# Direct-Laser-Written Polymer Nanowire Waveguides for Broadband Single Photon
Collection from Epitaxial Quantum Dots into a Gaussian-like Mode

Edgar F. Perez<EMAIL_ADDRESS>Joint Quantum Institute, NIST/University of
Maryland, College Park, USA  Microsystems and Nanotechnology Division,
National Institute of Standards and Technology, Gaithersburg, USA  Cori Haws
Department of Engineering, University of Cambridge, Cambridge, CB3 0FA, United
Kingdom  Marcelo Davanco  Microsystems and Nanotechnology Division, National
Institute of Standards and Technology, Gaithersburg, USA  Jindong Song  Center
for Opto-Electronic Materials and Devices Research, Korea Institute of Science
and Technology, South Korea  Luca Sapienza  Department of Engineering,
University of Cambridge, Cambridge, CB3 0FA, United Kingdom  Kartik Srinivasan
<EMAIL_ADDRESS>Joint Quantum Institute, NIST/University of
Maryland, College Park, USA  Microsystems and Nanotechnology Division,
National Institute of Standards and Technology, Gaithersburg, USA

(August 28, 2024)

###### Abstract

Single epitaxial quantum dots (QDs) embedded in nanophotonic geometries are a
leading technology for quantum light generation. However, efficiently coupling
their emission into a single mode fiber or Gaussian beam often remains
challenging. Here, we use direct laser writing (DLW) to address this challenge
by fabricating 1 $\mu$m diameter polymer nanowires (PNWs) in-contact-with and
perpendicular-to a QD-containing GaAs layer. QD emission is coupled to the
PNW’s HE11 waveguide mode, enhancing collection efficiency into a single-mode
fiber. PNW fabrication does not alter the QD device layer, making PNWs well-
suited for augmenting preexisting in-plane geometries. We study standalone
PNWs and PNWs in conjunction with metallic nanoring devices that have been
previously established for increasing extraction of QD emission. We report
methods that mitigate standing wave reflections and heat, caused by GaAs’s
absorption/reflection of the lithography beam, which otherwise prevent PNW
fabrication. We observe a factor of ($3.0\leavevmode\nobreak\
\pm\leavevmode\nobreak\ 0.7)\times$ improvement in a nanoring system with a
PNW compared to the same system without a PNW, in line with numerical results,
highlighting the PNW’s ability to waveguide QD emission and increase
collection efficiency simultaneously. These results demonstrate new DLW
functionality in service of quantum emitter photonics that maintains
compatibility with existing top-down fabrication approaches.

Figure 1:  (a-d) 3D FDTD simulations of systems with and without polymer
nanowires (PNWs). For each system (a-d), the top panel is a schematic of the
physical device, the middle panel is a cross section of the system’s 3D FDTD
simulation, and the bottom panel is the far-field projection of the system’s
emission. The black dashed rectangles in the top panel frame the cross
sectional planes displayed in the middle panels, and the white lines in the
middle panels indicate the height at which the emission was sampled for far-
field projections shown in the bottom panels. (a) A reference system,
consisting of an x-polarized dipole in the middle of a 190 nm thick GaAs layer
on top of an Au back reflector, taken as a starting point for systems in
(b-d). (b) A standalone PNW system, with a 0.7 $\mu$m diameter PNW of 4 $\mu$m
length, centered over the dipole, showing emission confined- and guided-by the
PNW waveguide. (c) A metallic nanoring (NR) system, consisting of an Au NR of
inner diameter 236 nm and outer diameter of 437 nm centered above the QD. (d)
A metallic NR system with the same dimensions as in (c) and a concentric 0.7
$\mu$m diameter PNW of 4 $\mu$m length (i.e., the NR+PNW system). (e) Line
scans ($\phi=90\degree$, y-axis) of the $|E_{x}|^{2}$ far-field projections
for each system. The PNW (purple) and NR+PNW (green) systems have monotonic
and Gaussian-like distributions, whereas the reference (pink) and NR(orange)
systems without PNWs have wide and nonmonotonic distributions. (f) The ratio
of $|E_{x}|^{2}$ intensity emitted by the the PNW (pruple), the NR (orange),
and the NR+PNW (green) systems compared to the reference system, as a function
of polar angle $\theta$. See text for details. (g) The transmission of each
system through a plane 200 nm above the substrate, showing that all four
schemes are broadband. (h) Transmission into the various optical modes of the
PNW system (dashed) and the PNW+NR system (solid) as a function of PNW
diameter. Insets display the $|E_{x}|$ component of the $HE_{11}$ mode (green)
and $HE_{13}$ mode (orange) of a PNW with 1.3 $\mu$m diameter (circumference
shown as white line). The $HE_{12}$ mode (purple) of the system is only weakly
excited due to poor overlap with an x-polarized dipole.

As fundamental building blocks, single photons (SPs) and entangled photons
play key roles in the development of quantum science [1, 2], and their
efficient generation and collection into optical fibers is crucial for quantum
technologies such as quantum simulation and quantum communication [3, 4].
Among the many options for SP generation, semiconductor quantum dots (QDs) are
a favorable choice, as demonstrated performance has begun to approach the
challenging requirements of various applications [5, 6, 7, 8], with top-down
nanofabrication techniques, for creating photonic cavities and waveguides that
house the QDs, contributing significantly to the success of the platform.
However, in many such photonic geometries, realizing high fiber-coupled
collection efficiency of SP emission remains an important challenge that, if
unaddressed, limits the SP flux delivered to many downstream applications. A
viable solution to this problem should ideally increase the collection
efficiency without compromising other important performance characteristics,
such as SP purity and indistinguishability. To that end, several different
efforts to realize such solutions are underway [9, 10, 11]

In recent years, Direct Laser Writing (DLW) has been used to create a variety
of three-dimensional (3D) structures that improve fiber-to-chip coupling [12,
13, 14] with increasing levels of automation [15, 16], and complexity [17]. In
the context of SP emission, direct laser written solutions for epitaxially-
grown, semiconductor QDs have focused on the fabrication of micro-optics [18,
19, 14, 20] that shape and collect their far-field radiation. In addition, a
variety of DLW structures have been used in collection efficiency enhancement
from other single quantum emitters, such as color centers in diamond
nanocrystals [21] and organic molecules [22]. In this work, we use DLW to
fabricate high-index-contrast cylindrical waveguides, hereafter referred to as
polymer nanowires (PNWs), perpendicular to the surface of a semiconductor-
based SP emitter substrate. The PNWs operate on the near-field radiation of a
SP emitter to directly waveguide-couple its emission to an $HE_{11}$ optical
mode that can be well-coupled to a downstream optical fiber. Additionally, the
fabrication of PNWs does not require etching of the underlying substrate,
which limits potential negative effects on underlying emitters [23]. As a
result, PNWs may operate as standalone devices or in conjunction with existing
on-chip solutions - like other broadband collection-enhancing devices or
resonant cavities.

In this work, PNWs are studied as standalone devices and in conjunction with
metallic nanorings (NRs), which are broadband collection-enhancing devices
[24, 25], to improve the collection efficiency from epitaxially grown
InAs/GaAs QDs. PNWs prove to be effective at waveguide-coupling the emission
from QDs and we observe a factor of ($3.0\leavevmode\nobreak\
\pm\leavevmode\nobreak\ 0.7)\times$ improvement in collection efficiency in a
NR system with a PNW compared to the same system without a PNW. The inherently
broadband nature of waveguide collection, together with the low dispersion of
the materials comprising the PNW, results in improvements in collection
efficiency over a large bandwidth. Moreover, the collection into an HE11
optical mode is advantageous for direct fiber-coupling applications.

Section I contains a numerical investigation comparing systems with and
without PNWs, including the effect of PNW geometry, and the excitation of the
various modes of the PNW waveguide. Two key challenges to the fabrication of
these devices are standing wave reflections and heating; we present DLW
strategies that mitigate these problems in Section II. Optical
characterization of the fabricated PNWs is presented in Section III, and we
conclude by commenting on the utility that PNWs bring to integrated quantum
light sources. PNWs extend the role DLW plays in SP collection by working with
near-field emission to directly waveguide-couple SP radiation and increase
collection efficiency.

##  Polymer Nanowire Design

Polymer nanowires are shown as stand alone devices in Fig. 1(a-b), and as
complementary devices in Fig. 1(c-d). For each system, Fig. 1(a-d) provides a
schematic of the device (top), a cross section of 3D finite-difference time-
domain (FDTD) simulations of the system (middle), and far-field projections of
each system’s emission (bottom). The dashed black rectangle in the top panels
indicates the cross sectional plane displayed in the middle panels. Likewise,
the dashed white line in each middle panel indicates the distance from the
GaAs substrate at which the emission was sampled for the far-field
projections. The device illustrated in Fig. 1(a) consists of an x-polarized
dipole source (emission wavelengths from 880 nm to 980 nm) embedded in the
middle of a 190 nm layer of GaAs with an Au back reflector. This system has
been used in recent studies for broadband collection enhancement [26, 24], and
this work takes it as a reference point for understanding the improvements
offered by PNWs.

The fundamental concepts of PNW-guided emission can be understood by comparing
the reference system in Fig. 1(a) to the standalone PNW system in Fig. 1(b).
The reference system shows in-plane dipole emission that is significantly
trapped in the GaAs layer, with the limited free-space emission quickly
diverging. The $|E_{x}|$ component of the far-field projection of the system’s
emission shows a local minimum at its center and strong radiation at polar
angles greater than 40$\degree$, which is not well suited for coupling to the
$LP_{01}$ (fundamental, linearly polarized) mode of a single-mode fiber. In
contrast, simulating a 4 $\mu$m tall PNW with a 700 nm diameter concentric to
the dipole, as shown in Fig. 1(b), illustrates that the PNW laterally confines
radiation as it propagates through the PNW, along the z-axis, with a far-field
distribution that resembles the $LP_{01}$ mode of a fiber. Line scans along
the $\phi=90\leavevmode\nobreak\ \degree$ axis (i.e., the y-axis) of the
$|E_{x}|^{2}$ far-field distributions are directly compared in Fig. 1 (e),
which verifies that the distribution of the standalone PNW system (purple) is
more Gaussian-like, with a single maximum of greater amplitude at its center
compared to the reference system (pink).

The use of a PNW as a complementary device is studied in Figs. 1(c-d), where
it is simulated above a metallic NR. As previously reported [24, 27, 25], the
NR system shown in Fig. 1(c) shows an increase in vertical radiation compared
to the reference system, yet displays a local minimum at its center and a
large divergence angle. When the NR system is complemented with a PNW
(referred to as the NR+PNW system) the emission from the NR is coupled to the
optical modes of the PNW. As shown in Figs. 1(d-e), this results in a far-
field projection with a single maximum at its center that is of greater
amplitude than that of the NR system alone. As a complementary device, the PNW
has shifted the far-field $|E_{x}|^{2}$ distribution towards smaller angles by
coupling it to the $HE_{11}$ mode of the PNW.

Figure 2:  (a) A standard approach to DLW structures may use a flat substrate,
uniform laser power, and a solid-core design. (b,i) False-color SEM images
showing a modulation in the PNW diameter with periodicity of $\approx$230 nm
due to standing wave reflections of the pulsed 780 nm lithography beam. (b,
ii) Reflections from the substrate also cause a local increase in the
effective laser power near the substrate, which increases the diameter of the
PNW near the surface. (b, iii) Absorption of the lithography beam further
contributes to local heating of resist, which can lead to deformations and
resist vaporization (e.g., "bubbling"). (c) The exposure strategy used in this
work with a substrate mounted at a 10$\degree$ angle, reduced-power base
layers, and a hollow core. (d) False-color SEM images showing PNWs with
improved uniformity and decreased corrugation amplitudes realized with the
proposed exposure strategy. The 3D flexibility of DLW is used to correct for
the angle induced by the angled substrate in (d) (see Fig. 3), but is
intentionally included in this device for illustrative purposes. All scale
bars correspond to 1 $\mu$m .

For each of the PNW, NR, and NR+PNW systems, Figure 1(f) plots the ratio of
the integrated electric field intensity within a solid polar angle $\theta$,
calculated as $\int{|E_{x}|^{2}d\Omega}$, in the system to that of the
reference system. As expected, the PNW system (purple) and the NR+PNW system
(green) increase the radiation at small angles. At large angles, the total
extracted power of the PNW systems approaches the total extracted power of the
underlying system, suggesting that the PNWs have limited effect on the
extraction efficiency of the underlying devices. In other words, the PNWs
operate on the near field emission of the QD systems to increase collection
efficiency without significantly modification to their performance. For
$\theta\approx 12\degree$, the divergence angle of SM980 fiber [28], the PNW
(NR+PNW) system shows an increase of approximately 8.5$\times$ (41.0$\times$)
in collection efficiency compared to the reference system. For the same angle,
the NR+PNW system shows approximately 3.3$\times$ the collection efficiency of
the NR system without a PNW (orange curve). Finally, Fig. 1(g) compares the
broadband performance of each system, and shows that PNWs (purple) are
broadband devices, making them compatible with NR systems (orange), endowing
the NR+PNW system (green) with broadband performance as well.

Like most waveguides, the optical properties of a PNW will depend on its
geometry. Figure 1(h) shows the simulated transmission of dipole radiation
into various optical modes of the PNW as a function of nanowire diameter $D$
for the standalone system (dashed) and the NR+PNW system (solid). In general,
the two systems display similar behavior even with the collection from the
NR+PNW system being approximately 4$\times$ to 6$\times$ greater. As expected,
there is an optimal diameter $D\approx 700$ nm at which coupling into the
fundamental $HE_{11}$ mode of the PNW is maximized, with a monotonic decrease
for $D>700$ nm. This monotonic decrease is not associated with the excitation
of higher order modes, so it is attributed to a mismatch in the PNW mode
profile and the emission of the underlying device, meaning that it may be
possible to design a PNW in conjunction with underlying devices to prevent
this decrease. When $D\approx 1.3$ $\mu$m, coupling to the $HE_{13}$ mode of
the PNW begins to dominate and coupling to the $HE_{11}$ mode is reduced by
half. We note that coupling to the $HE_{12}$ mode of the PNW is inefficient at
all diameters due to poor overlap with an x-polarized dipole.

In summary, numerical studies of PNWs support their use as interfaces for
direct waveguide-coupling of dipole emission from solid-state SP emitters. In
both standalone and cooperative systems the PNWs offer waveguiding, $HE_{11}$
emission profiles, and significant farfield enhancement for small emission
angles $\theta\lessapprox 20\degree$. QD emission couples to the fundamental
mode of PNWs for $D\leq 1$ $\mu$m , with an ideal diameter of $700$ nm.
However, beyond $700$ nm, the large degree of overlap between the $HE_{11}$
mode of the PNW and the $LP_{01}$ mode of a single-mode fiber, together with
the small divergence of PNW emission, may still provide an overall increase in
the fiber collection efficiency of a system.

##  Fabrication of PNWs

The direct laser writing used in this study employs strongly focused 780 nm
femtosecond laser pulses to polymerize a small voxel of photoresist through
two photon excitation. Despite the minimum resolution of DLW systems routinely
reaching sub-micron scales [29, 30, 31], the DLW of sub-micron features
requires special attention to proximity effects during exposure [32] and
structural deformations during development [33]. Near the surface of
reflective and absorptive substrates like GaAs, additional challenges arise.
The partial reflection of the high intensity lithography pulses induces
standing waves that lead to modulations of the effective exposure dose.
Furthermore, the partial absorption of the pulses causes local heating of the
substrate, resist, and any underlying structures, which affects the
polymerization threshold of the resist [34]. Each of these effects deteriorate
the quality of small features near a substrate, and realizing sub-micron
diameter PNWs requires their mitigation.

A standard approach to DLW may use a flat substrate, uniform laser power, and
a solid-core design in the fabrication of PNWs, like that illustrated in Fig.
2(a). Fabrication outcomes from the use of this scheme with IP-Dip photoresist
[28] are shown in Fig. 2(b, i-iii), where unmitigated reflections cause
standing-wave-induced deep corrugations that can separate PNWs at their base
(i), an increase in the diameter of the PNW near its base (ii) (due to
increased effective dose), and a shift of the polymerization/damage thresholds
that can cause vaporization of the resist (e.g., "bubbling") near the
substrate (iii). As shown in Fig. 2(b,i) the period of the corrugations are
approximately 230 nm, which roughly correlate with the expected period of 260
nm for a 780 nm continuous wave laser in IP-Dip.

To mitigate heat generation and reflections, we employed the exposure strategy
shown in Fig. 2(c). In this strategy, a custom mount positions the GaAs
substrate at a 10$\degree$ angle relative to the lithography beam to limit the
overlap between incident and reflected pulses; base layers of lower
lithography power rectify variations in effective dose; and a hollow-core
design reduces local heating by limiting the total dose required to fabricate
the PNW. After exposure, samples were UV-cured in a solvent bath to polymerize
their cores and prevent structural deformation of the structures [33]. The
scanning electron micrograph (SEM) shown in Fig. 2(d) demonstrates the
successful fabrication of a PNW at the 10$\degree$ angle provided by the
custom mount. In all subsequent fabrication runs, a $-10\degree$ correction
was applied to the PNW design to compensate for the $+10\degree$ angle
introduced by the mount, which is possible due to the 3D flexibility of DLW.
The angled PNW shows greatly reduced corrugation amplitudes and improved
uniformity compared to those in Fig. 2(b).

To validate the general exposure strategy proposed in Fig. 2(c), a total of
120 PNWs of varying diameters were fabricated on the reference substrate shown
in Fig. 1(a). The nanowires were fabricated using IP-Dip photoresist [28],
6.25 mW to 12 mW of time-averaged laser power, with 80 fs to 100 fs pulses
focused by a numerical aperture (NA) 1.4 objective at an 80 MHz repetition
rate and a laser scan speed of 1 mm/s. As shown in Fig. 3(a-b), the
fabrication had a 100 percent yield of angle-corrected (i.e., straight-
standing and perpendicular to the substrate) PNWs with reduced corrugation
depths. Figure 3(c) shows PNWs with diameters varying from $0.9$ $\mu$m to
$1.8$ $\mu$m , showing the uniformity of each design with respect to diameter.
Despite the Au back reflector in the reference design providing very strong
reflections, the angled substrate reduced the depth of the corrugations to
$\approx 150$ nm for the reference system and $\approx 50$ nm for PNWs printed
on GaAs with no back reflector (Fig. 2(d)).

Figure 3: (a) False-color SEM images of PNWs fabricated on GaAs substrates
with Au back reflectors with 100 % yield using the strategy proposed in Fig.
2(c). (b) A perspective view of the central set of devices in (a), showing
straight-standing PNWs of different diameters. (c) A lateral view of a PNW
array, showing greatly reduced sidewall corrugations at all diameters compared
to those fabricated using a standard strategy (Fig. 2(b)). Figure 4: (a) Close
up scanning electron micrograph of a PNW on a GaAs substrate with an Au back
reflector and showing an $\approx$ 150 nm corrugation amplitude. (b) FDTD
simulation of a corrugated NW showing that light is still confined in a PNW
mode propagating along the z axis (top) and far-field emission is still
azimuthally symmetric and Gaussian-like. (c) The coupling efficiency into the
$HE_{11}$ modes of a 1 $\mu$m diameter PNW as a function of corrugation
amplitude. (d) The excitation of higher order modes for a fixed corrugation
amplitude but varying PNW diameter, showing similar performance to the
uncorrugated device in Fig. 1(h).

Despite the progress on PNW fabrication, the persistence of the corrugations
warrants a numerical understanding of their influence on device performance.
Figure 4(a) shows the fabrication of a PNW on the reference substrate (inset)
with various dimensions highlighted to show diameter variation along the z
axis. In particular, the device shows corrugation amplitudes that decrease as
a function of the distance $z$ from the substrate surface. Corrugations were
introduced into FDTD simulations as a variation of the diameter
$D(z)=D_{0}+\delta(z)$ with $\delta(z)=\frac{2A}{1+\gamma
z}cos^{2}(z\frac{\pi}{\lambda_{c}})$, where $A$ is the corrugation amplitude,
$\gamma$ linearly decreases the amplitude for increasing $z$, and
$\lambda_{c}$ is the corrugation wavelength. Figure 4(b) shows an FDTD
simulation for a PNW on the reference substrate with $D_{0}=0.7$ $\mu$m ,
$A=150\leavevmode\nobreak\ $nm, $\gamma=0.75$, and $\lambda_{c}=230$ nm. As
shown in the simulation, the corrugated device still confines emission to the
z-axis and has a Gaussian-like far-field distribution amenable to fiber-
coupling. The effect of the corrugation amplitude is investigated in Fig.
4(c), which shows that the corrugation depth monotonically reduces the
coupling efficiency from the dipole to the $HE_{11}$ mode of the PNW. Even so,
for $A=200$ nm the corrugations introduce $<20\leavevmode\nobreak\ \%$ loss
compared to the ideal PNW with $A=0$ nm. The modulations tend to shift the
average diameter of the PNW, so that a small shift in the optimal waveguide
dimensions is expected. Fixing the corrugation depth to $150$ nm depth, like
that of the fabricated device in Fig. 4(a), and varying $D_{0}$ (Fig. 4(d))
verifies that the optimal diameter decreases to $\approx 600$ nm. In general,
the corrugations reduce the optimal PNW diameter and the HE11 mode
transmission, but they do not prevent the PNW from confining radiation and
emitting a directional gaussian-like mode.

##  Optical Characterization of PNWs

Figure 5:  (a) Schematic of the micro-photoluminescence setup used for PNW
characterization (see main text for details). (b) Images captured by the EMCCD
camera when an excitation beam is aligned-to and confined by a PNW (left) and
when the beam is laterally displaced from that PNW (right) showing beam
divergence. Substrate illumination in this image is provided by an incoherent
LED. A PNW array makes up the dark circles in the images. (c) False color SEM
image of 9 NRs (yellow) with PNWs fabricated on top of 6 of the NR locations.
Data from the highlighted NR+PNW is presented in panels (d-e) before and after
PNW fabrication. (d) Emission spectra collected from the test site indicated
in panel (c) before (i.e., a NR only system) and after the fabrication of the
PNW (i.e., a NR+PNW system), showing a broadband spectral enhancement of
emission lines in the NR+PNW system over a span of 9 nm. Spectral shift
discussed in main text. (e) Power series for the highest intensity peak of the
NR system (orange) and the NR+PNW system (green), showing a factor of $\approx
2.6\times$ enhancement at QD saturation. The spectra shown in (d) correspond
to the circled data points in (e).

Implementing the fabrication strategy proposed above, PNWs were fabricated on
both the reference structure (shown in Fig. 3) and on the NR devices, as shown
in Fig. 5(c). To avoid spurious reflections from the Au NR, the PNWs
fabricated on NRs had $D_{0}\approx 1.4$ $\mu$m, which reduces the PNW-to-NR
coupling efficiency, as shown in Fig. 4(d), but provides an emission profile
that overlaps well with the $LP_{01}$ mode of a single mode fiber. The
standalone PNW and the NR+PNW systems were optically characterized using the
micro-photoluminescence set up shown in Fig. 5(a). The devices were cooled to
a temperature of $\approx$ 4 K in a closed-loop cryostat, and illuminated
using a 980 nm light emitting diode (LED) or a 780 nm tunable laser. The laser
was operated with continuous-wave emission for above-band QD excitation and
the LED provided broadband wide-field illumination of the substrate. The laser
source is focused onto the sample by a 0.7 NA objective to a spot
approximately 1.4 $\mu$m in diameter. On the other hand, the LED source is
collimated on the sample to provide wide-field illumination. During data
acquisition, only the excitation beam was active, i.e., the widefield LED
illumination was turned off. The focal plane of the objective is at the top of
PNWs (NRs) for measurements of PNW (NR) emission, and the collected signal is
routed to an electron multiplying charge-coupled device (EMCCD) camera and a
0.5 m long grating spectrometer through a series of beamsplitters with
splitting ratios and positions as indicated in Fig. 5(a).

Figure 5(b) shows a representative image captured by the EMCCD when a PNW
array is illuminated by the LED and the laser simultaneously. The objective is
focused on the top plane of a PNW array, and each PNW appears as a small
darkened dot in the image. Using a piezo stage within the cryostat, the
excitation can be aligned to a PNW, the result of which is shown in the left
panel of the figure. In this image, the laser appears as a bright illuminated
circle. On the other hand, displacing the excitation beam in a lateral
direction produces the image shown in the right panel, where the excitation
beam is not confined by the PNW, thus diverging to a large out-of-focus spot
spread out on the substrate surface. These images demonstrate that the PNWs
are functioning as waveguides perpendicular to the substrate surface.

In order to quantify the impact of PNWs on a QD’s emission, the same QD should
be measured before and after the fabrication of a PNW. The metallic NR
platform is well suited for this comparison, given that the centers of the
rings provide a well-defined location for optical measurements before and
after PNW fabrication. Figure 5(c) shows a set of six PNWs printed directly on
an array of metallic NRs, which were fabricated on a GaAs substrate with a
high density of emitters. As a representative device, the PNW highlighted by
the green arrow, which is centered over a NR, was studied before and after
fabrication of the PNW. Figure 5(d) shows the emission spectra of this NR
before (orange) and after (green) the fabrication of the PNW. The top and
bottom axes of this figure correspond to the emission wavelengths for each
system, and we note that the spectra of the NR+PNW system was shifted by
$\approx$ 2 nm relative to that of the NR alone. This spectral shift may be
due to polymer-induced strain on the substrate from possible shrinkage of the
cold DLW polymer [19, 35]. Nevertheless, the emission lines can be uniquely
identified by the structure of the spectra over a wide bandwidth, as shown in
the figure. The spectra in Fig. 5(d) were taken near QD saturation, at powers
indicated by the open circles in Fig. 5(e). We observe a broadband spectral
enhancement of QD emission in the NR+PNW system compared to the NR system
alone.

As a representative single-QD comparison, the emission of the spectral line at
$\approx$ 962 nm was studied for increasing amounts of excitation power, as
shown in Figure 5(e) in units of NR saturation power. At saturation, the
maximum count rates measured at the spectrometer were $\approx$ 42000 s-1 for
the NR system and $\approx$ 108000 s-1 for the NR+PNW. This observed
enhancement factor of 2.6$\times$ is inline with the $\approx$3.3$\times$
enhancement predicted in Fig. 1(f) for an SM980 (NA = 0.21) fiber-coupled
input to the spectrometer. We note however, that the count rate enhancement is
achieved at an excitation power 3$\times$ greater than that of the NR device
alone. The PNW was designed with a 1.4 $\mu$m diameter to prevent spurious
reflections at the ring’s surface during fabrication but at the cost of
becoming a multi-mode waveguide for light at 950 nm, as shown in Fig. 1(h).
Thus, the 780 nm excitation beam likely couples to an even greater number of
modes, some of which may not excite the QD in the NR configuration with the
same efficacy as the free-space beam in the NR configuration. In principle,
the excitation efficiency can be optimized by using a PNW that is single mode
at both the excitation and emission wavelengths, but in this study the minimum
PNW diameter is restricted to avoid the NR reflections. On average, we observe
a ($3.0\leavevmode\nobreak\ \pm\leavevmode\nobreak\ 0.7)\times$ enhancement
over the spectral window shown in Fig. 5(e), where the error represents the
standard deviation of five prominent spectral lines and the leading source of
error is likely the distribution of the underlying QDs near the principal axis
of the PNW. In general, the PNW has enhanced the fiber-coupling of the NR
platform by directly waveguide-coupling its emission to the $HE_{11}$ optical
mode, and we expect further improvements to be possible through the use of
modified PNW designs (e.g., elliptical PNWs), modified NRs (e.g., optimized
for PNW coupling), different underlying devices (e.g., circular Bragg gratings
[36, 37, 38]), or individually pre-positioned QDs.

##  Discussion and context

We have demonstrated that DLW can be used to fabricate PNWs that directly
waveguide-couple the emission from InAs/GaAs QDs while increasing collection
efficiency into a down-stream fiber. Using numerical simulations, we show that
dipole emission can be coupled to the optical modes within a PNW, which is
expected to increase the collection efficiency by a down-stream single mode
fiber due to the large overlap of a PNW’s $HE_{11}$ mode with the $LP_{01}$
mode of a single mode fiber. We have also shown that PNWs are compatible with
other on-chip devices like metallic NRs, since they do not require etching or
modification of the underlying substrate. PNWs were fabricated on reflective
substrates with DLW by suppressing standing wave reflections and mitigating
heat generation. Comparing a NR system before and after the fabrication of a
PNW, we observe an approximately three-fold increase in the collection of the
saturated flux of a single QD emission line when coupling the excitation light
through the PNW. Our realization of wavelength-scale PNWs near the surface of
a substrate that is both reflective and absorptive brings new functionality to
the expanding field of 3D quantum photonic circuitry, and we expect that
advances in DLW fabrication, PNW design, and modified on-chip devices will
continue to improve the performance of PNW-enhanced systems.

This investigation has focused on azimuthally symmetric PNWs that are
perpendicular to the device substrate, but a broadband PNW (or NR+PNW), like
those in this study, also offers full 3D flexibility. This may make PNWs well
suited for use with other solid state devices, like micro-pillars and circular
Bragg gratings. For example, the confined photons can be rerouted to other on-
chip elements as in various examples of photonic wire-bonding [13]. In
particular, PNWs may be especially well suited for this function when used in
conjunction with III-V nanowires [11], where the $HE_{11}$ mode of the III-V
nanowire can be well coupled to the $HE_{11}$ mode of the PNW, which then
routes the SP emission. We further note that the use of anti-reflection
coatings (at the DLW lithography wavelength) on the surface of the GaAs may
further improve PNW quality, as would the use of a distributed Bragg
reflection mirror as the system’s back reflector (at the cost of reduced
reflection bandwidth). Finally, other possibilities include the use of
elliptical nanowires for polarization-maintaining emission, or tapered PNWs
that adiabatically transfer power from the higher order modes to the
fundamental $HE_{11}$ mode for further-improved performance.

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Data availability The data that supports the plots within this paper and other
findings of this study are available from the corresponding authors upon
reasonable request.

Acknowledgments This work is supported by the NIST-on-a-chip program and the
Leverhulme Trust, Grant IAF-2019-01. J.D.S. would like to acknowledge the
partial support received from the IITP grant, which is funded by the Korean
government (MSIT 2020-0-00841).

Author contributions E. P. led the project, PNW design and fabrication, and
conducted experiments. C.H. conducted optical characterization experiments,
contributed to theoretical understanding and data analysis. M. D. contributed
to theoretical understanding, the design of the PNWs, and the interpretation
of data. J. D. S. grew the high density InAs/GaAs QDs. L. S. contributed to
the theoretical understanding of PNWs, their design, and the fabrication of
devices. K. S. contributed to the theoretical understanding of PNWs, standing
wave mitigation, and data analysis. E. P. and K. S. prepared the manuscript.
All authors contributed and discussed the content of this manuscript.