This article has been accepted for publication in IEEE Journal of Selected Topics in Quantum Electronics.

This is the author's version which has not been fully edited and
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Deep Learning Assisted Microwave Photonic

Dual-parameter Sensing
Xiaoyi Tian, Luping Zhou, Senior Member, IEEE, Liwei Li, Member, IEEE, Giorgio Gunawan,
Linh Nguyen, and Xiaoke Yi, Member, IEEE

Abstract— The combination of optical microresonators and existing chip-based technologies, have led to a broad range of
the emerging microwave photonic (MWP) sensing has recently applications [3-8].
drawn great attention, whereas its multi-parameter sensing Conventionally, the interrogation of resonant mode changes
capability mainly relies on adopting multiple resonance modes.
By incorporating deep learning (DL) into MWP sensing, we
relies on directly measuring the optical transmission using an
propose a new sensing paradigm, which has the simplified design, optical spectrum analyzer. This is simple but of limited speed,
reduced fabrication requirement, and the capability of sensing especially when high resolution is needed, and the
more than one parameter. The MWP interrogation transforms performance largely depends on the fabrication accuracy of
the spectral response of a single optical resonance (SOR) that can optical microresonator devices [9-14]. In the pursuit of
be at arbitrary coupling conditions into the variations of the zero- achieving high speed and high resolution to meet the ever-
transmission profile of microwave signals, providing improved
interrogation resolution regardless of the resonance parameters.
increasing demand in modern sensor networks, the Internet of
A DL unit is used to exploit the raw interrogation output to Things, and the frontiers in medical and biochemical fields,
simultaneously estimate the target measurands. As the proof-of- microwave photonics (MWP), which has been bringing
concept demonstration, simultaneous temperature and humidity together and benefiting the two worlds of microwave
sensing using a SOR is conducted, where the convolutional engineering and photonics [15-19], has been applied into
neural tangent kernel (CNTK) is used as the DL model to reduce optical sensing in recent years [20,21]. Different MWP
the demand for experimental data. The established CNTK-DL
model consistently outperforms the support vector regression
interrogation schemes have been proposed for optical
model that relies on handcrafted features and demonstrates an microresonators. The basic idea is to transfer the resonant
over 2-fold higher estimation accuracy with the laser drift wavelength shift of optical microresonators in the optical
interference and a lower mean absolute error in the presence of domain into the frequency changes in the microwave domain,
strong noise, showing the power of DL for boosting MWP where fast and precise measurements are easier to conduct [9-
sensing. 12]. With the recent advances in photonic integration, which
have propelled MWP to a new height by allowing enriched
Index Terms—Microwave photonics, optical resonators, deep
learning, sensors, machine learning, optical signal processing. functionality in a dramatically reduced footprint [22], the
MWP sensors using integrated devices are promised to be a
I. INTRODUCTION preferred solution in various high-demanding sensing
scenarios. However, the related research effort on the on-chip

O
PTICAL microresonators, such as microrings, MWP sensing mainly centers on single-parameter sensing,
microdisks, and microspheres, can strongly enhance while the achievement of sensing more than one parameter,
the light-matter interaction by confining the resonant which is often required or even indispensable in real-life
light at specific wavelengths through total internal reflection applications, is still challenging. Along with the variations of
along the sidewalls of a microscale cavity. Optical the measurands of interests, the undesired perturbations can
microresonator based sensors have been attracting great also be encoded in the optical resonant mode changes,
attention [1,2]. Their remarkable properties, including the affecting the sensing selectivity. The ability to effectively
label-free detection and real-time monitoring capabilities and distinguish different factors is thus vital to achieving accurate
the exceptional sensitivity to any environmental perturbation and reliable sensing with no ambiguity. Conventional
that can influence the optical mode distribution, coupled with approaches to realizing optical multi-parameter sensing rely
their diverse fabrication platforms and compatibility with the on the usage of multiple resonator devices or resonance modes
with different sensitivities [9,23], which increases the
complexity of the design, implementation, and interrogation of
The work was supported in part by the Australian Research Council.
(Corresponding author: Xiaoke Yi). the sensors. This challenge becomes increasingly pronounced
Xiaoyi Tian, Luping Zhou, Liwei Li, Linh Nguyen, and Xiaoke Yi are with as the required number of resonance modes multiplies. It is,
the School of Electrical and Information Engineering, The University of therefore, necessary to find a new way to enable the MWP
Sydney, Sydney, NSW 2006, Australia (e-mail: xiaoyi.tian@sydney.edu.au;
luping.zhou@sydney.edu.au; liwei.li@sydney.edu.au; linh.n@sydney.edu.au; sensors to simultaneously detect more than one measurand.
xiaoke.yi@sydney.edu.au). Recently, deep learning (DL) has gained ever-increasing
Giorgio Gunawan is with the School of Aerospace, Mechanical and attention, as it allows computational models consisting of
Mechatronic Engineering University of Sydney, Sydney, NSW 2006,
Australia (e-mail: ggun7030@uni.sydney.edu.au).
multiple processing layers to learn to automatically extract
optimal feature representations from the raw input for making

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 This article has been accepted for publication in IEEE Journal of Selected Topics in Quantum Electronics. This is the author's version which has not been fully edited and
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(a)

(b)
Fig. 1. The proposed new MWP sensing scheme consists of (a) the high-resolution MWP interrogation system for the optical microresonator sensors, which
uses a DDMZM to map the single optical resonance responses, including the resonance wavelength shift and the variations of ER and FWHM, in the optical
transmission of a MRR into the zero-transmission profile of the SFS, where H and H’ are the optical transmissions before and after the measurands change
and T and T’ are the corresponding SFS transmissions, respectively, and (b) the DL processing of the raw interrogation output, where the DL model
automatically extracts the optimal feature representations and is capable of generating the accurate estimation the measurands of interest (M1’ and M2’)
after being sufficiently trained.

accurate decisions, even for highly complex problems [24-33]. small datasets is adopted to establish the DL model to reduce
It has shown great promises to directly decouple the combined the demand for a large amount of experimental data. In
response to different measurands [26-30]. In comparison with comparison with the ML model based on support vector
the traditional machine learning (ML) approaches which regression (SVR) and two handcraft features extracted from
require handcrafted input [34-36], the excellent capabilities of the interrogation output, the DL-assisted MWP sensor
DL make it a promising tool to process the interrogation consistently shows superior performance, demonstrating a
results by automatically recognizing and learning the optimal nearly 2-fold and 3-fold higher estimation accuracy with and
informative feature representations, rather than solely relying without the interference of laser drift, respectively, and
on handcrafting features, for complex mapping [37-39]. To remains a lower mean absolute error (MAE) in a high noise
date, however, to our best knowledge, the DL has not been level. These results demonstrate the superiority of MWP
applied in emerging MWP sensing. sensing assisted by DL and boost the microresonator for multi-
In this article, by combining MWP sensing with DL for the parameter sensing.
first time, we propose a new MWP sensing paradigm using a
single optical resonance (SOR), which has the minimum II. PRINCIPLES AND METHODS
requirement for the design and fabrication of the optical
A. Principle of Operation
microresonator sensor and the capability of simultaneously
sensing more than one measurand of interest. Through the Figure 1(a) depicts the schematic diagram of the high-
MWP sideband processing, the spectral response of the SOR resolution MWP interrogation system for the optical
to the measurands of interest can be transformed into the zero- microresonator sensors in our proposed new sensing approach
transmission profile of the interrogation microwave signals using only a SOR. The proposed scheme is compatible with
with high resolution. The interrogation output is then directly any optical microresonator. Here, a standard all-pass MRR,
used as the input for DL processing, where multiple which consists of simply a cavity waveguide and a bus
processing layers automatically extract optimal feature waveguide, is used as an example. The optical transmission
representations and achieve accurate simultaneous prediction profile of a SOR of the MRR at arbitrary coupling conditions
of the measurands of interest through supervised training. As a is continuously interrogated with high speed and high
proof-of-concept, we experimentally demonstrate the resolution by using a swept-frequency signal (SFS) modulated
achievement of simultaneous sensing of temperature and onto the excitation light in a dual-drive Mach Zehnder
relative humidity (RH) via DL of the MWP interrogation modulator (DDMZM) via an electrical 90-degree hybrid
output of a SOR of a generic silicon-on-insulator (SOI) coupler. By conducting the MWP sideband processing of the
microring resonator (MRR) top-coated with the hygroscopic modulated light, the transmitted SFS constantly exhibits an
polymethyl methacrylate (PMMA). The convolutional neural ultradeep spectral notch with a sharp tip, indicating the SOR
tangent kernel (CNTK) that approximates a convolutional responses to the measurand changes with greatly enhanced
neural network with infinite layer width and is amiable to resolution. The raw SFS transmission is later used as the direct

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 This article has been accepted for publication in IEEE Journal of Selected Topics in Quantum Electronics. This is the author's version which has not been fully edited and
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1 4 40
input for DL processing which enables the simultaneous 0.4 ncladding = 1.485 neff = 2.3550
ng = 4.3874
neff ng
0.1
r/r

Y (um)

1×10-4
prediction of more than one measurand of interest. 0.2

pm
220 nm 0 0 0
0
For the MRR with a self-coupling coefficient of 𝑟 and a 0.2 450 nm 0.1
0 -4 -40
cavity length of 𝐿 , its optical field transmission, 𝐻 , with (a)
-0.5 0
X (um)
0.5 -4 0
(b) n of cladding (1×10-4)
4 -4 0 4
(c) n of cladding (1×10-4)
respect to the wavelength of 𝜆 and the effective index of 𝑛𝑒𝑓𝑓 Fig. 2. (a) The simulated cross-section view of the optical field
can be expressed as [40] distribution of light transmitted in a standard SOI waveguide shows the
strong evanescent waves on the waveguide surface that intimately
𝑎−𝑟𝑒 −𝑖Ɵ
𝐻= 𝑒 𝑖(𝜋+Ɵ) (1) interact with the top claddings; (b) The variation of the refractive index
1−𝑟𝑎𝑒 𝑖Ɵ of top cladding (∆n) results in the change of effective index (∆n eff) and
where 𝑎 is the single-pass amplitude transmission that reflects group index (∆ng) and hence the distinct shift of resonance wavelength
the transmission loss in the cavity, and Ɵ is defined as Ɵ = (∆λres); (c) The simulated change of self-coupling coefficient (∆r) of a
2𝜋 straight directional coupler as the cladding refractive index varies.
𝑛 𝐿. Each resonance mode thus corresponds to an optical
𝜆 𝑒𝑓𝑓
power transmission dip at the resonance wavelength, 𝜆𝑟𝑒𝑠 , features from the raw spectrum and compares the resulting
with the notch depth or extinction ratio (ER) equal to estimated measurand values in the output layer against the
(𝑎+𝑟)2 (1−𝑎𝑟)2
𝐸𝑅 = (2) ground truth. Errors are then used to adjust the network
(𝑎−𝑟)2 (1+𝑎𝑟)2
coefficients and hyperparameters in the direction of achieving
The full width at haft maximum (FWHM) of notch width is
given by better estimation accuracy. This process occurs over and over
(1−𝑟𝑎)𝜆𝑟𝑒𝑠 2
through the training dataset until the model has been fitted
𝐹𝑊𝐻𝑀 = (3) appropriately with the optimal parameters. Once the DL model
𝜋𝑛𝑔 𝐿√𝑟𝑎
where 𝑛𝑔 is the group index. When the laser wavelength, 𝜆𝐶 , is established, the different target measurands of interest can
is placed close to the selected SOR for sensing at the longer be accurately and simultaneously estimated with the MWP
wavelength side, as the SFS-modulated optical field, 𝐸𝑚 , interrogation output of the SOR. In this way, the high-
transmits in the MRR, the optical notch of the SOR will then sensitivity and high-resolution MWP sensing of more than one
be scanned by the upper or lower sideband (USB or LSB), parameter is achieved, which has the minimum requirement on
consequently resulting in a transmission dip of the SFS. Figure the design and fabrication of the optical microresonator sensor
1(a) shows an example of using the USB in MWP probe.
interrogation. The instantaneous intensity of the transmitted Figure. 2(a) presents the simulated optical mode field
SFS after the photodetector (PD) can be expressed as [9] distribution in the cross-section of the SOI waveguide. A
1
𝐼 2 = ℛ 2 𝑃𝐶 {𝑃𝐿𝑆𝐵 + 𝑃𝑈𝑆𝐵
′ ′
+ 2√𝑃𝐿𝑆𝐵 𝑃𝑈𝑆𝐵 cos Δ𝜑} (4) finite-difference eigenmode (FDE) solver (Ansys Lumerical)
2
where ℛ is the responsivity of the PD, 𝑃𝐶 , and 𝑃𝐿𝑆𝐵 are the was adopted to numerically calculate the TE mode optical
initial optical power of the optical carrier and LSB, electric field distribution within cross-section area of the
′
respectively. 𝑃𝑈𝑆𝐵 represents 𝑃𝑈𝑆𝐵 |𝐻(𝜆𝑈𝑆𝐵 )|2 , which is the waveguide. The simulation was conducted at a wavelength of
instantaneous USB power, 𝑃𝑈𝑆𝐵 , being filtered by the SOR 1550 nm, with the silicon waveguide dimensions set to 450
power transmission dip at the wavelength position of 𝜆𝑈𝑆𝐵 . Δ𝜑 nm in width and 220 nm in height, and the refractive index of
is the phase difference between the two photocurrent terms the top cladding layer fixed at 1.485. As the results indicate,
resulting from the carrier beating with USB and LSB, the optical mode field of the transmitted light distributes
respectively, which is dependent on the phase transmission of throughout both the waveguide core and the cladding layers.
the SOR and adjustable by the DC bias of DDMZM. The Thus, any environmental changes that can perturb the optical
changes of different measurands of interest can lead to a mode field, especially those as evanescent waves along the
combined variation in the spectral line shapes of the SOR. waveguide surface, will cause the optical mode indices to
Through the MWP sideband processing by tailoring the vary. Figure 2(b) shows the changes of 𝑛𝑒𝑓𝑓 and 𝑛𝑔 of the
optical power and phase profiles of the optical components in simulated optical mode at 1550 nm and the consequent
Eq. (4) via tuning the DC bias voltage of the modulator, the resonance wavelength shift, when the refractive index of the
superposed responses of the SOR, which can have arbitrary
top cladding, 𝑛𝑐𝑙𝑎𝑑𝑑𝑖𝑛𝑔 , undergoes a variation. Therefore, by
coupling states and parameters, can be transformed into the
variations of an ultra-deep notch in the SFS transmission using the MRR as the sensor, a tiny index change can be
spectrum with high resolution. transformed into a distinct resonance wavelength shift. In the
The output of the MWP interrogation is used as the input of meantime, as shown by the simulation results of the self-
the DL for learning and estimation, as shown in Figure 1(b). coupling coefficient of a straight directional coupler which
The SFS transmission spectrum is measured at various uses the same SOI waveguide geometry and has a coupling
measurand conditions in the target sensing area to establish the length of 15 um and a gap distance of 300 nm in Fig. 2(c), 𝑟 in
DL-based estimation model. The acquired raw spectra labeled Eq. (1) is also varying with the optical index of the cladding.
with the ground-truth measurand values then comprise the Given that the optical indices are wavelength dependent [41],
dataset to train the DL model, where the raw spectrum along with the resonance wavelength shift, the overall
composed of a length of point transmission directly functions resonance line shape, therefore, also responds with altered
as the input layer without experiencing any pretreatment. In characteristics, such as the ER and FWHM, as indicated by
the supervised training, the DL neural network containing Eqs. (2) and (3).
multiple hidden layers automatically extracts high-level

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0 2 0 1 filter size:
filter size: J×
J×1

π rad

π rad
-5 1 0
dB

dB
-5

|H(λ)|2 |H(λ)|2
H(λ) H(λ)
-10 -0.1 0 0.1 0 -10 -0.1 0 0.1 -1
(a) λ (nm) (b) λ (nm)
40 4 2 40 4 2
8 8
π rad

π rad
4 4
dB

dB
3
20 0 20 0
-4 2 π rad -4 2
0 0.15 0.3

π rad
0 0.15 0.3
λUSB (nm) λUSB (nm)
0 1 0 1
dB

dB
-20 -20 Input N infinite-width convolutional layers Flattening Output
-40 0 -40 0 Fig. 4. The experimental CNTK-DL model approximates a convolutional
0 0.2 0.4 0.6 0.8 1 1 1.2 1.4 1.6 1.8 2
(c) VDC / Vπ (d) VDC / Vπ neural network with one input layer of raw transmission spectrum, N
infinite-width convolutional layers, and one flattening layer connected to
Fig. 3. The optical sideband processing via the DC bias voltage. The the output estimations of temperature (T) and RH. Each convolutional
simulated power and phase transmission of (a) over-coupled and (b) filter has a size of J, and all the weights and biases are initialized by
under-coupled resonant modes show the integer number of π rad phase using the normal distribution.
changes at the resonance wavelength. The simulated power ratio between
′
the USB filtered by the SOR ( 𝑃𝑈𝑆𝐵 ) and the LSB ( 𝑃𝐿𝑆𝐵 ) and the chip sensor probe. Due to the high thermal-optic coefficient of
concurrent Δφ at different DC bias conditions show that there is always a
DC bias voltage in the first and second Vπ range for the (c) over-coupled
silicon [43] and the humidity-sensitive refractive index of
and (d) under-coupled SOR, respectively, to create the zero transmission. PMMA [44], the transmitted optical resonance modes in the
The insets show the instantaneous sideband power ratio and Δφ as the MRR are thus sensitive to the environmental temperature and
USB sweeps through the resonance wavelength at the corresponding
RH level. The MWP interrogation of the selected SOR of the
optimal DC bias condition.
MRR was carried out at a series of different temperature and
′
Figure 3 shows the simulated power ratio between 𝑃𝑈𝑆𝐵 and humidity conditions to obtain sufficient transmission spectra
𝑃𝐿𝑆𝐵 and the concurrent Δ𝜑 at different DC bias voltages, to comprise the dataset for DL processing and model testing.
when the USB sweeps through the resonance wavelength of an To reduce the high demand for training data, CNTK [45-47],
over-coupled (Fig. 3(a)) and under-coupled (Fig. 3(b)) which approximates a convolutional neural network with
resonance mode, respectively. Since the optical phase infinite layer width and has been demonstrated to be suitable
transmission at the resonance wavelength is always equal to for small dataset problems [45], is adopted to build the DL
the integer number of π rad, as shown in Fig. 3(c) and Fig. model. CNTK is a kind of kernel method that works by
3(d), there always exists one DC bias point in the first and transforming input from the original dimension space into a
second Vπ (half-wave voltage) range to allow the transmitted higher dimensional space and searching for an optimal linear
SFS in Eq. (4) for the over-coupled and under-coupled SOR, function, which may be a highly nonlinear function in the
respectively, to satisfy the following conditions original space, to make the prediction. Therefore, the CNTK
′
𝑃𝐿𝑆𝐵 = 𝑃𝑈𝑆𝐵 (5a) allows the DL of transmission spectra with a much lower
cosΔ𝜑 = −1 (5b) number of parameters.
Therefore, a zero transmission of the SFS (𝐼 2 = 0) can always The approximation of infinite-width neural networks as
be created regardless of the coupling state of SOR, via kernels depends on three conditions: over-parameterization,
automatically controlling the DC bias voltage of the DDMZM proper initialization of parameters, and a sufficiently small
[42]. The zero transmission is manifested as the ultradeep dip learning rate [46]. Given these conditions, as the neural
in the SFS transmission spectrum, where the dip location and network model becomes over-parameterized, the weight
spectral line shape are subject to the concurrent resonance changes are observed to decrease proportionally. The weights
wavelength and the original optical resonance line shape. will hence remain static during the gradient descent
Overall, based on the MWP sideband processing technique, optimization process, even if each layer is built with infinite
the wavelength position of the selected SOR, which can be at neurons. This unique feature thus allows the infinite-width
arbitrary coupling states, can be continuously interrogated by
neural network to be approximated as its Taylor’s expansion
locating the zero-transmission point of the SFS. The spectral
around the initialized weights, 𝒘𝟎 , as [48]
profile at the output of MWP interrogation output, which
contains the sharp tip of the ultradeep spectral notch enabling 𝑓(𝑥, 𝒘) ≈ 𝑓(𝑥, 𝒘𝟎 ) + 〈∇𝑤 𝑓(𝑥, 𝒘𝟎 ), 𝒘 − 𝒘𝟎 〉 (6)
the high interrogation resolution, is used as the input of the DL where 𝑓(𝑥, 𝒘) refers to the neural network function, 𝒘
model for measurand prediction. represents weights, 𝑥 stands for the input, and ∇𝑤 𝑓(𝑥, 𝒘𝟎 ) is
the gradient vector at initialization. As the weights are
B. Deep Learning Model completely static when the network is highly over-
As a proof-of-concept, the proposed DL-assisted MWP parameterized, 𝒘𝟎 can be considered a constant. Equation (6)
sensing scheme using a SOR is validated in the case of is thus simply a linear model of the weights 𝒘. As proved in
simultaneous sensing of temperature and humidity by using a [46,49], training such infinite-width neural network by
SOI MRR, top-coated with hygroscopic PMMA, as the on- gradient descent is equivalent to conducting kernel regression

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expressed as 1 1

𝑓(𝑥) = 𝐾(𝑥, 𝑫) ∙ 𝐾(𝑫, 𝑫)−1 ∙ 𝑦(𝑫)

Transmission

Transmission
(7)
where 𝑥 stands for the test data as the input, which can be 0.5 Q=23600 0.5
20 um
assigned with a transmission spectrum acquired from the Q 38700
0
MWP interrogation during the sensing process, 𝑫 = (a) (b) 1548.80 1548.90 1549.00 (c)
0
1548.60 1548.70
Wavelength (nm) Wavelength (nm)
[𝑥̂1 , … , 𝑥̂𝑁 ]′ , is the training dataset with a size of N, which is Fig. 5. (a) Scanning electron microscope image shows the racetrack
implemented with a collection of the transmission spectra shape of the fabricated SOI MRRs for experiments; Measured optical
acquired by the MWP interrogation of the SOR at N different power transmissions of the MRRs with the waveguide width of (b) 420
nm and (c) 450 nm, respectively.
known conditions of the measurands of interest throughout the
target sensing range, 𝑦(𝑫) corresponds to the ground-truth Air pumps
Hybrid
values, i.e., the N known conditions of the measurands of Chamber Coupler
interest, 𝐾(𝑥, 𝑥 ′ ) is the kernel function that computes the Water
DDMZM 1.801V
+-
similarity between two samples, 𝑥 and 𝑥 ′ , by Thermistor PolC Power Supply
fmin[.]
Tavg[.]

Desiccant RH =
Temp =

𝐾(𝑥, 𝑥′) = 〈𝛻𝒘 𝑓(𝑥, 𝒘𝟎 ), 𝛻𝒘 𝑓(𝑥′, 𝒘𝟎 )〉 (8) Laser Control & DL

%RH Peltier PD Computer
EDFA
where the gradient vector works as the feature map that 11.02 K
Port 1 Port 2
VNA
TC
transforms the input to higher-dimensional space. The CNTK- Hygrometer

DL model thus can be established simply by incorporating the Fig. 6. Schematic of the experimental setup of the proposed SOI based
gradient vector function of the convolutional neural network MWP sensor using ML and DL for the simultaneous measurement of
temperature and humidity. The PMMA coated SOI MRR sits close to a
[47], which can be numerically calculated in practical thermistor on a Peltier, which is connected to a temperature controller
implementations, into Eq. (7) and determining the and is enclosed in a homemade chamber where the RH level is monitored
hyperparameters, including only the filter size and the number by a reference hygrometer and adjustable via controlling the wet and dry
of layers, through the grid search. As for the weights and air flows.
biases in each infinite layer, the normal distributions with the
nm-SOR has a Q factor of around 23600, while the 450 nm-
variance of 1 and 0 are used, respectively, for the
initialization, following an identical configuration in [50]. SOR shows a relatively larger Q factor of around 38700.
Figure 4 depicts the equivalent network structure of the B. Experimental Setup
experimental CNTK-DL model. Compared with the deep The experimental setup of the simultaneous measurement of
neural network model, the CNTK-DL model uses multiple
temperature and humidity with the proposed DL-assisted
layers with infinite width to learn the features of the input, but
MWP sensing scheme using a SOR is illustrated in Fig. 6. The
only has a few parameters to optimize, which, therefore,
on-chip PMMA-coated SOI MRR, working as the sensor
makes it a more efficient choice for implementing the
proposed DL scheme in experiments. probe, sits close to a thermistor on a Peltier cooler and is
enclosed in a homemade chamber made with an inlet and an
III. EXPERIMENTAL SECTION outlet and proper holes for wires and fibers. The humidity
inside the chamber is constantly monitored using a
A. Device Fabrication and Characterization commercially available hygrometer (IC-Center 317) as the
The experimental SORs are contributed from SOI MRRs humidity reference sensor. The hygrometer has a measurement
fabricated in the same racetrack shape, as shown in Fig. 5(a), range of 0-99% RH, a resolution of 0.1% RH, and an accuracy
using standard electron-beam lithography technology on a SOI of ± 2.5% RH. The interior RH level can be gradually adjusted
wafer where the silicon waveguides are 220 nm thick and sit to and stabilize at the desired value by carefully changing the
on top of a 2 um buried oxide layer above a 725 um thick power of the pumps that bring in the surrounding air into the
silicon substrate. The bending radius of the curved waveguides chamber via tubes filled with water and desiccant. To ensure a
is around 27 um, and the length of the straight waveguides is reliable reference RH measurement, the MWP interrogation
about 20 um. The light coupling between the on-chip MRR was only performed when the RH level had stabilized, and the
device and fibers is realized via vertical grating couplers at the concurrent reference RH level was recorded at the same time
end of the bus waveguides. Once fabricated, the SOI MRRs of the spectrum acquisition. Meanwhile, the temperature
were then spin-coated with the hygroscopic PMMA layer to variation is achieved by using a temperature controller (TC)
make the waveguide cladding index sensitive to the (Newport 325), which detects the thermistor and drives the
environmental humidity, where the thickness of the PMMA Peltier cooler. A polarization controller (PolC) is added
cladding was made to be around 450 nm to envelop the between the laser source (Keysight, 81960A) and the
evanescent waves surrounding the MRR waveguides DDMZM to align the polarization of the light according to the
completely. Figures 5(b) and 5(c) present the optical quasi-transverse electric mode of the chip waveguides to
transmission of the experimental SORs of PMMA-coated minimize the optical loss. The vector network analyzer (VNA)
MRR with a 420 nm and a 450 nm waveguide width, (Keysight, N5234A) is used to generate the SFS, which drives
respectively, which were measured at room temperature and the DDMZM via a 90-degree electric hybrid coupler (Marki
humidity conditions. Both resonances exhibit a small ER and a microwave, QH0444). The DDMZM bias voltage is supplied
wide tip, indicating a limited resolution performance. The 420 by a DC power supply (Keysight, E3632A) which is

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programmable with a voltage resolution of 1 mV. To

0
compensate for the coupling loss between the on-chip

Normalized transmission (dB)

23

Dip frequency (GHz)

waveguides and optical fibers, an Erbium-doped fiber
19 -30
amplifier (EDFA) is added at the output of the sensor probe
before the optical detection in a high-speed PD (u2t). The 15 RH 52.0%
22.63 °C
detected photocurrent is then sent to the VNA, which 11 -60 22.55 °C
22.46 °C
22.37 °C
measures the demodulated SFS and provides the SFS 7 22.29 °C
35 22.20 °C
transmission. In practice, the optical modulator, optical 22.3 45 -90
2 6 10 14 18 22
frequency (GHz)
microresonator, and PD can be integrated into a single 22.5 55 RH(%)
(a) T (°C) 22.7 65
platform to enhance the system compactness and portability
[22], while the VNA, which works as a radio frequency

Transmission average (dBm)

0
transceiver, can be replaced with a compact RF source and

Normalized transmission (dB)

-45
power meter to reduce the system volume and cost. The power
-30
supply and VNA are connected to a computer that
dynamically adjusts the DC bias voltage to maintain the -55 T 42 °C
39.9% RH
-60 44.1% RH
conditions for the high-resolution MWP interrogation during 48.2% RH
52.0% RH
the sensing and processes the acquired interrogation results -65
56.0% RH
60.5% RH
65 -902
with ML and DL techniques to enable the sensing of dual 22.6 55
6 10 14 18
frequency (GHz)
22
RH(%)
parameters. T (°C) 22.4 45
(b) 22.2 35

IV. RESULTS AND DISCUSSIONS Fig. 7. The flat and rugged distribution of the (a) dip positions and (b)
transmission averages extracted from the transmission spectra obtained
In this section, the performance of the proposed SOR-based in Scenario 1, showing their linear and nonlinear relationships with the
MWP sensing scheme using the CNTK-DL model in the temperature and RH, respectively. The inset in (a) and (b) presents the
transmission spectra (referenced to -20 dBm) collected at a fixed
simultaneous measurement of temperature and humidity is
humidity of 52.0% RH and a fixed temperature (T) of 22.42 °C,
demonstrated and analyzed. To evaluate the robustness and respectively, which demonstrates the constant high interrogation
versatility of the DL-based sensing model, the experiment was resolution and varied line shapes at varying temperature and humidity
carried out in three different scenarios: the SOR-based MWP conditions.
temperature and humidity sensing under (i) no additional RH 60.2%
interference, (ii) laser drift, and (iii) strong noise. Laser drift is 23 Scenario 1 0
Scenario 1
0
Scenario 2
Dip frequency (GHz)

22.63 °C 22.37 °C

Normalized transmission (dB)

Normalized transmission (dB)

Scenario 2 22.55 °C 22.29 °C
a common problem in optical systems and critical for long- 19 -20 22.46 °C 22.20 °C -20

term operation, while noise resistance is desired for practical -40 -40
15
deployment. In each experiment, the laser wavelength was -60 -60
11
kept on the longer-wavelength side of the selected SOR, and -80 -80 22.63 °C 22.37 °C
36 spectra in total were acquired in the MWP interrogation of 7
45
35 22.55 °C
22.46 °C
22.29 °C
22.20 °C
22.3 -100
2 7 12 17 22
-100
2 7 12 17 22
22.5 55
the SOR at six different RH levels, ranging from around 40% (a) T (°C) 22.7 65 RH(%) frequency (GHz) frequency (GHz)

RH to around 60% RH in a step of about 4% RH, while the T 22.68 °C

Transmission average (dBm)

Scenario 1 Scenario 2
temperature of the MRR chip was set to six equally spaced -20 Scenario 1 0 39.8% RH 52.0% RH 0
Normalized transmission (dB)

Normalized transmission (dB)

Scenario 2 44.0% RH 55.6% RH
values, ranging from 22.20 °C to 22.63 °C, via a temperature -30 -20 48.0% RH 59.7% RH
-20

controller. Each spectrum acquired has a frequency range of -40 -40 -40

20 GHz and a sample length of 1001, which corresponds to a -50 -60 -60

wavelength resolution of about 0.16 pm at the wavelengths -60 -80 -80 39.9% RH 52.4% RH
around 1550 nm. The small temperature and humidity -70 65 -100 -100 47.9% RH 60.4% RH
44.2% RH 56.5% RH

22.6 55 2 7 12 17 22 2 7 12 17 22
increments were adopted to test the interrogation resolution. 22.4
22.2 35
45
RH(%)
frequency (GHz) frequency (GHz)
(b) T (°C)
Although the measurement range of the MWP system
demonstrated in this paper is limited by the experimental Fig. 8. The (a) dip positions and (b) transmission averages extracted from
the transmission spectra collected in Scenario1 and Scenario 2. The laser
devices and instrument, such as the PD and VNA, it can be drift makes the two spectral features ambiguous and lose validity as
extended by utilizing a tunable laser to conduct the multi- individual sensing parameters. The inset in (a) and (b) compares the
channel interrogation via changing the carrier wavelength measured spectra (referenced to -20 dBm) in Scenario1 and Scenario 2,
at the fixed humidity of 60.2% RH and the fixed temperature (T) of
[51]. The collected transmission spectra labeled with the 22.68 °C, respectively, showing the clear shape deformations.
ground-truth temperature and RH values comprise the datasets
for DL processing. For comparison, in parallel with
establishing the CNTK-DL model, the SVR-ML model (see A. Data Description
Appendix) was also conducted to do the simultaneous sensing First, as in Scenario 1, the MWP simultaneous sensing of
of temperature and humidity with the same spectrum datasets temperature and humidity was carried out without additional
and procedures by using two handcrafted spectral features: the interference. The SOR was selected from a fabricated PMMA-
transmission dip position and overall average. coated SOI MRR with a waveguide width of 420 nm. The

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ratio of the transmission dip is still preserved, and the

0 spectrum generally shows a similar response to the

Normalized transmission (dB)

Dip frequency (GHz)

34
measurands. However, at each temperature and humidity
32 -30 condition point, the data shows a clear position deviation in
30
RH % both horizontal and vertical directions. As the laser
28 22.63 °C
-60 22.55 °C
22.46 °C
wavelength drift directly superimposes on the resonance
26 22.37 °C
22.29 °C wavelength shift, all the transmission dips appear at a higher
24 35 22.20 °C
22.3 45
-90
22 26 30 34 38 42 frequency, while each of the offsets slightly varies with one
frequency (GHz)
22.5 55 RH(%) another due to the non-zero filtering effect of resonance, in
(a) T (°C) 22.7 65 practice, on the optical carrier. At the same time, all the
transmission spectra are integrally lifted, to different extents,
Transmission average (dBm)

Normalized transmission (dB)

0 due to the increased optical power, whereas consequently
-60 becoming more overlapped.
-30 In Scenario 3, a SOR selected from a fabricated PMMA-
-70 T 60 °C coated SOI MRR with a waveguide width of 450 nm was used
40.0% RH
-60 44.4% RH
48.0% RH
in the temperature and humidity sensing experiment in the
52.0% RH
56.1% RH
presence of a high noise level which is realized by decreasing
-80 35 60.1% RH
the experimental optical power and also shifting the MWP
-90
22.3 45 22 26 30 34 38 42
22.5 55 RH(%)
frequency (GHz) interrogation window to higher frequencies [9]. The collected
(b) T (°C) 22.7 65 spectrum data constitute Dataset 3 and are shown in Fig. 9.
Fig. 9. The (a) dip positions and (b) transmission averages extracted Compared with Dataset 1, the total resonance wavelength shift
from the transmission spectra obtained in Scenario 3, where there is in response to the humidity variation is evidently smaller due
intentionally induced strong noise interference, exhibit nonlinear to the wider waveguide width that leads to the less distribution
variation with respect to the temperature and humidity changes. The
inset in (a) and (b) presents the noisy transmission spectra (referenced to of the transmitted optical mode field in the claddings, although
-40 dBm) collected at a fixed humidity of 60.1% RH and a fixed the high rejection ratio of the transmission dip is still retained.
temperature (T) of 22.60 °C, respectively. The noisy spectra become distorted and blurry and overlap
obtained dataset is named Dataset 1. Two series of spectrum with one another in a wide frequency range. Moreover, the dip
position now shifts nonlinearly, and similar to Dataset 2, the
data collected at the same temperature of around 22.42 °C and
change of transmission average at different environment
the same RH level of around 52.0%, respectively, are shown
conditions (humidity and temperature) becomes less obvious,
in Fig. 7, where the transmission dip position and overall
showing the deterioration in the signal quality undoubtedly
average extracted from each spectrum data are presented
poses challenges to the measurand estimation.
altogether as well. Under different environmental conditions,
the transmission dip remains a high rejection ratio of around B. Experimental Modeling and Testing Results
50 dB, which is over 47 dB larger than the ER of the selected As shown in Figures 7-9, for each dataset, each spectrum
SOR shown in Fig. 5(b), showing the constant high-resolution data can be identified by a unique pair of dip frequency and
performance of the MWP interrogation. When any of the two transmission average, which indicates that the spectrum data
measurands varies, the transmission spectrum exhibits clear points in each dataset are unambiguous. The 6-fold cross-
line shape variations, as manifested by the horizontal shifts of validation was adopted to establish and test the CNTK-DL
dip position and the vertical shifts of the transmission average, model that enables the simultaneous sensing of temperature
which is calculated by the sum of the transmission at every and humidity using the collected datasets (Datasets 1-3). In
frequency point in the measured transmission spectrum each 6-fold cross-validation process, the in-use dataset was
divided by the sample length. As the temperature or humidity first permutated and then split into six subsets. One by one, a
level rises, the dip position shifts to the lower frequencies, subset was selected as the test set, and the rest of the subsets
while the overall transmission average moves in an increasing were used as the training sets until all possible combinations
trend. This nonlinear response of transmission average can be were evaluated. In this way, every data point in the dataset
explained by the nonlinear variation of ER, as shown in Eq. was all used as the testing data once. In each validation round,
(2), which constantly changes the average transmitted the MAE between the estimated and ground-truth measurand
intensity of SFS via regulating the DC bias voltage of values were calculated. The hyperparameters of both CNTK
DDMZM according to the matching conditions. and SVR models were determined by-way-of grid search in a
Second, as in Scenario 2, the experiment was conducted range of values based on the resulting MAE values during a
with the same 420 nm-SOR and the same experimental preliminary validation process. The convolutional layer
conditions as in Scenario 1, but with altered laser wavelength number and filter size of the CNTK-DL model were
and power. The obtained dataset is named Dataset 2. Figure 8 determined as 8 and 11, respectively, which indicates a low
compares the spectrum data before and after tunning the laser complexity that is beneficial to mitigating overfitting. To
and the corresponding dip positions and transmission ensure a thorough evaluation, five 6-fold cross-validations
averages. After introducing the laser drift, the high rejection with different initial permutations were performed with each

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22.8 65 22.8 65
CNTK CNTK CNTK CNTK

Temperatures (°C)
Temperatures (°C)

SVR SVR SVR SVR

RH Levels (%RH)
Humidity (%RH)
22.6 Ground truth 55 Ground truth 22.6 Ground truth 55 Ground truth

Estimated
Estimated

Estimated
Estimated
22.4 45 22.4 45

22.2 35 22.2 35
T1 T2 T3 T4 T5 T6 RH1 RH2 RH3 RH4 RH5 RH6 T1 T2 T3 T4 T5 T6 RH1 RH2 RH3 RH4 RH5 RH6
(a) Test temperatures (b) Test RH (a) (b)
0.25 7 0.25 7
CNTK CNTK CNTK CNTK
6 SVR 6 SVR
0.20 SVR SVR 0.20
5

MAE (%RH)
5
MAE (°C)

MAE (°C)
MAE (%RH)
0.15 4 0.15 4
0.10 3 0.10 3
2 2
0.05 0.05
1 1
0 0 0
(c) 1 2 3 4 5 (d) 0 1 2 3 4 5 (c) 1 2 3 4 5 (d) 1 2 3 4 5
5 Cross-validations 5 Cross-validations 5 Cross-validations 5 Cross-validations
Fig. 10. The CNTK-DL model and SVR-ML model were established Fig. 12. The CNTK-DL model and SVR-ML model were established
with Dataset 1, where the median values of the estimation results of with Dataset 3, which has degraded signal quality caused by strong noise,
CNTK-DL (red dots) are located closer to the ground-truth values (black where the median values of estimated (a) temperatures and (b) RH levels
crosses) than that of the SVR-ML model (blue diamonds) at all the by CNTK-DL model (red dots) still show a better precision than that by
experimental (a) temperature and (b) humidity points. The boxplot of SVR-ML model (blue diamonds). The boxplot of MAE of (c)
MAE of (c) temperature and (d) humidity estimations in the five 6-fold temperature and (d) humidity estimations in the five 6-fold cross-
cross-validations further demonstrate the superiority of DL of the entire validations further demonstrate the better robustness and spectrum
spectrum over ML of handcrafted features. The dotted lines indicate the resolving power of the CNTK-DL model than that of the SVR-ML
overall average MAE values. model. The dotted lines indicate the overall average MAE values.

22.8 65 cross-validations demonstrate a more centralized distribution

CNTK CNTK
around small values of around 0.04 °C and 1.30% RH,
Temperatures (°C)

SVR SVR
RH Levels (%RH)

22.6 Ground truth 55 Ground truth respectively, while the MAE of the SVR-ML model fluctuates
Estimated

Estimated

severely in a wide range and results in an overall average

22.4 45 MAE being nearly 3-fold worse than that of CNTK-DL
model. Although the currently achieved estimation
22.2
T1 T2 T3 T4 T5 T6
35
RH1 RH2 RH3 RH4 RH5 RH6
performance is restricted by the size of the experimental
(a) Test Temperatures (b) Test RH Levels dataset, the superiority of DL of the entire raw spectrum over
0.25 7 the ML of handcrafted spectral features for sensing is
CNTK CNTK
SVR 6 SVR
0.20 pronounced clearly.
MAE (%RH)

5
MAE (°C)

0.15 4
Next, the CNTK-DL and SVR-ML models were
3
established with the combined Dataset 1 and Dataset 2, for the
0.10
2 case where there are strong laser drift interferences. The
0.05
1 estimation results in the same validation process are shown in
(c)
0 1 2 3 4 5 (d)
0 1 2 3 4 5 Fig. 11. The CNTK-DL model continues to demonstrate a
5 Cross-validations 5 Cross-validations considerably better estimation accuracy with the average
Fig. 11. The CNTK-DL model and SVR-ML model were established estimation MAEs around 2.1-fold smaller than that of the
with combined Dataset 1 and Dataset 2 in the presence of laser drift, SVR-ML model. Compared with the performance indicated in
where the median values of estimated (a) temperatures and (b) RH levels
by CNTK-DL model (red dots) are still located in closer proximity to the Fig. 10, the laser drift causes a small deviation to the median
ground truth values (black crosses) than that by SVR-ML model (blue prediction by the CNTK-DL model, indicating the excellent
diamonds). The boxplot of MAE of (c) temperature and (d) humidity resistance of DL-based MWP sensing models to the laser
estimations in the five 6-fold cross-validations further demonstrate the drifts.
resistance of the ML and DL models to the laser drift problem. The
dotted lines indicate the overall average MAE values. Finally, Dataset 3, with a high noise level, was employed
for establishing the CNTK-DL and SVR-ML models to test
CNTK-DL and SVR-ML model. their tolerance to signal degradation. The estimation results are
First, the modeling and testing were carried out with shown in Fig. 12. In this case, the SVR-ML model remains an
Dataset 1. Figure 10 shows the estimation results by the estimation performance similar to that with no additional
established CNTK-DL and SVR-ML models. At every testing interferences. Although the average MAEs of temperature and
temperature and humidity condition point, the median humidity estimation of CNTK-DL increase to around 0.10 °C
estimation values by CNTK-DL are constantly located in and 3.25% RH, respectively, they are still notably smaller than
closer proximity to the ground truth than that of the SVR-ML that of the SVR-ML model. This might be due to the fact that
model, indicating the better estimation accuracy of the CNTK- the automatically extracted high-level features by the CNTK-
DL model. Besides, the total MAEs of the CNTK-DL model DL model contain not only the dip position and power
for the temperature and humidity estimation in the five 6-fold transmission that the SVR-ML model solely relies on but also

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other hidden features which can benefit the estimation but are complexity in hardware to combat cross-sensitivity or
now overwhelmed by the strong noise and interfered by the interference is shifted to software using the DL engine.
wide spectrum overlapping. This also suggests that increasing
the size of the training dataset might be beneficial for the DL APPENDIX
model to learn the features in a noisy environment. The higher The ML algorithm of SVR has been demonstrated to
estimation precision of the CNTK-DL model compared with
perform well in small dataset scenarios [34,35,52,53]. For
that of the SVR-ML model, even in the strong noise situation,
example, it outperformed the classification and regression
further indicates the benefit of conducting DL of the raw
spectrum rather than relying on handcrafted features for trees [52] and the multi-layer perceptron neural network [53]
sensing. As DL is a data-driven method capable of learning when the size of the training data was even decreased to below
features automatically, by adopting a deeper neural network thirty-six. The SVR by itself is designed to mitigate overfitting
and training it with a large dataset involving all the possible via choosing a specific hyperplane via the max-margin
environmental interferences, the resulting sensing model criterion towards better model generalization, among many
should achieve a higher capability level and preserve excellent hyperplanes that can separate data in the feature space. To
performance in practical use. further mitigate overfitting for the small experimental datasets,
the soft margin SVR, which allows a trade-off between
V. CONCLUSION maximizing the margin and minimizing the loss, is adopted.
In summary, we have proposed and demonstrated the use of The SVR-ML approach for comparison purposes in the
DL to enable the MWP sensing of more than one measurand experiments is shown in Fig. 13. Unlike the CNTK-DL model
sensing with the minimum requirement on the number of that directly accepts the interrogation results as input, the
optical resonances as well as the design and fabrication of SVR-ML model requires a preliminary procedure to extract
optical microresonators. As a proof-of-concept, the proposed the dip position and the transmission average of each
scheme is implemented in the simultaneous sensing of transmission spectrum from the microwave photonic
temperature and humidity via DL of the MWP interrogation interrogation to constitute its input space. As the extension of
result of a SOR of a PMMA-coated SOI MRR, where the the SVR model in our previous work [34,35], the SVR-ML
CNTK is adopted as the DL model to reduce the demand on model in this work simultaneously predicts the temperature
experimental data. The CNTK-DL model has been established and humidity and no longer needs the DC bias voltages
and further evaluated in the presence of laser wavelength and beyond the interrogation results, since the transmission
power drifts and strong noise, respectively, in comparison average is dominated by the passband transmission off the
with the SVR-ML model, which requires two handcrafted resonance dip region, where the instantaneous transmitted
spectral features as the input. Despite the usage of a small power of the swept frequency signal is subject to the DC bias
dataset in training, the CNTK-DL model consistently voltage of the modulator. The experimental SVR-ML model
outperforms the SVR-ML model, showing better robustness uses radial bias function kernel [54] to make the similarity
with high tolerance on the interference and noise and
comparison between the input vector and the support vectors
demonstrating nearly 2-fold and 3-fold higher accuracy with
in a sufficiently higher dimension, where the support vectors
and without the interference of laser drift, respectively.
are the training samples around the 𝜀 tube [55] that determines
Besides, within the system frequency range, the proposed
sensor can be configured for any other measurand ranges by a linear fitting function. The similarity tolerance is controlled
simply retraining the DL models with the MWP interrogation by 𝛾. The proportion of the number of points outside the 𝜀
results collected in the new target range. With such low tube is adjustable via the regularization parameter, 𝐶. After
complexity in realizing the optical microresonator probe, the being multiplied by learnable weights 𝛼 and 𝛽 , the
proposed MWP sensing scheme paves the way for the comparison results are then summed to be the estimated
realization of cost-effective multi-parameter sensing and temperature and humidity, respectively. In the experiment, the
opens a new avenue for boosting the integrated optical sensing hyperparameters of 𝜀=0.1, 𝐶=10, and 𝛾=2 were determined in
and the development of smart MWP sensors in which the the preliminary validation process and used for the SVR-ML
model.
k (x1, x) α1
Transmission spectrum

ACKNOWLEDGMENT
x β1
T
k (x2, x)
transmission
Photonic waveguide fabrication and scanning electron
(

average
Feature X(1)
extraction
microscopy were conducted at the Research and Prototype
X(2)
dip
αm
RH Foundry, a core research facility at the University of Sydney
)

position
βm
and a part of the Australian National Fabrication Facility. L.
k (xm, x) Li acknowledges the support of Sydney Research Accelerator
Input
vector Kernels Weights Output Fellowship. X. Tian acknowledges the support of Research
Preprocessing SVR-ML model Training Program Scholarships from the University of
Fig. 13. The schematic diagram of the experimental SVR-ML approach Sydney.
that relies on two extracted spectral features to estimate the temperature
(T) and relative humidity (RH).

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