# Hybrid Au-Si microspheres produced by laser ablation in liquid (LAL) for
temperature-feedback optical nano-sensing and anti-counterfeit labeling†

S. Gurbatov  Far Eastern Federal University, Vladivostok 690090, Russia
Institute of Automation and Control Processes, Far Eastern Branch, Russian
Academy of Science, Vladivostok 690041, Russia  V. Puzikov  Far Eastern
Federal University, Vladivostok 690090, Russia  Institute of Automation and
Control Processes, Far Eastern Branch, Russian Academy of Science, Vladivostok
690041, Russia  D. Storozhenko  Institute of Automation and Control Processes,
Far Eastern Branch, Russian Academy of Science, Vladivostok 690041, Russia  E.
Modin  CIC nanoGUNE BRTA, E-20018 Donostia - San Sebastian, Spain  E. Mitsai
Institute of Automation and Control Processes, Far Eastern Branch, Russian
Academy of Science, Vladivostok 690041, Russia  A. Cherepakhin  Institute of
Automation and Control Processes, Far Eastern Branch, Russian Academy of
Science, Vladivostok 690041, Russia  A. Shevlyagin  Institute of Automation
and Control Processes, Far Eastern Branch, Russian Academy of Science,
Vladivostok 690041, Russia  A.V. Gerasimenko  Institute of Chemistry FEB RAS,
Vladivostok 690022, Russia  S.A. Kulinich  Far Eastern Federal University,
Vladivostok 690090, Russia  Research Institute of Science and Technology,
Tokai University, Hiratsuka, Kanagawa 259-1292, Japan  A. Kuchmizhak
<EMAIL_ADDRESS>Institute of Automation and Control Processes, Far
Eastern Branch, Russian Academy of Science, Vladivostok 690041, Russia
Pacific Quantum Center, Far Eastern Federal University, 8 Sukhanova Str.,
Vladivostok, Russia

###### Abstract

Recent progress in hybrid nanomaterials composed of dissimilar constituents
permitted to improve performance and functionality of novel devices developed
for optoelectronics, catalysis, medical diagnostic and sensing. However, the
rational combination of such contrasting materials as noble metals and
semiconductors within individual hybrid nanostructures $via$ a ready-to-use
and lithography-free fabrication approach is still a standing challenge. Here,
we report on a two-step synthesis of Au-Si microspheres generated by laser
ablation of silicon in isopropanol followed by laser irradiation of the
produced Si nanoparticles in presence of HAuCl4. Thermal reduction of [AuCl4]-
species to metallic gold phase, along with its subsequent mixing with silicon
under laser irradiation creates a nanostructured material with a unique
composition and morphology revealed by electron microscopy, tomography and
elemental analysis. Combination of such basic plasmonic and nanophotonic
materials as gold and silicon within a single microsphere allows for efficient
light-to-heat conversion, as well as single-particle SERS sensing with
temperature feedback modality and expanded functionality. Moreover, the
characteristic Raman signal and hot-electron induced nonlinear
photoluminescence coexisting within Au-Si hybrids, as well as commonly
criticized randomness of the nanomaterials prepared by laser ablation in
liquid, were proved useful for realization of anti-counterfeiting labels based
on physically unclonable function approach.

††preprint: AIP/123-QED

##  I Introduction

Resonant interaction of optical radiation with the matter is in the heart of
modern sensors, as well as of light-emitting and optoelectronic devices.
Coupling of light waves with resonant oscillations of free electron plasma
supported by noble-metal nanostructures and metal-dielectric interfaces (i.e.
localized and propagating surface plasmons Maier  _et al._ (2007)) provides an
efficient way to boost this interaction, giving rise to a number of
practically important interface phenomena and their related applications, such
as efficient light-to-heat conversion, surface-enhanced Raman scattering
(SERS), plasmon-mediated generation of hot electrons, etc Sobhani  _et al._
(2013); Baffou  _et al._ (2020); Langer  _et al._ (2019). An alternative way
recently suggested to advance light-matter interactions consists in the use of
nanophotonic (all-dielectric) platforms made of optically resonant dielectric
or semiconductor materials that exhibit high refractive index and low optical
losses (e.g., Si, Ge, TiO2, etc.) Kuznetsov  _et al._ (2016). Related
nanostructures and their ordered arrangements, i.e. metasurfaces, permit to
achieve full control over the properties of scattered/ reflected/ transmitted
light waves, offering resonant light absorption and enhanced light emission/
nonlinear effects Yu and Capasso (2014); Koshelev  _et al._ (2020); Koshelev
and Kivshar (2020). These features are partially related to the ability of
all-dielectric nanostructures to confine incident radiation inside their bulk,
which cannot be achieved with their lossy plasmonic counterparts.

Due to a limited choice of basic materials with on-demand properties,
integration of plasmonic and nanophotonic approaches within hybrid
nanostructures is considered a key strategy for designing next-generation
optoelectronic devices and optical sensors Soukoulis and Wegener (2011); Jiang
_et al._ (2014); Makarov  _et al._ (2017); Fusco  _et al._ (2020). Meanwhile,
along with their ability to integrate such contrasting materials as noble
metals and semiconductors at the nanoscale, the related fabrication approaches
should meet simultaneously a number of practical requirements such as
scalability, simplicity, attractive production yield, etc. Beyond the multi-
step and expensive lithography-based approaches, laser-assisted technologies
have recently appeared as a promising route towards environment friendly high-
yield preparation of hybrid nanomaterials Zeng  _et al._ (2012); Zhang  _et
al._ (2017); Amendola  _et al._ (2020); Shabalina  _et al._ (2022a). In
particular, laser ablation in liquid (LAL) presents a flexible experimental
approach that utilizes intense laser pulses to ablate a target material placed
in a liquid medium. Spatially and temporally confined laser radiation can be
used to create unique experimental conditions (high pressures and temperature,
fast quenching rates), also driving chemical interactions of ejected
nanomaterial with surrounding liquid. This provides a pathway for the
preparation of nanomaterials with a wide range of morphology, structure and
composition (including meta-stable and non-equilibrium phases). Laser
irradiation of LAL-generated dispersions can further expand the method
functionality, allowing for high-performance preparation of diverse hybrid
nanomaterials for photovoltaics Tarasenka  _et al._ (2021); Furasova  _et al._
(2021), photothermal conversion Nastulyavichus  _et al._ (2020); Gurbatov  _et
al._ (2021), catalysis Zhang  _et al._ (2020); Forsythe  _et al._ (2021);
Shabalina  _et al._ (2022b), nonlinear optics Gurbatov  _et al._ (2022),
sensing Amendola  _et al._ (2014); Scaramuzza  _et al._ (2017); Bharati  _et
al._ (2019); Guadagnini  _et al._ (2021) and medical applications Torresan
_et al._ (2020); Amendola  _et al._ (2021).

Gold, the most chemically stable plasmon-active metal, and silicon, an earth-
abundant semiconductor widely applied for all-dielectric metasurface design,
present an intriguing combination, in which the advantages of plasmonic and
nanophotonic concepts can be merged within unified nanostructures. Although
extensive research was conducted and reported over years on products of Au and
Si ablation in various liquids Simakin  _et al._ (2004); Amendola and
Meneghetti (2009); Al-Kattan  _et al._ (2018); Zabotnov  _et al._ (2020), few
papers reported on formation of Au-Si hybrids with various morphologies (nano-
alloys, core-satellites, etc.Liu  _et al._ (2015); Saraeva  _et al._ (2018);
Ryabchikov (2019); Kutrovskaya  _et al._ (2017); Al-Kattan  _et al._ (2021)).
However, no general assessment of their nanophotonic properties and/or
demonstration of material’s suitability for related applications was shown.
Here, hybrid Au-Si microspheres (MSs) were produced $via$ ablation of Si wafer
by nanosecond (ns)-pulsed laser in isopropanol followed by further irradiation
of the as-produced Si dispersion in presence of HAuCl4. Formation of Au
nanoparticles on the surface of Si particles through the thermal reduction of
[AuCl4]- species, as well as further mixing of the metal and semiconductor
phases upon remelting and recrystallization, were found to result in a novel
hybrid Au-Si product. By combining transmission electron microscopy (TEM),
electron tomography, energy-dispersive X-ray spectroscopy (EDX) elemental
analysis, X-ray diffraction (XRD) and Raman spectroscopy, we revealed the
unique structure of the newly prepared hybrids, in which nanocrystalline Si
inclusions are wrapped and decorated with nanostructured Au. Strong light
absorbing properties, characteristic Raman signal and nonlinear hot-electron-
induced photoluminescence coexisting in the novel Au-Si MSs were proved to be
useful for realization of single-particle SERS sensors with temperature-
feedback modality and fabrication of unclonable anti-counterfeit labels.

Figure 1: Fabrication of Au-Si MSs. (a) Schematic presentation of preparation
of Au-Si hybrid structures $via$ LAL. (b) Representative top-view SEM images,
(c) size distributions and (d) normalized UV vis absorbance spectra
(isopropanol suspensions) of Si precursor (top row) and hybrid Au-Si MSs
(bottom row, Sample #2). (e) SEM images of Au-Si MSs produced by varying the
amount of HAuCl4 (0.25, 0.5 and 0.75 mM) added to laser-treated suspension.

##  II Results and discussion

###  II.1 Preparation of Au-Si microspheres $via$ LAL

Hybrid Au-Si microstructures were produced using a simple two-step protocol
schematically illustrated in Figure 1a (see also Methods section). Briefly, a
dispersion with Si MSs with an average diameter of $\approx$0.6 $\mu$m was
first produced by ablating a bulk monocrystalline Si wafer immersed in
isopropanol (Figure 1b). Next, a certain amount of aqueous HAuCl4 (10-3M) was
added to the as-produced dispersion with Si MSs followed by its laser-
irradiation for an additional 1 h using the same LAL parameters (pulse energy
of 0.4 mJ and pulse repetition rate of 20 Hz). The resultant Au-Si product
obtained after adding 0.5 mL of HAuCl4 solution is shown in the SEM image
(Figure 1b) revealing the average particle diameter of $\approx$1.2 $\mu$m.
Comparative UV-vis absorbance spectra of the dispersions containing the
initial Si precursor and the Au-Si product are presented in Figure 1c. The
spectrum of the product is seen to reveal a characteristic absorption band at
530 nm, which confirms appearance of metallic Au phase formed $via$ thermal
reduction processes.

To demonstrate the ability to control the composition of the produced
material, we first fixed the laser irradiation conditions varying only the
amount of HAuCl4 (0.25, 0.5 and 0.75 mL) added to the processed liquid. UV-vis
spectra of the three produced dispersions (hereafter referred to as Samples
#1, #2 and #3) all demonstrated absorption band at 530 nm whose intensity
gradually increased along with the amount of HAuCl4 added during preparation.
This clearly indicates the increase in the content of Au within the product
structures (Figure S1, ESI). The resultant Au-Si materials (Samples #1 to #3)
were then taken from each dispersion and drop-cast on Si wafer for further
analysis. Close-up SEM images of Au-Si MSs produced at three different
concentrations of HAuCl4 are shown in Figure 1e, revealing complex morphology
and composition of the obtained product. It is worth noting that Si and Au
elements demonstrate remarkably different contrast when visualized by SEM with
any secondary or back-scattered electrons detector. This permits to
distinguish both elements within the bulk of spherically shaped MSs (mainly in
Samples #2 and #3). Moreover, nano-sized Au particles decorating Si-based MS
surface are also clearly identified in the SEM images of all samples.

Figure 2: Characterization of Au-Si MSs. (a) XRD patterns of Au-Si MSs
produced at different concentrations of HAuCl4 added to laser-processed
dispersion (Samples #1 - #3). Stars denote XRD peaks attributed to the Si
substrate used. (b) TEM image and EDX composition mapping of a representative
Au-Si MS (Sample #2). (c) HR-TEM image of an isolated Au nanoparticle on the
surface of Au-Si MS, with a well-seen SiO2 shell. (d) 3D model of an isolated
Au-Si MS reconstructed from a series of 50 cross-sectional FIB cuts. Several
representative cuts are shown as insets. Au nanoparticles on the surface of a
Au-Si MS are highlighted by green color to distinguish them from Au material
(orange) mixed with Si within the particle.

Analysis of SEM images shows that the increase of the amount of HAuCl4 added
to laser-treated mixture results in a visually larger amount of Au (both
inside the MSs and on their surface). This finding was confirmed by systematic
EDX studies of as-prepared hybrid MSs (Figure S2, ESI), showing the average
content of Au (in wt.%) gradually increases from 26$\pm$1 (Sample #1) to
48$\pm$2.5 wt.% (Sample #3). EDX characterization also revealed almost
constant content of carbon atoms ($\approx$ 4.5$\pm$0.5 wt.%) in the product,
which presumably resulted from decomposition of isopropanol molecules upon
laser irradiation. In this study, alcohol medium was used to minimize Si
oxidation during material preparation. According to EDX analysis, the oxygen
content increased from 3$\pm$0.5 (Sample #1) to 5.2$\pm$0.7 wt.% (Sample #3)
which could also originate from laser-induced Si oxidation stimulated by
adding aqueous HAuCl4.

The same Au-Si MSs deposited on Si(001) substrate (Samples #1-#3) were further
systematically analyzed by XRD (see Methods section) revealing several key
features regarding the composition and crystal structure of the LAL-prepared
hybrids. First of all, clear signatures of both cubic Au (Fm3m, JCPD04-0784)
and Si (Fd3m, JCPD27-1402) can be identified in the corresponding XRD patterns
of all samples with no signs of metastable Si phases often associated with LAL
processing Liu  _et al._ (2013). The intensity of the main Au-related peaks
(2$\theta\approx$ 38.1o, 44.4o, and 81.8o) was found gradually to increase
with the amount of HAuCl4 added to the processed liquid, thus confirming the
EDX measurement results. Moreover, at higher HAuCl4 addition, a larger number
of peaks related to Au (2$\theta\approx$ 64.7o and 77.6o) are seen in Figure
2a, as well as peaks of Au silicide with composition Au81Si19 (seen at
2$\theta\approx$ 32.2o; 39.7o and 67.1o; JCPD39-0735, Sample #3).

Also, at higher HAuCl4 concentration in the LAL-processed liquid, the most-
intense Au-related XRD peak changes from Au(200) to Au(111), indicating that
the Au-Si system tends to the most favorable orientation of Au(111)——Si(111)
which is resulted from the minimum crystal lattice mismatch between Au
particles and their Si support Langford and Wilson (1978). The average grain
size of Si phase in the MSs $D_{g}$ calculated using Scherrer s equation
$D_{g}$=(K$\cdot\lambda_{X-ray}$)/($\beta\cdot$cos$\theta$) (K is a constant
depending on grain shape and crystal symmetry, $\lambda_{X-ray}$ is the X-ray
wavelength, $\beta$ is the FWHM of the diffraction peak, and $\theta$ is the
diffraction angle Daudin  _et al._ (2012)) was found to be $\approx$
125$\pm$10 nm and nearly same for all tested samples. The lattice of Si phase
was found to be completely relaxed as its interplanar distances corresponded
to those of bulk Si, with residual strain not exceeding 0.01%.

High-resolution TEM (HR-TEM) was carried out further to study the inner
structure and composition of the Au-Si MSs (Samples #1 and #3). Focused ion
beam (FIB) milling procedure was undertaken for isolated MSs to prepare their
nm-thick lamellae whose representative HR-TEM image is provided in Figure 2b
along with superimposed EDX elemental maps. Both images shed light onto a
complex inner structure of the product where Au material fills in the space
between irregularly shaped Si nanocrystals. The crystalline structure of Si
inclusions was confirmed by HR-TEM images and by single-particle Raman
spectroscopy (see Section 2.2). Along with single Au nanoparticles located on
the surface of Au-Si MSs, a nm-thick oxide shell can be observed all around
the entire Au-Si microsphere (Figure 2b,c). A similar oxide shell was also
found in the product obtained at the smallest amount of HAuCl4 added to the
laser-processed dispersion (Sample #1; Figure S3, ESI). To study the inner
structure of the Au-Si hybrids more systematically, a series of consecutive
FIB cuts of an isolated MS was prepared, while its 3D model was then
reconstructed from a series of corresponding SEM images (see Methods and
Figure 2d). The performed studies revealed that Si nanocrystals are mainly
located near the MS’s surface, while its core was mostly formed by Au-based
phase.

Figure 3: Light-to-heat conversion and single-particle SERS sensing with Au-Si
hybrids. (a) Reflectance spectrum of Au-Si MS coating. Inset: Optical
photograph of coating made of Au-Si MSs (Sample #2) dried over a glass slide.
(b) Representative series of normalized Raman spectra (c-Si band) of separate
Au-Si MSs (Samples #2 and #3) measured at varied intensity of pump laser
radiation $I$. (c) Spectral shift of the c-Si Raman band $\Delta\Omega$ and
the average MS temperature increase $\Delta$T versus pump laser intensity $I$
measured for Au-Si MSs from Sample #1 (gray), Sample #2 (red), and Sample #3
(yellow). (d) Correlated SEM, reflection and SERS (at 520.8$\pm$1 and
612$\pm$1 cm-1) images of a single Au-Si MS functionalized with R6G molecules.
(e) Averaged SERS spectra of the R6G detected from the Au-Si MS and smooth Au
mirror sites. Characteristic bands related to crystalline Si and R6G used for
mapping are marked by stars. Circle indicates the geometric position of the MS
in the optical and Raman images.

The unveiled 3D morphology of the Au-Si MSs produced at higher amounts of
HAuCl4 allowed us to make the following justification regarding the physical
and chemical processes underlying the hybrid structure formation. Keeping in
mind the transparency of isopropanol at 532 nm, the formation of Au
nanoparticles via thermally-induced reduction of HAuCl4 is expected to be
preferentially facilitated near the interface of precursor Si particles that
efficiently absorbed laser radiation. Formation of Au nanoparticles on the Si
surface further boosts the light-to-heat conversion via plasmon-mediated
enhancement of the electromagnetic field at 532 nm (see Figure S4, ESI). Then,
taking into account the comparable melting temperatures of Au and Si, this may
result in remelting of Si surface and capping the formed Au nanoparticles. The
molten Au can form a continuous nm-thick coating (Figure S3, ESI) or penetrate
between Si nanocrystallites formed under fast recrystallization. The latter
effect is associated with weak solubility of Au in Si and was previously
predicted by molecular dynamic modeling Larin  _et al._ (2020). Subsequent
irradiation by laser pulses causes multiple melting/resolidification cycles
for highly absorbing Au-Si MSs and formation of Au nanoparticles on their
surface.

###  II.2 Optical sensing and anti-counterfeiting with Au-Si material

Rational combination of Au and Si elements within a hybrid structure with a
well-developed surface morphology permits to create functional nano/micro-
materials with linear and nonlinear optical properties attractive for various
applications. First of all, combination of plasmon-active nanomaterial with an
indirect bandgap semiconductor provides conditions for efficient light
absorption. Reflection spectra of the prepared Au-Si powder (Sample #2) drop-
cast on a glass slide indicates its average reflectivity $\approx$4 % in the
visible spectral range with the minimal value ($\approx$3.5%) achieved near
the plasmonic absorption band of Au constituents (Figure 3(a,b)). The absorbed
laser energy is converted to heat, while the efficiency of this process can be
assessed by tracing the spectral position of the main phonon-mediated Raman
band of crystalline Si (at 520.8 cm-1) Zograf  _et al._ (2017); Mitsai  _et
al._ (2019). The spectral shift $\Delta\Omega$ of this band can be
recalculated to local temperature increase $\Delta$T using the following
expression: Balkanski  _et al._ (1983)

$\Delta\Omega(T)=\Omega_{0}+A(1+\frac{2}{e^{x}-1})+B(1+\frac{3}{e^{y}-1}+\frac{3}{(e^{y}-1)^{2}})$
(1)

where $\Omega_{0}$=528 cm-1, A= -2.96 cm-1, A= -0.174 cm-1,
$x$=$\hbar\Omega_{0}$/2$\kappa$T and $y$=$\hbar\Omega_{0}$/3$\kappa$T.

Two representative series of Raman spectra measured at different laser pump
intensities from isolated MSs randomly chosen from Samples #1 and #3 (top and
bottom plots in Figure 3b) demonstrate the remarkably different efficiency of
their laser-induced heating. For example, upon excitation at 3.3 mW/$\mu$m2
(maximal laser intensity available in these experiments) the MS containing
less Au (Sample #1) can be heated up to about $\Delta$T$\approx$200 K, while a
similar excitation of the Au-rich MS (Sample #3) resulted in a trice larger
temperature increase $\Delta$T$\approx$600 K (Figure 3c). Systematic studies
performed for multiple isolated Au-Si MSs produced at varied HAuCl4 content in
the processed dispersion (Samples #1-#3) confirm the direct relationship
between Au content and light-to-heat conversion efficiency (Figure 3c).
Meanwhile, further increase in Au content within the MS is expected to
decrease their heating efficiency. Importantly, even for highly heated hybrids
the spectrum of their phonon-mediated Si Raman band was found to preserve a
Gaussian-shaped profile, thus indicating their uniform heating by laser
radiation Aouassa  _et al._ (2017).

Figure 4: Optical PUF labeling with Au-Si hybrids. (a) Schematically
illustrated fabrication process of PUF labels and their optical readout by
mapping characteristic optical fingerprints: Raman signal and nonlinear
broadband photoluminescence associated with crystalline Si inclusions. (b)
Correlated SEM, Raman (at 520.8 cm-1) and nonlinear PL images of two
representative labels composed of random arrangements of the Au-Si MSs. (c)
Sketch of label digitization and authentication. (d) Hamming intra- and inter-
distances estimated for 10 different PUF labels.

Inherent Raman signal enhanced by efficient light absorption and plasmon-
mediated electromagnetic fields near the Au-Si interfaces make the LAL-
prepared MSs promising for nano-sensing based on surface-enhanced Raman
scattering (SERS) and photoluminescence (SEPL) effects. The complex chemical
composition of the generated structures (Au, Si, and SiO2) can significantly
expand the range of molecules that can functionalize their surface using the
toolbox of synthetic organic chemistry Linford and Chidsey (1993). The
temperature-feedback Raman signal can be used to maintain temperature in the
analyte-MS system to avoid excessive heating of attached organic molecules,
most of which are rather prone to thermal decomposition. Also, the Raman
signal of Si permits easily to correlate a certain surface site with the MS
and corresponding signal from analyte molecules, thus ensuring more reliable
SERS measurements. To illustrate nano-sensing modality of the prepared Au-Si
material acting as SERS-active structures, their surface was functionalized
with Rhodamine 6G molecules (see Methods). The MS concentration in the
dispersion was optimized to yield in deposition of isolated MSs on a smooth Au
mirror upon drop-casting. Figure 3d provides correlated SEM, laser confocal
(reflectivity at pump laser wavelength of 633 nm) and SERS (intensity at
520.8$\pm$1 and 612$\pm$1 cm-1) image of a single 1.1-$\mu$m-sized Au-Si MS
confirming its ability to detect adsorbed analyte molecules at pump intensity
($\approx$ 0.3 mW/$\mu$m2) while preserving the sensor temperature below that
of the analyte’s thermal decomposition Qiu  _et al._ (2016). At such pump
intensity, the R6G Raman signal measured from a smooth Au reference is
indistinguishable over the noise level. Meanwhile the laser pump, which is
several orders of magnitude higher by intensity, provides a non-zero signal
from the R6G on a smooth Au film allowing for systematic measurements to
estimate reliably the SERS enhancement factor (EF) for a single Au-Si MS of
$\approx$ (6.1$\pm$2.7)$\times$104 as a ratio of signals of the main R6G Raman
bands normalized to collection time and laser pump intensity (see Figure S5,
ESI). Such an EF value can be largely attributed to the plasmon-mediated
enhancement of the electromagnetic field amplitude as chemical enhancement is
expected to act equally for both Au-Si MS and Au reference. Considering that
chemical EF is estimated to be $\approx$10-102, the total SERS EF factor of
the isolated hybrid Au-Si particle is varied between $\approx$106-107, which
meets the modern requirements for SERS-active substrates Langer  _et al._
(2019). In particular, the hybrid MSs permit to combine the benefits of
plasmonic and nanophotonic approaches for efficient hot-spot engineering with
the ability of versatile liquid-phase functionalization and physical analyte
concentration in the process of deposition Lee  _et al._ (2019).

Mixing nanocrystalline Si with plasmon-active materials is known to provide
promising strategy to boost non-linear optical response of such hybrid
nanomaterialsKnight  _et al._ (2011); Cho  _et al._ (2013); Makarov  _et al._
(2018); Larin  _et al._ (2020). In particular, injection of photo-generated
hot electrons from bulk Au inclusions and from surface Au nanoparticles into
Si nanocrystals upon excitation with femtosecond IR laser pulses was
previously shown to provide conditions for observation of nonlinear broadband
visible-light PL from the LAL-generated Au-Si nanomaterial Gurbatov  _et al._
(2022). In the present work, we carried out systematic studies revealing that
the highest nonlinear PL yield does not correlate with the amount of Au
species added to the laser-treated dispersion (see Methods). This probably
indicates the existence of an optimal ratio between the amount of light-
emitting Si nanocrystals in the top hemi-sphere of a laser-pumped MS and the
light-absorbing Au fraction therein. In particular, the Au-Si MSs produced at
moderate HAuCl4 content (Sample #2) demonstrated the highest integral PL
signal (see Figure S6, ESI).

The coexistence of nonlinear PL and characteristic Raman signal within Au-Si
MSs makes them quite a unique nanomaterial that can be used to create state-
of-the-art optical labels for anti-counterfeiting applications based on
physically unclonable function (PUF) strategy Pappu  _et al._ (2002); McGrath
_et al._ (2019). The PUF approach suggests introduction of some stochastic
processes into the label fabrication, thus making them almost unclonable.
Optical PUF labels (i.e labels with a read-out based on a certain optical
signal such as Raman-scattering, PL and reflection Arppe and Sørensen (2017))
created using various light-emitting materials have recently gained a lot of
research interest owing to simplicity of realization (for example, $via$
simple drop-casting onto the substrate) and authentication. Organic-based
light emitters suffer from degradation caused by UV light or elevated
temperature, which is why inorganic nanomaterials with unique optical response
are beneficial for realization of robust labels. Moreover, the commonly
criticized randomness of LAL-produced nanomaterials (and their related
properties), if combined with the randomness of drop-cast deposition from
dispersion and agglomeration on the surface, are expected to provide unique
conditions for the fabrication of physically unclonable tags that cannot be
replicated by chance or with any deterministic approach.

Here, we produced security tags by drop-casting 0.5-$\mu$L drops of as-
generated isopropanol dispersion with Au-Si MSs on glass slides or Au mirrors
(Figure 4a). Upon drying, the drop-cast material created random arrangements
on the surface which are impossible to replicate by chance upon subsequent
deposition cycles. Meanwhile, the wafer usually demonstrates very good
wettability with respect to isopropanol, which results in spreading and
deposition of material over centimeter-sized surface area. Consequently, this
increases the material consumption and makes either visual or optical
microscopy analysis of the deposition area rather complicated. Typically, a
certain randomly chosen area within a relatively large deposition area (in the
form of so-called “coffee rings”) is analyzed, which makes finding and
recognition of the tags an extremely hard task for the end user (in absence of
additional marking) Gu  _et al._ (2020). To avoid the above-mentioned issues,
a certain amount (about 5 - 10 vol. %) of distilled water was added to the as-
prepared isopropanol dispersion, which remarkably changed its wetting and
drying behavior. We found experimentally that dispersions with different
isopropanol/water ratio spread and evaporated at different rates, which
allowed us to find conditions when the MSs tended to concentrate within a
small droplet that evaporated over a smaller area. Eventually, tags with sizes
as small as $\approx$80$\times$80 $\mu$m2 were produced by means of an
ordinary syringe, which was achieved through the optimization of the
isopropanol/water ratio in drop-cast droplets and concentration of the Au-Si
MSs (Figure S7, ESI). Typical examples of Au-Si MS deposits are illustrated by
the SEM images in Figure 4b.

The produced tags can be characterized by using certain unique optical
fingerprints, for example, their Raman signal (at 520.8$\pm$2 cm-1) associated
with nanocrystalline Si inclusions in the Au-Si hybrids and/or a related
nonlinear broadband PL signal. In Figure 4b, corresponding Raman and nonlinear
PL maps (40$\times$40 pixels) reveal close correlation between the real
position of MSs (marked by white/yellow circles) and the characteristic
distribution of both optical signals. The variation of both signal intensities
depends on the local nanostructure of produced Au-Si MSs and their number
within each individual pixel as several agglomerated particles can contribute
to the overall detected signal. Figure 4c schematically illustrates the
authentication/validation procedure of the produced labels. First, coarse-
grained discretization of fingerprint signals (either Raman or PL spectra) to
a certain number of intensity levels $N$ is performed for each pixel in the
Raman/PL map. The end user can repeat optical mapping and leveling procedures
validating the PUF label $via$ the pair-wise pixel-by-pixel comparison of
signal intensities. Considering the independence of both fingerprint signals,
the encoding capacity for the designed tags based on the novel hybrid Au-Si
material can be assessed as $N^{2\cdot m}$ (where $m$ is a total number of
pixels in the obtained maps). For the illustrated maps (40$\times$40 pixels)
the corresponding encoding capacity reaches $\approx$101500 at $N$=3 intensity
levels for both characteristic signals, which meets the requirements for
modern anti-counterfeit labeling. To justify the ability of the proposed
algorithm reliably to distinguish different labels, we characterized 10 random
realizations of PUF tags calculating their similarity $\alpha$ (the ratio of
zero-intensity pixels to the total pixel number with initial non-zero
intensity) or Hamming intra-distance (1 - $\alpha$/100%). The obtained results
are presented in Figure 4d, giving the average inter-Hamming distance of
$\approx$0.94$\pm$0.05 for different PUF labels analyzed by mapping both
(Raman and PL) signals. Next, each label was scanned one more time and pair-
wise comparison of the digitized maps was carried out between the scans of the
same label, revealing their strong similarity with the average Hamming intra-
distance of $\approx$0.55$\pm$0.04 (Figure 4d). This finding indicates the
stability of the developed algorithm and its capability to reliably
distinguish between the real (stored in the database) and fake (duplicated)
labels.

##  III Conclusion and Outlook

To conclude, this study highlights the potential of a scalable laser ablation
in liquid combined with laser irradiation to create functional micro/nano-
materials in which such contrasting constituents as Si and Au can be
efficiently mixed within unified structures that exhibit promising optical
properties. The combination of plasmon-active Au and nanophotonic Si was found
to be useful for the realization of reliable SERS sensors that provide, for
isolated hybrid Au-Si structures, an average enhancement factor as high as 107
and permit to maintain the local temperature of the sensor system below that
of analyte’s thermal decomposition. The light-to-heat conversion efficiency of
the novel hybrid structures was controlled by tuning their Au content, which
was confirmed by Raman spectroscopy. Importantly, our preliminary studies also
showed the ability to downscale the average diameter of the hybrid Au-Si MSs
by using pure Si precursor with smaller diameter (see Figure S8, ESI).

In addition, the commonly criticized randomness of LAL-prepared nanomaterials
was utilized in this study to produce physically unclonable anti-
counterfeiting labels with encoding capacity of 101500. Larger encoding
capacity of the PUF labels can be easily achieved by increasing the number of
pixels analyzed in Raman/PL maps or by functionalizing the hybrid Au-Si
product with Raman-active molecules capable of providing additional bands for
mapping Gu  _et al._ (2020). The PUF labels were produced by optimized drop-
casting of the as-prepared Au-Si dispersions. The ability to concentrate
produced MSs is very advantageous for SERS applications as well as for
adequate characterization of the nanomaterial on the stage of synthesis
optimization, especially when the droplet contains a small amount of analyzed
nanoparticles.

##  IV Materials and Methods

###  IV.1 LAL-based preparation of hybrid Au-Si structures

The dispersion of pure polycrystalline Si MSs was first produced by ablating
bulk monocrystalline Si wafer placed in isopropanol. We used second-harmonic
(532 nm) laser pulses generated with a pulse width of 7-ns and repetition rate
of 20-Hz by a Nd:YAG source (Ultra, Quantel). Laser pulses with a constant
pulse energy of 0.4 mJ were focused on a Si wafer surface by a lens with a
focal distance of 20 mm. Then, a certain amount (ranging from 0.25 to 0.75 mL)
of aqueous HAuCl4 (10-3M) was added to the as-prepared Si dispersion, after
which the mixture (6 mL in volume) was further irradiated for another 1 h
keeping the same laser parameters.

###  IV.2 Characterization

Initial assessment of the morphology and composition of the prepared hybrid
MSs was carried out using a SEM tool (Ultra 55+, Carl Zeiss) equipped with an
EDX detector (X-max, Oxford Instruments). EDX measurements were performed at
accelerating voltage of 5 kV.

Absorbance spectra of the dispersions containing LAL-generated Si
nanoparticles and the final hybrid Au-Si structures (Samples 1-3) were
recorded using a UV Vis spectrophotometer (UV-2600, Shimadzu) equipped with an
integrating sphere (ISR-2600 Plus). The measurements were carried out at room
temperature using a quartz cuvette and absorbance spectrum of pure isopropanol
as reference. Reflection spectra of the dry powder of Au-Si MSs (Sample #2)
were obtained using a spectrophotometer (Cary Varian 5000) equipped with an
integrating sphere.

XRD patterns of hybrid Au-Si MSs on Si wafer were collected on a
diffractometer with CuKα radiation operated in the 2$\Theta$/$\omega$ mode
(SmartLab, RIGAKU). The incident beam size did not exceed 0.1 mm, and the XRD
peaks were identified in accordance with the ICDD database.

Imaging of the MSs combined with their focused-ion beam (FIB) milling modality
was performed with a SEM instrument (Helios 450s Nanolab, Thermofisher). FIB
milling permitted to prepare precise cross-sectional cuts of isolated MSs
which were then examined by SEM. By repeating milling procedure, we realized
the FIB tomography to create a 3D reconstruction of the internal and external
features of the prepared MSs. Series of slices were obtained automatically via
the FEI AutoSlice & View G3 software (Thermofisher). The MS surface was
protected by a locally deposited Pt layer. Ion beam was operated at the energy
of 30 keV and a beam current of 24 pA. The total number of slices was about
110 per one MS, with an approximate slice thickness of 7 nm. SEM image
acquisition was set up for recording images with 1536 x 1024 pixels (with
pixel size being 1.3 nm x 1.3 nm). As a result, the 3D volume of 2 $\mu$m x
1.3 $\mu$m x 0.7 $\mu$m was collected. Further, the resulting volume was
processed with the Avizo 8.1 software (Thermofisher). FIB milling was also
used to prepare thin samples for TEM studies. HR-TEM images were acquired at
the acceleration voltage of 80 kV (Titan 80-300, Thermofisher).

Modeling of the normalized electromagnetic field amplitude ($E$/$E_{0}$) near
a pure and Au-decorated Si MSs was carried out using the Comsol Multiphysics
package. We considered excitation of an isolated particle in isopropanol
(refractive index of 1.385) by a linearly polarized plane wave with a
wavelength of 532 nm. Temperature profiles under single-pulse excitation of
the MS were then calculated by numerically solving the heat equation using the
same software package.

###  IV.3 Raman thermometry, sensing and PUF labeling

Raman micro-spectroscopy was carried out using a multifunctional optical
system (Spectra II, NT-MDT) equipped with a CW He-Ne laser (central wavelength
of 633 nm), a femtosecond-pulse IR laser (TOPOL-1050-C, Avesta Project; pulse
repetition rate of 80 MHz, central wavelength of 1050 nm) and grating-type
spectrometer with a monochromator (M522, Solar Laser Instruments) and
electrically cooled CCD camera (i-Dus, Oxford Instruments). Pump laser
radiation was focused on the sample surface with a dry microscope objective
(100$\times$, M Plan Apo, Mitutoyo) having a numerical aperture of 0.7. Light-
to-heat conversion measurements were carried out with isolated Au-Si MSs drop-
cast on a monocrystalline Si wafer. Raman maps (40$\times$40 pixels) of the
PUF labels were recorded from 80$\times$80 $\mu$m2 surface areas at pump
intensity of 0.5 mW/$\mu$m2 and signal accumulation time of 0.1 per pixel.
Correlated nonlinear PL maps (40$\times$40 pixels) were acquired by scanning
the same surface area with fs-laser radiation at a pulse energy of $\approx$
0.8 nJ and collecting the integral PL intensity within the visible spectral
range (400 - 700 nm).

R6G molecules were used as a probe for the assessment of SERS performance of
the Au-Si hybrids owing to its strong affinity to noble metals and high Raman
cross-section. The Au-Si MSs (Sample #2) were functionalized with R6G
molecules by mixing a freshly prepared MS dispersion in isopropanol with
aqueous R6G (10-6 M). The obtained mixture was kept for 1 h and then drop-cast
on a bulk Au mirror reference. A similar analyte functionalization procedure
was carried out for Au reference to evaluate the SERS EF. The PUF labels were
created by drop-casting droplets (0.5 $\mu$L) of as-produced Au-Si dispersion
on Ag mirror/glass slides using a conventional syringe.

## Supporting Information

There are no conflicts to declare.

## Acknowledgements

This work was supported by the Russian Science Foundation (Grant no.
21-79-00302). S.G. expresses his gratitude to the Ministry of Science and
Higher Education of the Russian Federation (Grant Nos. MK-4321.2021.1.2).

## Conflicts of interest

The authors declare no conflict of interest.

## Data Availability Statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

## Keywords

Laser ablation in liquids; Hybrid nanomaterials; Au-Si microspheres; SERS;
Optical labels

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Further author information: (Send correspondence to G.P.S.)
G.P.S.: E-mail<EMAIL_ADDRESS>
* NASA Hubble Fellow

# Thermal control of long delay lines in a high-resolution astrophotonic
spectrograph

Gregory P. Sercel  Department of Astronomy, California Institute of
Technology, 1200 E California Blvd, Pasadena, CA, 91125, USA  Pradip R.
Gatkine  Department of Astronomy, California Institute of Technology, 1200 E
California Blvd, Pasadena, CA, 91125, USA  Department of Physics and
Astronomy, University of California Los Angeles, 475 Portola Plaza, Los
Angeles, CA, 90095, USA  Nemanja Jovanovic  Department of Astronomy,
California Institute of Technology, 1200 E California Blvd, Pasadena, CA,
91125, USA  Jeffrey B. Jewell  Jet Propulsion Laboratory, California Institute
of Technology, 4800 Oak Grove Drive, Pasadena, CA, 91109, USA  Luis Pereira da
Costa  Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak
Grove Drive, Pasadena, CA, 91109, USA  J. Kent Wallace  Jet Propulsion
Laboratory, California Institute of Technology, 4800 Oak Grove Drive,
Pasadena, CA, 91109, USA  Dimitri P. Mawet  Department of Astronomy,
California Institute of Technology, 1200 E California Blvd, Pasadena, CA,
91125, USA

###### Abstract

High-resolution astronomical spectroscopy carried out with a photonic Fourier
transform spectrograph (FTS) requires long asymmetrical optical delay lines
that can be dynamically tuned. For example, to achieve a spectral resolution
of R = 30,000, a delay line as long as 1.5 cm would be required. Such delays
are inherently prone to phase errors caused by temperature fluctuations. This
is due to the relatively large thermo-optic coefficient and long lengths of
the waveguides, in this case composed of SiN, resulting in thermally dependent
changes to the optical path length. To minimize phase error to the order of
0.05 radians, thermal stability of the order of 0.05° C is necessary. A
thermal control system capable of stability such as this would require a fast
thermal response and minimal overshoot/undershoot. With a PID temperature
control loop driven by a Peltier cooler and thermistor, we minimized
interference fringe phase error to +/- 0.025 radians and achieved temperature
stability on the order of 0.05° C. We present a practical system for precision
temperature control of a foundry-fabricated and packaged FTS device on a SiN
platform with delay lines ranging from 0.5 to 1.5 cm in length using
inexpensive off-the-shelf components, including design details, control loop
optimization, and considerations for thermal control of integrated photonics.

###### keywords:

Thermal control, astrophotonics, spectrographs, photonic delay lines

##  1 INTRODUCTION

The Fourier transform spectrograph (FTS) is a common and essential tool in
spectroscopy, in which flux of interest is passed through a scanning
interferometer, producing sinusoidal interference fringes [1]. As the delay
path length in the interferometer is modulated, the measured optical power of
the resulting fringes may be used to generate an interferogram. Taking the
Fourier transform of the interferogram yields the optical spectrum of the
input flux [2]. However, the resulting reconstructed spectrum is extremely
susceptible to path length error within the interferometer; accurate and
precise control of optical path length to a fraction of a wavelength is
necessary. [3]

Fourier transform spectrographs have been demonstrated in integrated photonic
platforms, in the conformation of Mach-Zehnder interferometers (MZIs),
constructed on both silicon-on-insulator (SOI) and SiN-on-silica
($Si_{3}N_{4}/SiO_{2}$) platforms [4, 5, 6]. Tunable optical path lengths in
photonic FTS chips are possible due to the relatively high thermo-optic
coefficients of these materials, however, this property results in a
temperature-dependent optical path difference error. The optical path length
of each arm of the interferometer, l, is given by $l=n\times d$, where n is
the refractive index of the waveguide and d is the physical length of the
waveguide.[7] Assuming the reference arm and delayed arm of the interferometer
possess different physical path lengths, the optical path difference between
the two will vary with global chip temperature. Thus, precise thermal
stabilization of photonic FTS chips is necessary to minimize phase error
resulting from fluctuating optical path differences.[8]

We present a thermal control system to minimize thermally induced phase errors
in a photonic FTS chip fabricated with SiN waveguides, shown in Fig. 1,
designed for astronomical spectroscopy.

---
Figure 1:  Top view (left) and side view (right) of fully packaged photonic
FTS chip mounted on thermoelectric cooling element.

##  2 EXPERIMENTAL SETUP

###  2.1 Spectrograph Chip

The Fourier transform spectrograph chip shown in Fig. 1 was designed by JPL,
Caltech, and Bright Photonics, fabricated by LioniX International, and mounted
and packaged with a V-groove fiber-optic pigtail by Phix Photonic Assembly.
The FTS chip contains several large MZI structures, of which one is concerned
in this paper. This large MZI, shown in Fig. 2, is composed of cascaded
Archemedian spiral delay lines separated by smaller 2x2 MZIs labeled as
switches that are constructed from multi-mode interferometers (MMIs) and
thermo-optic phase modulators (TOPMs). To differentiate between the smaller
MZI stages and the larger overarching MZI structure, the smaller MZIs will be
called MZI switches, while the large cascaded structure will be called the
main MZI.

Each MZI switch is used to control the transmission of optical power through
each of their two outputs, which is accomplished via TOPMs. Each TOPM is a
thin chrome trace that runs along one waveguide within each MZI switch, to
which a voltage bias is applied by a computer-controlled power supply. The
resulting high current density heats the trace, thermally inducing a local
change in the refractive index of the waveguide. Thus, through electrical
control, flux may be directed through one output while suppressing flux at the
other output, and vice versa. Figure 3 demonstrates the suppression of flux by
an MZI switch at several wavelengths. Large drops in throughput are seen at
voltage biases of 16-17 V for all wavelengths, indicating large bandwidths can
be controlled simultaneously.

---
Figure 2:  Top: Main MZI mask layout depicting TOPMs (yellow), regions heated
by TOPMs (green), and waveguides (pink). Bottom: Functional schematic
depicting Archemedian spiral delay lines interspersed by MZI switches.

The operation of an MZI is fairly simple: input flux is split down two paths,
one of which contains a path delay while the other is a straight path,
considered to be the reference path. Light traveling along the delayed path
has a phase shift relative to the path without a delay, which can be
modulated. The two paths are recombined and interfere constructively and
destructively. By modulating the relative phase difference between the delayed
path and reference path, an interference fringe can be reconstructed. The main
MZI depicted in the functional schematic in Fig. 2 follows this principle,
where input flux enters a controllable MZI switch that splits light down both
the delayed path and reference path, denoted as S1. Then, additional MZI
switches along the delayed path, denoted as S2, S3, and S4, each are set to
configure the optical path to either a straight waveguide which bypasses a
delay, or an Archemedian spiral waveguide delay. By electrically setting
switch states of S2, S3, and S4, the length of the delayed path can be varied
from 0 to 1.5 cm, in 0.5 cm steps. Finally, the delayed path is passed along a
thermal phase shifter, denoted as PM, that enables additional phase
modulation, and then recombined with the reference path.

A stand-alone MZI switch is present on the chip for calibration purposes; it
is used to determine the corresponding switching voltage for each optical path
length configuration. The same experimentally determined switching voltages
from this test structure are used to control the MZI switches within the main
MZI.

---
Figure 3:  Left: Throughput of an MZI output as a function of wavelength,
demonstrating broadband switchability and suppression of up to 50 dB around
1566 nm. Right: Throughput of the same MZI output as a function of voltage,
showing suppression can be achieved over broad bands with voltages in the
range of 16-17 V.

###  2.2 Thermal Control

A thermoelectric cooling device (TEC) is used to control chip temperature. The
FTS chip is fixed on a brass mounting plate which is thermally coupled to the
cold side of a 30-watt TEC via thermal paste, as can be seen in Fig. 1. The
TEC’s hot side is thermally coupled to a steel cooling plate, from which heat
is dissipated with an aluminum heat sink and cooling fan, as well as copper
thermal straps fixed to an optical bench. The TEC is powered by a 5-volt
supply with a 1-amp current limit through an N-MOS driver. The output power of
the N-MOS is modulated with an Arduino Uno microcontroller via pulse-width
modulation (PWM).

---
Figure 4:  Electrical layout of the thermal control system.

A thermistor is fixed in a bore in the brass mounting plate underneath the FTS
chip and is used for temperature feedback to drive a PID control loop. Analog
voltage from the thermistor is amplified by a factor of 10 using a rail-to-
rail op-amp, boosting the temperature sensitivity of the thermistor. This
maintains temperature precision otherwise lost in quantization by the 10-bit
analog-to-digital converter of the microcontroller. The electrical schematic
of the entire thermal control apparatus is shown in Fig. 4.

PID control was implemented on the microcontroller using a built-in PID
library, and the control loop has been manually tuned to achieve a fast
settling time and minimal overshoot/undershoot using a PID tuning guide from
Thorlabs.[9] An additional oversampling algorithm averages 10-sample bins in
every loop cycle to mitigate the effects of electrical noise. The control loop
maintains the chip at 18° Celsius, slightly below the ambient temperature of
the laboratory.

###  2.3 Characterization

Identifying the switching voltages: Using the aforementioned standalone MZI
switch test structure, voltage biases corresponding to each switch
configuration were experimentally determined by modulating the applied voltage
from 0 V to 18 V in 0.1 V steps, while illuminating the device with an L-band
monochromatic source and measuring optical power at both outputs with an
optical power meter. The voltage biases associated with each switch state for
the test structure were translated into truth tables for the main MZI, in
which voltages applied to each of its switch stages will engage or disengage
optical delay lines to set desired path lengths (see Fig. 5).

---
Figure 5:  Each MZI switch can be configured to transmit flux from the same
side as the input waveguide at a 16.5 V bias, or the opposing side at a 5.6 V
bias.

Balancing the power in reference and delayed arms: Once each MZI path length
configuration is set, the initial split-ratio-controlling MZI switch (S1 in
Fig. 2) was incrementally modulated from 0 V to 18V in 0.25V steps while a
1550 nm super-luminescent diode (SLD) source was used to illuminate the
device. The MZI output was passed to an optical spectrum analyzer (OSA) that
was used to analyze the resulting interference fringes for each S1 voltage
sweep. The experimentally determined S1 voltage that yields maximized
interference fringe amplitude is considered to provide the optimal splitting
ratio of flux between the delayed path and reference path (see Fig. 6-left).
This process was repeated for each delay path length configuration.

Measuring the long-term phase error: The MZI, once set to a given path length
with an optimized splitting ratio, was fed with an L-band monochromatic source
of constant flux, which was achieved with a variable optical attenuator. The
wavelength-phase relationship of interference fringes, which may be
approximated as sinusoids, is controlled by modulation of the PM thermal phase
shifter (see Fig. 6-right). Assuming an amplitude A for the sinusoidal fringe
at given wavelength $\lambda$, we get,

$\mathrm{Optical~{}power}~{}P=A\times sin(\phi)$ (1)

$\delta P=A\times\delta\phi~{}cos(\phi)$ (2)

At the point of inflection of the sinusoidal fringe (i.e. where $sin(\phi)$ =
0) at a given $\lambda$, cos($\phi$) $\sim$ 1\. Thus, the phase error
($\delta\phi$) can be inferred as:

$\delta\phi=\delta P/A$ (3)

To experimentally determine A at a given $\lambda$, we modulated the MZI’s
thermal phase shifter to sweep over an interference fringe and measured the
optical power at the fringe peak, trough, and point of inflection. After
measuring the amplitude A, we set the MZI’s thermal phase shifter to the point
of inflection and leave it there for $\sim$ 2 hours while keeping the thermal
control loop on. During this time, the optical power is continuously measured
at a sampling rate of 15 Hz and used to compute phase error (using Eq. 4) as a
metric of fringe stability. The phase error is calculated as

$\delta\phi=\sigma/A\,,$ (4)

where $\sigma$ is the measured standard deviation in the optical power at the
point of inflection of the fringe throughout the measurement (i.e. over 2
hours), and A is the fringe amplitude measured at the beginning of the
experiment.

---
Figure 6:  Left: Non-optimized and optimized sinusoidal interference fringes
from MZI configured with a 1.5 cm delay path, demonstrating amplitude
modulation by the initial splitting ratio MZI switch, S1. Right: Optical power
as a function of the voltage applied to the thermal phase shifter, PM, at 1550
nm.

##  3 RESULTS AND DISCUSSION

###  3.1 Calibration

The voltage biases found to direct all optical power from one input to each of
the two outputs of the single-stage 2x2 MZI switch test structure, identical
to those in each MZI variant, were found to be 5.6 V and 16.5 V, respectively.
Figure 5 depicts the optical path of a hypothetical MZI switch set to each
corresponding voltage state, for a given input waveguide.

The S1 initial split-ratio MZI switch swept from 0 V to 18 V in 0.25 V steps
for each path length configuration was found to produce maximized interference
fringes at a 12 V bias in all cases.

###  3.2 Thermal Control

After manually tuning PID coefficients to $K_{p}$, $K_{i}$, and $K_{d}$ values
of 700, 25, and 1, respectively, the thermal control system demonstrated rapid
settling and precise thermal stability at 18° C.

---
Figure 7:  Settling curve of thermal control loop following activation (left),
histogram of chip temperature over 2-hour monitoring period (right).

As the settling curve and histogram in Fig. 7 show, the device stabilizes to
its set point from room temperature in under 60 seconds with minimal
overshoot/undershoot once activated. Additionally, once stabilized, a standard
deviation of +/- 0.028° C was achieved over a monitoring period of 2 hours.

Once the thermal control system has been activated and stabilizes to the set
temperature, the delay path length of the MZI is configured. This causes
additional chip temperature swings which have been observed to settle in as
little as 30 seconds.

###  3.3 Stability

For each configuration of delay path length, phase error was measured over
2-hour-long monitoring periods. Without any thermal stabilization in place,
accurate computation of phase error was not possible due to thermal drift.
Large changes in optical power over time were observed due to a slow global
increase in chip temperature from heat dissipated by the MZI switches, as can
be seen in the left plot of Fig. 8. The increase in chip temperature affects
both the phase and period of the fringes, as well as the switching behavior of
each MZI switch.

---
Figure 8:  Flux at fringe inflection point over a 30-minute period without
thermal stabilization (left) and with thermal stabilization (right), with a 1
cm delay path.

The same measurements were repeated with active thermal stabilization, which
made computation of phase error metrics possible. The maximum phase error
observed amongst all path length configurations was +/- 0.025 radians. No
large fluctuations in optical power at the fringe inflection point were
observed, as shown in the right plot of Fig. 8. The phase error computed for
each delay configuration is given in Table 1.

Table 1: Phase error in radians and as a percent of fringe amplitude for each delay path length, measured over 2-hour-long periods. Path Length (cm) | 0 | 0.5 | 1 | 1.5
---|---|---|---|---
Phase Error (rad) | +/- 0.015 | +/- 0.025 | +/- 0.015 | +/- 0.015
Phase Error (%) | +/- 1.46 | +/- 2.45 | +/- 1.51 | +/- 1.52

##  4 CONCLUSIONS AND FUTURE WORK

###  4.1 Conclusions

We demonstrate a system to precisely control the global temperature of a
photonic chip with long delay lines, thus minimizing phase error originating
from thermally induced changes to optical path lengths. The apparatus is
constructed from inexpensive and readily available off-the-shelf components,
exhibits high thermal stability of the order of +/- 0.028° C, and sub-minute
settling time with minimal thermal overshoot/undershoot. This system
successfully stabilized the interference fringes of a photonic Fourier
transform spectrograph chip, reducing phase error to under +/- 0.025 radians
for delay path lengths of up to 1.5 cm.

###  4.2 Potential Improvements

While the stability achieved with this system is sufficient to carry out
spectral reconstructions, further tuning and implementation of adaptive PID
control algorithms would allow for more rapid stabilization of delay
configurations and thus allow faster acquisition of spectra. In an adaptive
PID loop, a more aggressive set of PID coefficients would be used when there
is a large deviation between the actual chip temperature and the set
temperature, while a less aggressive set of coefficients is used when the chip
temperature is near the set point. Additionally, increasing the thermal mass
of the heat sink coupled to the hot side of the TEC would improve the
efficiency of heat transfer of the TEC, further improving the stability of the
device.

###### Acknowledgements.

Support for P Gatkine was provided by NASA through the NASA Hubble Fellowship
Grant HST-HF2-51478.001-A awarded by the Space Telescope Science Institute,
which is operated by the Association of Universities for Research in
Astronomy, incorporated, under NASA Contract NAS5-26555. This work was
supported by the Wilf Family Discovery Fund in Space and Planetary Science,
funded by the Wilf Family Foundation, as well as the support from Keck
Institute for Space Studies at Caltech. Some of this research was carried out
at Caltech and the Jet Propulsion Laboratory and funded through the
President’s and Director’s Research & Development Fund program. This work was
supported by NASA through the Center Innovation Fund. The authors would like
to thank the staff at Lionix for the fabrication of the photonic chips
presented herein.

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