of 28
3D-Patterned Inverse-Designed Mid-Infrared
Metaoptics Supplementary
Contents
1 Two-Photon Polymerization (TPP) Accuracy
2
2 Laguerre Gaussian Modes for Angular Momentum Splitter
2
3
12
-Layer Stokes Polarimetry Device
2
4 Polarimetry Splitting Bounds
3
4.1
Maximum transmission into each analyzer state . . . . . . . . . . . .
3
4.2
Minimum overlap between analyzer states . . . . . . . . . . . . . . .
4
5 Polarimetry Contrast Bounds
5
5.1
Analyzer state transmission to all quadrants . . . . . . . . . . . . . .
5
5.2
Extinguishing orthogonal state to analyzer quadrant . . . . . . . . . .
6
6 Polarimetry Analyzer States
6
7 Device Index of Refraction Profiles
7
8 Polarimetry Reconstruction
7
8.1
Reconstruction Method . . . . . . . . . . . . . . . . . . . . . . . . .
8
8.2
Reconstructing Pure Polarization States . . . . . . . . . . . . . . . .
9
8.3
Reconstructing Mixed Polarization States . . . . . . . . . . . . . . .
9
9 Angular Momentum Sorting Device Outside of Design Points
9
9.1
Illumination with Different Spin Values . . . . . . . . . . . . . . . . 10
9.2
Illumination with Different OAM Values . . . . . . . . . . . . . . . . 10
10 Supplementary Figures
11
10.1 Optical setup for characterization of multispectral and polarimetry
devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
10.2 Stokes state creation and verification . . . . . . . . . . . . . . . . . . 11
10.3 Simulation performance for Stokes polarimetry device with
additional degrees of freedom compared to Stokes polarimetry device
from the main text . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
10.4 Schematic of simulation geometry for optimization and evaluation . . 15
10.5 Schematic of fabrication process . . . . . . . . . . . . . . . . . . . . 16
10.6 Conceptual diagram of the Stokes polarimetry device . . . . . . . . . 16
10.7 Index of refraction profiles for multispectral and angular momentum
devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
10.8 Index of refraction profiles for Stokes polarimetry devices . . . . . . 19
10.9 Stokes polarimetry reconstruction for pure states . . . . . . . . . . . 21
10.10Stokes polarimetry reconstruction for mixed states . . . . . . . . . . 23
1
10.11Angular momentum device under different spin excitation . . . . . . 24
10.12Angular momentum device under different OAM excitation . . . . . . 26
References
28
1 Two-Photon Polymerization (TPP) Accuracy
Fabrication via TPP is a flexible and powerful method, but also has known challenges
in printing accuracy [1]. We observe shrinkage of the structure, which is dependent
on the height of the layer from the substrate. Material printed on the bottom layer
is not able to shrink from its printed size because it is physically adhered to the
substrate. The topmost layer is roughly
90%
of the desired lateral size and the bottom
layer is close to the expected size. We also observe dilation of the smallest features in
the design. Designs were compensated for this effect by pre-eroding features in the
STL file before printing. Finally, the Nanoscribe had a mismatch between the feature
size in each lateral direction. This is not a limitation of TPP, but likely the result of
astigmatism in the optical alignment of our specific tool.
2 Laguerre Gaussian Modes for Angular Momentum
Splitter
A spatially varying field can carry orbital angular momentum (OAM). Discrete values
of OAM,
l
, can be found in the Laguerre-Gaussian orthonormal basis for solutions of
the paraxial wave equation [2]. We used a simplified set with
p
= 0
, such that each
mode was defined at its waist (
z
= 0
) with spatial profile in cylindrical coordinates:
u
(
r,φ,z
= 0) = (
r
2
w
0
)
|
l
|
e
r
2
w
2
0
e
ilφ
(1)
where
w
0
is the waist radius of the beam. We chose
w
0
= 8
.
5
μ
m
to ensure the mode
was confined to the device. Transmission plots shown are geometrically normalized
against the transmission of this beam through the device aperture with no device
present. We can further assign a spin angular momentum of the mode by choosing the
handedness of its circular polarization. The following pairs of OAM values
l
and spin
values
s
were used in the optimization:
(
l,s
) = (
2
,
1)
,
(
1
,
1)
,
(1
,
1)
,
(2
,
1)
.
These states were assigned to quadrants starting with the top right (blue) and moving
counterclockwise (green, red, magenta).
3
12
-Layer Stokes Polarimetry Device
The polarimetry device in the main text consists of six
3
μ
m
layers and struggles to
achieve equal contrast for all four analyzer states with the circular polarization state
lagging the others. We speculate this may be due to lack of degrees of freedom in
the thickness of device. As a comparison, we optimize a thicker device consisting of
twelve
3
μ
m
layers to see if the solution will display better contrast for all analyzer
2
states. In
Fig. S3
we show the comparison of the thicker device to the original.
While the quadrant transmission per analyzer state is slightly reduced, the contrast
metric is improved for the circular polarization state without sacrificing the other
analyzer state contrasts.
4 Polarimetry Splitting Bounds
We can model the Stokes polarimetry device as a linear system that projects an input
Jones state describing the x- and y-polarized electric field components onto several
analyzer states. The Jones polarization is a 2-dimensional complex vector. The four
analyzer states for our device are specifically chosen Jones vectors. In
Fig. S6
,
analyzer states correspond to
|
v
i
, where
N
= 4
for the device in the paper. We
assume the device outputs into four spatially distinct modes
|
w
k
, such that we take
them to be orthogonal (
w
i
|
w
k
=
δ
ik
). Specifically, we model each output mode as
a focused spot in a different quadrant of the focal plane and thus we assume the lack
of spatial overlap implies orthogonality to a good approximation. The functionality
of the device is described by an operator
ˆ
Q
where projection of an input state on each
analyzer direction modulates the amplitude of an outgoing mode. We write
ˆ
Q
=
X
i
α
i
|
w
i
⟩⟨
v
i
|
(2)
Without loss of generality, we assume
α
i
is real. Any complex phase can be included
in output mode
|
w
i
.
4.1 Maximum transmission into each analyzer state
Next, we assume for simplicity that all states have the same projection efficiency,
such that
α
i
=
α
. The transmission bound will differ from the following if each state
does not split at the same projection efficiency. Consider an arbitrary state
|
a
and it’s
orthogonal complement
|
̄
a
. The action of
ˆ
Q
on
|
a
is
ˆ
Q
|
a
=
α
X
i
|
w
i
⟩⟨
v
i
|
a
(3)
Taking the vector magnitude squared of the resulting state
a
|
ˆ
Q
ˆ
Q
|
a
=
α
2
X
i,j
w
i
|
w
j
⟩⟨
v
j
|
a
⟩⟨
a
|
v
i
(4)
Since
w
i
|
w
k
=
δ
ik
, the double sum reduces to
a
|
ˆ
Q
ˆ
Q
|
a
=
α
2
X
i
v
i
|
a
⟩⟨
a
|
v
i
=
α
2
X
i
|⟨
a
|
v
i
⟩|
2
(5)
3
Following this pattern, we also have
̄
a
|
ˆ
Q
ˆ
Q
|
̄
a
=
α
2
X
i
v
i
|
̄
a
⟩⟨
̄
a
|
v
i
=
α
2
X
i
|⟨
̄
a
|
v
i
⟩|
2
(6)
Due to energy conservation, we cannot have gained any magnitude through applying
ˆ
Q
on the state so
a
|
ˆ
Q
ˆ
Q
|
a
⟩ ≤
1
and
̄
a
|
ˆ
Q
ˆ
Q
|
̄
a
⟩ ≤
1
. Summing these together, we
get
a
|
ˆ
Q
ˆ
Q
|
a
+
̄
a
|
ˆ
Q
ˆ
Q
|
̄
a
=
α
2
X
i
(
|⟨
a
|
v
i
⟩|
2
+
|⟨
̄
a
|
v
i
⟩|
2
)
2
(7)
Because the Jones vector space is 2-dimensional,
|
a
and
|
̄
a
form an orthonormal
basis, so by definition
(
|⟨
a
|
v
i
⟩|
2
+
|⟨
̄
a
|
v
i
⟩|
2
) = 1
. Thus, the sum simply becomes
a
|
ˆ
Q
ˆ
Q
|
a
+
̄
a
|
ˆ
Q
ˆ
Q
|
̄
a
=
2
2
(8)
If we assume
α
is the largest it can be, then
α
2
=
2
N
. For
N
= 4
as is the case for
the device in this manuscript,
α
2
= 0
.
5
. Thus, the maximum transmission we can
achieve for each analyzer state into its output mode is
0
.
5
.
4.2 Minimum overlap between analyzer states
Given a maximum transmission efficiency of
0
.
5
for each analyzer state, we can set
a minimum overlap,
β
, for Jones vector analyzer states used in the splitter. While the
choice is not unique, a maximally spaced set of vectors will have a common mutual
overlap. Assume for our set of analyzer states,
|⟨
v
i
|
v
j
⟩|
2
=
(
1
if
i
=
j
β
2
if
i
̸
=
j
(9)
Sending in an analyzer state to the device
ˆ
Q
|
v
k
=
α
X
i
|
w
i
⟩⟨
v
i
|
v
k
(10)
Taking the magnitude like before and using the orthogonality of the
|
w
i
states
v
k
|
ˆ
Q
ˆ
Q
|
v
k
=
α
2
X
i
v
i
|
v
k
⟩⟨
v
k
|
v
i
=
α
2
X
i
|⟨
v
k
|
v
i
⟩|
2
(11)
Using the common overlap between states in the analyzer set and requiring that by
energy conservation this magnitude squared is bound by
1
,
v
k
|
ˆ
Q
ˆ
Q
|
v
k
=
α
2
(1 + (
N
1)
β
2
)
1
(12)
4
The relation between
α
and
β
, then is given by
α
2
1
1 + (
N
1)
β
2
(13)
Suppose we specialize to the case where the transmission is maximized into each
analyzer state (
α
2
=
2
N
) and we have no lost transmission for any given analyzer
state through the system (
v
k
|
ˆ
Q
ˆ
Q
|
v
k
= 1
). Then,
α
2
(1 + (
N
1)
β
2
) = 1
2
N
(1 + (
N
1)
β
2
) = 1
1 + (
N
1)
β
2
=
N
2
(
N
1)
β
2
=
N
2
2
β
2
=
N
2
2(
N
1)
(14)
Note the case of
N
= 2
requires no overlap between the vectors with
β
2
= 0
and
α
2
=
2
N
= 1
because that matches the dimensionality of the Jones vector space.
However, from two measurements, we cannot reconstruct the full Stokes vector
where in order to do so we need at least
N
= 4
. As stated before, for
N
= 4
,
α
2
= 0
.
5
at best and with no lost transmission for the analyzer states,
β
2
=
1
3
.
5 Polarimetry Contrast Bounds
The contrast figure of merit for the Stokes polarimetry device is independent
of overall transmission. For a given quadrant corresponding to analyzer state
|
v
i
and orthogonal complement
|
̄
v
i
, the contrast is related to the analyzer
transmission
T
analyzer
and orthogonal transmission
T
orthogonal
to the quadrant as
C
=
T
analyzer
T
orthogonal
T
analyzer
+
T
orthogonal
. In order to get a contrast of
C
= 1
, we need to be able to
completely extinguish light in the analyzer quadrant for the orthogonal state.
5.1 Analyzer state transmission to all quadrants
We first show that a given analyzer state must necessarily appear in more than just
the desired quadrant. Following from the notation above, the action of the device on
an analyzer state,
|
v
k
is given by
ˆ
Q
|
v
k
=
X
i
α
i
|
w
i
⟩⟨
v
i
|
v
k
(15)
5
We ask how much overlap does this have with one of the output modes
|
w
j
not
corresponding to the analyzer quadrant (i.e.
i
̸
=
j
).
w
j
|
ˆ
Q
|
v
k
=
X
i
α
i
w
j
|
w
i
⟩⟨
v
i
|
v
k
=
α
j
v
j
|
v
k
(16)
where we used
w
j
|
w
i
=
δ
ij
to eliminate the sum. However, as we showed above,
with four analyzer states,
v
j
|
v
k
⟩ ̸
= 0
even for
j
̸
=
i
. So there is energy in the
other quadrants according to the splitting efficiency of the
j
th
analyzer state and the
overlap between the
j
and
k
analyzer states.
5.2 Extinguishing orthogonal state to analyzer quadrant
We now check if an orthogonal state can be completely extinguished to the analyzer
quadrant, which will determine if we can achieve a contrast of
C
= 1
. When we send
in the orthogonal state to a given analyzer,
|
̄
v
k
, the device output is given by
ˆ
Q
|
̄
v
k
=
X
i
α
i
|
w
i
⟩⟨
v
i
|
̄
v
k
(17)
Since it is true that
v
k
|
̄
v
k
= 0
by definition, the sum is reduced to
ˆ
Q
|
̄
v
k
=
X
i
̸
=
k
α
i
|
w
i
⟩⟨
v
i
|
̄
v
k
(18)
Now, we ask how much overlap does this have with the output mode corresponding
to this analyzer quadrant,
|
w
k
, since we are interested in seeing if this overlap can
be zero.
w
k
|
ˆ
Q
|
̄
v
k
=
X
i
̸
=
k
α
i
w
k
|
w
i
⟩⟨
v
i
|
̄
v
k
= 0
(19)
where
w
k
|
w
i
=
δ
ki
is only nonzero for
i
=
k
, but the sum explicitly ranges
over values of
i
̸
=
k
. Thus, we can extinguish a quadrant completely for a given
orthogonal state and a contrast of
1
is theoretically achievable even if we transmit all
incident light through the device to the focal plane.
6 Polarimetry Analyzer States
The choice of analyzer states that fits the above criteria is not unique, but will
correspond to a tetrahedron with points lying on the Poincar
́
e sphere. First, we
choose evenly spaced pure polarization states in Stokes space and then evaluate
their mutual overlaps in Jones space. One state is fixed in Stokes space to be right
circular polarization (RCP), which is encoded as

1
,
0
,
0
,
1

. This choice is arbitrary
and different starting states will generate equally suitable sets of analyzer states.
Staying on the Poincar
́
e sphere surface means the first entry is fixed to
1
(from
6
here, we write the vector in terms of
S
1
,S
2
,
and
S
3
). The other three states should
lie on a circle with a fixed polar angle from this first state such that all mutual
overlaps are the same. For polar angle
θ
and azimuthal angle
φ
, these states can
be parameterized

sin
θ
cos
φ,
sin
θ
sin
φ,
cos
θ

. To evenly spread out these states
azimuthally, the spacing should be
φ
=
2
π
3
. We make the non-unique choice to
set the first
φ
= 0
. The first two states on the circle, then are

sin
θ,
0
,
cos
θ

and

sin
θ
cos
2
π
3
,
sin
θ
sin
2
π
3
,
cos
θ

. Evaluating the dot product between any of the
states on the circle and the right circular polarization state yields
cos
θ
. The first two
states on the circle have a dot product of
sin
2
θ
cos
2
π
3
+ cos
2
θ
. Equating these two
values generates the relation:
sin
2
θ
cos
2
π
3
+ cos
2
θ
= cos
θ
(20)
Solving for
cos
θ
gives
cos
θ
=
1
3
. Completing the tetrahedron, the final Stokes
states (rounded to the thousands place) are:

1
,
0
,
0
,
1


1
,
0
.
471
,
0
.
816
,
0
.
333


1
,
0
.
943
,
0
,
0
.
333


1
,
0
.
471
,
0
.
816
,
0
.
333

(21)
Converting these states to Jones vectors, the analyzer states we used (rounded to the
thousands place) are given by:

0
.
707
,
0
.
707
j


0
.
514
,
0
.
794 + 0
.
324
j


0
.
986
,
0
.
169
j


0
.
514
,
0
.
794 + 0
.
324
j

(22)
The squared overlap magnitudes between any of these states,
β
2
=
1
3
as desired for
equally split analyzer states.
7 Device Index of Refraction Profiles
Optimized index of refraction profiles for the multispectral and angular momentum
sorting devices are shown in
Fig. S7
and those for the Stokes polarimetry device
from the main text and the one from the supplement with more layers are shown in
Fig. S8
.
8 Polarimetry Reconstruction
The following section shows how the polarimetry device presented in the main text
can be used to recover the Stokes parameters of arbitrarily polarized inputs. This
7
addresses interpretation of quadrant outputs when the excitation is different than the
four analyzer states used in the design. It further addresses the ability of the device
to utilize the four measurements to recover the degree of polarization for partially
polarized light. This exploration is done in simulation, but the same calibration and
reconstruction procedure can be used experimentally as well.
8.1 Reconstruction Method
The problem of converting the signal in each of the four quadrants into the incident
polarization state can be phrased as follows:
M
S
=
T
(23)
where
M
is the forward model that maps the Stokes vector,
S
, to the observed
quadrant transmissions,
T
. We utilize the common definition of the Stokes
parameters:
S
=
S
0
S
1
S
2
S
3
=
E
2
x
+
E
2
y
=
E
2
45
+
E
2
45
=
E
2
R
+
E
2
L
E
2
x
E
2
y
E
2
45
E
2
45
E
2
R
E
2
L
(24)
where
E
x
,
E
y
,
E
45
, and
E
45
are projections onto horizontal, vertical, 45-degree,
-45-degree linear polarizations, respectively and
E
R
and
E
L
are projections onto
right- and left-circular polarizations, respectively. To calibrate the device, we input
each of these individual polarization components and observe the transmission into
each of the four quadrants. Then, we form:
M
σ
=
τ
σ
=

S
x
S
y
S
45
S
45
S
R
S
L

R
4
x
6
τ
=

T
x
T
y
T
45
T
45
T
R
T
L

R
4
x
6
M
R
4
x
4
(25)
where
S
x
=

1 1 0 0

,
S
y
=

1
1 0 0

,
S
45
=

1 0 1 0

,
S
45
=

1 0
1 0

,
S
R
=

1 0 0 1

,
S
L
=

1 0 0
1

and
T
α
are the four quadrant
transmissions under excitation by the the
S
α
state. We solve for
M
by taking the
pseudo-inverse of
σ
and applying it on the right side,
M
=
τ
σ
. Then, we form
the solution or reconstruction matrix by taking the inverse of
M
, such that given a
set of measurements
T
, we compute the Stokes parameters as
S
=
M
1
T
. We note
this calibration could alternatively be done with the four analyzer states used in the
design and we expect the results would be similar.
8
8.2 Reconstructing Pure Polarization States
The reconstruction method applied to pure polarization states is shown in
Fig. S9
for different amounts of added noise in the transmission measurements to simulate
different signal-to-noise ratios in the sensor detection. For
p
added noise, we add
a normally distributed random variable with a mean of
0
and a standard deviation
equal to
p
T
avg
where
T
avg
is the mean transmission across the four quadrant
transmissions. As can be seen for increasing noise, the
S
3
parameter is the most
susceptible to a reduced signal-to-noise ratio. This is likely due to the circular
polarization analyzer state exhibiting the lowest contrast and the
S
3
Stokes parameter
being a direct measure of the handedness of the circular polarization in the input.
8.3 Reconstructing Mixed Polarization States
The use of four projective measurements means information about partially polarized
input states is contained in the quadrant transmissions. To test our ability to recover
this property, we consider the situation where the polarization vector input into the
device is randomly changing. We input a series of random polarization states into
the device, and average the resulting quadrant transmission values for each quadrant.
From these averaged transmission values, we reconstruct the Stokes vector in the
same way as above. This reconstructed vector is compared to the averaged Stokes
vectors for all the states input into the device. The degree of polarization of the light
is computed as
p
=
S
2
1
+
S
2
2
+
S
2
3
S
0
.
Fig. S10
shows the results of reconstructing mixed polarization states. As the
number of averaged states increases, the degree of polarization starts dropping. When
noise is added per averaged state (using the same type of distribution as above), the
squared error for the reconstruction is highest for the smaller number of averaged
states. As this number of states increases, the fluctuating noise term starts averaging
to zero thus decreasing the overall effect of noise on the reconstruction.
9 Angular Momentum Sorting Device Outside of Design
Points
Fig. S11
and
Fig. S12
demonstrate the behavior of the angular momentum
sorting device for different values of spin and OAM, respectively, than the design
states. In an optical communication application, controlling the behavior of the device
at these alternate points will depend on the amount noise present and mode distortion
between communication links. However, in an advanced imaging context where
information about the scene is inferred through the spatially resolved projection
of the input onto different angular momentum states, the response of the device
to other mode inputs needs to be at least characterized if not explicitly designed
for the given application. As a note, the optimization technique used here was not
directed to explicitly minimize or control the behavior of the device under these
other excitations. By adding more simulations to each iteration to capture the effect
of illuminating with these other modes, we can compute a gradient that either
9
enables control over the quadrant these other modes couple to or extinguishes their
transmission.
9.1 Illumination with Different Spin Values
In
Fig. S11
, we observe the device behaves similarly upon a flip in the handedness
of the circular polarization for each angular momentum state. This can be seen
through similar contrast and transmission profiles albeit at lower overall values. Thus,
the optimization solution for the device relied primarily on the different OAM values
for splitting and does not have strong polarization discriminating behavior.
9.2 Illumination with Different OAM Values
In
Fig. S12
, we observe the device output changes drastically when illuminated
with different OAM values. Most of the light for each of the four states goes to the
quadrants designed for the original higher design OAM values (i.e. -
l
=
2
,
+2
).
This is the reason for the negative contrast in the other two quadrants. Further, overall
transmission values are significantly reduced with the higher transmission occurring
for OAM values closer to the design points (i.e. -
l
=
3
,
+3
).
10
10 Supplementary Figures
10.1 Optical setup for characterization of multispectral and
polarimetry devices
Camera
L2
L1
LPHWP1
PM
QCL
DUT
HWP2
QWP1LP
HWP2
QWP1 QWP2LP
L1
L2
PM
PM
QCL
WP
a
b
Mirror
Supplementary Fig. 1
:
(a)
Configuration for imaging of device focal plane and
power normalization. Without the mirror in place, the lens images focal planes of the
device onto the camera. Normalization of the device transmission is done with the
mirror and power meter path of the setup. For these measurements, net power through
an empty aperture is used to normalize net power through an aperture of the same
size with the device on top of it. The power meter is aligned to the beam center, which
is aligned to the pinhole centers during measurement. QCL: MIRcat-QT Mid-IR
Quantum Cascade Laser (DRS Daylight Solutions); HWP1: Thorlabs WPLH05M-
4500, Low-Order 4.5
μ
m
Half-Wave Plate; HWP2: Thorlabs WPLH05M-5300,
Zero-Order 5.3
μ
m
Half-Wave Plate; QWP 1: Thorlabs WPLQ05M-4500, Low-Order
4.5
μ
m
Quarter-Wave Plate; LP: Thorlabs WP25M-IRA, Wire Grid Polarizer; L1:
Thorlabs AL72525-E1, ZnSe Aspheric Lens, NA=0.42; L2: Thorlabs AL72512-E1,
ZnSe Aspheric Lens, NA=0.67; Camera: Electrophysics PV320L IR Camera.
(b)
Configuration for verifying the polarization states used to test the Stokes polarimetry
device. The second quarter-wave plate is moved to three distinct positions and
the power in each linear polarization component separated by the Wollaston prism
is recorded. QWP2: Thorlabs WPLQ05M-3500, Low-Order 3.5
μ
m
Quarter-Wave
Plate; WP: Thorlabs WPM10, Wollaston Prism.
10.2 Stokes state creation and verification
11
linear
polarizer
half-wave
plate
quarter-wave
plate
to device
or
to QWP/WP
quarter-wave
plate (QWP)
Wollaston
prism (WP)
x-polarization
component
y-polarization
component
a
b
c
Supplementary Fig. 2
:
(a)
Polarization states are created through choice of angles
of the linear polarizer, half-wave plate, and quarter-wave plate (
θ
1
,
θ
2
, and
θ
3
).
(b)
Each state is verified by measuring the horizontal and vertical polarization
component magnitudes output from the Wollaston prism after the state passes through
a quarter-wave plate under three different rotations,
φ
.
(c)
Plot of measured Jones
vector overlap for the
4
analyzer states and their
4
orthogonal complements for each
measurement wavelength used in the experiment.
12
10.3 Simulation performance for Stokes polarimetry device with
additional degrees of freedom compared to Stokes
polarimetry device from the main text
13
a
b
d
b
Analyzer States:
Orthogonal States:
orthogonal
states
analyzer
states
orthogonal
states
analyzer
states
c
Supplementary Fig. 3
:
(a)
Polarization contrast (
C
)
and transmission (
T
) for device
from the main text showing low contrast for the circular polarization analyzer state.
For input
k
,
C
k
=
T
|
S
k
⟩→
Q
k
T
|
ˆ
S
k
⟩→
Q
k
T
|
S
k
⟩→
Q
k
+
T
|
ˆ
S
k
⟩→
Q
k
.
(b)
Polarization contrast and transmission for
device with additional degrees of freedom showing high contrast for all four analyzer
states at the cost of slightly reduced analyzer state transmission.
(c)
Focal intensity
images for device from the main text with the top row showing the analyzer states and
the bottom row showing their orthogonal complements. Intensity units are arbitrary
but comparable between all plots in (c). The focal plane size is same as device
aperture (
30
μ
m
x
30
μ
m
).
(d)
Focal intensity image comparison for the device with
additional degrees of freedom. Intensity units are arbitrary but comparable between
all plots in (d). The focal plane size is the same as device aperture (
30
μ
m
x
30
μ
m
).
14
10.4 Schematic of simulation geometry for optimization and
evaluation
PML
PML
PML
PML
TFSF Source
Region
Focal Plane
Device
Optimization
Region
Plane Wave Source
PML
PML
PML
PML
Focal Plane
Device
Optimization
Region
Gaussian Source
a
b
Supplementary Fig. 4
:
(a)
Simulation geometry for optimization of the multispectral
and Stokes polarimetry devices using a plane wave excitation. The angular
momentum devices are optimized using focused angular momentum states with
different circular polarization handedness for spin.
(b)
Evaluation geometry for the
multispectral and Stokes polarimetry devices where the plane wave excitation is
replaced with a defocused Gaussian source intended to match with the experimental
source. Angular momentum devices are evaluated with the same sources as used for
optimization.
15
10.5 Schematic of fabrication process
a
b
c
d
e
f
g
sapphire substrate
photolithography
(negative resist)
Al deposition
liftoff in acetone
drop IP-Dip resist
direct laser write
(two photon polymerization)
develop (PGMEA)
and rinse (IPA)
Supplementary Fig. 5
:
(a)
Fabrication starts with a sapphire substrate (Al
2
O
3
,
C-plane (0001), double side polished, 2-inch diameter, 0.5mm thickness).
(b)
Using a negative tone photoresist, apertures are patterned onto the substrate using
photolithography.
(c)
After direct oxygen and argon plasma cleaning to remove
undesired residual resist on the substrate, 150
nm
of Al is deposited on top using an
electron beam evaporator.
(d)
The liftoff procedure is finished in acetone to remove
remaining photoresist followed by cleaning in IPA and then DI water.
(e)
The IP-
Dip resist from Nanoscribe is dropped onto the substrate.
(f)
Alignment is done
by keeping the laser power below polymerization threshold and using fluorescence
from its focused spot to align to the aperture centers for printing.
(g)
Development
in propylene glycol methyl ether acetate (PGMEA) for 20 minutes followed by two
three-minute rinses in IPA reveals the final device.
10.6 Conceptual diagram of the Stokes polarimetry device
16