect incident light with
different wavelengths over a continuous broadband wave-
length range at a fixed angle. According to reported work
[35] and the results above, we artificially design an array
to obtain the required phase profile:
ϕ(x,λ)=2π
λxsin θ,(6)
where xis the spatial coordinate, λis the wavelength,
and θis the deflected angle of the transmitted beam (i.e.,
the RCP-light-beam deflection under LCP incidence). To
achieve achromatic deflection, the designed unit elements
should satisfy the phase profile for achromatic deflection
metasurfaces with a bandwidth of λ =λmax −λmin,as
plotted in Fig. 4(a). Similarly, the phase profile ϕ(x,λ) can
be rewritten as follows:
ϕ(x,λ)=ϕ(x,λmax)+ϕ (x,λ)(7)
with
ϕ (x,λ)=2πxsin θ1
λ−1
λmax .(8)
(a)
(c) (d)
(b)
3.7 µm3.9 µm4.1 µm4.3 µm4.5 µm
FIG. 4. Broadband achromatic deflection metasurfaces. (a) Phase profile for a broadband achromatic deflection metasurface at arbi-
trary incident wavelength bandwidth between λmin and λmax.ϕ(x,λ) expressing the phase difference within the given bandwidth. (b)
The deflection angles of the designed achromatic deflector as a function of the incident wavelength. (c) The electric field distribution
of the deflected RCP light under normal incidence for different wavelengths. The top panel shows the case indicated by the red circles
in (b) and the bottom panel shows the case indicated by the black squares in (b). (d) Simulated deflection angle for different wavelenths
of incident light from 3.7 to 4.5 μm.
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To realize the phase requirement for deflection of light with
an unchanged angle within the given wavelength range,
the significant phase difference ϕ (x,λ)needs to be taken
into consideration in the design to reduce the chromatic
effect, combining the PB phase to achieve the required
function.
For verification, we construct two achromatic beam
deflectors under normal incidence with deflection angles
of −18.2◦and −28◦by using 18 and 19 unit elements,
respectively. Figure 4(b) shows the deflection angles of
the designed achromatic deflector as a function of the inci-
dent wavelength. As shown, all the RCP light is deflected
at almost unchanged angles when the incident wavelength
is varied from 3.7 to 4.5 μm, demonstrating a broadband
achromatic performance in beam deflection. In addition,
we also simulate a beam deflector without elimination of
the chromatic effect, presenting significant dependence of
the deflection angle on the incident wavelength, denoted
by the black squares in Fig. 4(b).
Figure 4(c) displays the electric field distributions of
the deflected RCP light under normal incidence with dif-
ferent wavelengths. The top and bottom panels show the
angle offsets of the red circles and black squares in Fig.
4(b), respectively. For the achromatic case, the wavefront
of the transmitted beams is deflected to almost unchanged
−18.2◦for incident wavelengths of 3.7, 3.9, 4.1, 4.3, and
4.5 μm, which agrees greatly with the theoretical value.
In contrast, for the chromatic case, the wavefront of the
transmitted beams is deflected to different oblique angles
for different incident wavelengths, showing smaller angles
for shorter wavelengths. Figure 4(d) shows the transmitted
field intensity of RCP light as a function of the deflection
angle for the achromatic deflector in the top panel and the
chromatic deflector in the bottom panel, further showing
the high performance of the designed achromatic deflector.
Overall, the comparison between our achromatic deflec-
tor and the common one demonstrates the validity of our
proposed method in designing achromatic devices in the
mid-IR range. Compared with other mid-IR designs, our
BAML has the advantages of light weight, small size, easy
integration, and continuous broadband wavelength range.
Wan g et al. [39] designed a grating surface microstructure
for chromatic aberration correction in two infrared bands
of 4.7–4.9 μm and 10.5–10.7 μm. Their proposed structure
is simple but with relatively narrow bandwidth compared
with our proposed BAML with a broadband wavelength
range of 3.7–4.5 μm. Zhang et al. [40] fabricated a metal-
ens to focus light into a substrate with increased efficiency
(average value of 70%) as compared with focusing light
in air in normal cases. The increased efficiency resulted
from the enhanced numerical aperture of the metalens
in Ref. [40] in comparison with that of free space as in
our designs. The results for the chromatic and achromatic
cases were compared. Nevertheless, the achromatic focus-
ing results were not discussed well as in this paper. In
addition, we further investigate achromatic deflection in
which the wavefront of the transmitted beam is deflected
in an unchanged direction with angles of −18.2◦and −28◦
over the broadband wavelength range of 3.7–4.5 μm. To
this extent, we believe that the BAML can be useful in the
development of integrated mid-IR devices.
V. CONCLUSION
In summary, we demonstrate an achromatic metalens in
transmission over a continuous and broadband wavelength
range in the mid-IR region by simultaneously controlling
the geometric phase and phase compensation. To demon-
strate this, we chose the wavelength range from 3.7 to
4.5 μm, which is limited by computing ability and can
be extended further by engineering of the metasurface
structure. Our metalens consists of only a single layer of
nanobricks on the substrate, whose thickness is on the
order of the wavelength, and does not involve spatial mul-
tiplexing or cascading. The design has an efficiency of
about 20.7% at 4.5 μm, focusing light in the same focal
plane in the wavelength region of interest. Through varia-
tion of the geometry of Si-based unit elements, the meta-
surfaces can provide corresponding phase compensation
for broadband achromatic devices such as a converging
metalens and a metasurface deflector. This represents a
significant achievement for expanding the applications of
mid-IR metalenses, which have been limited by intrinsic
dispersion of the material and the geometric arrangement
of the devices.
ACKNOWLEDGMENTS
This research was funded by the National Natural Sci-
ence Foundation of China (Grants No. 61775050 and
No. 11505043), the Natural Science Foundation of Anhui
Province, China (Grants No. 1808085MF188 and No.
1808085QA21), and the Fundamental Research Funds for
the Central Universities (Grants No. JD2017JGPY0005,
No. JZ2018HGBZ0309, and No. JZ2018HGTB0240).
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