# Scattering holography designed metasurfaces for channeling single-photon
emission

Danylo Komisar<EMAIL_ADDRESS> Center for Nano Optics, University of
Southern Denmark, DK-5230 Odense M, Denmark  Shailesh Kumar<EMAIL_ADDRESS>Center for Nano Optics, University of Southern Denmark, DK-5230 Odense M,
Denmark  Yinhui Kan  Center for Nano Optics, University of Southern Denmark,
DK-5230 Odense M, Denmark  Chao Meng  Center for Nano Optics, University of
Southern Denmark, DK-5230 Odense M, Denmark  Liudmilla F. Kulikova  L.F.
Vereshchagin Institute for High Pressure Physics, Russian Academy of Sciences,
Troitsk, Moscow, 142190, Russia  Valery A. Davydov  L.F. Vereshchagin
Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk,
Moscow, 142190, Russia  Viatcheslav N. Agafonov  GREMAN, CNRS, UMR 7347, INSA
CVL, Université de Tours, 37200 Tours, France  Sergey I. Bozhevolnyi  Center
for Nano Optics, University of Southern Denmark, DK-5230 Odense M, Denmark
Danish Institute for Advanced Study, University of Southern Denmark, DK-5230
Odense M, Denmark

###### Abstract

Channelling single-photon emission in multiple well-defined directions and
simultaneously controlling its polarization characteristics is highly
desirable for numerous quantum technology applications. We show that this can
be achieved by using quantum emitters (QEs) nonradiatively coupled to surface
plasmon polaritons (SPPs), which are scattered into outgoing free-propagating
waves by appropriately designed metasurfaces. The QE-coupled metasurface
design is based on the scattering holography approach with radially diverging
SPPs as reference waves. Using holographic metasurfaces fabricated around
nanodiamonds with single Ge vacancy centers, we experimentally demonstrate on-
chip integrated efficient generation of two well-collimated single-photon
beams propagating along different $15^{\circ}$ off-normal directions with
orthogonal linear polarizations.

###### pacs:

Valid PACS appear here

## Introduction

Single-photon emission is an essential part in different quantum information
technologies, including quantum communication and cryptography [1], sensing
[2], and in fundamental studies of quantum phenomena [3, 4]. Solid-state
systems like single molecules [5, 6], color centers in diamonds [7, 8, 9],
quantum dots [10, 11, 12], and defects in 2D materials [13] are reported to
serve as robust single-photon sources [14, 15]. Germanium vacancy (GeV)
centers in diamonds have emerged as a promising candidate for use in single-
photon experiments due to their brightness, high emission into zero-phonon
lines and ability to operate at room temperatures [16, 17, 18, 19, 20, 21,
22]. However, the spontaneous emission of quantum emitters located in free
space is, in general, not well-directed and poorly polarized. Rapidly
developing quantum technologies require a technological platform that would
provide a reliable method for realizing, preferably on-chip, versatile and
efficient single-photon sources with controlled emission directions and
polarizations.

Various plasmonic antennas have been utilized for engineering the single
photon properties and have been used for generation of radially-polarized
[23], circularly polarized [24] and vortex [25] beams, polarization encoded
multichannel emission [26], cavity-enhanced emission [27] and beam steering
[28]. Many of these plasmonic antennas represent optical metasurfaces, i.e.,
dielectric ridge structures fabricated around QEs, that are utilized to
scatter QE-excited SPPs into outgoing free-propagating waves, enabling thereby
control over the QE emission into free space [23, 24, 25]. These metasurfaces
feature, however, a fundamental limitation, which is associated with the
isotropic nature of SPP scattering by continuous antenna ridges and which
results in an inherent inability to efficiently control the emission
polarization, unless the radially polarized emission is targeted [23]. The
diverging QE-excited SPP is radially polarized in the surface plane. This
polarization is then projected onto the polarization of the outgoing free-
propagating waves produced by a metasurface. This allows for control over the
polarization of the outcoupled beam. For example, the generation of the the
left and right circularly polarized beams with specific angular optical
momenta [25, 29]. The metasurface design can be described within the framework
of the scattering-holography approach [29] that allows one to accurately
design metasurfaces for single-channel photon emission into well-defined
arbitrary, including off-normal, directions. We have developed this approach
further , extending it to the case of photon emission into multiple different
directions and circumventing the above limitation, at least in the case of
generation of orthogonally and lineraly polarized single-photon beams.

In this article, we report on the design, fabrication and characterization of
hybrid QE-SPP coupled metasurfaces that enable generation of two well-
collimated (divergences $<6.5^{\circ}$) single-photon beams propagating along
different 15∘ off-normal directions and featuring orthogonal linear
polarizations. We find that the conversion efficiency of QE power into photons
forming these two beams can exceed 80%, depending on the metasurface
realization. Highly compact and efficient planar photonic components
demonstrated in our work represent essentially single-photon sources,
collimators and polarizing beam splitters integrated together in on-chip
devices, showcasing thereby the potential of QE-SPP coupled holographic
metasurfaces for a wide range of quantum technology applications.

## Results

### Performance of plasmonic metasurface

The operation principle and performance of the designed QE-SPP coupled
metasurface is illustrated in Figure 1. The fabricated metasurface consists of
a single GeV center in a nanodiamond (ND) with an emission peak at 602 nm
placed atop an optically thick silver (Ag) film with a thin SiO2 overlayer and
surrounded by dielectric outcoupling ridges. When pumped with a 532 nm laser,
the GeV-ND center, which is selected to have the radiative transition dipole
oriented perpendicular to the sample surface, excites radially diverging SPPs
that propagate along the Ag-SiO2 interface. The SPP excitation efficiency
depends on configuration material, optical and geometrical parameters,
influencing the loss through nonradiative and radiative channels, and can
exceed 85% [30, 23]. These SPPs are then out-of-plane scattered by an array of
hydrogen silsesquioxane (HSQ) ridges into outgoing free-propagating waves in
the form of two single-photon beams, featuring orthogonal linear polarizations
and propagating along different directions. The inevitable absorption of SPPs
occurring during their propagation (before being out-of-plane scattered) can
be minimized by using high-refractive index ridges to increase the scattering
efficiency and high-quality metal films to reduce the ohmic losses. For
example, in the case of generation of radially polarized single photons in a
similar metasurface configuration with the bullseye ridge pattern, the
external quantum efficiency can reach 95% [23]. The external quantum
efficiency is defined as a fraction of the total dipole power radiated into
outgoing waves, propagating within a $64^{\circ}$ cone (collected by an NA =
0.9 objective). For the considered configuration, the corresponding external
quantum efficiency is evaluated at the level of 60% (see for details
Supporting Information, SI, Section 1).

### Holography approach to metasurface design

The QE-SPP coupled metasurface design is based on the scattering-holography
approach with the QE-excited radially diverging SPPs serving as reference
waves [29], which we further extend to the case of photon emission into
multiple different directions. This is achieved by multiplexing holograms,
i.e., the intensity interference patterns, computed when using the in-plane
field distributions of signal beams with desired sizes, polarizations and
propagation directions. For clarity, we consider only the in-plane electric
field components, as they are the ones responsible for scattering in the
directions close to normal to the surface. In our case, the electric fields of
the signal waves are represented by their in-plane field components $E_{x}$
and $E_{y}$ for either X- or Y-polarized beams propagating along different 15∘
off-normal directions. Note that, due to the orthogonal polarizations of the
two signal waves, the hologram can be computed in one step (SI, Section 2)
instead of computing holograms separately with their subsequent multiplexing.
Importantly, in this special case of orthogonal linear polarizations, two
constituting holograms complement each other resulting in the efficient use of
the available metasurface area [Figure 2(b-c)]. Generally speaking, the
efficiency of isotropic holographic metasurfaces for producing linearly
polarized free space emission cannot exceed 50%, because in-plane radially
polarized SPPs contain equal amount of two orthogonal linear polarizations.
For this reason, designing the QE-SPP coupled metasurface for generating two
single-photon beams with orthogonal linear polarizations is attractive apart
from realizing a useful single-photon functionality also from the viewpoint of
maximizing the external quantum efficiency.

The practical design of the metasurface ridges builds upon the calculated
smooth interference patterns, requiring their conversion into patterns of
ridges of the same height but different width. Note that the presence of
dielectric ridges influences the SPP propagation constant and has to be
properly taken into account already at the stage of calculating the
interference pattern [23, 24, 29]. To simplify the design procedure we adjust
our design so that the ridge filling factor varies around 0.5, and use this
filling factor and the ridge height of 200 nm to evaluate the SPP propagation
constant for computing the interference patterns [23]. Importantly, when
calculating a particular interference pattern we use radially increasing SPP
field as reference wave. This is done to compensate for the radial decay of
QE-excited SPP wave due to it divergence, absorption and out-of-plane
scattering (SI, Section 1.1). This procedure results in widening of outer
metasurface ridges and thus enhancing the SPP scattering. As a result, when
the designed metasurface interacts with diverging and radially attenuating SPP
waves, the out-of-plane scattered field reconstructs a predefined amplitude
and polarization profile [29].

### Pattern optimization

The optimization of the holographic metasurface to be fabricated was conducted
numerically at the wavelength of 602 nm corresponding to the zero-phonon line
(ZPL) of the GeV center. In particular, we optimized the metasurface diameter
along with the ridge width variations in order to maximize the external
quantum efficiency and minimize the divergence of each beam, while preventing
the fabrication of unnecessarily large metasurface structures. The metasurface
size is determined by the SPP decay due to its absorption and scattering on
the ridges. By considering these factors, we calculated an effective structure
diameter of 17 µm (SI, Section 1.2). The resulting metasurface presented in
Figure 2(a) is expected to produce two well-separated (overlap $<13$%) beams
with the full angular width at half maximum (FWHM) of $\uptheta_{1/2}$<5.2∘
and the external quantum efficiency of 63%. At the same time, the polarization
states of generated beams characterized by the Stokes parameter S1, which is
determined as $S_{1}=(I_{x}-I_{y})/(I_{x}+I_{y})$ with $I_{x}(I_{y})$ denoting
the intensities of the linear X(Y) polarizations, are expected to be
orthogonal with high degrees of linear polarizations [Figure 2(d)]. Finally,
we assessed the robustness of the resulting metasurfaces design for eventual
ND misalignments with respect to the metasurface ridges, and found that the ND
displacements in the surface plane below 100 nm do not noticeably perturb the
far-field emission pattern and thereby the metasurface performance (SI,
Section 3).

A scanning electron microscope (SEM) image of the fabricated Gev-ND-coupled
metasurface with a diameter of 17 µm is shown in Figure 3(a-b). A typical
fluorescence scan of the properly oriented GeV-ND, coupled to the metasurface
and measured with a narrow-band spectral filter at $605\pm 8$ nm, is shown in
Figure 3(c). The doughnut-shaped pattern of fluorescence confirms that the
considered ND contains a GeV center with a radiative dipole oriented
perpendicularly to the sample surface, as required for maximizing SPP
excitation and for proper operation of the metasurface designed for the dipole
source normal to the surface. Fabrication details are described in SI, Section
4.

### Single-photon source characterisation

We characterize properly oriented GeV-NDs before and after the metasurface
fabrication. Typical normalized emission spectra of a GeV-ND center obtained
before and after its coupling to the metasurface [Figure 4(a)] feature a
characteristic ZPL centered at 602 nm with 7 nm FWHM [31, 32]. After the
coupling to the metasurface in this particular case, the ZPL signal became
enhanced by 20%, an enhancement which is related to the efficient SPP
outcoupling by the metasurface ridges. The lifetime measured for the GeV-ND
before and after fabrication of the metasurface are $\tau_{uc}$=16 ns and
$\tau_{c}$=19 ns, respectively, corresponds to typical values [16, 27, 33]. An
increase in lifetime after fabrication is attributed to a destructive feedback
by metasurface ridges surrounding the GeV-ND asymmetrically Figure 3(b). A
single exponential model, $I=A_{0}+Ae^{-t/\tau}$, is used for fitting the
experimental data, where $\tau$ is a characteristic lifetime of the decay
process with $A_{0}/A$ accounting for a background contribution [Figure 4(b)].

To estimate the GeV-ND center brightness, we measured emission rates while
increasing the excitation power and fitted the data to estimate the saturated
emission rate and excitation power [Figure 4(c)]. The data was fitted to
$I=I_{sat}[P/(P+P_{sat})]$, where I and P are experimentally measured emission
rate and excitation power, respectively, whereas $I_{sat}$ and $P_{sat}$ are
the fitting parameters. It is seen that the saturated emission rate before
coupling to the metasurface, $I_{sat}=1$ Mcps while $P_{sat}=1.8$ mW,
increased after the coupling by 30%, $I_{sat}=1.3$ Mcps while $P_{sat}=1.3$
mW. The increased single-photon emission rate observed is consistent with the
increased ZPL signal [Figure 4(a)] and related to the efficient SPP
outcoupling by the metasurface that outweighs the influence of its destructive
feedback.

Finally, we verified the single-photon nature of emission from the
investigated GeV-ND by characterizing the autocorrelation of its emission and
observing anti-bunching minima well below 0.5 both before,
$g^{(2)}_{u}(0)=0.08$, and after, $g^{(2)}_{c}(0)=0.16$, coupling to the
metasurface [Figure 4(d)]. We attribute a slight increase in $g^{(2)}(0)$ to
the background fluorescence of the HSQ traces around the GeV-ND.

### Polarization splitting and beams collimation

Having confirmed the single-photon emission from the GeV-SPP coupled
metasurface, we investigated angular distribution and polarization
characteristics of the single-photon emission, observing in the Fourier plane
two bright emission spots with orthogonal linear polarizations as expected
[Figure 5(a)]. The spot locations are equally displaced from the normal to the
surface by 15∘ as designed and also predicted by FDTD calculations [Figure
5(b)], demonstrating good agreement between experimental and calculated
angular distributions. The generated beams are expected to be collimated
better in the direction of the emission polarization due to a better coverage
by the corresponding metasurface region [Figure 2(b-c)], a feature that is
ultimately related to the longitudinal orientation of the in-plane SPP
polarization. Nevertheless, the experimentally measured angular FWHM of the
generated beams for both polarizations was found within 6.5∘, securing thereby
sufficient angular separation of the emission channels with orthogonal linear
polarizations. A small difference in experimental X and Y peak intensities
[Figure 5(c)] is believed to result from imperfection of the metasurface
positioning, whose precision is evaluated being 50 nm. The experimentally
realized degree of linear polarization can be judged upon from the normalized
Stokes parameter $S_{1}$ distribution in the Fourier plane, reaching 0.79 for
X- and 0.82 for Y-linear polarizations at the corresponding intensity maxima
[Figure 5(d)].

## Discussion

The experimental characterization reveals the metasurface performance being
worse than expected from the numerical simulations, a deterioration that is
understandable for several reasons. First, the simulations were performed for
monochromatic (602 nm) fields, whereas optical characterization involved the
use of a 16-nm-wide bandpass filter. Second, a GeV-ND is perfectly located
with respect to the metasurface in the design, while the experimental
precision of ND positioning is limited to 50 nm. Additionally, the radiating
dipole is oriented perfectly perpendicular to the surface in the design,
whereas that of a GeV-ND center selected for the metasurface fabrication might
have nonzero projections on the surface plane. Finally, geometrical parameters
of fabricated metasurfaces differ, although on the nm-scale, from the
optimized ones. All these factors would result in deteriorated performance,
such as broadening of the generated beams, polarization cross talk and other
distortions in the emission pattern, in comparison with the results of
numerical modeling. At the same time, the developed approach for generating
two spatially separated single-photon beams propagating along different
directions with orthogonal linear polarizations was found to be sufficiently
robust and amenable to different radiation wavelengths. The experiments
similar to the described above were successfully conducted with another single
GeV-ND center as well as with NDs containing multiple Si vacancy (SiV) centers
emitting at 738 nm and coupled to metasurfaces with different diameters (SI,
Section 6).

To summarize, we have developed the approach to realize the on-chip integrated
efficient single-photon sources of well-collimated beams propagating along
different off-normal directions and featuring different linear polarizations.
Using single GeV-ND centers embedded in holographic dielectric metasurfaces
supported by silver substrates, we have demonstrated efficient (63%)
generation of two well-collimated (divergences $<6.5^{\circ}$) single-photon
beams propagating along different 15∘ off-normal directions and featuring
orthogonal linear polarizations. It should be noted that the efficiency can be
further increased by using high-refractive index metasurface ridges to boost
their out-of-plane scattering and high-quality monocrystalline metal films to
reduce the ohmic losses [34]. Thus, simply by changing the ridge material to
titanium dioxide (TiO2), the external quantum efficiency is expected to exceed
80%, even without further optimization of ridge parameters as described for
the bullseye pattern [23]. Importantly, we have shown that the developed
approach is robust and flexible and thus can readily be applied to a wide
range of QEs, including quantum dots and individual molecules. We believe that
on-chip integrated, highly compact and efficient, multifunctional single-
photon components demonstrated in our work convincingly showcase the potential
of QE-SPP coupled holographic metasurfaces for a wide range of quantum
technology applications.

Authors gratefully acknowledge Torgom Yezekyan and Volodymyr Zenin for
assistance with experimental setup as well as Xujing Liu and Cuo Wu for
fruitful discussions on all research steps. SK acknowledges financial support
from VILLUM FONDEN by a research grant (35950). YK acknowledges the support
from European Union’s Horizon Europe research and innovation programme under
the Marie Skłodowska-Curie Action (Grant agreement No. 101064471). CM
acknowledges the EU Horizon 2020 research and innovation program (Marie
Skłodowska-Curie grant agreement No. 713694). SIB acknowledges the support
from the Villum Kann Rasmussen Foundation (Award in Technical and Natural
Sciences 2019).

## Methods

### Device fabrication

Metasurfaces are fabricated in a two-step process of electron beam lithography
(EBL) using a scanning electron microscope JOEL JSM-6490LV with an
acceleration voltage of 30 keV. The substrate consists of a polished Si wafer
coated with 3 nm Ti, followed by 150 nm Ag, another 3 nm Ti, and a 30 nm SiO2
layer, which protects the silver from atmospheric influence. The Ti is added
for better adhesion between the materials. In the first lithography step, 35
nm thick golden alignment markers are deposited using 200 nm thick PMMA
positive resist. Further, a water dispersion of GeV-NDs with an average size
of $\sim$100 nm is spin-coated on the sample. The choice of NDs is made using
a strongly focused radially polarized excitation beam. This beam produces a
strong out-of-plane field component in the focal point and consequently
excites GeV centers with a predominant out-of-plane dipole moment most
efficiently. In the second lithography step, 200 nm thick HSQ holographic
metasurfaces are deposited around individual GeV-NDs with alignment relative
to the golden markers. HSQ is a negative resist. Precise fabrication
parameters can be found in Section 4 of the Supplementary Information.

### Experimental optical characterization

All measurements are performed at room temperature under 532 nm laser
excitation. The experimental setup scheme is presented in SI, Section 1. The
excitation laser beam is purified by passing through a single mode
polarization maintaining fiber, then converted to radially polarized beam
using a Radial Polarization Converter. The Olympus MPLFLN x100 objective with
0.9 NA focuses the beam onto the sample surface, exciting GeV-ND quantum
emitters with a strong normal to surface field component. The optical signal
scattered from the metasurface is collected by the same objective. Laser light
is filtered out using dichroic mirrors and long-pass filters. Decay-rate
measurements are performed using time-correlated single photon counting
technique under weak 10 µW excitation power to keep the GeV in unsaturated
emission regime. To purify the emission a narrow-band $605\pm 8$ nm filter was
used for all presented optical measurements except spectral ones. For
g${}^{(}2)$ correlation function measurements 256 ps time-bin width was
used.Saturation curves of GeV emission are measured by accumulating counts
from both APDs with excitation laser power varying in range from 10 µW to 7
mW. Back focal plane images are captured with a CCD camera , with emission
polarization properties measured using a Glan-Thompson polarizer. Exact
specifications of the set-up components can be found in Supplementary, Section
5.

### Pattern generation

The metasurface pattern was generated using Matlab software, calculating the
interference between X and Y-polarized beams as signal waves and SPP as the
reference wave of a hologram. The pattern was designed considering only in-
plane field components on the metal-dielectric interface. The refractive
indices of the dielectrics were set to n(SiO2) =1.45 and n(HSQ)=1.41. The real
part of the SPP mode index in the antenna domain was calculated as the average
of Neff(Air)=1.12 and Neff(HSQ)= 1.52, due to the 50% filling factor. These
values correspond to the mode indices of SPP propagation on the Ag-SiO2-Air
and Ag-SiO2-HSQ-Air interfaces, respectively. The fixed filling factor allowed
to simplify calculations by utilizing the constant SPP mode index and
wavelength along the structure. The generation of the pattern is illustrated
in the SI, Section 2.

### Numerical modelling

Numerical simulations were performed using FDTD simulations (Lumerical) in a
3D domain. The simulations were conducted at an operating wavelength of 602 nm
corresponding to the zero-phonon line (ZPL) of the GeV center. The GeV-ND was
modeled as a vertically oriented electric dipole positioned 30nm above the 30
nm thick SiO2 spacer. The Ag layer had a thickness of 300 nm. The far-field
angular distributions were calculated using the built-in Lumerical near-to-far
field transformation procedure. The near-field data was collected from the
monitor positioned 50 nm above the HSQ structure. Quantum efficiency was
calculated by integrating the Poynting vector on a box covering the
metasurface, positioned 150 nm above the substrate to avoid encountering the
SPP field. The refractive index of HSQ was set to be n(HSQ) = 1.41, extinction
coefficient k = 0 [35]. The optimal dipole separation distance from the SiO2
surface was determined to be between 15 and 80 nm [9]. Optical constants for
silver and SiO2 were taken from [36] and [37], respectively.

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## Acknowledgements

Authors gratefully acknowledge Torgom Yezekyan and Volodymyr Zenin for
assistance with experimental setup as well as Xujing Liu and Cuo Wu for
fruitful discussions on all research steps. SK acknowledges financial support
from VILLUM FONDEN by a research grant (35950). YK acknowledges the support
from European Union’s Horizon Europe research and innovation programme under
the Marie Skłodowska-Curie Action (Grant agreement No. 101064471). CM
acknowledges the EU Horizon 2020 research and innovation program (Marie
Skłodowska-Curie grant agreement No. 713694). SIB acknowledges the support
from the Villum Kann Rasmussen Foundation (Award in Technical and Natural
Sciences 2019).

## Author contributions

S.I.B. conceived the experiment and developed the metasurface design method.
D.K. performed numerical optimization, fabrication, and experimental
characterization of the device. S.K. assisted the experiment. C.M. and Y.K.
contributed to numerical simulations of device design and optimization.
L.F.K., V.A.D. and V.N.A synthesized the GeV nanodiamonds. All authors
contributed to discussion and interpretation of the results. D.K. wrote the
manuscript with contributions of S.I.B. and S.K. S.I.B. and S.K. supervised
the project.

## Competing interests

The authors declare no competing interests.

## Figures and Captions

Figure 1: Schematic of a QE-SPP coupled metasurface. QE-excited radially-
diverging SPPs are scattered by metasurface dielectric ridges into outgoing
free-propagating waves, producing two spatially separated single-photon beams
with orthogonal linear polarizations. Figure 2: Hologram metasurface design
and operation. (a) Optimized pattern of HSQ ridges composing the polarization-
splitting metasurface. (b) Illustration of the operation principle behind
generation of orthogonally polarized beams: red and blue colored areas
indicate metasurface domains responsible for generating predominantly X- and
Y-polarized outgoing waves, respectively. Grey colored domains contribute to
both X- and Y-polarized beams. Metasurfaces designed for generating either
X-(red) or Y-(blue) polarized beams are illustrated in (c). (d) Calculated 3D
angular distributions of the superimposed beam intensity shown by height and
polarization Stokes parameter S1 encoded by color. These simulations are
conducted for the optimized metasurface configuration described further in the
paper. The occurrence of blue and red peaks demonstrates spatial separation of
two emission channels featuring orthogonal linear polarizations. Figure 3:
Images of the fabricated metasurface and Gev-ND. (a) Tilted SEM image of the
holographic metasurface. (b) Zoom on the central area showing an ND with a GeV
center properly positioned with respect to metasurface ridges. (c) Fluorescent
scan (3x3 µm2) showing emission of the GeV with out of plane dipole moment.
Figure 4: Characterization of GeV-ND emission. (a) Emission spectra of GeV-ND
center characterized before (blue) and after (red) coupling to the metasurface
featuring the resonant peak at 602 nm. (b) Lifetime measurements using a
pulsed laser with 1 MHz rate show single-exponent emission decays along with
the instrument response function (IRF). (c) Emission rate power-saturation
dependencies. (d) Correlation data and a model fit to the g(2) correlation
function.  Figure 5: Angular and polarization emission distribution. (a)
Fourier-plane emission images collected with NA=0.9 objective from the GeV-ND
coupled to the holographic metasurface. From left to right: images taken
without analyzer, with analyzer parallel to X-axis, and to Y-axis of the
metasurface.(b) Corresponding simulated far-field intensity distributions.
Dashed circles mark 15o angular displacements from the normal to the surface.
(c) Intensity circular cross section distributions (along the dashed lines)
showing clear separation between X- and Y-polarized emission channels. (d) 3D
representation of the superimposed experimental distributions of emission
intensity (height) and polarization (color) Stokes parameter S1. Height
represents the intensity and color indicates the polarization