[1]Varun Dolia

[4]Mark Lawrence [3]Jack Hu [1]Jennifer Dionne

1]Department of Materials Science and Engineering, Stanford University, 496
Lomita Mall, Stanford, 94305, CA, USA

2]Department of Electrical Engineering, Stanford University, 350 Jane Stanford
Way, Stanford, 94305, CA, USA

3]Pumpkinseed Technologies, Inc., 380 Portage Ave, Palo Alto, 94306, CA,
Country

4]Department of Electrical & Systems Engineering, Washington University in St.
Louis, 1 Brookings Drive, St. Louis, 63130, MO, USA

# Very-Large-Scale Integrated High-Q Nanoantenna Pixels (VINPix)

<EMAIL_ADDRESS>Halleh Balch  Sahil Dagli  Sajjad Abdollahramezani  Hamish
Carr Delgado  Parivash Moradifar  Kai Chang  Ariel Stiber  Fareeha Safir
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>[  [  [  [

###### Abstract

Metasurfaces provide a versatile and compact approach to free-space optical
manipulation and wavefront-shaping.[1, 2, 3, 4, 5] Comprised of arrays of
judiciously-arranged dipolar resonators, metasurfaces precisely control the
amplitude, polarization, and phase of light, with applications spanning
imaging,[6, 7, 8] sensing,[9, 10, 11] modulation,[12, 13, 14] and
computing.[15, 16] Three crucial performance metrics of metasurfaces and their
constituent resonators are the quality-factor (Q-factor), mode-volume (Vm),
and ability to control far-field radiation. Often, resonators face a trade-off
between these parameters: a reduction in Vm leads to an equivalent reduction
in Q, albeit with more control over radiation. Here, we demonstrate that this
perceived compromise is not inevitable – high-Q, subwavelength Vm, and
controlled dipole-like radiation can be achieved, simultaneously. We design
high-Q, very-large-scale integrated silicon nanoantenna pixels – VINPix – that
combine guided mode resonance waveguides with photonic crystal cavities. With
optimized nanoantennas, we achieve Q-factors exceeding 1500 with Vm less than
0.1 (/nair)3. Each nanoantenna is individually addressable by free-space
light, and exhibits dipole-like scattering to the far-field. Resonator
densities exceeding a million nanoantennas per cm2 can be achieved. As a
proof-of-concept application, we demonstrate spectrometer-free, spatially
localized, refractive-index sensing utilizing VINPix metasurfaces. Our
platform provides a foundation for compact, densely multiplexed devices such
as spatial light modulators, computational spectrometers, and in-situ
environmental sensors.

##  1 Main

Photonic resonators are often evaluated by two key metrics: the quality factor
(Q-factor) and the mode volume (Vm). The Q-factor of a resonator describes the
degree of temporal confinement or enhancement of electromagnetic waves within
the resonator, characterized by the linewidth of a mode in frequency space. On
the other hand, Vm quantifies the spatial extent where electromagnetic modes
are primarily concentrated. Metasurfaces – arrays of nanoscale optical
resonators, stand as some of the most recent significant innovations in
photonics.[17, 18, 2, 9, 19] Owing to each resonator’s ability to control the
phase, amplitude, and polarization of light, metasurfaces enable precise
control of far-field radiation in a compact, subwavelength-thick footprint.
They promise to address the growing demand for photonic devices applicable for
wearable, deployable, or point-of-care scenarios such as health and
environmental monitoring,[20, 9, 21, 22, 23, 24] wireless communications,[25,
26, 27] LiDAR systems,[28, 29] wavefront shaping,[30, 31, 32, 33, 1, 34, 35,
36] on-chip lasing,[37, 38] and computational spectrometry.[39, 40]
Metasurfaces have added another key metric to photonic resonators beyond
Q-factor and Vm: the ability to control free-space radiation.

Mie-resonators, foundational elements of metasurfaces, confine light to deep
subwavelength mode volumes and excel at manipulating light waves and
controlling far-field radiation.[5, 41, 2, 42, 43, 44] However, such
nanostructures generally display only modest Q-factors (around 10) due to
their increased radiative channels. More recently, high-Q metasurfaces merging
high-Q cavities with Mie antennas have emerged. These metasurfaces enable high
Q-factors (>1000), controlled far-field radiation, and wavefront control,
operating on the principle of free-space excitation of guided mode resonances
that scatter orthogonally as a dipole.[33, 45, 46, 47, 10] Yet, maintaining
high Q-factors often requires at least one translationally invariant
dimension, rendering subwavelength mode volumes a challenge. Meanwhile, high-Q
photonic crystal defect cavities[48, 49, 50, 51, 52, 53, 54, 55] have
demonstrated high Q-factors with subwavelength mode volumes, around
$10^{-4}(\lambda/n)\textsuperscript{3}$, through in-plane band-gap
confinements. However, they scatter light arbitrarily with limited control
over free-space radiation: the free-space emission often spreads out in many
directions, without a distinct or intended pattern, which leads to losses in
devices. Whispering gallery resonators such as ring resonators, microtoroids,
and microspheres[56, 57, 58, 59] achieve even higher Q-factors ranging from
thousands to billions. However, these ultra-high Q-factor structures exhibit
relatively large Vm values (on the order of a few to hundred cubic
wavelengths). Additionally, they require fibers prism- or grating-couplers to
address wave-vector mismatches due to their limited free-space coupling
efficiencies. These results beg the question: can optical resonators be
designed that simultaneously provide a high Q-factor, small Vm, and controlled
dipolar radiation?

In this work, we present high-Q antennas that sculpt free-space light into
subwavelength volumes while controlling far-field radiation with a dipole-like
scattering profile. These structures merge high-Q guided mode resonance
waveguides[33, 10] with photonic crystal cavities[48] to create free-space
ultra-small mode volume, high-Q resonators. Owing to their very large-scale
integration (patterned at >1M antennas per cm2 and pixelated design, we term
these nanoantennas VINPix. Experimentally, we achieve Q-factors as high as
$\sim$4700 for individual VINPix resonators with normally incident free-space
light. By incorporating a slot in our design, we predict deep subwavelength
mode volumes (around $0.07(\lambda/n\textsubscript{air})\textsuperscript{3}$)
with experimental Q-factors surpassing 1500, showcasing heightened sensitivity
to surrounding refractive index variations. As a proof of concept, we create a
dense VINPix metasurface to image local refractive index variations for high-
resolution and high-sensitivity spectrometer-free hyperspectral mapping.

##  2 The VINPix Resonator Design

Figures 1a and 1b depict the schematics of our setup and the structural design
of a VINPix, respectively. Our antenna design comprises: (i) a photonic cavity
section, (ii) tapered photonic mirrors sections, and (iii) padding photonic
mirrors sections. Figures 1c-1f display SEM images of various antenna designs
that demonstrate the variations within these sections, as will be discussed
ahead. Throughout this article, all structures are based on arrays of 600 nm
tall Si nanoblocks on a sapphire substrate. The first design feature of our
VINPix is the cavity section. The optical cavity supports bound modes that can
be coupled to normally incident free-space light as guided mode resonances by
introducing a bi-periodic width perturbation, $\Delta d$, in the waveguide
cavity (Supplementary Figure 1).[60, 61, 62, 63, 33, 64, 65] To achieve
optical resonances in the near-infrared telecommunication frequency range, we
select the average block width, $d$, to be 600 nm (Supplementary Figure 3).
The bonding and anti-bonding guided mode resonances of interest are at 207 THz
($\sim$1448 nm) and 262 THz ($\sim$1144 nm) respectively for normally incident
light with an infinitely long waveguide cavity (Figure 2a, Supplementary
Figure 1). The perturbation magnitude ($\Delta d$) controls the lifetime of
the guided mode resonances. Decreasing the perturbation increases the Q-factor
of the modes to values as high as $\sim$240,000 with a 10 nm perturbation
(Supplementary Figure 4) for the bonding guided mode resonance (GMR) of
interest. The long resonant lifetime results in a strong $\sim$40-fold
increase in the electric near-field enhancement, with significant field
enhancements at the nanoblocks’ surface (Figure 2b). Taking into account the
fabrication limitations, $\Delta d$ was chosen to be 50 nm for our cavities,
throughout the article, unless specified otherwise.

The second design feature of our VINPix resonator is the integration of
tapered photonic mirrors. These mirrors allow us to truncate the cavity
length, i.e., decrease the mode volume ($V_{m}$), while still preserving high
Q-factors. Without these mirrors, the Q-factor drops by orders of magnitude
due to radiation losses when we reduce the waveguide cavity length (Figure
2c). For example, the Q-factor drops from $\sim$12,000 to 600 when the cavity
length is shortened from semi-infinite to 5 $\mu$m without photonic mirrors.
Notably, tapered photonic crystal mirrors have been used to confine modes
within traditional one-dimensional photonic crystal cavities through band-gap
effects.[66, 67, 68] Here, we employ nanoblocks of the same thickness but
varying widths ($d$) as our individual mirror segments to create our tapered
photonic mirrors section. Varying the width changes the reflection strength of
a given mirror segment. The mirror strength can be calculated from a band
structure calculation. Figure 2d presents a simplified band structure for a
mirror segment with $d=600$ nm. The mode gap indicates the range of forbidden
frequencies, reflected by the mirror segment. The reflection strength is
contingent on the relative positions of the segment’s bands and the target GMR
frequency according to the formula:

$\sqrt{\frac{(\omega_{2}-\omega_{1})^{2}}{(\omega_{2}+\omega_{1})^{2}}-\frac{(\omega_{res}-\omega_{o})^{2}}{(\omega_{o})^{2}}}$
(1)

where $\omega_{2}$, $\omega_{1}$, and $\omega_{0}$ are respectively the
frequencies for the air band edge, dielectric band edge, and midgap frequency
of the mirror segment, and $\omega_{res}$ is the GMR frequency.[66] By
tracking the positions of the dielectric (bonding mode) and air (anti-bonding
mode) bands of mirror segments with varying widths ($d$), we can determine
their respective strengths (Supplementary Figure 2 and Figure 2e). Based on
these calculations, we opted for a mirror segment with $d=2.5$ $\mu$m as the
strongest mirror and a segment with $d=600$ nm as our weakest mirror.

Creating a Gaussian field envelope using rationally tapered mirrors minimizes
radiation losses and maximizes mode confinement in photonic crystal cavities,
as demonstrated by out-of-plane Fourier analyses.[48] To achieve such a
Gaussian field profile within our 15 $\mu m$-long VINPix antenna, the width of
each mirror segment ($d$) progressively increases from the cavity end to
establish a polynomial taper, adhering to the formula $X=AY^{p}+C$. In this
expression, $X$ symbolizes the width of the mirror segment ($d$), $Y$
represents the position of the mirror segment from the end of the cavity
section, $p$ indicates the polynomial’s order, and $A$ and $C$ are constants
dictated by the minimal and maximal widths of the mirror segments in the
tapered mirrors section (further details can be found in the Supplementary
Information). We systematically arrange these mirror segments in an ascending
order of strength within the 5 $\mu m$-long tapered mirrors sections on two
ends of a 5 $\mu m$-long cavity. We examined seven distinct polynomial
functions, spanning from $p=0$ (signifying no taper or a consistent $d$) to
$p=6$. The mode confinement in the vertical (out-of-plane) dimension was
evaluated by performing Fourier transforms of the cross-sectional electric
near-field profile, to quantify the scattering within the light cone.[48, 69]
Figure 2f displays a cross-sectional near-field representation of the
x-component of the electric field and its corresponding Fourier transform (FT)
spectrum for a VINPix resonator devoid of any perturbation ($\Delta d=0$),
with mirror sections exhibiting a zeroth-order polynomial taper. In this
instance, a pronounced intensity within the radiation zone is apparent,
signifying substantial radiation losses in this design. This results in a
modest simulated $Q$-factor of approximately 1900. In stark contrast, Figure
2g showcases comparable findings for a VINPix resonator, with mirror sections
illustrating a fourth-order polynomial taper. A more Gaussian-like field
envelope is discerned, which correspondingly causes a marked decrease in
intensity within the radiation zone and a remarkably superior $Q$-factor of
approximately 615,000 (Supplementary Figure 5 encompasses one-dimensional line
traces of the field profiles and FT spectra). Therefore, by employing rational
taper functions for the mirror sections, we gain Gaussian-like field profiles
inside our devices that minimize radiative losses.

##  3 Optimization and Measurements of High-$Q$ VINPix Resonators

We further optimize our VINPix design with width perturbations in the cavity
region, with the aim to maximize $Q$-factors while retaining the capability
for free-space light excitation. Figure 3a illustrates simulated $Q$-factors
for a 15 $\mu m$-long VINPix resonator with a 5 $\mu m$-long cavity, subject
to varying perturbations ($\Delta d$), truncated by 5 $\mu m$-long tapered
mirrors sections with different polynomial orders ($p$). We ascertain that a
fourth-order polynomial taper yields the most optimal confinement for a vast
range of perturbation magnitudes, consistent with simulations sans
perturbations (Figure 2g). Employing a fourth-order polynomial taper, we
conduct a coarse optimization analysis to discern optimal length ratios for
various sections of the VINPix resonator. The length of the cavity section
emerges as the most crucial determinant in realizing elevated $Q$-factors
(Figure 3b). This observation is intuitive, given that the cavity section
primarily facilitates coupling of free-space light into individual resonators.
The taper section assumes secondary importance, dictating the count of
individual mirror segments and enabling intricate tapering profiles. The
padding section is a set of strong mirrors that can be added to the end of the
tapered photonic mirrors to increase confinement. We achieve calculated
$Q$-factors, exceeding 10,000 by configuring the VINPix resonator with a
cavity length of 7 $\mu m$ and 4 $\mu m$-long mirror sections (Figure 3b).
Figure 3c depicts the simulated normalized electric near-field intensity (log
scale) at the cross-section of the optimized VINPix resonator design. The most
pronounced field enhancements are discernible at the nanoblock surfaces within
the cavity section. Utilizing this near-field profile, we compute the far-
field response, shown in Figure 3d. Along with a near-field profile of a
cross-sectional x-z monitor at the GMR wavelength (Figure 3e), our simulations
culminate in a refined 15 $\mu m$-long, free-space-excitable, high-$Q$ antenna
design that produces a dipole-like far-field radiation profile with suppressed
radiations to higher-orders.

We experimentally validate our VINPix resonator design using a home-built
reflection microscope (detailed in Supplementary Figure 6 and Methods). Guided
by insights from Figure 3b, we opt for a 7 $\mu m$-long cavity section and 4
$\mu m$-long tapered mirrors sections, wihtout any padding sections. We
fabricate and charcaterize individual resonators with varied polynomial orders
(ranging from $p=1$ to 6) and perturbation magnitudes ($\Delta d$ = 50 nm and
100 nm). Figure 3f shows a scanning electron microscope (SEM) image of a
representative section of an array of 15 $\mu m$-long VINPix resonators,
patterned on a sapphire substrate. Illuminating the metasurface through the
substrate, we employ a supercontinuum near-infrared (NIR) light source, and
subsequently capture the reflected intensity using an imaging spectrometer.
Figure 3g presents a spectral image obtained from five individual VINPix
resonators showing that our high-$Q$ GMRs do not rely on interdevice coupling.
This makes each VINPix individually addressable enabling higher packing
densities, exceeding millions per $cm^{2}$. The characterized GMR wavelength
resonates with our theoretical predictions (detailed in Supplementary Figure
7), with the manifested Fano-lineshape emerging as a byproduct of the guided
mode coupling with radiative Fabry-Perot modes. Figure 3h presents $Q$-factors
obtained from this experiment – we observe the highest confinement with a
fourth-order polynomial, as anticipated from simulations. Experimentally, we
achieve $Q$-factors peaking at roughly 4700 with $\Delta d$ = 50 nm (and
approximately 2000 with $\Delta d$ = 100 nm) for individual VINPix resonators.

##  4 Spatial Refractive Index Mapping on a VINPix Metasurface

We subsequently fabricated a dense VINPix metasurface to showcase potential
applications in high-density, multiplexed computational spectrometry and
biosensing, among others. Here, each VinPix reports the local refractive index
via its spectral resonance shift, which we can record via spatially-dependent
intensity variations. As illustrated in Figure 4a, we employ hyperspectral
imaging to concurrently extract spectral and spatial data of individual VINPix
resonators. This is achieved through a time-series of wide-field images
captured on a 2D CCD array, rendering a data cube.[21, 9] We pattern the top
layer of 126 VINPix resonators with PMMA resist in the shape of an “S”. Inside
the “S” is water (with refractive index $\sim$1.33), while outside the “S” is
PMMA resist (with refractive index $\sim$1.47) as shown in Figures 4c and 4d
(see Methods for details). We illuminate the metasurface with a narrow-
linewidth NIR tunable laser and sweep the wavelength from 1560 nm to 1620 nm
in 0.05 nm increments. Each image frame corresponds to a single illumination
wavelength as schematically shown in Figure 4a and 4b. By sweeping the
illumination wavelength across the resonances, we simultaneously image and
collect spectra for hundreds of individually addressable resonators in a
single experiment (Figure 4e).

We extract the spectral information for each resonator as schematically shown
in Figures 4a and 4b. Here, $R_{\text{PMMA}}$ is a VINPix situated outside the
“S”, while $R_{\text{water}}$ is located within the “S”. The detected
resonance wavelengths at $\sim$1570 nm ($\lambda_{\text{water}}$) and
$\sim$1610 nm ($\lambda_{\text{PMMA}}$) for the two resonator groups agree
with our theoretical calculations (Supplementary Figure 8). As anticipated,
the resonance wavelength for VINPix resonators enveloped by PMMA is longer,
attributable to the higher effective refractive index of the encompassing
medium. A spatially-resolved map of resonance shifts spanning the entire
field-of-view is presented in Figure 4f. The appended histogram manifests the
GMR wavelengths for all the VINPix resonators recorded in the experiment
(Figure 4f).

##  5 Introduction of a Slot for Higher Spatial Confinement and Sensitivity

To augment the sensitivity of our imaging array, we further decrease the
$V_{m}$ of our VINPix resonators by incorporating a slot. Photonic crystals
localize light to subwavelength mode volumes, leveraging bandgap confinements
in-plane and total internal reflection out-of-plane.[70] However, by
introducing a secondary step in the light confinement strategy, slotted
photonic crystal cavities have attained even smaller mode volumes on the order
of $\sim$0.01 $(\lambda/n_{\text{air}})^{3}$.[71] Owing to electromagnetic
boundary conditions, this secondary level of spatial localization mandates the
field, which was formerly confined within the dielectric, to now concentrate
within the air section, yet maintaining the high-Q character of the modes.[50,
72, 73]

In order to calculate the mode volume ($V_{m}$), we utilize the conventional
definition wherein $V_{m}$ is determined using the electric field intensity
($E$) and permittivity ($\epsilon$):

$V_{m}=\frac{\int\epsilon|E|^{2}\,dV}{\max(\epsilon|E|^{2})}$ (2)

By introducing a slot along the length of the VINPix, we reduce the mode
volume $V_{m}$, while still maintaining relatively high $Q$-factors (Figure
5a, schematic, and Figure 1f, SEM image). Figure 5b compares the theoretically
calculated effective $V_{m}$ values for different device lengths of our
waveguide cavity, VINPix design, and slotted VINPix with a 30 nm wide slot
(see Supplementary Figure 9 for similar comparisons of $Q$-factors and
$Q/V_{\text{eff}}$). The length ratios for the cavity, tapered mirrors, and
padding mirrors sections are kept the same across all different device
lengths, using the ratio that yielded the highest $Q$-factor in our
optimizations (Figure 3b). Our VINPix resonators exhibit $V_{m}$ values close
to $1(\lambda/n_{\text{eff}})^{3}$ and as small as $\sim
0.07(\lambda/n_{\text{air}})^{3}$ after introducing a 30 nm wide slot. Here,
$n_{\text{eff}}$ is taken as 2.24, the average of the refractive indices of
air and Si based on our waveguide cavity’s design, and is used to calculate
the effective $V_{m}$ for both the waveguide cavity and VINPix designs. For
the slotted VINPix design, the field confinement is maximum within the air
slot, so $n_{\text{eff}}=n_{\text{air}}=1$, in that case. Figure 5c
illustrates the normalized cross-sectional electric field intensity of a 15
$\mu m$ slotted VINPix with a 30 nm wide slot, showing an electric field
enhancement of approximately 110-fold within the slot. This enhancement is
significantly greater than what was observed in our infinitely long waveguide
cavity ($\sim 40$-fold, Figure 2b) and a VINPix resonator without a slot
($\sim 10$-fold, Figure 3c).

In Figure 5d, we compare the experimentally measured $Q$-factors (circles) of
the slotted VINPix with the theoretically predicted values (stars). We perform
our measurements on 15 $\mu m$-long slotted VINPix resonators with $p=4$,
featuring 70 nm and 100 nm wide slots. Both simulations and experiments
exhibit a decrease in the $Q$-factor compared to a VINPix resonator (from an
average of $\sim 3500$ to $\sim 1200$) as the field is now localized within a
lower refractive index medium. Nevertheless, while $Q$-factor decreases by
$\sim 3\times$, $V_{m}$ shrinks by $\sim 100$-fold in simulations, boosting
the effective $Q/V_{\text{eff}}$ ratio significantly (Supplementary Figure 9).
Higher $Q/V_{\text{eff}}$ and more accessible enhanced electric fields boost
the sensitivity of our slotted VINPix design. In Figure 5e, we exemplify this
increased sensitivity. It is well documented that increasing NaCl
concentrations increases the refractive index of water.[74] Slotted VINPix
resonators demonstrate significantly higher shifts in resonant wavelength due
to a stronger field overlap in the surrounding medium. The resonator’s sensing
figure of merit is defined as sensitivity (resonant wavelength shift per
refractive index unit or RIU change) divided by the full width at half maximum
(FWHM) of the mode. We observe considerably higher resonant wavelength shifts
per RIU change – 437.2 nm RIU-1 with our slotted VINPix resonators – compared
to 355.6 nm RIU-1 without the slots. State-of-the-art affinity-based
biosensors are plasmonic sensors that combine small-mode volumes with
controlled dipolar radiation but generally achieve FOM values of ca. 1-10
RIU-1.[75, 76] With much higher $Q$-factors and subwavelength $V_{m}$, our
optimized slotted VINPix design achieves an excellent FOM of $\sim 440$ RIU-1
with effortless free-space excitation and efficiently captured controlled
radiation. Notably, while ensemble sensitivity sees an averaged response
manifested by the radiating field in the vicinity of the resonators, a single
or few molecules adeptly placed in the slot region of high electromagnetic
intensity would experience a much more pronounced interaction. This implies
that, for sparse-molecule measurements in the slot region, the sensitivity
enhancement is expected to be substantially greater.

##  6 Conclusion

In this study, we introduced densely integrated high-$Q$ photonic
nanoantennas—VINPix—that combine key features of high-$Q$ GMR waveguide
cavities and tapered photonic crystal cavities. We simultaneously achieved
high $Q$-factors, subwavelength $V_{m}$, and controlled dipole-like radiation,
with effortless free-space coupling. Utilizing rationally designed tapered
photonic mirrors to truncate perturbed waveguide cavities, we experimentally
showcased average $Q$-factors of approximately 3500 in 15 $\mu m$-long VINPix
resonators. Given optimal fabrication techniques that accentuate design
intricacies and mitigate flaws, our VINPix design is poised to reach
$Q$-factors in the million range. Recognizing the burgeoning need for photonic
platforms in deployable and wearable applications, we demonstrate high-
resolution, high-sensitivity spatial resonance shift mapping using a
spectrometer-free hyperspectral imaging setup. The introduction of a slot
further refines the spatial localization in our VINPix resonator, enabling
subwavelength volumes as low as $\sim 0.07$ ($\lambda/n_{\text{air}})^{3}$ and
heightened sensitivity to refractive index variations with an ROI of $\sim
440$ RIU. Notably, this sensitivity could significantly escalate, especially
when analyzing isolated or few molecules – if these particles are adeptly
positioned within slots where field enhancement is at its maximum. The compact
footprint of our antenna imparts the potential to integrate millions of
individually addressable resonators per square cm. Our work opens avenues for
developing innovative integrative and/or wearable and deployable photonic
platforms for multiplexed health and environmental monitoring, enhanced
vibrational spectroscopy, wavefront shaping, and on-chip spectrometry.

Figure 1: Schematic and scanning electron microscopy (SEM) images of VINPix
resonators: (a) Schematic of a metasurface of individually addressable 15 $\mu
m$-long high-Q photonic antennas (VINPix) made of Si nanoblocks on a sapphire
substrate. The resonances are excited using a normally incident near-infrared
(NIR) laser source and the scattered light is recorded using a camera or an
imaging spectrometer. (b) Representation of a VINPix’s structural design,
broken into three sections: a photonic cavity section, a tapered mirrors
section, and a padding mirrors section. (c) Top view (SEM image) of VINPix
resonators with different tapering functions – polynomials of order, p = 0 to
6 from top to bottom – without any padding sections. (d) Angled SEM images of
VINPix without padding sections, and p = 1, 2, 4 and 6 as labeled. (e) Angled
SEM image, with enlarged inset of the cavity section, of a representative 15
$\mu m$-long VINPix consisting of a 7 $\mu m$-long cavity section, 3 $\mu
m$-long tapered mirrors sections and 1 $\mu m$-long padding sections. (f)
Angled SEM image, with enlarged inset of the cavity section, of a slotted
VINPix with a 70 nm wide slot.

Figure 2: Tapered photonic mirrors confine guided mode resonances to shorter
resonator lengths: (a) Simplified TE band diagram of our infinitely long
photonic cavity with average width, $d=600$ nm and $\Delta d=50$ nm, the unit
cell size or periodicity ($b_{y}$) = 660 nm. Bands at 207 THz and 262 THz (for
$k_{||}=0$) are the bonding and anti-bonding guided mode resonances of
interest. Refer to Supplementary Figure 1 for a schematic of our waveguide
cavity and band diagram calculations (b) Simulated normalized electric field
enhancements at the cross-section of the unit cell of an infinitely long
cavity with $\Delta d=50$ nm, of the bonding guided mode resonance (GMR).
Geometrical parameters of the resonator unit cell are: height = 600 nm,
average width ($d$) = 600 nm, thickness ($t$) = 160 nm, block spacing
($a_{y}$) = 330 nm. Scale bar 200 nm. (c) Simulated $Q$-factors of the GMR for
waveguide cavities of different lengths. Stars correspond to waveguide
cavities of infinite length (d) Simplified TE band diagram for a mirror
segment with $d=600$ nm with labeled radiation or leaky zone, light line, the
bonding and anti-bonding guided mode resonances of interest, and the
corresponding mode gap. Simulated mode profiles of the bonding and anti-
bonding modes are shown in the Supplementary Figure 1. (e) Mirror strength
calculated using band positions for mirror segments of different widths. Refer
to Supplementary Figure 2 for band positions of the bonding mode (dielectric
band edge), anti-bonding mode (air band edge), and the mid-gap frequency for
mirror segments of different widths. (f) and (g) Left: simulated cross-
sectional field profiles for the x-component of the electric field; and Right:
corresponding Fourier transform spectra on a logarithmic scale to visualize
the out-of-plane scattering for a VINPix with $\Delta d=0$, with a tapered
mirrors section of orders, $p=0$ and $p=4$, respectively. The region inside
the circle is the radiation zone. Nanoblocks are marked with black borders in
the cross-sectional field profiles to aid visualization. Scale bar 1 $\mu$m.

Figure 3: Optimized VINPix resonators show dipole-like radiation and high
Q-factors in experiments: (a) Simulated $Q$-factors of 15 $\mu m$-long VINPix
with a 5 $\mu m$-long cavity of different perturbation magnitudes ($\Delta
d$), and 5 $\mu m$-long tapered mirrors sections of different polynomial
orders. (b) Simulated $Q$-factors of 15 $\mu m$-long VINPix with varying
fractional configurations of the lengths of the cavity section, tapered
mirrors sections ($p=4$), and padding mirrors sections. Black arrows point
towards the respective axes for one representative configuration having 0.2,
0.4 (combined, for both sides of the VINPix), and 0.4 (combined, for both
sides of the VINPix) fractions of the VINPix’s total length for each of the
three sections respectively. (c) Simulated normalized electric near-field
enhancements at the cross-section of a VINPix with 7 $\mu m$-long cavity
section of $\Delta d=50\,\text{nm}$, 3 $\mu m$-long tapered mirrors sections
of $p=4$, and 1 $\mu m$-long padding sections on each end. (d) Far-field
simulation plot of the optimized VINPix. Concentric circles represent
$10^{\circ}$, $30^{\circ}$, $60^{\circ}$, and $90^{\circ}$ from the center
respectively. (e) Simulated electric near-field profile through the cavity of
the optimized VINPix. (f) Representative SEM image of an array of 15 $\mu
m$-long VINPix with $p=4$ and $\Delta d=50\,\text{nm}$. (g) (Left panel)
Spectral image from five individual VINPix as marked in (f) and (Right panel)
normalized row-averaged reflected intensities corresponding to each of the
five VINPix. (h) Experimentally characterized $Q$-factors of 15 $\mu m$-long
VINPix with 7 $\mu m$-long cavity sections of $\Delta d$ = 50 nm and 100 nm,
and 4 $\mu m$-long tapered mirrors sections of different polynomial orders.
Average values and standard deviations correspond to 30 VINPix resonators
measured for each set.

Figure 4: VINPix metasurface successfully senses changes in the local
refractive index using high-resolution hyperspectral imaging: (a) Schematic of
our hyperspectral imaging setup. A VINPix metasurface patterned with a PMMA
layer on top in the shape of an “S” is illuminated using a normally incident
narrow band tunable NIR light source and the reflected images are recorded on
a camera. (b) Extracted spectral data corresponding to $R_{\text{PMMA}}$ and
$R_{\text{water}}$ – a VINPix resonator outside, and inside, the “S”,
respectively. (c) Schematic of the PMMA patterned metasurface where certain
VINPix structures are covered under PMMA. (d) Optical microscopic image of the
VINPix metasurface after patterning a PMMA layer in the shape of the “S” where
the resonators inside the “S” are exposed to the top medium and the rest are
covered under PMMA resist. (e) Image frames recorded on the camera at the two
resonance wavelengths where $\lambda_{\text{water}}$ corresponds to $\sim
1570\,\text{nm}$ for GMR wavelengths of VINPix inside the “S”, and
$\lambda_{\text{PMMA}}$ corresponds to $\sim 1610\,\text{nm}$ for GMR
wavelengths of VINPix outside the “S”. (f) (Top) Spatial resonance-shift map
generated by extracting spectral information for all the 126 VINPix resonators
recorded in the data cube. (Bottom) Histogram displaying the GMR wavelengths
of all the recorded VINPix resonators.

Figure 5: Slots boost light confinement within our VINPix resonators: (a)
Schematic of a slotted VINPix. (b) A comparison of simulated effective mode
volumes for our perturbed waveguide cavity, optimized VINPix and a slotted
VINPix with a $30\,\text{nm}$ wide slot. (c) Simulated normalized electric
field enhancements at the cross-section of a 15 $\mu\text{m}$-long slotted
VINPix with a $30\,\text{nm}$ wide slot. (d) Simulated (stars) and
experimentally characterized (circles) $Q$-factors of slotted VINPix with
$70\,\text{nm}$ and $100\,\text{nm}$ wide slots. Average values and standard
deviations correspond to 30 slotted VINPix resonators measured for each set.
(e) Resonant wavelength measurements as a function of background medium
refractive index with slotted VINPix. Average values and standard deviations
correspond to 30 resonators measured for each set. Lines represent linear fits
to the data.

##  7 Methods

###  7.1 Computational Design

Simulations were performed using the Lumerical FDTD solver (Lumerical 2023
R1.3). PML boundary conditions in $x$ and $y$ directions were used for
structures with finite lengths. PML boundary conditions were used in the $z$
direction in all cases. Localized dipole sources were used to excite
structures with no perturbations ($\Delta d=0$). For structures with non-zero
perturbations ($\Delta d\neq 0$), a plane wave excitation source was used in
the case of periodic boundary conditions, whereas a total-field scattered-
field (TFSF) excitation source was used otherwise. Consistent $Q$-factors were
observed with all three sources for waveguide cavities of different lengths
(see Supplementary Figure 11). Standalone device simulations, for example for
VINPix optimizations, were performed in air as the medium. Simulations to
replicate experimental results were performed in water as the medium.

###  7.2 Fabrication

Photonic structures were fabricated using standard lithographic procedures.
First, $600\,\text{nm}$, single crystal silicon-on-sapphire (MTI Corporation
and University Wafer) substrates were cleaned by rinsing with acetone,
methanol, and isopropanol, followed by sonication in acetone and isopropanol
followed by a dehydration bake at $180^{\circ}\text{C}$ for 2 minutes. The
substrates were spin-coated with hydrogen silsesquioxane (HSQ) negative tone
resist (XR-1541-006, DuPontTM) at 1500 RPM. The resist was baked for 5 minutes
at $80^{\circ}\text{C}$. To reduce charging, a charge dissipation layer
(e-spacer, Showa Denko) was spin-coated at 2000 RPM over the HSQ resist and
baked again for 2 minutes at $80^{\circ}\text{C}$. The patterns were defined
using electron beam lithography (Raith Voyager) with a $50\,\text{kV}$
accelerating voltage and developed in a solution consisting of 4% sodium
chloride and 1% sodium hydroxide in water. After exposure and development, the
patterns were transferred to the chip using reactive ion etching (Oxford III-V
Etcher) using HBr and Cl2 chemistry for an anisotropic silicon etch. Lastly,
the resist was removed using 2% hydrofluoric acid in water, followed by
cleaning in a Piranha solution at $120^{\circ}\text{C}$ to remove any organic
residue. Further, for preparing VINPix metasurface for hyperspectral imaging,
patterned silicon on sapphire metasurface was cleaned by rinsing with acetone,
methanol, and isopropanol, followed by sonication in acetone and isopropanol
followed by a dehydration bake for 2 minutes. The metasurface was spin-coated
with PMMA 950A4 positive resist at 3000 RPM, followed by a 2-minute bake at
$110^{\circ}\text{C}$. A charge dissipation layer (e-spacer, Showa Denko) was
spin-coated at 2000 RPM over the HSQ resist and baked again for 2 minutes at
$110^{\circ}\text{C}$. The PMMA patterns were defined using electron beam
lithography (Raith Voyager) with a $50\,\text{kV}$ accelerating voltage and
developed in a solution consisting of a 1:3 ratio of MIBK and IPA.

###  7.3 Scanning Electron Microscopy Characterization

Representative images were taken using a FEI Magellan 400 XHR scanning
electron microscope with a field emission gun source. A representative sample
was coated with a $\sim 5\text{-nm}$ film of Au to reduce charging. For side
and tilted views, the stage was titled by $30^{\circ}$. Images were typically
acquired with an accelerating voltage of $5-10\,\text{kV}$.

###  7.4 Optical Characterization

Resonator spectra were measured in a home-built near-infrared reflection
microscope shown in Supplementary Figure 6. Samples were illuminated via a
broadband supercontinuum laser (NKT SuperK EXTREME) or a tunable narrow-
linewidth laser (SANTEC TSL-550), with a collimated fiber output. A polarizer
$P1$ was set to create linearly polarized incident illumination at a
45$\mathrm{\SIUnitSymbolDegree}$ angle with respect to the metasurface
resonators. The illuminating beam is focused on the back focal plane of a 5X
objective (Mitutoyo Plan Apochromat NIR) with a lens $L1$ ($f=75$ mm or
$f=100$ mm) to produce a collimated plane wave at the sample. The devices were
illuminated through the sapphire substrate. To demonstrate general
applicability, we characterized our VINPix metasurface under a droplet of
water, following the common practice employed in biomolecular sensing. The
scattered light is directed through a cross-polarized polarizer $P2$ at
-45$\mathrm{\SIUnitSymbolDegree}$ to reduce the substrate Fabry-Perot signal.
The scattered light is then focused via a lens $L2$ ($f=75$ mm) into a
spectrometer (Princeton Instruments SPR-2300). The broadband signal is
diffracted via a diffraction grating (600 g/mm, blaze wavelength 600 nm,
Princeton Instruments) and focused onto a TE cooled InGaAs CCD detector
(NiRvana, Princeton Instruments). While using the Santec for hyperspectral
imaging, the diffraction grating is eliminated and the images are recorded
straight on the InGaAs CCD detector. Throughout the paper, the measured
resonant spectral features were first normalized and then analyzed by fitting
the diffraction efficiency data with the function

$T=\left|\frac{1}{1+F\sin^{2}(n_{s}kh_{s})}\right|^{2}\cdot\left|a_{r}+a_{i}i+\frac{b}{f-f_{0}+i\gamma}\right|^{2}$
(3)

The first term accounts for the Fabry–Perot interference through the substrate
of thickness $h_{s}$ and refractive index $n_{s}$. $k$ is the free-space
wavevector ($\frac{2\pi}{\lambda}$) and $F$ accounts for the reflectivity of
the interfaces. The second term represents the superposition between a
constant complex background, $a_{r}+a_{i}i$, and a Lorentzian resonance with
resonant frequency ($f_{0}$) and full-width at half-maximum $(2\gamma)$. The
Q-factor of this resonance is calculated as $Q=\frac{f_{0}}{2\gamma}$.

###  7.5 Analysis of Hyperspectral Data Cube

Each image frame in the hyperspectral data cube corresponds to a single
illumination wavelength. A time series of widefield image frames representing
intensity mappings were collapsed by uniform summation into a singular frame
to locate VINPix centers. Pixel rows and columns corresponding to maximum
intensity in the image frames were selected by determining peaks via local
maxima, and manual adjustments were made based on physical VINPix spacing
constraints to remove spatial overlap. VINPix centers were then assigned and
labeled at each row and column cross-section. Because our VINPix size is
greater than the individual pixels of our CCD camera, a $9\times 9$ pixel
intensity integration centered at our VINPix centers was performed for each
frame in the hyperspectral stack. Spectral features were then extracted from
each VINPix region and fitted to a Fano lineshape using the above-mentioned
formula.

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# Photonic sampled and quantized analog-to-
digital converters on thin-film lithium niobate platform

Donghe Tu  1,2 Xingrui Huang  1,2 Yang Liu  1,2 Zhiguo Yu  1 and Zhiyong Li1
1State Key Laboratory on Integrated Optoelectronics, Institute of
Semiconductors, Chinese Academy of Sciences, Beijing 100083, China
2College of Materials Science and Opto-Electronic Technology, University of
Chinese Academy of Sciences, Beijing 100083, China<EMAIL_ADDRESS>
###### Abstract

In this paper, an on-chip photonic sampled and quantized analog-to-digital
converter (ADC) on thin-film lithium niobate platform is experimentally
demonstrated. Using two phase modulators as a sampler and a 5$\times$5
multimode interference (MMI) coupler as a quantizer, an 1 GHz sinusoidal
analog input signal was successfully converted to a digitized output with a 20
GSample/s sampling rate. To evaluate the system performance, the quantization
curves together with the transfer function of the ADC were measured. The
experimental effective number of bits (ENOB) was 3.17 bit. The demonstrated
device is capable of operating at a high frequency up to 70 GHz, making it a
promising solution for on-chip ultra-high speed analog-to-digital conversion.

††journal: osajournal††articletype: Research Article

##  1 Introduction

The analog-to-digital converter (ADC), which converts analog signals to
digital signals, plays an important role in modern advanced information
systems, such as radars, high speed communication systems, and precision
measuring instruments. Nevertheless, conventional electronic ADCs are not
suitable for ultra-high speed signal processing and large bandwidth
applications since the serious aperture jitter and limited comparator
bandwidth [1]. To overcome these bottlenecks, optical ADCs which utilize
photonic components to implement the conversion were proposed and have become
a hotspot in the field of optoelectronic technologies [2].

In recent years, many optical ADC schemes have been proposed and demonstrated,
which can be divided into four major types [1]: photonic assisted (PA) ADC [3,
4], photonic sampled (PS) ADC [2, 5, 6], photonic quantized (PQ) ADC [7] and
photonic sampled and quantized (PSQ) ADC [8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 27]. PA, PS and PQ ADCs still require several high speed electronic ADCs
for either sampling or quantizing, resulting in additional power consumption
and system complexity. The PSQ scheme, which performs sampling and
quantization both in the optical domain, can avoid these problems and has
attracted much attention in recent years [8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 27]. PSQ ADC can be further subdivided into two broad categories by
different quantization methods: optical amplitude quantization (OAQ) schemes
[10, 11, 12, 13] and phase-shifted optical quantization (PSOQ) schemes [8, 9,
14, 15, 16, 17, 27]. In OAQ schemes, different optical amplitude was
distinguished via high optical nonlinearities . For example, Ref. [13]
reported a 2 bit all optical ADC using photonic crystal based cavities. In
[10], an optical ADC with a sampling rate of 40 GS/s and the effective number
of bits (ENOB) of 3.79 was demonstrated by using a highly non-linear fiber to
induce soliton self-frequency shift. However, OAQ schemes usually require high
input optical power and a long interactive length, which lead to additional
power consumption and difficulty of chip level integration. As for PSOQ
schemes, the quantization is accomplished by the interference of the lights
with different phases. The interference can be achieved by on-chip Mach-
Zehnder interferometers, and the requirement of high optical nonlinearities in
OAS schemes is avoided. Thus, the optical power could be more efficient and
the footprint could be relatively small. In Ref. [9], an optical ADC with
sampling rate of 40 GS/s and ENOB of 3.45 using a phase shifter array was
reported. In Ref. [14, 15], an optical analog-to-digital conversion scheme
using Mach–Zehnder modulators (MZM) with identical half-wave voltages was
reported. Compared with the OAQ schemes, the above-mentioned PSOQ schemes
effectively reduced the input optical power, but they still used discrete
devices. In order to achieve an on-chip integration and further downsize the
footprint of the system, a quantization approach using a 3$\times$5 step-size
multimode interference (MMI) coupler was proposed [16]. The scheme in Ref.
[16] was further investigated in Ref. [17]. A quantizer utilizing integrated
photonics with ENOB of 3.31 was fabricated on SOI platform. However, the
authors in [17] only focused on the quantizer, which is only one part of the
PSQ ADC. The sampling process and the complete analog-to-digital conversion
were not engaged. Furthermore, sampling a high speed analog signal for PSOQ
schemes on SOI platform is challenging due to three main drawbacks. Firstly,
the large half wave voltage ($V_{\pi}$) of high speed SOI phase modulators
makes it difficult to meet the 2$\pi$ phase shift requirement in PSOQ schemes.
The electrical divers that can provide enough output power are hard to
achieve, and a breakdown may occur when using reverse biased PN junction
modulators. Next, the nonlinearities of the SOI modulators would lead to
sampling errors. The modulation efficiency decreases when the input voltage
increasing because of the nonlinearities of the plasma dispersion effect.
Finally, the relatively small electro-optical (EO) 3-dB bandwidth of SOI
modulators limits the sampling bandwidth of the ADC, which makes it difficult
to competent ultra-fast applications.

To overcome these above-mentioned shortcomings, an on chip PSQ ADC on thin-
film lithium niobate (TFLN) platform was demonstrated in this paper. The
Pockels effect of lithium niobate provides a linear modulation on TFLN
platform. And over the past 4 years, many high speed and low $V_{\pi}$
electro-optical modulators on TFLN platform are reported [18, 19, 20]. In
[18], a EO 3-dB bandwidth of a 80 GHz and $V_{\pi}$ of 2.3 V modulator was
demonstrated. It showed the capability of TFLN platform for large bandwidth
sampling and meeting the 2$\pi$ phase shift requirement for the MMI quantizer
with a lower drive voltage.

In our work, a PSQ ADC on a TFLN chip consisting of two beyond 70 GHz EO 3-dB
bandwidth phase modulators and a 5$\times$5 MMI was demonstrated. The input
analog signal was sampled by an optical pulse train using the two phase
modulators. An optical 72∘ hybrid based on the 5$\times$5 MMI proposed in our
previous study [21] was used for a 10-level quantization. The quantization
results were then coded and converted to a digital output with 10 digitized
levels. To evaluate the system performance, the quantization curves and the
transfer function of our proposed ADC were measured and analyzed. And an 1 GHz
electrical analog sinusoidal signal was converted to a digital output with a
20 GS/s sampling rate. To the best of our knowledge, this is the first time
that the sampling and the quantization were demonstrated on a single chip for
PSQ ADCs. The ENOB was measured to be 3.17 and the input sampling EO 3-dB
bandwidth was beyond 70 GHz. Therefore, our work has provided a potential
solution towards high-bandwidth on-chip analog-to-digital conversions and
optical signal processing systems.

##  2 Methods

Figure 1: Conceptual diagram of our proposed PSQ ADC

A conceptual diagram of our proposed PSQ ADC is shown in Fig. 1. An analog
signal is sampled by an optical pulse train using two identical 1-cm long
phase modulators with opposite modulation phase shift. Next, the two sampled
lights are quantized by a 5$\times$5 MMI. Following by a photodetector (PD)
array and a digital signal processing (DSP) unit, the signal is then coded and
transferred to digitized values. The following contents in this section will
introduce the operation principles of sampling and quantization, which are the
two main functions of our proposed ADC.

###  2.1 Sampling

As shown in Fig. 1, an optical pulse train is fed into the TFLN ADC chip as an
optical source. The optical pulse train can be represented as

$E_{\textup{input}}=A\cdot e^{-j\omega t}\cdot f(t)$ (1)

where $A,\omega,f(t)$ represent the amplitude, angular frequency and the
normalized envelope of the pulse shape, respectively. To simplify the
calculation, the initial phase of the optical pulse is considered to be zero.
After the input analog signal is phase modulated, the amplitude of the two
output lights ($E_{0}$, $E_{1}$) can be expressed as

$\begin{split}E_{\textup{1}}=\frac{\sqrt{2}}{2}A\cdot e^{-j\omega t}\cdot
e^{-j(\phi_{1}+\frac{1}{2}\Delta\phi_{\textup{signal}})}\cdot f(t)\\\
E_{\textup{2}}=\frac{\sqrt{2}}{2}A\cdot e^{-j\omega t}\cdot
e^{-j(\phi_{2}-\frac{1}{2}\Delta\phi_{\textup{signal}})}\cdot f(t)\end{split}$
(2)

where $\phi_{1}$ and $\phi_{2}$ are the random phase shifts induced by the
non-uniformity of the waveguides of the two phase modulators due to
fabrication errors. $\frac{1}{2}\phi_{\textup{signal}}$ represent the amount
of change in phase by both phase modulation. Since the modulation on TFLN
platform utilizes the Pockels effect, the phase change
($\frac{1}{2}\phi_{\textup{signal}}$) is proportional to the amplitude of the
input analog signal, which can be expressed as

$\frac{1}{2}\Delta\phi_{\textup{signal}}=\frac{\pi
V_{\textup{analog}}}{V_{\pi}}$ (3)

where $V_{\textup{analog}}$ is the amplitude of the input analog signal and
$V_{\pi}$ is the half wave voltage of the phase modulators. The phase
difference between the two modulated lights ($\Delta\phi$) can be written as

$\Delta\phi=\phi_{1}-\phi_{2}+\Delta\phi_{\textup{signal}}$ (4)

where $\phi_{1}-\phi_{2}$ is a constant. According to Equation (3) and (4),
the sampling process induces an additional phase difference ($\Delta\phi$)
between the two modulated lights, which increases linearly with the amplitude
of the input analog signal.

###  2.2 Quantization

Figure 2: (a) Schematic diagram of the optical 72∘ hybrid. (b) Quantization
curves of the quantizer. (c) The corresponding quantization codes for ten
quantization levels

The quantization process in our proposed ADC converts the two modulated lights
with different phases into 5-channel outputs with 10 quantization levels. As
shown in Fig. 2 (a), after the analog signal is sampled, the two lights with a
phase difference ($\Delta\phi$) are fed into a 15-um wide and 235-um long
5$\times$5 MMI. According to our previous study [21], when the input channels
are the first and the third ports, the 5$\times$5 MMI can be used as an
optical 72∘ hybrid with an acceptable phase deviation in a relatively large
wavelength range. The output optical power intensities of the five channels of
the MMI ($I_{1}\sim I_{5}$) can be successively expressed as

$\displaystyle I_{1}$
$\displaystyle=\frac{1}{5}A^{2}[1+cos(\Delta\phi-\frac{2}{5}\pi)]$ (5)
$\displaystyle I_{2}$ $\displaystyle=\frac{1}{5}A^{2}[1+cos(\Delta\phi)]$
$\displaystyle I_{3}$
$\displaystyle=\frac{1}{5}A^{2}[1+cos(\Delta\phi-\frac{4}{5}\pi)]$
$\displaystyle I_{4}$
$\displaystyle=\frac{1}{5}A^{2}[1+cos(\Delta\phi+\frac{2}{5}\pi)]$
$\displaystyle I_{5}$
$\displaystyle=\frac{1}{5}A^{2}[1+cos(\Delta\phi+\frac{4}{5}\pi)]$

Equation (5) shows that the optical power intensity of each channel is
sinusoidally related to $\Delta\phi$. As one can see in Fig. 2 (b), a 72∘
phase shift is induced between the adjacent quantization curves. Next, a
threshold power is set at the middle of the normalized power to determine the
digital output of each channel. For instance, if the output power intensity of
one channel is above the threshold, it is decided to be 1. Otherwise is
decided to be 0. The five transmission curves divide the threshold line into
10 regions, corresponding to 10 quantization levels. In Fig. 2 (c), 10 groups
of codes for the 10 quatization levels are shown. According to
$log_{2}10=3.32$, the above analysis indicates that the theoretically
quantization bit of the 5$\times$5 MMI is 3.32.

##  3 Device fabrication and experimental results

In this section, the fabrication process of the proposed optical ADC on the
TFLN platform was illustrated. Then, the measurements of the quantization
curves and the transfer function of the proposed ADC were introduced, and the
equivalent ENOB was obtained. Finally, the experiment of digitizing an 1 GHz
sinusoidal signal with a 20 GS/s optical pulse train was demonstrated.

###  3.1 Device fabrication

Figure 3: (a) Microscope image of the demonstrated ADC. SEM image of the
fabricated 5$\times$5 MMI (b) and the grating coupler (c).

Fig. 3(a) shows the microscope image of the demonstrated ADC, and Fig. 3(b)
and (c) show the scanning electron microscope (SEM) image of the 5$\times$5
MMI and the grating coupler. The detailed fabrication process of the devices
can be found in our previous work [23]. The devices were fabricated on a x-cut
lithium niobate-on-insulator with a 400-nm thick TFLN and a 3-$\mu$m buried
oxide. Firstly, the wafer was cleaned by a piranha solution (H2SO4/H2O2 = 3:1,
80∘C) and an oxygen plasma. Next, a microlithography adhesion promoter named
Surpass 3000 and e-beam hydrogen silsesquioxane (HSQ) were sequentially spin-
coated to the surface at 3000 rpm for 60s. After a 80∘C, 4 min pre-bake, the
e-beam lithography was performed by the JBX-8100FS system with an accelerating
voltage of 100 KV. Followed by the resist development, the TFLN was partially
dry-etched by 200 nm using argon-based inductively coupled plasma reactive ion
etching with approximately 1:2.5 etch selectivity between TFLN and HSQ.
Finally, 1-$\mu$m thick gold electrodes were fabricated using UV lithography
and a standard lift-off process. The total area of our demonstrated ADC
(including the grating couplers) is approximately 0.33$\times$11.8 mm2.

###  3.2 Measurement of quantization curves and tranfer function

Figure 4: Experimental setup of measuring the quantization curves and transfer
function

Fig. 4 shows the experimental setup of the quantization curves and transfer
function measurements. The ENOB can then be obtained from the experimental
results. The input light was generated by a continuous wave (CW) laser. It was
amplified by an erbium-doped fiber amplifier (EDFA) to 20 dBm and then
connected to a polarization controller (PC). Next, it was fed into the ADC
chip using a grating coupler and split into two lights by an 1$\times$2 MMI.
After oppositely modulated by an 1 MHz triangular signal generated from an
arbitrary waveform generator (AWG), the two modulated lights were connected to
the input channels of the 5$\times$5 MMI. Therefore, the phase difference
between the two lights ($\Delta\phi$) changed linearly over the half period of
the triangular signal. After passing through the 5$\times$5 MMI, the output
lights were amplified by another EDFA to 3 dBm and then transferred to
electrical signals by a PD with a responsibility of 0.7 A/W. The signals were
recorded by an oscilloscope (OSC) and processed into quantization curves by a
linear time-phase mapping.

Figure 5: (a) Normalized quantization curves. (b) Transfer function of the
optical ADC and the ideal value. Insets: the maximum and the minimum phase
errors.

The normalized quantization curves of the 5 channels are shown in Fig. 5(a).
The measured curves were smoothed to reduce the white noise induced by the PD.
A decision threshold represented as the black dash line are set at the middle
of the normalized power to determine the 10 quantization levels mentioned
above. The dots are the intersections of the curves and the threshold, which
represent the measured phase of the 10 quantization levels. The ideal phases
of the 10 quantization levels are marked with triangles. Fig. 5(b) shows the
transfer function of our proposed ADC. The transfer function is obtained based
on the quantization curves. The blue line is the measured value while the red
line is the ideal one. The maximum and minimum phase errors of the
quantization levels,${\Delta\phi_{step-7}}$ and ${\Delta\phi_{step-0}}$, are
shown in the upper and the lower insets respectively. ${\Delta\phi_{step-7}}$
is 9.29∘ while ${\Delta\phi_{step-0}}$ is 0.9∘, which means the maximum
relative error is 12.9$\%$ and the minimum one is 1.25$\%$. The equivalent
ENOB can be calculated using Equation (6) according to Ref. [22].

$ENOB=\frac{20}{6.02}log_{10}\frac{P_{\textup{FS}}/\sqrt{12}}{\sqrt{\frac{1}{12}(\frac{P_{\textup{FS}}}{Q})^{2}+\frac{1}{Q}\sum_{i=0}^{Q-1}{\Delta\phi_{step-i}^{2}}}}$
(6)

where $\Delta\phi_{step-i}$ represents the phase error of each quantization
level. $P_{\textup{FS}}$ is the maximum value of the phase difference
${\Delta\phi}$. Q is the total number of the quantization levels. Thus, the
ENOB was calculated to be 3.17.

The decrease between the theoretically quantization bit of 3.32 and the ENOB
of 3.17 is induced by the phase errors mentioned above, which is mainly cause
by the inherent phase deviation of a 5$\times$5 MMI, the fabrication errors
and the PD noise. The asymmetric input channels lead to a inherent phase
deviation of the 5$\times$5 MMI. A 5$\times$5 MMI with input ports of channel
2 and 4 can reduce the inherent phase deviation at a specific wavelength
according to Ref. [21]. However, it would limit the operating wavelength range
and lessen the fabrication tolerances. In order to lower the impact of the PD
noise, larger output optical power is needed. One can design and manufacture
MMI and phase modulators with lower insertion losses. Also, grating couplers
can be replaced by edge couplers to reduce the coupling loss. To reduce the
impact of fabrication errors, a compact MMI with sub-wavelength gratings [26]
can be used to mitigate the effects of etching and substrate non-uniformity.
Additionally, an optimized 5$\times$5 MMI design, such as using sub-wavelength
structures in Ref. [25], can further decrease the phase errors, which is the
research direction in our future works.

###  3.3 Analog to digital conversion experiment

Figure 6: Experimental setup for digitizing an 1 GHz sinusoidal electrical
signal.

Using our presented optical ADC, an 1 GHz sinusoidal electrical analog signal
was sampled and quantized. The experimental setup is shown in Fig. 6. Light
generated from a CW was modulated by a commercial MZM. The amplitude of the
input 20 GHz analog signal was 0.51 times of the $V_{\pi}$ of the commercial
MZM, and the bias point induced by a DC source was $3/4V_{\pi}$. Thus, a 20
GS/s optical pulse train with a duty cycle of 37$\%$ was generated. After
amplified by an EDFA to the peak power of 20 dBm and connected to a PC, the
pulse train was fed into the ADC chip. An 1 GHz sinusoidal electrical analog
signal was sampled by the pulse train and then quantized by the 5$\times$5
MMI. The 5 outputs were amplified by another EDFA to the maximum peak power of
3 dBm, and then filtered by a band pass filter (BPF). Finally, an OSC with
optical ports was used to recorded the 5 output waveforms.

Figure 7: Normalized waveforms of the 5 output channels and ideal simulated
envelopes.

The blue lines in Fig. 7 show the normalized recorded waveforms of the 5
output channels. The red dash lines are the ideal simulated envelopes of the
pulses. The simulation results were based on Equation (5), where the power was
normalized and
$\Delta\phi=(V_{\pi}/\pi)V_{pp}cos(\omega_{m}t)+\phi_{1}-\phi_{2}$. $V_{\pi}$
is the half wave voltage of the phase modulator. $V_{pp}$ and $\omega_{m}$ are
the peak-to-peak voltage and angular frequency of input 1 GHz analog signal.
$\phi_{1}-\phi_{2}$ is the initial phase difference mentioned above that can
be adjusted by a DC source. The measured waveforms are generally consistent
with the simulation results, and the mismatches are mainly due to the PD noise
and the phase errors mentioned above. The black dash lines represent the
threshold power. For each pulse in the waveforms, if the maximum power is
larger than the threshold, the output value of this pulse is decided to be 1,
and vice versa. Then, combining the output values of the 5 channels, the
quantization codes are obtained. The corresponding digitized values overlaid
with the input 1 GHz sinusoidal wave are shown as the circles and the solid
line in Fig. 8. As a result, the analog-to-digital conversion of an 1 GHz
sinusoidal wave was successfully implemented. Noted that only 7 of the 10
quantization levels are used in this proof-of-concept experiment, which is due
to the $V_{pp}$ of the input analog signal could only be amplified to 0.6
times of the $V_{\pi}$ of the phase modulators by the amplifier we used.

Figure 8: Digitized values and the input 1 GHz sinusoidal wave.

##  4 Discussion

Figure 9: Measured and simulated EO response as a function of frequency. Table
1: Comparison of reported optical ADCs

Year |  Type |  Sampling 3-dB bandwidth |  Platform |  Footprint |  Ref.
---|---|---|---|---|---
2011 |  PSQ |  20 GHz |  Discrete |  / |  [27]
2012 |  PS |  12 GHz |  SOI |  7$\times$3.25 mm${}^{\textup{2}}$ |  [2]
2020 |  PS |  45 GHz |  SOI ${}^{\textup{a}}$ |  3.3$\times$5 mm${}^{\textup{2}}$ |  [5]
2021 |  PA |  100 GHz ${}^{\textup{b}}$ |  Discrete |  / |  [4]
2021 |  PSQ |  / |  SOI |  7.5$\times$95 $\mu$m${}^{\textup{2}}$ ${}^{\textup{c}}$ |  [17]
2022 |  PSQ |  $>$70 GHz |  TFLN |  0.33$\times$11.8 mm2 |  This work

${}^{\textup{a}}$The filters were on the SOI platform while the modulator for
sampling was discrete and off the shelf. ${}^{\textup{b}}$An EO 3-dB bandwith
of 100 GHz modulator was used to sample a 320 GHz signal. ${}^{\textup{c}}$The
footprint was only for the quantizer while the sampling experiment was not
carried out.

The above experimental results show the ENOB of 3.17 and the capability of
digitizing analog signals. To further evaluate the ADC performance, we
measured the input sampling 3-dB bandwidth. The characterizations of the small
signal were performed using a 67 GHz vector network analyzer (VNA). Fig. 9
shows the EO response as a function of frequency. The measured result decays
about 2.6 dB from 10 MHz to 67 GHz. The simulated EO response was based on the
average modulation voltage model described in [24], which can be expressed as

$r(f_{m})=20log_{10}\frac{\lvert V_{avg}(f_{m})\rvert}{\lvert
V_{avg}(DC)\rvert}$ (7)

where $r(f_{m})$ is the EO response of a frequency $f_{m}$, and $V_{avg}$ is
the the average voltage experienced by a photon as it traverses through the
modulator, which is given as

$V_{avg}=\frac{V_{g}(1+\rho_{1})e^{\gamma
i\beta_{o}l}(V_{+}+\rho_{2}V_{-})}{2[e^{\gamma l}+\rho_{1}\rho_{2}e^{-\gamma
l}]}$ (8)

where $V_{g}$ is the amplitude of the driving voltage.
$\rho_{1}=(Z_{c}-Z_{s})/(Z_{c}+Z_{s})$ and
$\rho_{2}=(Z_{t}-Z_{s})/(Z_{t}+Z_{s})$ are the input and output reflection
coefficients. $V_{+}$ and $V_{-}$ are the single pass average voltage due to
co-propagation and counter-propagation between microwave and optical wave,
where $V_{\pm}=e^{\pm i\phi_{\pm}}sin\phi_{\pm}/\phi_{\pm}$, and
$\phi_{\pm}=(\beta_{e}\mp\beta_{o})l/2$, l is the length of the phase shifter
length. $\beta_{o}$ is the complex phase of the optical wave, and $\gamma$ is
the propagation constant of microwave. The values of $Z_{c}$,$\gamma$ and
$\beta_{o}$ used in this simulation were all extracted from experiments.

As shown in Fig. 9, the simulation result agrees with the measured result, and
the EO 3-dB bandwidth is expected to be beyond 70 GHz. This suggests that our
presented ADC is capable of operating well with the input frequency up to 70
GHz. In order to accurately sample such high speed analog signals, a pulse
source with ultra-narrow pulse width, such as a femtosecond mode-locked laser,
should be used to further exploit the performance of the ADC.

A comparison of the sampling 3-dB bandwidth and the footprint for various
types of optical ADCs is shown in Table 1. Compared to those reported optical
ADCs, our proposed work has a relatively large sampling 3-dB bandwidth and is
on-chip implemented with a compact footprint at the same time, which makes it
a potential integrated solution for high-bandwidth analog-to-digital
conversions in the field of all-optical signal processing.

##  5 Conclusion

To draw a conclusion, we present an on-chip PSQ ADC on thin-film lithium
niobate platform using two phase modulators for sampling and a $5\times 5$MMI
for quantization. The quantization curves and the transfer function were
measured and analyzed. The ENOB, obtained from the experimental results, was
3.17 bit. Using a 20 GS/s pulse train as an optical source, an 1 GHz input
analog signal was converted to a digitized output. The footprint of the ADC is
approximately 0.33$\times$11.8 mm2. Furthermore, the demonstrated devices are
capable of operating at a high frequency up to 70 GHz. Therefore, the
presented ADC provides a promising solution for ultra-high speed analog-to-
digital conversions.

Funding This work is supported by the National Key Research and Development
Program of China under Grant 2018YFE0201900.

Disclosures The authors declare no conflicts of interest.

Data availability 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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