# Target-wavelength-trimmed second harmonic generation with gallium phosphide-
on-nitride ring resonators

Lillian Thiel  1,* Alan D. Logan  1 Srivatsa Chakravarthi  1 Shivangi Shree  2
Karine Hestroffer  3 Fariba Hatami  3 and Kai-Mei C. Fu1,2  1Department of
Electrical and Computing Engineering, University of Washington, Seattle WA
98195
2Department of Physics, University of Washington, Seattle WA 98195
3 Department of Physics, Humboldt-Universitat zu Berlin, 12489 Berlin, Germany
<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

We demonstrate post-fabrication target-wavelength trimming with a gallium
phosphide on silicon nitride integrated photonic platform using controlled
electron-beam exposure of hydrogen silsesquioxane cladding. A linear
relationship between the electron-beam exposure dose and resonant wavelength
red-shift enables deterministic, individual trimming of multiple devices on
the same chip to within 30 pm of a single target wavelength. Second harmonic
generation from telecom to near infrared at a target wavelength is shown in
multiple devices with quality factors on the order of $10^{4}$. Post-
fabrication tuning is an essential tool for targeted wavelength applications
including quantum frequency conversion.

††journal: oe

##  1 Introduction

Nanophotonic devices have transformed frequency conversion processes, enabling
conversion efficiencies orders of magnitude higher than in bulk materials by
confining light and controlling mode dispersion. To fully leverage the
potential of nanophotonic platforms for frequency conversion, multi-resonant
devices are desirable; for example, in a $\chi^{(2)}$ nonlinear media, doubly
resonant devices for second-harmonic generation (SHG) and parametric down-
conversion (PDC) and triply resonant devices for difference- and sum-frequency
generation. Moreover, applications are emerging in which an absolute frequency
of one or more interacting fields is required. Examples of this include PDC
entangled photon sources for optical quantum computing [1, 2, 3, 4] and
frequency conversion of single visible or NIR photons, emitted by ions or
solid-state defects, for long-distance fiber transmission [5, 6, 7, 8, 9].
Toward this latter application, multi-resonant frequency conversion of photons
to/from the telecom band has been demonstrated in nanophotonic structures
fabricated from non-linear materials such as gallium phosphide (GaP) [10],
aluminum nitride [11], lithium niobate [12, 13] and silicon nitride [14, 15].
However, tight fabrication tolerances for such devices typically cause
resonant wavelengths to differ significantly from their designed values,
presenting a challenge for practical device implementation. Here we introduce
a promising technique for post-fabrication nanoscale control of photonic
resonances to address this challenge via electron-beam modification of
hydrogen silsesquioxane (HSQ) cladding.

Generally, photonic resonators can be tuned by altering the physical
dimensions or optical properties of the structure. For a ring resonator,
tuning variables include ring width and height, resonator refractive index,
and cladding refractive index. Resonances may be either tuned via processes
that require constant active control (e.g. temperature [16, 17], electric
field [18, 19]) or trimmed via processes that permanently change device
parameters (e.g. etching [20, 21, 22], introducing strain [23, 24],
modification of cladding material [25, 26, 27, 28]). Resonant wavelength
modification of ring resonators for frequency conversion processes presents a
particularly complex challenge due to the simultaneous involvement of multiple
wavelengths. Any tuning or trimming process will cause a shift in both
absolute resonant wavelength and relative spacing between the two or more
required resonances. Thus, realizing multiple independent tuning mechanisms
and/or developing techniques which offer the spatial resolution to
preferentially tune certain resonator modes are particularly interesting.
Further, a tuning mechanism that can be readily integrated into a well
established fabrication process is preferred.

HSQ is heavily utilized for high-resolution electron-beam lithography [29, 30]
of photonic devices and is fully compatible with most materials and
fabrication processes. Prior studies have investigated the utility of HSQ for
resonance tuning using thermal annealing [31] to convert the cage-like
structure of uncured HSQ into a denser cross-linked silica structure,
increasing the index of refraction from n = 1.45 to n = 1.51. Similarly,
localized laser[26] and in situ[25] annealing of HSQ on individual silicon
micro-ring resonators has been utilized to shift resonances by up to 2 nm.
Both techniques involve heating the devices to high temperatures, thus
limiting integration of III-V non-linear photonic materials such as GaAs and
GaP. Additionally, long-term, the spatial resolution afforded by thermal
processes will be inadequate for multi-resonance frequency conversion
applications. High-energy electron-beam exposure allows high spatial and
tuning resolution [28]. In this work we investigate the utility of HSQ
electron-beam exposure as a method for high-resolution, post-fabrication,
single device trimming, with the potential for mode-selective trimming.
Electron-beam exposure of HSQ has been shown to induce cross-linking similar
to thermal annealing, while high exposure intensity enables further refractive
index tuning (up to $\mathrm{n=1.62}$) via the formation of silicon-rich SiO2
[32, 33]. Our results indicate that the induced wavelength shift is linearly
dependent on the electron-beam exposure dose, with an observed trimming range
of $\sim$ 5 nm for the applied doses. We demonstrate high spatial and tuning
resolution, resonance stability, and minimal impact on device quality factor
(Q), making HSQ electron-beam trimming a promising candidate for use in
quantum frequency conversion applications. Finally, we demonstrate successful
target-wavelength second harmonic generation with multiple devices and provide
an outlook toward utilizing this technology for simultaneous multiple
resonance tuning.

Figure 1: (a) SEM image of the fabricated GaP-on-Si3N4 resonator with
accompanying grating couplers. The device is excited with telecom band tunable
laser (red) and the SHG signal is measured out of the vis/NIR output grating
(yellow). (b) Simulated resonator $\vec{E}$-field profiles of the quasi-phase
matched telecom and second-harmonic modes. (c) Pre and post trimming optical
images of a device. The ring was exposed with a donut pattern. The waveguide
and grating structures were utilized for exposure alignment. To reveal the
exposed HSQ pattern during the trimming process, the post-trimmed optical
image was acquired after developing the exposed HSQ in a 25% TMAH solution.
Note that all optical characterizations were performed before the development.

##  2 Resonator design, fabrication and testing

The ring resonators were designed and fabricated in a 250 nm (100) GaP
photonic layer on an epiwafer substrate with 220 nm LPCVD silicon nitride on 4
µm silicon oxide on silicon. A ring radius of 7.77 µm and width of 940 nm were
selected to satisfy a quasi-phase matching condition for a TE00 fundamental
mode and TM03 second harmonic (SH) mode at $\mathrm{\lambda_{0}\approx
1550\,nm}$ and $\mathrm{775\,nm}$, respectively [10]. Each ring mode is
evanescently coupled to a different input/output waveguide leading to a pair
of cross-polarized grating couplers. A device SEM image and schematic are
shown in Fig. 1a, with the relevant mode profiles in Fig. 1b. Additional
design details can be found in Appendix A1.

Eigenmode simulations of the ring resonator predict that an increment in
refractive index of $\mathrm{\Delta n_{HSQ}=+\,0.1}$ in a 100 nm thick
conformal HSQ cladding will red-shift the resonant wavelength of the
fundamental mode by $\sim$ 2.98 nm and SH mode by $\sim$ 1.07 nm. With changes
in HSQ refractive index as high as 0.22 reported [32, 33], the predicted
trimming range is capable of compensating for typical device-to-device
fabrication variations.

To fabricate the structure, the 250 nm GaP layer was released from a GaP
substrate by etching an intermediate $\mathrm{Al_{0.8}Ga_{0.2}P}$ sacrificial
layer with dilute HF. The GaP was then transferred to the Si3N4-on-SiO2/Si
substrate using a wet transfer process [34, 35, 36, 10]. Electron-beam
lithography using HSQ resist and subsequent plasma reactive-ion-etching (RIE)
of the GaP layer forms the photonic devices. Two chips (A and B) were
fabricated with identical device dimensions. After fabrication, a layer of
developed HSQ mask remains. This HSQ layer is removed with a vapor-HF etch,
enabling the spin-on of a new conformal coating of HSQ for the resonance
trimming process. After HSQ spin-on, each device was trimmed by exposing a
donut-shaped region extending 1 µm beyond the inner and outer device radii at
a beam voltage of 5 keV (Fig. 1c). Further details of the fabrication are
provided in Appendix A2. The fabrication process is compatible with diamond
substrates for GaP-on-diamond or GaAs-on-diamond photonic circuits integrated
with solid-state defects [35, 36, 37].

The fundamental resonances of individual devices were identified by sweeping a
continuous-wave telecom laser (1530 to 1565 nm) and detecting transmission
spectra using a InGaAs photodiode. In the visible band a supercontinuum laser
(550 to 1350 nm) was used for excitation and the transmission spectra is
detected with a grating spectrometer. The excitation polarization was set to
excite TE (1550 nm) or TM (775 nm) modes, as depicted in Fig. 1a. Scattered
excitation light was filtered out of the collection path via polarization and
spatial filtering. Chip-A exhibited resonances with Q-factors of 7 $\pm$ 2.2
$\times$103. Chip-B exhibited narrower resonances with Q-factors of 3 $\pm$
1.7 $\times$104.

##  3 HSQ target-wavelength trimming

The first goal is to establish a relationship between exposure dose and
resonant wavelength shift to deterministically tune the resonant wavelength of
individual devices on-chip. Approximately 24 hours after HSQ spin-on, 13
devices (chip-A) were selected for a dose-test and exposed with electron-beam
lithography. Three devices each received doses of 1000, 1750, and 2500 µC/cm2
respectively and four devices received no exposure. Transmission spectra of
one specific fundamental mode taken before and after exposure show a linear
relationship between resonance shift and exposure dose (Fig. 2a). On average,
the exposed devices exhibit a tuning rate (red-shift) of 1.4 $\pm$0.1
pm/µC/cm2, with the maximum tested dose (2500 µC/cm2) giving an average shift
of 3.08 nm.

Figure 2: Chip-A: (a) Relationship between HSQ exposure dose and observed
wavelength shift at the fundamental wavelength. (b), (c) A target trim-test
showing the fundamental wavelength resonances for nine devices with
identically designed resonator dimensions pre- and post-exposure,
respectively. The target wavelength was selected to be 1540.5 nm, however a
systematic overexposure resulted in resonances trimmed to 1540.91$\pm$0.19 nm.

In the next step, a set of nine identically designed devices were identified
(Fig. 2b) with initial resonances near $\mathrm{\lambda=1540.5}$ nm to trim to
mutual resonance. Before trimming, the spread of resonant wavelengths was
measured to be $\approx$ 3 nm. We used the above linear dose-shift
relationship to determine the necessary exposure dose for targeted trimming of
each device resonance to $\mathrm{\lambda=1540.5}$ nm. With a single exposure
of each device, all resonances were trimmed to the target wavelength with an
offset of 0.41$\pm$0.19 nm (Fig. 2c).

Post-tuning analysis (Appendix A3) of the transmission spectra determined that
the tuning rate is different for various families of modes supported by the
ring. The highest observed shift was 4.92 nm (Fig. A1a, mode-1). The
significant mode-sensitivity suggests deterministic inter-modal control could
be developed within this platform. Further, we observed an average post-trim
resonance drift of 10.6 pm/day (corresponding to 0.7% of average trimmed red-
shift or 5% of the average target resonance linewidth) over 12 days. This
minor drift followed a non-monotonic trend for all tested devices. The source
of the post-exposure drift requires further investigation.

##  4 Target-wavelength-trimmed SHG

In a second experiment (chip-B), we expanded the scope of our dose-test to
incorporate both the fundamental and SH modes. Using the same dose-test
procedure, a linear dose-shift relationship is found for the fundamental mode
with a nearly identical tuning rate (1.2 $\pm$0.1 pm/µC/cm2) to the chip-A
dose-test. The largest dose (2500 µC/cm2) corresponds to an average shift of
3.0 nm. This matches the simulated resonance shift for a cladding index change
of $\mathrm{\Delta n_{HSQ}\approx 0.1}$, which is reasonable for the large
electron-beam exposure dose [32]. A linear dose-shift relationship (0.5
$\pm$0.2 pm/µC/cm2) is also established for the SH mode (Fig. 3a). Due to the
highly multi-mode nature of the ring at 775 nm, difficulty in consistently
identifying radial modes prevented us from accurately determining the mode-
specific trimming rate of the targeted SH mode. Thus, we focus on HSQ target
trimming of the fundamental mode to demonstrate target-wavelength-trimmed SHG
in multiple devices.

We selected three nominally identical devices with telecom resonances that
exhibited strong SH conversion. The initial spread of resonances was 1.11 nm.
Each device was exposed to a calibrated HSQ electron-beam dose for trimming to
a target wavelength of $\mathrm{\lambda=1533.75}$ nm. All three devices were
trimmed to within $\mathrm{\approx 30\,pm}$ of the target wavelength (Fig.
3b). The strong temperature dependence of the SHG signal (Fig. 3c), indicates
that the devices were close to quasi-phase matched double resonance after the
trimming process. The SH and fundamental resonances red-shift at different
rates with increasing temperature, causing the SHG conversion efficiency to
peak as the SH resonance tunes into and out of double resonance with the
fundamental. All three devices gain some double-resonant SHG enhancement at
the target wavelength (1533.75 nm), but due to remaining variations in the SH
resonant wavelength after the HSQ exposure trimming, each resonator reaches
its maximum SHG efficiency at a slightly different temperature and wavelength.

Figure 3: Chip-B: (a) Linear dependence of resonant wavelength shifts with the
doses for both fundamental and SH (blue) wavelengths with estimated slopes of
1.18 and 0.47 pm/µC/cm2 respectively. (b)The dose-test data is utilized to
trim the fundamental wavelength resonance of three near-quasi-phase-matched
devices. (c) Peak SHG intensity (blue) and corresponding input (fundamental
resonance) wavelength (red) as a function of temperature for each trimmed
device. The fundamental and SH resonance red-shift linearly with different
rates with increasing temperature. The SHG intensity depends on how close the
device is to double resonance (SH resonance at exactly half the input
wavelength). (d) A simulated trimming scenario showing two ring resonators
with different initial fundamental and SH resonant frequencies (points A and
B). Blue and red regions show the range of resonant wavelengths that can be
reached using a combination of temperature tuning (10 to 60∘C) and HSQ
exposure (0 to 2500 µC/cm2), with the overlap (green) showing that each ring
could be tuned to double resonance (dotted red line) over a range of
wavelengths including the design wavelength (point C). Wavelength shift
dependence on temperature and HSQ exposure are derived from experimental data
for the fundamental and simulations for the SH resonances.

SHG efficiency is also very sensitive to the Q-factors of the resonant modes.
The narrow resonances observed on chip-B enable us to investigate the effect
of trimming on the fundamental mode Q-factor. Initially the average Q-factor
for 15 devices was 3 $\pm$1.7$\times$104. The Q-factor is observed to both
decrease and increase with the average Q decreasing by 5.1 $\pm$6.1$\times$103
after exposure. It is likely that the majority of this variation in Q can be
attributed to exposure of the coupling region, altering the coupling-Q as
described in Appendix A1. An exposure pattern that avoids the coupling region
could maintain the device Q through the trimming process. Further, selective
exposure of the coupling regions could be utilized to tune devices to the
critical-coupling regime in addition to resonant wavelength trimming.

##  5 Outlook and Conclusion

In this work we demonstrated that HSQ exposure is a promising post-fabrication
trimming method for photonic resonators. With a simple calibration process, we
target-wavelength trim a large set of identically designed devices with
typical post-fabrication variations. HSQ trimming will be an important tool in
the larger effort towards target-wavelength frequency conversion. For example,
combined with temperature tuning, HSQ trimming should enable dual target-
wavelength trimming for doubly resonant quasi-phase matched frequency
conversion processes. The devices in this work that were trimmed to correct
variance at the telecom wavelength at room temperature still had some variance
in the SH resonance, resulting in maximum SHG conversion at different
temperatures and wavelengths. By taking the effect of temperature tuning into
account when selecting exposure doses, Fig. 3d illustrates how multiple
resonators could be trimmed to provide their maximum SHG conversion efficiency
at the same target wavelength. Two simulated devices (A, B) with fundamental
wavelengths differing by 1.3 nm at room temperature and $\mathrm{\sim
5.5\,nm}$ at their optimal SHG temperatures can be target wavelength tuned
within the green dose-temperature area. A third independent tuning mechanism
will be required to achieve optimal efficiency for a specific sum- or
difference-frequency conversion process needed for quantum frequency
conversion applications.

The attractive properties of HSQ exposure trimming include tuning range,
resolution and precision, low post-trim drift and minimal effect on quality
factor. We expect that additional process development will further improve the
accuracy and precision. Better mode identification will reduce uncertainty in
mode-specific trimming rates enabling the implementation of multiple tuning
mechanisms. Improved understanding of sources of drift will allow us to design
for or mitigate post-trim resonant shifts. The spatial resolution afforded by
electron-beam lithography for HSQ trimming creates potential for applications
beyond resonance shifting. Selective exposure of coupling regions could allow
post-fabrication fine tuning of coupling Q. Other works have shown that
periodic nanometer-scale variations along the ring inner radius can target
specific modes for mode-splitting [38]. Electron-beam lithography-based
trimming makes target mode trimming and splitting a realistic opportunity. We
have shown HSQ exposure to be a simple and effective post fabrication trimming
technique. With further development it stands to become a process widely
utilized by the photonics community.

## Appendix

##  A1 Device design and simulation details

The ring resonators were designed using bent-waveguide eigenmode simulations
in Lumerical MODE. Using ring radius $r$ and width $w$ as design variables,
the resonator was optimized to maximize nonlinear overlap $\beta$ while
satisfying the mode polarization and quasi-phase matching (QPM) requirements
imposed by the zincblende crystal symmetry and (100)-normal orientation of the
GaP photonic layer [10, 39, 40]. At each design point, the target modes
($\mathrm{TE_{00}}$ at $\mathrm{\lambda_{1}\,=\,1550\,nm}$ and
$\mathrm{TM_{03}}$ at $\mathrm{\lambda_{2}\,=\,775\,nm}$) were simulated in a
ring cross section. The nonlinear overlap $\beta$ was calculated from the mode
profiles, along with fractional azimuthal mode numbers
$\mathrm{(m_{i}\,=\,2\pi\cdot r\cdot n_{eff,i}/\lambda_{i})}$ for each mode,
which are used to check the QPM condition
$\mathrm{(2m_{1}\,-\,m_{2}\,=\,\pm\,2)}$. Integer azimuthal mode numbers at
the simulated wavelengths are preferred, but not required; a design with non-
integer $m_{i}$ is expected to have QPM modes that are near double resonance
at wavelengths that are not exactly 1550 nm and 775 nm in ambient conditions,
which is acceptable if within the tolerance of our tuning capabilities. Based
on previous experiments in similar material platforms (GaP-on-Diamond, GaP-on-
oxide), intrinsic quality factor is expected to be dominated by fabrication-
related factors such as sidewall roughness, so the simulated radiative quality
factor was not considered for the design process.

The ring resonator coupling regions were designed to provide specific coupling
quality factors using a supermode analysis method. For a range of coupling
waveguide widths and ring-to-waveguide distances, the target ring and
waveguide modes were simulated with each structure alone, and then all guided
modes were simulated for the combined structure. Mode overlap between each
coupling region mode and the ring/waveguide modes were calculated and used to
numerically find the total power transfer from the ring mode to waveguide mode
as a function of coupling region length. The coupling quality factor $Q_{c}$
was derived from the simulated free spectral range $\Delta\lambda_{FSR}$ of
the resonator mode and the field coupling coefficient $\kappa$ from a single
pass through the coupling region:

$Q_{c}=\frac{2\pi\lambda}{\left|\kappa^{2}\right|\Delta\lambda_{FSR}}.$ (1)

To provide a consistent interface to the rest of the coupling photonic
circuit, a constant waveguide width and propagation length was selected for
each ring mode’s coupling region, with only the separation distance varied to
set $\mathrm{Q_{c}}$.

Coupling quality factor depends significantly on how well the HSQ fills the
space between the ring and the waveguide, as well as HSQ exposure dose; the
coupling regions were simulated with a 100 nm conformal HSQ layer. The telecom
ring mode is coupled to a 440 nm wide waveguide wrapped around a
$\mathrm{45^{\circ}}$ arc of the ring, and the SH mode is coupled to a 120 nm
waveguide with a $\mathrm{30^{\circ}}$ wrap. For the telecom mode, a ring-to-
waveguide gap distance of 240 nm gives $\mathrm{Q_{c}\approx 24000-11000}$
with increasing ebeam exposure, and a distance of 360 nm gives
$\mathrm{Q_{c}\approx 90000-55000}$. For the SH mode, a gap distance of 120 nm
gives $\mathrm{Q_{c}\approx 4500-5500}$, and 160 nm gives
$\mathrm{Q_{c}\approx 11000-13500}$.

The grating couplers were designed to provide coupling to free space with
minimal footprint and low back reflections. For each wavelength band and
polarization, an aperiodic grating coupler design was found using a sampled
hill climbing optimization algorithm with a simplified model of grating
behavior as an objective function. The performance of the final design was
verified with a 3D FDTD simulation. To suppress on-chip back reflections,
which cause Fabry-Perot interference patterns in transmission spectra, the
grating designs were implemented as elliptically-shaped focusing grating
couplers. The grating notches are shaped as sections of progressively larger
ellipses with one focus centered on the end of the waveguide. Back reflections
from the waveguide are directed toward the second focus of the ellipse instead
of going back into the waveguide mode [41]. The design variables used for the
elliptical grating were: eccentricity, the angle between waveguide and major
axis, the arc angle of the elliptical section, and major axis length of first
grating notch. Designs were evaluated with 3D FDTD simulations to find a
combination of parameters that sufficiently suppresses back reflection in the
the same mode while maintaining a reasonable spot shape for light scattered
into free space.

##  A2 Fabrication details

The GaP material used for the photonics layer was grown by molecular beam
epitaxy on a 300 nm $\mathrm{Al_{0.8}Ga_{0.2}P}$ sacrificial layer on a GaP
substrate. This epitaxial GaP layer was released in 2% HF solution, followed
by a H2O rinse and wet transfer to the nitride substrate. To improve GaP
adhesion, prior to transfer, a 5 nm layer of SiO2 was thermally evaporated
onto the substrate, which was then treated with hexamethyldisilizane vapor.
The transferred GaP was allowed to dry overnight on a hotplate at 80 ∘C.
Electron beam lithography (JEOL-6300, 100 kV, 1 nA beam current) was utilized
to pattern the designed photonic structures on a thin (150 nm) HSQ resist
layer on top of the GaP-on-nitride stack. Multiple arrays of devices were
patterned with the resonator and coupling region dimensions varying across the
pattern to compensate for fabrication variations. A reactive-ion etch (RIE)
step (3.0 mTorr, 45 W RF, 60 W ICP, 235 V DC-bias, 1.0/6.0/3.0 sccm Cl2/Ar/N2
flow) was used to etch the GaP layer. The residual HSQ mask had to be removed.
Initial attempts at HSQ removal using a dilute HF (0.5%) dip revealed low
adhesion of the GaP devices to the substrate: stiction from the wet process
damaged the waveguide coupling regions. Thus, a HF vapor-etch process was
investigated. After the successful HSQ vapor-etch, the chip was heated to 200
∘C for 5 min to remove etch byproducts. This provided a clean surface for a
$\sim$150 nm layer of HSQ electron-beam resist that was spun-on and exposed
for device trimming. The thickness of this HSQ layer is expected to shrink by
up to 33% due to e-beam exposure [32].

##  A3 Post-tuning analysis

Figure A1: (a) Resonance shift as a function of HSQ exposure dose shows a
linear relation for two different modes: Mode-1 (red) and Mode-2 (blue) at
telecom wavelength range. The slope is different for the two modes indicating
that a different dose would be required for the same shift for a specific
mode. (b) Temporal stability of the trimming process for a subset of eight
devices. Day-0 data shows initial resonance wavelengths of all devices without
HSQ exposure. Device 5 did not receive any e-beam exposure. The large shift at
day-1 is observed due to coarse e-beam trimming. Devices 1, 2, 6 and 7 were
re-exposed for fine target wavelength trimming.

The dose-shift relationship is dependent on the overlap of the target mode
with the surrounding cladding. Analysis of the chip-A trim-test data (Fig.
A1a) reveals that two families of modes were observed in the transmission
spectra (1530 to 1565 nm) with significantly different tuning rates. Mode-1
(FSR = 13.61 $\pm$0.14 nm) exhibits a sensitivity of 2.11 pm/µC/cm2, and
mode-2 (FSR = 12.91 $\pm$0.05 nm) exhibits a lower sensitivity of 1.45
pm/µC/cm2. From simulations, the fundamental TE00 mode is expected to have an
FSR$\approx$14.7 nm. Given the smaller observed FSR, we suspect both these
families of resonances are higher order hybrid TE01/TM00 modes. Simulations
show these hybrid modes tune about twice as fast as the fundamental mode, with
a change in HSQ cladding index of 0.1 shifting the wavelength by about 6.25 nm
and 7.32 nm respectively instead of 2.98 nm.

To monitor the temporal stability of the trimming process, after HSQ exposure,
room temperature transmission spectra of eight identically designed devices
were periodically collected over a 12 day period. Devices 1, 2, 6 and 7 were
re-exposed for fine target wavelength trimming. Therefore, we only included
the remaining devices for detailed analysis of the resonance shift. One
possible reason for the observed shift could be the change in refractive index
of the cladding over time (possibly from uptake of ambient moisture by the
exposed HSQ [26, 25]) and further investigation is required for identification
of the source of the drift.

Funding

Acknowledgments This material is based upon work supported by the National
Science Foundation under Grants EFMA-1640986 (photonic design and fabrication)
and U.S. Department of Energy, Office of Science, National Quantum Information
Science Research Centers, Co-design Center for Quantum Advantage (C2QA) under
contract number DE-SC0012704 (HSQ tuning and testing). The photonic devices
were fabricated at the Washington Nanofabrication Facility, a National
Nanotechnology Coordinated Infrastructure (NNCI) site at the University of
Washington which is supported in part by funds from the National Science
Foundation (awards NNCI-1542101, 1337840 and 0335765).

Disclosures The authors declare that there are no conflicts of interest
related to this article.

Data Availability Statement Data underlying the results presented in this
paper are not publicly available at this time but may be obtained from the
authors upon reasonable request.

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