Lens with focusing metasurface and low chromatic aberration
View Patent ↗The invention relates to a metasurface lens using a planar array of elementary resonators, each elementary resonator being the shape of a cross the arms of which are of unequal length. The phase shift applied by an elementary resonator is dependent on its orientation in the plane of the lens, the orientation of the various elementary resonators being determined depending on the shape of the desired wavefront. Such a lens has a substantially uniform transmission-coefficient distribution and a low chromatic aberration. Furthermore, it has a very good spectral selectivity.
1. A lens with a metasurface intended to receive an incident wave of a given wavelength, the lens comprising:
at least one first array of resonators, said resonators of the first array being crosses having identical shapes, said first array being located in a plane of the lens, each cross comprising at least one first arm, called long arm, extending along a first axis and a second arm, called short arm, having a length strictly less than the long arm and extending along a second axis, substantially orthogonal to the first axis, each cross phase shifting the incident wave by introducing a specific phase shift (φ i ) depending on the orientation of the cross (ψ i ) with respect to a reference direction in the plane of the lens, the crosses of the first array not having one single orientation.
2. The lens with a metasurface according to claim 1 , wherein the length of the long arm is greater than the length of the short arm by 5% to 10%.
3. The lens with a metasurface according to claim 1 , wherein the lengths of the long and short arm are chosen in such a way that the difference between the resonance frequency of the long arm and the resonance frequency of the short arm is less than the width at half height of the transmission spectral response of each of said arms.
4. The lens with a metasurface according to claim 1 , wherein the crosses are made by apertures in a metal layer, the metal layer being deposited on a first dielectric layer transparent to said given wavelength.
5. The lens with a metasurface according to claim 4 , wherein the apertures are filled by a material having an optical index greater than the optical index of the first dielectric layer.
6. The lens with a metasurface according to claim 4 , wherein the first dielectric layer is itself deposited on a semiconductor substrate transparent to said given wavelength, the optical index of the substrate being greater than the index of the first dielectric layer.
7. The lens with a metasurface according to claim 4 , wherein a second dielectric layer is deposited on the metal layer, said second dielectric layer being made from the same material as the first dielectric layer and having a thickness of
λ
2
n
where λ is said given wavelength and n is the index of the first and second dielectric layer.
8. The lens with a metasurface according to claim 4 , wherein the lens with a metasurface is a convergent lens, having a focal distance f, and the orientation of a cross, the centre of which is located at a point P i having the coordinates (x i ,y i ) in a reference frame (O, x, y) in the plane of the lens, is chosen in such a way as to generate a specific phase shift
φ
i
=
2
π
n
o
λ
(
f
-
x
i
2
+
y
i
2
+
f
2
)
with
φ
i
<
π
2
where λ is said given wavelength and n o is the index of the output medium of the lens.
9. The lens with a metasurface according to claim 7 , wherein the lens with a metasurface is a convergent lens, having a focal distance f, and the orientation of a cross, the centre of which is located at a point P i having the coordinates (x i ,y i ) in a reference frame (O, x, y) in the plane of the lens, is chosen in such a way as to generate a specific phase shift
φ
i
=
ϕ
i
mod
π
2
with
ϕ
i
=
2
π
n
o
λ
(
f
-
x
i
2
+
y
i
2
+
f
2
)
,
where n o is the index of the output medium of the lens, a third dielectric layer having a thickness of
λ
2
n
being deposited only above the crosses for which
π
2
<
ϕ
i
<
π
.
10. The lens with a metasurface according to claim 1 , wherein the orientation of the crosses can only take on a finite set of discrete angular values.
11. The lens with a metasurface according to claim 1 , wherein the first array is periodic.
12. The lens with a metasurface according to claim 4 , further comprising a second array of resonators, the resonators of the second array being crosses having identical shapes, the second array being located in the plane of the lens, each cross of the second array being further located in an effective cross-section having a size of
(
λ
2
)
2
of a cross of the first array, the crosses of the second array having a size smaller than that of the crosses of the first array, each cross of the second array also comprising a long arm and a short arm, each cross of the second array phase shifting the incident wave by a specific phase shift depending on its orientation, in the plane of the lens, with respect to said reference direction.
13. The lens with a metasurface according to claim 12 , wherein the incident wave comprises a first spectral component at a first wavelength λ 1 and a second spectral component at a second wavelength λ 2 the lens with a metasurface is a convergent lens, having a focal distance f, the orientation of a cross of the first array, the centre of which is located at a point P i having the coordinates (x i ,y i ) in a reference frame (O, x, y) of the plane of the lens, is chosen in such a way as to generate a specific phase shift
φ
1
,
i
=
2
π
n
o
1
λ
1
(
f
-
(
x
i
-
x
1
)
2
+
(
y
i
-
y
1
)
2
+
f
2
)
with
φ
1
,
i
<
π
2
where n o 1 is the optical index of the output medium of the lens, at the wavelength λ 1 , and the orientation of a cross of the second array, the centre of which is located at a point P j having the coordinates (x j ,y j ) in the reference frame (O, x, y), is chosen in such a way as to generate a specific phase shift
φ
2
,
j
=
2
π
n
o
2
λ
2
(
f
-
(
x
j
-
x
2
)
2
+
(
y
j
-
y
2
)
2
+
f
2
)
with
φ
2
,
j
<
π
2
where n o 2 is the optical index of the output medium of the lens, at the wavelength μ 2.