Full Stokes imaging polarimetry using dielectric metasurfaces
Ehsan Arbabi,
1
Seyedeh Mahsa Kamali,
1
Amir Arbabi,
2
and Andrei Faraon
1,
∗
1
T. J. Watson Laboratory of Applied Physics, California Institute of Technology,
1200 E. California Blvd., Pasadena, CA 91125, USA
2
Department of Electrical and Computer Engineering,
University of Massachusetts Amherst,
151 Holdsworth Way, Amherst, MA 01003, USA
∗
Corresponding author: A.F.: faraon@caltech.edu
1
arXiv:1803.03384v1 [physics.optics] 9 Mar 2018
Polarization is a degree of freedom of light carrying important information that is usually
absent in intensity and spectral content. Imaging polarimetry is the process of determin-
ing the polarization state of light, either partially or fully, over an extended scene. It has
found several applications in various fields, from remote sensing to biology. Among different
devices for imaging polarimetry, division of focal plane polarization cameras (DoFP-PCs)
are more compact, less complicated, and less expensive. In general, DoFP-PCs are based
on an array of polarization filters in the focal plane. Here we demonstrate a new principle
and design for DoFP-PCs based on dielectric metasurfaces with the ability to control po-
larization and phase. Instead of polarization filtering, the method is based on splitting and
focusing light in three different polarization bases. Therefore, it enables full-Stokes charac-
terization of the state of polarization, and overcomes the 50
%
theoretical efficiency limit of
the polarization-filter-based DoFP-PCs.
Polarimetric imaging is the measurement of the polarization state of light over a scene of inter-
est. While spectral and hyperspectral imaging techniques provide information about the molecular
and material composition of a scene [1, 2], polarimetric imaging contains information about the
shape and texture of reflecting surfaces, the orientation of light emitters, or the optical activity of
various materials [3, 4]. This additional information has led to many applications for imaging po-
larimetry ranging from astronomy and remote sensing to marine biology and medicine [3, 5–11].
Therefore, several methods have been developed over the past decades to enable mapping of the
polarization state over an extended scene [11–18].
Generally, polarimetric imaging techniques can be categorized into three groups: division of
amplitude, division of aperture, and division of focal plane [3]. All of these techniques are based
on measuring the intensity in different polarization bases and using them to estimate the full Stokes
vector or a part of it. Among various systems, DoFP-PCs are less expensive, more compact, and
require less complicated optics [16–18]. In addition, they require much less effort for registering
images of different polarizations as the registration is automatically achieved in the fabrication of
the polarization sensitive image sensors. The advances in micro/nano-fabrication have increased
the quality of DoFP-PCs and reduced their fabrication costs, making them commercially available.
DoFP-PCs either use a birefringent crystal to split polarizations [19, 20], or thin-film [17, 21]
or wire-grid [11, 16, 22] polarization filters. To enable the measurement of degree of circular
polarization, form-birefringent quarter waveplates were integrated with linear polarizers in the
mid-IR [23]. Recently, liquid crystal retarders have been integrated with linear polarization filters
2
to enable full Stokes polarimetric imaging by implementing circular [24] and elliptical polarization
filters [25, 26]. An issue with the previously demonstrated DoFP-PCs is that they all have a
theoretical efficiency limit of 50
%
due to using polarization filters [3], or spatially blocking half
of the aperture [20].
Optical metasurfaces are a category of nano-fabricated diffractive optical elements comprised
of nano-scatterers on a surface [27–42] that are judiciously designed to control the wavefront.
They have enabled high-efficiency phase and polarization control with large gradients [30, 31, 36,
37, 41, 43]. In addition, their compatibility with conventional microfabrication techniques allows
for their integration into optical metasystems [44–47].
Metasurfaces have previously been used for polarimetry [48–53], but not polarimetric imaging.
An important capability of high contrast dielectric metasurfaces is the simultaneous control of
polarization and phase [43]. Here, we use this capability to demonstrate a dielectric metasurface
mask for DoFP-PCs with the ability to fully measure the Stokes parameters, including the degree
of circular polarization and helicity. Since the mask operates based on polarization splitting and
focusing instead of polarization filtering, it overcomes both the 50
%
theoretical efficiency limit,
and the one-pixel registration error (resulting from distinct physical areas of the polarization filters)
of the previously demonstrated DoFP-PCs [3]. In addition, unlike the previously demonstrated full
Stokes DoFP-PCs, the metasurface is fabricated in a single dielectric layer and does not require
integration of multiple layers operating as retarders and polarization filters. The mask is designed
for 850-nm center wavelength. The polarization cross-talk ranges from 10
%
to 15
%
for pixel
sizes from 7.2
μ
m to 2.4
μ
m when using an 850-nm LED as the light source. In addition, we use a
polarization mask to demonstrate that the metasurface DoFP-PC can be used to form polarization
images over extended scenes. To the best of our knowledge, this is the first demonstration of a
DoFP-PC mask that measures the polarization state completely and is not based on polarization
filtering.
There are several representations for polarization of light [54]. Among them, the Stokes vec-
tor formalism has some conceptual and experimental advantages since it can be used to represent
light with various degrees of polarization, and can be directly determined by measuring the power
in certain polarization bases [54]. Therefore, most imaging polarimetry systems determine the
Stokes vector [3], which is usually defined as
S
=
(
1
/
I
)[
I
,
(
I
x
−
I
y
)
,
(
I
45
−
I
−
45
)
,
(
I
R
−
I
L
)]
, where
I
is the total intensity,
I
x
,
I
y
,
I
45
, and
I
−
45
are the intensity of light in linear polarization bases
along the x, y, +45-degree, and -45-degree directions, respectively.
I
R
and
I
L
denote the inten-
3
sities of the right-hand and left-hand circularly polarized light. To fully characterize the state of
polarization, all these intensities should be determined. A conventional setup used to measure the
full Stokes vector is shown in
Figure 1
a: a waveplate (half or quarter), followed by a Wollaston
prism and a lens that focuses the beams on photodetectors. One can determine the four Stokes pa-
rameters [54] from the detector signals without a waveplate, with a half-waveplate (HWP), and a
quarter-waveplate (QWP). An optical metasurface with the ability to fully control phase and polar-
ization of light [43] can perform the same task over a much smaller volume and without changing
any optical components. The metasurface can split any two orthogonal states of polarization and
simultaneously focus them to different points with high efficiency and on a micron-scale. This
is schematically shown in
Figure 1
a. Such a metasurface can be directly integrated on an image
sensor for making a polarization camera. To fully measure the Stokes parameters, the projec-
tion of the input light on three different polarization basis sets should be measured. A typical
choice of basis is horizontal/vertical (H/V),
±
45
◦
linear, and right-hand-circular/left-hand-circular
(RHCP/LHCP) that can be used to directly measure the Stokes parameters.
Figure 1
b shows a
possible configuration where the three metasurface polarization beam-splitters (PBS) are multi-
plexed to make a superpixel, comprising of six image sensor pixels. Each image sensor pixel can
then be used to measure the power in a single polarization state. A schematic illustration of a su-
perpixel is shown in
Figure 1
c. The colors are only used to distinguish different parts of the super
pixel more easily, and do not correspond to actual wavelengths. The blue nano-posts, separate and
focus RHCP/LHCP, the green ones and the red ones do the same for
±
45
◦
and H/V, respectively.
The metasurface platform we use here is based on the dielectric birefringent nano-post struc-
ture [43]. As seen in
Figure 2
a, the metasurface is composed of
α
-Si nano-posts with rectangular
cross-sections on a low-index fused silica substrate. With a proper choice of the
α
-Si layer thick-
ness and lattice constant (650 nm and 480 nm, respectively at a wavelength of 850 nm), the nano-
posts can provide full and independent 2
π
phase control over x and y-polarized light where x and
y are aligned with the axes of the nano-post (see Supplementary Information Fig. S1) [55]. Using
the phase versus dimension graphs, one could calculate the nano-post dimensions required to pro-
vide a specific pair of phase values,
φ
x
and
φ
y
, as shown in
Figure 2
b. This allows for designing a
metasurface that controls x and y-polarized light independently. With a simple generalization, the
same can be applied to any two orthogonal linear polarizations using nano-posts that are rotated
around their optical axis with the correct angle to match the new linear polarizations (e.g., the
x
′
-y
′
axis in
Figure 2
c). An important and interesting point demonstrated in [43] is that this can
4
be done on a point-by-point manner, where the polarization basis is different for each nano-post.
This property allows us to easily design the metasurface PBS for the two linear bases of interest.
Moreover, as demonstrated in [43], an even more interesting property of this seemingly simple
structure is that the independent control of orthogonal polarizations can be generalized to ellipti-
cal and circular polarizations as well (with a small drawback that will be discussed later). To see
this, here we reiterate the results presented in the supplementary material of [43], as it is important
to make the design process clear. The operation of a nano-post can be modeled by a Jones matrix
relating the input and output electric fields (i.e.,
E
out
=
TE
in
). For the rotated nano-post shown in
Figure 2
c, the Jones matrix can be written as:
T
=
T
x x
T
x
y
T
y
x
T
yy
=
R
(
θ
)
e
i
φ
x
′
0
0 e
i
φ
y
′
R
(−
θ
)
,
(1)
where
R
(
θ
)
denotes the rotation matrix by an angle
θ
in the counter-clockwise direction. Here
we have assumed a unity transmission since the nano-posts are highly transmissive. We note here
that the right hand side of Equation 1 is a unitary and symmetric matrix. Using only these two
conditions (i.e., unitarity and symmetry), we find
T
x
y
=
T
y
x
,
|
T
y
x
|
=
√
1
−|
T
x x
|
2
, and
T
yy
=
−
exp
(
i2
∠
T
y
x
)
T
x x
. As one could expect, these reduce the available number of parameters of the
matrix to three (
|
T
x x
|
,
∠
T
x x
,
∠
T
y
x
), corresponding to the three available physical parameters (
φ
x
′
,
φ
y
′
, and
θ
). Using these relations to simplify
E
out
=
TE
in
, we can rewrite it to find the Jones
matrix elements in terms of the input and output fields:
E
out
∗
x
E
out
∗
y
E
in
x
E
in
y
T
x x
T
y
x
=
E
in
∗
x
E
out
x
,
(2)
where
∗
denotes complex conjugation. Equation 2 is important as it shows how one can find
the Jones matrix required to transform any input field with a given phase and polarization, to
any desired output field with a different phase and polarization. This is the first application of the
birefringent meta-atoms, i.e.,
complete and independent polarization and phase control
. The Jones
matrix is uniquely determined by Equation 2, unless the determinant of the coefficients matrix on
the left hand side of Equation 2 is zero (i.e., the matrix rows are proportional). Since the Jones
matrix is unitary (i.e., the input and output powers are equal), the proportionality coefficient must
have a unit amplitude:
E
out
1
=
exp
(
i
φ
1
)
E
in
∗
1
, where we are using numeral subscripts to distinguish
5
between two different sets of input/output fields. This means that
E
out
1
and
E
in
1
have the same
polarization ellipse, but an opposite handedness. In this case, a second equation is required to
uniquely determine the Jones matrix. To impose only one equation, the second set of input and
output polarizations should also satisfy the same condition as the first ones:
E
out
2
=
exp
(
i
φ
2
)
E
in
∗
2
. If
φ
1
and
φ
2
can be independently controlled, one can see using a conservation of energy argument,
that
E
in
1
and
E
in
2
(as well as
E
out
1
and
E
out
2
) should be orthogonal to each other. Using these two
conditions, we can write the final equation as:
E
in
1
,
x
E
in
1
,
y
E
in
2
,
x
E
in
2
,
y
T
x x
T
y
x
=
E
out
1
,
x
E
out
2
,
x
=
exp
(
i
φ
1
)
E
in
∗
1
,
x
exp
(
i
φ
2
)
E
in
∗
2
,
x
.
(3)
This is the second important application of the method,
polarization controlled phase manipu-
lation
: given
any
two orthogonal input polarizations (denoted by
E
in
1
and
E
in
2
), their phase can
be independently controlled using the Jones matrix given by Equation 3. For instance, Arbabi et.
al. [43], demonstrated a metasurface that focuses RHCP input light to a tight spot, and LHCP input
light to a doughnut shape. The cost is that the output orthogonal polarizations have the opposite
handedness compared to the input ones. When the Jones matrix is calculated from Equation 3 (or
Equation 2, depending on the function), the two phases (
φ
x
′
and
φ
y
′
) and the rotation angle (
θ
)
can be calculated from Equation 1, by finding the eigenvalues and eigenvectors of the Jones ma-
trix. Let us emphasize here that since this is a point-by-point design, all the steps can be repeated
independently for each nano-post, meaning that the polarization basis can be changed from one
nano-post to the next.
Based on the concept and technique just described, the first design step is identifying the input
polarizations at each point. For the DoFP-PC, three different sets of H/V,
±
45
◦
, and RHCP/LHCP
(corresponding to the three distinct areas in the superpixel shown in
Figure 1
b) are chosen. Then,
the required phase profiles are determined to split each two orthogonal polarizations and focus
them to the centers of adjacent pixels on the image sensors (as shown schematically in
Figure
1
c). For a pixel size of 4.8
μ
m, the calculated phase profiles are shown in
Figure 2
d, where the
distance between the metasurface mask and the image sensor is assumed to be 9.6
μ
m. Since
each polarization basis covers two image sensor pixels, the phases are defined over the area of two
pixels. In addition, the calculated phases are the same for the three different polarization bases, and
therefore only one basis set is shown in
Figure 2
d. Using these phases and knowing the desired
6
polarization basis at each point, we calculated the rotation angles and nano-post dimensions from
Equations 3 and 1 along with the data shown in
Figure 2
b.
The metasurface mask was then fabricated in a process similar to Ref. [56]. A 650-nm-thick
layer of
α
-Si was deposited on a fused silica wafer. The metasurface pattern was defined using
electron-beam lithography, and transferred to the
α
-Si layer through a lift-off process (to make a
hard etch-mask) followed by dry etching.
Figure 2
e shows a scanning electron micrograph of a
fabricated superpixel, with the polarization bases denoted by arrows for each section. In addition
to the metasurface mask corresponding to a pixel size of 4.8
μ
m (mentioned above and shown in
Figure 2
e), two other masks with pixel sizes of 7.2
μ
m and 2.4
μ
m were also fabricated (with
metasurface to image sensor separations of 14.4
μ
m and 4.8
μ
m, respectively) to study the effect
of pixel size on the imaging performance.
To characterize the metasurface mask, we illuminated it with light from an 850-nm LED (fil-
tered by a 10-nm bandpass filter) with different states of polarization, and imaged the plane cor-
responding to the image sensor location using a custom-built microscope (see Supplementary Fig.
S2 for measurement details and the setup).
Figure 3
summarizes the superpixel characterization
results for the 4.8-
μ
m pixel design. The measured Stokes parameters are plotted in
Figure 3
a for
different input polarizations showing results with low cross-talk (<10
%
) between polarizations and
high similarity between different superpixels. The measurements were averaged over more than
120 superpixels (limited by the field of view of the microscope), and the standard deviations are
shown in the graph as error bars. In addition, the intensity distribution over a sample superpixel
area is shown in
Figure 3
b for the same input polarizations. The graphs show the clear ability
of the metasurface mask to route light as desired for various input polarizations. Similar char-
acterization results without a bandpass filter (i.e., for a bandwith of about 5
%
) are presented in
Supplementary Information Figure S3, showing slight performance degradation (with a maximum
cross-talk of
∼
13
%
) as the metasurface efficiency decreases with changing the wavelength. In ad-
dition, similar measurement results for metasurface masks with pixel sizes of 7.2
μ
m and 2.4
μ
m
are presented in Supplementary Information Figures S4 and S5, respectively. The results show a
degradation of performance with reducing the pixel size (the cross-talk is smaller than 7.5
%
and
13
%
for 7.2-
μ
m and 2.4-
μ
m pixels, respectively). To show the ability of the metasurface mask
to characterize the polarization state of unpolarized light, we repeated the same measurements
with the polarization filter removed from the setup.
Figure 3
c summarizes the results of this mea-
surement that determines the state of polarization of light emitted by the LED. The data given
7
in
Figure 3
a is used to estimate the calibration matrix. As expected, the emitted light has a low
degree of polarization (
<
0.08). We also characterized the polarization state of the emitted LED
light using a QWP and an LP, and found the degree of polarization to be equal to zero upto the
measurement error.
In addition, we measured the transmission efficiency of the metasurface mask and found it
to be in the range of 60
%
to 65
%
for all pixel size designs and input polarizations. The lower
than expected transmission is mainly due to a few factors. First, the metasurface has a maximum
deflection angle larger than 50
◦
, which results in lower transmission efficiency [36, 57]. Second,
the relatively large metasurface lattice constant of 480 nm does not satisfy the Nyquist sampling
theorem for the large-deflection-angle transmission masks inside the fused silica substrate [58].
This results in spurious diffraction of light inside the substrate. Finally, the mask is periodic with
a larger-than-wavelength period equal to the superpixel dimensions. This results in excitation
of higher diffraction orders especially inside the substrate that has a higher refractive index. It is
worth noting that the achieved
∼
65
%
efficiency is higher than the theoretical limit of a polarimetric
camera that is based on polarization filtering (e.g., uses a nano-wire grid polarizer).
Finally, we show that using the DoFP metasurface mask, one could perform polarimetric
imaging. To do this, we designed and fabricated a metasurface polarization mask (using the
polarization-phase control method described above, and a fabrication process similar to the DoFP
metasurface mask). The mask converts x-polarized input light to an output polarization state char-
acterized by the polarization ellipses and the Stokes parameters shown in
Figure 4
a and
Figure
4
b, respectively. Each Stokes parameter is +1 or -1 in an area of the image corresponding to
the specific polarization (e.g., S
3
being +1 in the right half circle and -1 in the left half circle
and 0 elsewhere). Using a second custom-built microscope, the image of the polarization mask
was projected on the DoFP metasurface mask (see Supplementary Information Figure S2 for the
measurement setup and the details). First, we removed the metasurface mask and performed a con-
ventional polarimetric imaging of the projected image using a linear polarizer (LP) and a QWP.
The results are shown in
Figure 4
c. Second, we removed the LP and QWP, and inserted the DoFP
metasurface mask in its place. The Stokes parameters were extracted from a single image cap-
tured at the location of the image-sensor plane in front of the DoFP metasurface mask. The results
are shown in
Figure 4
d, and are in good agreement with the results of regular polarimetric imag-
ing. The lower quality of the metasurface polarimetric camera image is mainly due to the limited
number of superpixels that fit inside the single field of view of the microscope (limited by the
8
microscope magnification and image sensor size,
×
22 and
∼
15 mm, respectively). This results in
a low resolution of 70-by-46 points for the metasurface polarimetric image versus the
∼
2000-by-
2000 point resolution of the regular polarimetric image. In addition, to form the final image, we
need to know the coordinates of each superpixel a priori. The existing errors in estimating these
coordinates (resulting from small tilts in the setup, aberrations of the custom-built microscope,
etc.) cause a degraded performance over some superpixels. In a polarization camera made using
the metasurface DoFP metasurface mask, both of these issues will be solved as the resolution can
be much higher, and the mask and the image sensor are lithographically aligned.
To extract the polarization information of the image, we integrated the intensity inside the area
of two adjacent image sensor pixels, and calculated the corresponding Stokes parameter simply
by dividing their difference by their sum. While straightforward, this is not the optimal method
to perform this task as there is non-negligible cross-talk between different polarization intensi-
ties measured by the pixels (
Figure 3
). The issue becomes more important as one moves toward
smaller pixel sizes (e.g., the 2.4-
μ
m pixel of Supplementary Information Figure S5). To address
this, a better polarization data extraction method is to form a matrix that relates the actual intensity
of different input polarizations to the corresponding measured values for a specific DoFP metasur-
face mask design (for instance using the data in
Figure 3
). This allows one to reduce the effect of
the cross-talk and measure the polarization state more precisely.
The designed small distance between the metasurface and the image sensor (e.g., 9.6
μ
m for the
4.8-
μ
m pixel) results in a diffraction-limited bandwidth of about 40
%
(assuming a constant phase
profile that doesn’t change with wavelength and using the criterion given in [44]). Therefore, the
actual bandwidth of the device is limited by the focusing and polarization control efficiencies that
drop with detuning from the design wavelength. In addition, it is expected that the same level
of performance achieved from the 2.4-
μ
m pixel in this work, can be achieved from a
∼
1.7-
μ
m
pixel if the material between the mask and the image sensor has a refractive index of 1.5, which
is the case when the DoFP mask is separated from the image sensor by an oxide or polymer
layer, as in a realistic device. To achieve smaller pixel sizes, better performance, and larger oper-
ation bandwidths one could use more advanced optimization [59] or chromatic-dispersion control
techniques [60], especially since the size of a single superpixel is small and allows for a fast sim-
ulation of the forward problem. In addition, a spatial multiplexing scheme [61–63] can be used
to interleave multiple superpixels corresponding to different optical bands, and therefore make a
color-polarization camera.
9
Using the polarization-phase control method and the platform introduced in [43], we demon-
strated a metasurface mask for DoFP-PCs. The mask is designed to split and focus light to six
different pixels on an image sensor for three different polarization bases. This allows for complete
characterization of polarization by measuring the four Stokes parameters over the area of each
superpixel, which corresponds to the area of six pixels on the image sensor. We experimentally
demonstrated the ability of the metasurface masks to correctly measure the state of polarization
for different input polarizations. In addition, we used the DoFP metasurface mask to form an
image of a complicated polarization object, showing the ability to make a polarization camera.
Many of the limitations faced here can be overcome using more advanced optimization techniques
or better data extraction methods. We anticipate that polarization cameras based on metasurface
masks will be able to replace the conventional polarization cameras for many applications as they
enable measurement of the full polarization state including the degree of circular polarization and
handedness.
MATERIALS AND METHODS
Simulation and design.
To design the DoFP metasurface mask, we first calculated the two phase
profiles required for the two polarization states [
Figure 2
d]. The phase profiles correspond to
decentered aspheric lenses that focus each polarization at the center of one image sensor pixel.
These phases are then used in Equation 3 along with the known input polarization states to cal-
culate the Jones matrix. To find the nano-post corresponding to each Jones matrix, the matrix is
diagonalized according to Equation 1, and the two phases (
φ
x
′
and
φ
y
′
) and the rotation angle
θ
are then extracted. The nano-post providing the required pair of phases is then found using the
data in
Figure 2
b.
The polarization target used for the imaging experiments in
Figure 4
was designed in a slightly
different manner, since in this case only the output polarization is of interest. Assuming an
x
-
polarized input light, the output polarization at each point on the mask was chosen according to
Figure 4
a. In the general case, the mask can then be designed using the Jones matrix found from
Equation 2, and calculating the corresponding phases and rotation from the Jones matrix. In this
especial case, however, the device is a set of nano-posts acting as quarter or half wave-plates.
Therefore, we deigned the nano-posts in a manner similar to [64] to make it robust to fabrication
errors.
10
To find the transmission amplitude and phase for the nano-posts [Supplementary Fig. S1], we
simulated a uniform array of nano-posts with rectangular cross-sections under normally incident
x
- and
y
-polarized light using the rigorous coupled wave analysis [55]. The resulting complex
transmissions were then used to find the best nano-post that provides each required phase pair
through minimizing the Euclidean distance between
[
e
i
φ
x
,
e
i
φ
y
]
and
[
t
x
,
t
y
]
, where
φ
x
and
φ
y
are
the desired phase values, and
t
x
and
t
y
are complex nano-post transmissions. The optimized nano-
post dimensions are plotted in
Figure 2
b.
Fabrication.
The fabrication process is the same for both the DoFP metasurface mask and the
polarization imaging target. The fabrication started with deposition of a 650-nm-thick layer of
α
-
Si on a 500-
μ
m-thick fused silica substrate. The metasurface pattern is defined in a
∼
300-nm-thick
ZEP-520A positive electron-beam resist using electron-beam lithography. After development of
the resist, a
∼
70-nm-thick layer of aluminum oxide is deposited on the sample using electron-beam
evaporation and lifted off to invert the pattern. The aluminum oxide is then used as a hard mask
in the reactive ion etching of the
α
-Si layer. Finally, the aluminum oxide mask is removed in a
solution of hydrogen peroxide and ammonium hydroxide.
Measurement.
The measurement setups (including part models) are schematically illustrated in
Supplementary Fig. S2 for different parts of the characterization process. To characterize the
DoFP super-pixel performance, light from an LED was passed through an LP and a QWP to set
the input polarization state. The six different polarization states [
Figure 3
a] were generated using
this combination. The intensity distribution patterns at the focal plane after the DoFP metasurface
mask were then imaged using a custom-built microscope. The data was analyzed by calculating
the Stokes parameters measured by each super-pixel, and averaging over all the super-pixels that
fit within the field of view. A 10-nm bandwidth filter with a center wavelength of 850 nm was
inserted in the path to characterize the narrow-band operation, and was then removed to acquire
the results for a wider-bandwidth source.
The imaging polarimetry experiments were performed in a similar way. For these experiments,
the polarization target was illuminated by
x
-polarized light out of a supercontinuum laser source
(filtered by the same 10-nm bandwidth filter). The target was imaged onto the DoFP metasurface
mask plane using a secondary custom-built microscope (operating as relay optics). The intensity
distribution at the focal plane after the DoFP metasurface mask was then imaged and analyzed
to generate the polarization images plotted in
Figure 4
d. For comparison, the DoFP metasurface
mask was removed and a polarization analyzer (i.e., a QWP and an LP) was inserted into the
11
system to form the reference polarization images plotted in
Figure 4
c.
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16
c
b
a
P
P
WP
Wollaston prism
Metasurface
Image Sensor
PD1
PD2
Lens
Pixel 1
Pixel 2
x
y
z
Figure 1
Concept of a metasurface polarization camera.
(a)
Top: Schematics of a conventional setup used
for polarimetry: a waveplate (quarter or half) followed by a Wollaston prism and a lens that focuses light
on detectors. Bottom: A compact metasurface implements the functionality of all three components
combined, and can be directly integrated on an image sensor. WP: waveplate; PD: photodetector.
(b)
A
possible arrangement for a superpixel of the polarization camera, comprising six image sensor pixels.
Three independent polarization basis (H/V,
±
45
◦
, and RHCP/LHCP) are chosen to measure the Stokes
parameters at each superpixel.
(c)
Three-dimensional illustration of a superpixel focusing different
polarizations to different spots. The colors are used only for clarity of the image and bear no wavelength
information.
17
0
0
S
S
S
S
b [nm]
I
x
[Rad]
I
y
[Rad]
0
0
S
S
S
S
a [nm]
I
x
[Rad]
I
y
[Rad]
ab
c
d
e
100
200
Side length [nm]
a
a
h
l
c
b
x
z
y
T
x
x’
y’
y
S
S
0
Phase [Rad]
)
1
[Rad]
0
0
4
-4
-2
2
x [
P
m]
y [
P
m]
)
2
[Rad]
0
0
4
-4
-2
2
x [
P
m]
y [
P
m]
Figure 2
Meta-atom and pixel design.
(a)
An
α
-Si nano-post with a rectangular cross section resting on a
glass substrate provides full polarization and phase control.
(b)
Design graphs used for finding the in-plane
dimensions of a nano-post that provides a required pair of transmission phases for the x and y-polarized
light. The nano-posts are 650 nm tall, and the lattice constant is 480 nm.
(c)
Schematic illustration of a
rotated nano-post, showing the rotation angle and the old and the new optical axis sets.
(d)
Required phase
profiles for a metasurface that does both polarization beam splitting and focusing at two orthogonal
polarizations. These can be any set of orthogonal polarizations, linear or elliptical. The focal distance for
these phase profiles is 9.6
μ
m, equal to the width of the superpixel in the x direction. The lateral positions
of the focal spots are x
=
±
2.4
μ
m and y
=
0.
(e)
Scanning electron micrograph of a fabricated superpixel.
The polarization basis for each part is shown with the colored arrows. Scale bar: 1
μ
m.
18
04
-4
x [
P
m]
0
4
-4
y [
P
m]
04
-4
x [
P
m]
04
-4
x [
P
m]
04
-4
x [
P
m]
04
-4
x [
P
m]
04
-4
x [
P
m]
S1
S2
S3
0
1
-1
S1
S2
S3
0
1
-1
S1
S2
S3
0
1
-1
S1
S2
S3
0
1
-1
S1
S2
S3
0
1
-1
S1
S2
S3
0
1
-1
a
b
0
Intensity [a.u.]
0
4
-4
y [
P
m]
04
-4
x [
P
m]
S1
S2
S3
0
1
-1
c
Figure 3
Characterization results of the superpixels of the DoFP metasurface mask.
(a)
Calculated
average Stokes parameters for different input polarizations (shown with colored arrows), and
(b)
the
corresponding intensity distributions for a sample superpixel. The Stokes parameters are averaged over
about 120 superpixels (limited by the microscope field of view), and the error bars represent the statistical
standard deviations.
(c)
Calculated Stokes parameters and the corresponding intensity distribution for the
LED light source without any polarization filters in the setup. All the measurements are performed with an
850-nm LED filtered by a bandpass filter (center: 850 nm, FHMW: 10 nm) as the light source.
19