# Broadband Cavity-Enhanced Kerr Comb Spectroscopy on Chip

Andrei Diakonov  Konstantin Khrizman  Eliran Zano  Liron Stern
<EMAIL_ADDRESS>Institute of Applied Physics, The Hebrew
University of Jerusalem, Jerusalem, 91904, Israel

###### Abstract

The broad and equidistant spectrum of frequency combs has had a profound
impact on spectroscopic studies. Particularly, experiments involving the
coupling of frequency combs to cavities have already enabled unprecedented
broadband and sensitive spectroscopy on a single-molecule level. The emergence
of integrated, compact and broadband Kerr-microcombs holds promise to bring
many metrological and spectroscopic studies outside of the lab. However,
performing cavity-enhanced direct frequency comb spectroscopy on-chip has
remained a challenge. Here, we couple a microcomb source with a microcavity to
extend the advantages of cavity-enhanced spectroscopy to photonically
integrated circuits. By harnessing the coherent nature of the Kerr-comb and
high-Q microcavity enhancement, we obtain a detailed dispersion landscape of
the guided-wave mode and comprehensive frequency-dependent cavity lineshapes.
Our microcomb-cavity coupling can facilitate photonically integrated cavity-
enhanced biochemical spectroscopy by evanescently coupling analytes to the
cavity’s guided mode, a mode of operation we analyze and provide guidelines
for. Demonstrated detailed dispersion measurements, overperforming state-of-
the-art table-top tunable lasers in available bandwidth, show potential for
integrated nonlinear optics applications, as precise dispersion management is
crucial for such processes. Our chip-scale comb-cavity coupled platform
suggests an integrated, broadband, cost-effective and accurate tool for the
nonlinear optics studies as well as for ultra-compact bio- and chemical-
sensing platform.

††preprint: APS/123-QED

##  I Introduction

The direct interaction of laser light with different states of matter
constitutes the cornerstone of modern spectroscopic studies. By confining
matter within a cavity, a multitude of important spectroscopic modalities are
made possible, such as enhanced sensing at the single-molecule level [1],
dramatic amplification of optical nonlinearities [2, 3, 4] and the
establishment of strong coupling for coherent energy flow between matter and
the cavity [5]. The advent of optical frequency combs (OFCs) provides a rich
array of spectroscopic tools, presenting a particularly intriguing avenue for
cavity-enhanced measurements. OFCs, consisting of ultra-wideband coherent
spectra in the form of equidistant sharp peaks, have become an essential
metrological tool to bridge the gap between optical and RF frequencies [6],
thus unveiling important applications in timekeeping [7] and frequency
synthesis [8]. The expansion of the utility of OFCs beyond coherent up and
down conversions has allowed them to play a significant role in a multitude of
novel applications such as spectroscopy [9], dimensional metrology [10, 11]
and environmental monitoring [12]. Naturally, OFCs may perfectly complement
cavities leading to the emergence of Cavity-Enhanced Direct Frequency Comb
Spectroscopy [13] (CE-DFCS), which allowed to probe complex molecular
structures with an extremely broad bandwidth and high sensitivity [14],
investigate the kinetics of different radicals [15, 16] and to provide a high-
resolution spectroscopy of gases [17] with a prominent application to human
breath analysis [18]. A further major development that broadens the
capabilities of comb spectroscopy is the use of two combs with offset
repetition rates, known as dual-comb spectroscopy [19]. Essentially, this
multi-heterodyne technique transfers the detection to the radio-frequency
range, allowing for increased acquisition speed and eliminating the need for
an optical spectrum analyzer [20, 21].

Recent years have shown the emergence of the field of integrated photonics,
introducing the manipulation of light on a chip by utilizing various photonic
components, such as waveguides, modulators, and detectors. This approach
promises to revolutionize sensing, data communication and quantum technologies
by enabling high-speed, low-power and compact photonic devices. Central to
these technologies are integrated micro-cavities, enabling unprecedented
levels of field confinement and enhancement, which in turn lead to novel
applications in both sensing and non-linear optics. Various integrated cavity
configurations have been implemented, such as Bragg-mirror based Fabry-Perot
cavities [22], whispering gallery mode (WGM) resonators [23], microring
resonators (MRRs) [24], and even the combination of thereof [25]. Arguably,
one of the most intensively used and investigated platforms to date is SiN MRR
configuration [26] , which benefits from extremely low-loss, wide operational
bandwidth and CMOS-compatible manufacturing process. Indeed, a plethora of
sensing modalities have been demonstrated using integrated silicon-based
micro-resonators, as for example concentration and temperature measurement of
glucose solution [27], iron corrosion sensing [28], and CES with microfluidic
channels [29], to name a few. Owing to to the inherent field enhancement in
optical cavities, the threshold for nonlinearities reduces significantly,
allowing to exploit $\chi^{(3)}$ process within the waveguide. In particular,
Kerr-comb generation may be initiated by a cascaded four-wave mixing process
producing coherent and octave-spanning spectrum [30]. Consequently, microcombs
have already been demonstrated to be extremely versatile in their applications
including ranging [31, 32], sensing and dual-comb spectroscopy [33], optical
clocks [34] and precision atomic spectroscopy [35]. The main challenge for
reaching wideband comb generation and a fully-coherent soliton state is
dispersion engineering [36]. In order to compensate for material non-linearity
through modal dispersion, the geometry of the MRR waveguide must be precisely
adjusted. Simultaneously, the modal dispersion landscape defines the existence
of dispersive waves, required to cover the octave range. This dictates the
necessity for the accurate and broadband dispersion measurement of the cavity.

Here, we demonstrate the coupling of a photonically-integrated microcomb
source with a microring resonator to showcase chip-scale cavity-enhanced
spectroscopy. By doing so, we introduce a universal platform allowing complete
microcomb dispersion characterization and microcomb-cavity enhanced
spectroscopy on-chip. In this study we use two identical MRRs which constitute
the comb and the cavity. Simple thermo-optic tuning of the cavity, probed by a
Kerr microcomb operating in a soliton regime, enabled us to thoroughly
characterize its guided-mode dispersion by providing detailed and broadband
cavity lineshapes and resonance frequency positions. Our results agree well
with comprehensive numerical simulations as well as reference measurements. In
our current demonstration, we were already able to provide a broad bandwidth
of nearly 250 nm. The effective bandwidth measurement obtained is already
highly competitive relative to contemporary table-top tunable laser sources
such as ECDLs and OPOs. Ultimately, our approach can support even larger
bandwidths approaching an octave span. Our demonstration exploits the
coherence and the high-Q of the cavity to allow cavity enhanced spectroscopy
of the guided-wave mode dispersion. By evanescently coupling molecules to the
guided mode, we can extend the spectroscopic approach to allow cavity-enhanced
direct frequency comb spectroscopy (CEDFCS) of anlaytes. In particular, we
numerically investigate the coupling of a microcomb to a water-cladded cavity,
enabling an extremely broad-band, sensitive, and photonic-integrated platform
for sensing. Our microcomb-cavity coupled system address key challenges in
integrated photonics, enabling rapid and precise mapping of the microresonator
dispersion landscape, while concurrently performing broadband resonantly
enhanced spectroscopy. As such, it paves the way for a variety of comb-cavity
experiments and applications in the fields of nonlinear integrated photonics,
as well as environmental and biomedical sensing.

##  II Comb-cavity coupling concept

In this part, we present the concept of photonically-integrated coupling of a
microcomb and a microring resonator. As will be shown and discussed later,
this concept can be simultaneously used for the direct cavity-enhanced
frequency comb evanescent spectroscopy as well as provide an ultra-wideband
measurement platform for thorough microcavity dispersion characterization. Our
conceptual arrangement is schematically depicted in the Fig.1(a).
Operationally, a Kerr-comb spectrum is initiated in the source MRR and
directly coupled to a target MRR. The latter frequency landscape is controlled
by means of thermo-optic effect, which can be routinely controlled by
integrated microheaters. Here, such an effect primarily alters the refractive
index of the constituting MRR materials, thus, shifting the resonance
frequencies. The Kerr-comb acts as a reference frequency source which tracks
the moving resonance transmission dips of the target cavity. As shown in
Fig.1(b) cavity transmission response can be extracted from monitoring the
power of a specific comb line, providing a detailed lineshape data and
consequently revealing the resonance frequency position, line-splitting,
contrast and linewidth. Cavity transmission acts as a filter which is shifting
in response to the temperature change effectively implementing the convolution
operation with respect to the comb signal. Resulting data (Fig.1(c)) naturally
represents the so-called integrated dispersion $D_{int}$ up to a linear term,
which results from a mismatch between the comb repetition rate and cavity free
spectral range (FSR). We can define $D_{int}$ in terms of the resonance
frequency positions with an angular number m
$\omega_{m}=\omega_{0}+D_{1}\mu+\frac{1}{2}D_{2}\mu^{2}+...$ as follows:

$D_{int}=\omega_{m}-\omega_{0}-D_{1}\mu$ (1)

, where $D_{1}/2\pi$ is an FSR of the cavity in Hz, the rest of the terms
define higher-order dispersion and $\mu$ is a longitudinal mode number with
respect to the reference mode $\mu=0$. Our results are acquired through a
continuous thermo-optical scan of the target cavity. Prior this process, we
synchronize the resonant frequency of the target cavity with the microcomb’s
pump frequency by applying a fixed thermal offset. To determine the magnitude
of this temperature offset, we measure the relative frequency position of the
pumped source MRR resonance with respect to the resonance of the target
cavity. This can be achieved by a laser frequency scan around the pump
resonance. Knowing the frequency scan rate and the temperature-to-frequency
resonance shift coefficient of the material, one can calculate the initial
temperature value and subsequent temperature change range for the target
cavity scan. Once calculated, the desired temperature profile is applied to
the target cavity, and the corresponding frequency sweep range is then
deduced. Above a certain power threshold, the resonant lineshape appears as a
triangular-like (often coined ’thermal triangle’) resonance instead of a
Lorentzian one. This is a consequence of a thermo-optic effect supported by
the small mode volume and field enhancement, [37]. Thus, the photodetected
signal of the scanning laser would consist of the source MRR thermal triangle
and a conventional Lorentzian resonance as is shown in Fig.1(a). Simultaneous
presence of the thermal triangle along with the Lorentzian resonance neatly
demonstrates the conceptual coexistence of the non-linear and linear effects
in a comb-cavity coupled system.

Figure 1: Photonically-integrated comb-cavity coupling concept a) Source Kerr-
comb is coupled to either a silicon-dioxide cladded cavity, allowing
waveguide-mode dispersion measurement or to an analyte-cladded cavity allowing
for the evanescent-mediated specimen-light interaction. Heaters are used to
set the appropriate pump wavelength of the comb source and to implement the
temperature sweep of the target cavity. b) Schematic description of the
mechanism: cavity resonances with a certain FSR shift in response to the
temperature change, while the stationary comb with a linespacing of $f_{rep}$
acts as a probe signal. Change in the intensity of a specific comb line,
resulting from the coupling of comb-tooth with a cavity resonance, provide a
complete dispersion data - relative frequency positions of the resonances
along with the corresponding lineshapes. Straight horizontal alignment of the
resonances corresponds to a perfect dispersionless cavity with FSR $=f_{rep}$,
linear one reveals the mismatch between FSR and $f_{rep}$, and parabolic
arrangement indicates a second-order dispersion characterizing group velocity
dispersion.

Repetition rate $f_{rep}$ of the frequency comb defines the even spacing of
the comb lines in the frequency domain, thus, scanning the target cavity
resonances with respect to the stable comb lines results in the partial
subtraction of the linear term defined in 1. In case of a closely matched comb
$f_{rep}$ and cavity FSR the remaining linear term can be negligibly small
which would naturally result in an integrated dispersion data representation
very close to its original definition. For the ideal scenario of a
dispersionless cavity with an FSR precisely matching $f_{rep}$ the measurement
would show the resonance positions perfectly aligned with respect to each
other, which implies that the overlap between the comb lines and corresponding
resonance dips during the shift occurred simultaneously. In case of a mismatch
between a dispersionless FSR and identical $f_{rep}$, linear term would show
up. Second-order dispersion, characterizing the group velocity dispersion
(GVD) for the pulse propagation, would have a parabolic shape with a concavity
defined by the normal or anomalous dispersion character. Analogously, if the
higher-order dispersion is presented, it would be captured by the measurement.
An access to the resonance lineshape data allows to use the aforementioned
setup for implementation of a photonically integrated cavity-enhanced
spectroscopy. Because such a method provides simultaneous information about
$D_{int}$ (real part of the refractive index) as well as the losses (imaginary
part of the refractive index and the resonance contrast) we term it as complex
$D_{int}$ throughout this paper. By exposing the MRR’s top cladding one can
evanescently couple a portion of the circulating light to a material under
investigation for the purpose of cavity-enhanced sensing. For example, liquid
or gas placed in the cladding of the MRR waveguide would alter the effective
refractive index of the transversal mode propagating along the cavity and
simultaneously induce frequency-dependent losses. By comparing the reference
complex $D_{int}$ with the one obtained after adding the material under the
investigation to the sensing cavity, absorption and dispersion spectroscopy
can be implemented. Integrated comb-cavity coupling constitutes a conceptually
universal, broadband and compact platform for cavity-enhanced direct frequency
comb spectroscopy and microcavity studies.

##  III Experimental results

The schematic representation of our experimental setup is illustrated in
Fig.2. To implement comb-cavity coupling we used two SiN chips with identical
design parameters. Yet, owning to manufacturing tolerances, the optical path
differs slightly and consequently the dispersion of the MRRs. The cross-
sectional dimensions have a crucial role in defining the dispersion of the
ring. In our work we targeted an anomalous dispersion that we achieved with
the microring waveguide of 1.55 $\mu$m width and 0.8 $\mu$m height for MRR and
1 $\mu$m width and 0.8 $\mu$m height for bus waveguide, correspondingly. A MRR
radius of 22.5 $\mu$m resulted in approximately a 1 THz separation between the
comb lines.

Figure 2: Chip-to-chip comb-cavity coupling experimental realization a)
Continuously tunable laser (CTL) is amplified by an Erbium-Doped Fiber
Amplifier (EDFA) with an amplified spontaneous emission filtered by a band-
pass Fiber Bragg Grating (FBG) filter. The first polarization controller (PC)
is used then to optimize the pump coupling to the SiN chip for the soliton
generation achieved by a forward-backward tuning of the CTL in the vicinity of
the source MRR resonance. The second PC in conjunction with an in-line
polarizer (IP) is used to eliminate the pump to prevent triggering non-linear
effects in the target cavity. Our target chip is placed on a copper stage with
the attached Peltier element for the temperature sweep, which is controlled by
means of Thermo-Electric Controller (TEC). Resulted comb signal is split for
the detection of the individual comb line power by an Optical Spectrum
Analyzer (OSA) simultaneously with monitoring the chip’s temperature. Another
part of the signal is photodetected for facilitating the soliton generation,
and the last portion is used for detecting the beat between the coherent comb
state and table-top Difference Frequency Comb (DFC). b) Comb coherence
verification by measuring the beat frequency between the comb line and DFC.
Standard deviation of 700 kHz is obtained for the 800 s measurement with a
sub-MHz linewidth.

Precise comb-assisted spectroscopy requires the source to be coherent.
Otherwise, the broad linewidth of comb-teeth [38] as well as their
corresponding jitter can hinder the measurement resolution and degrade the
available signal-to-noise ratio. This requirement can be matched by initiating
a soliton state. To that end, we employed a technique highly reminiscent of a
backward tuning reported by Guo et.al. [39]. Amplified continuously tunable
laser (CTL) was used to generate a multi-soliton state at first, which then
was converted to the single-soliton state by the backward tuning. In our case
no fast forward-tuning was required in order to get a multi-soliton state,
which we attribute to the presence of avoided mode-crossings around the pump
resonance [40]. Fiber Bragg grating (FBG) based band-pass filter was used to
filter out the amplified spontaneous emission of the Erbium-doped fiber
amplifier (EDFA). The first polarization controller (PC) was used to achieve
an optimal coupling of the pump to the chip, while the second PC in
combination with an in-line polarizer allowed us to reduce the pump power to
avoid triggering non-linear effects in the target MRR cavity.

To choose an appropriate temperature scan range and to control the laser
offset during the soliton generation, optical signal was photodetected and
monitored by an oscilloscope. We scanned the laser wavelength to obtain the
transmission signal of the target cavity simultaneously with the thermal
triangle of the source MRR to identify the initial value of the temperature
sweep. In order to verify the coherence of the microcomb we heterodyned an
adjacent line to the pump frequency with a table-top stabilized frequency-comb
line. The resulting beat-note was captured by an electrical spectrum analyzer
(ESA). Sub-MHz linewidth of the beat verifies the coherent nature of the
generated comb state. Fluctuation of the beat frequency during an 800 seconds
measurement did not exceed a peak-to-peak level of 3 MHz with a standard
deviation of approximately 700 kHz. As described in the previous section,
after propagating a comb light through the MRR cavity we initiated the
temperature sweep of the target chip. Target cavity chip was placed on a
copper stage connected to a Peltier element, which in turn was managed by a
thermo-electrical cooler (TEC) controller. An Optical Spectrum Analyzer (OSA)
was used to monitor comb lines power, while simultaneous temperature tracking
of the target chip was obtained using a thermistor. We used an apriori
temperature-to-frequency shift calibration to convert the temperature
measurement data into frequency shift values.

Figure 3: Microcomb enabled complex integrated dispersion of the high-Q MRR
cavity (a) Complex integrated dispersion measurement obtained from micocomb-
cavity coupling and subsequent temperature scan. Each row corresponds to a
specific comb line mode number $\mu$, ordered with respect to the pump (inset
in (b) shows $\mu$ ordering with respect to the comb lines), and represents
the cavity transmission as function of frequency. Light blue dots represent
the raw measurement data with the superimposed (red curves) fitted Lorentzian
lineshapes. (b) Reduced schematic of the setup where initial wide comb is
shown in comparison with the comb state after the propagation through the
target cavity. (c) Real integrated dispersion, extracted from the complex data
(a). The peaks of the split resonance are shown in light and dark orange, and
a single resonance is designated by the combination of thereof. Blue dots show
the result of a FEM simulation for $D_{int}$ with the blue light background
representing uncertainty in the WG dimensions. Inset demonstrates the WG
corss-sectional dimensions along with the basic TE mode intensity acounting on
the waveguide curvature. Wavelength meter measurement is depicted by black
dots and the obtained CTL range is shown (110 nm). (d) Q-factor distribution
extracted from (a) demonstrating the coupling-loss dependent loaded Q-factor
which is a consequence of our point coupling between the bus waveguide and
MRR. Measurement range obtained in the current study exceeds state-of-the-art
CTL range more than twice as much (246 nm).

Figure 3 shows the obtained complex integrated dispersion measurement and its
processing. Our single-shot measurement has the capacity to resolve 31 cavity
lines corresponding to a frequency (wavelength) deviation of 31 THz (246 nm).
Each row in Fig.3(a) is assigned a mode number $\mu$ with respect to the comb
pump mode number $\mu_{p}=0$, where $\mu$ decreases with the increasing
wavelength and increases with respect to the frequency. For clarity we show
the mode numbers related directly to the comb structure used in the experiment
in Fig.3(b). Raw measurements from the temperature scan are shown with light
blue dots with the processed fit data (red curve) on top of that. Apparent
slope in the demonstrated data of Fig.3(a) is due to the frequency-temperature
coefficient (GHz/∘C) frequency-dependent nature, the measurement was
calibrated with respect to it. The initial data in Fig.3(a) was acquired
simultaneously, after which every row was multiplied by a corresponding
frequency dependent temperature-to-frequency conversion coefficient resulting
in the scaling of the y-axis and appearance of the aforementioned slope. From
the complex $D_{int}$ picture we extracted the ordinary $D_{int}$, which
characterizes cavity modes shift with respect to their dispersionless evenly
spaced positions. The dominant parabolic nature of the frequency shifts shown
in Fig.3(b) and their concavity indicate the anomalous dispersion. The second-
order fit integrated dispersion coefficient $D_{2}/2\pi$ was calculated to be
24.8 MHz. To back-up our results we separately measured $D_{int}$ using a
wavelength meter, the result is depicted by black dots in Fig.3(b). It is
instructive to notice that the available measurement range obtained with a
state-of-the-art CTL and a wavelength meter (110 nm) is more than twice as
small as the range provided by the temperature scan (246 nm). We also
emphasize that our setup (Fig.2) was not optimized in terms of the available
comb probe signal bandwidth as we will discuss below. To further verify the
validity of the proposed method we executed numerical simulation by using a
finite-elements-method (FEM) mode solver. The refractive index from the
simulation was used to calculate $D$ coefficients for the integrated
dispersion [41]. The simulated $D_{int}$ (blue dots) is in a good agreement
with the measurements obtained, and the light blue background represents the
uncertainty range caused by manufacturing imperfections ($\pm$ 20 nm variation
in the height and width of the waveguide). The second-order dispersion
coefficient $D_{2}/2\pi$ obtained from the simulation was equal to 31.2 MHz,
which is in a good agreement with the measurement results, given the
uncertainties in refractive indices values, and geometry. Apart from the
frequency positions of the resonances, we are also able to to extract the
quality factors of the corresponding cavity resonances, which is presented in
Fig.3(d). The resulting data demonstrates a low-loss nature of the SiN
waveguide based cavity with Q-factors ranging approximately from 1 up to 2
millions. As a consequence of the the relatively high Q-factors, splitting of
some lineshapes is evident (owning to defects), which we include individually
in the plot. Another interesting feature of the Q-factor distribution is its
increasing trend with the increase of the mode number. We attribute this
behavior to the influence of the frequency-dependent point coupling between
the bus waveguide and the MRR itself, which is consistent with the study of
Moille et.al. [42].

Complex integrated dispersion representation is naturally appealing for the
cavity-enhanced spectroscopy applications. For the case of the integrated
photonic chip platform the sensing cavity can be realized by exposing the
cladding of the target MRR. The evanescently coupled guided wave would be
perturbed in the presence of a specimen such as a gas or liquid, resulting in
a modified frequency-dependent effective refractive index. Comparing the
reference complex $D_{int}$ obtained without the specimen with $D_{int}$
acquired after adding the specimen enables the identification of the spectral
components of the material under investigation.

High-Q cavities used in our experiment provide a potential platform for
dramatic sensitivity enhancement for spectroscopy experiments. Signal-to-noise
ratio improvement due to the presence of the low-loss cavity should be
approximately proportional to its Finesse, which defines the number of
roundtrips the light field would make until its energy would decay to the
$1/e$ with respect to the initial value. To verify this concept in context of
our proposed platform we performed rigours calculations where we used water as
the cladding of our cavity.

Figure 4: Cavity-enhanced comb-cavity water spectroscopy: (a)Schematic
comparison between a single-pass waveguide approach and a cavity-enhanced
approach with a sensing MRR. Here, the waveguide length is $L=2\pi R$, where
$R$ is the MRR radius. In both cases the waveguide upper cladding is exposed,
which allows the specimen to be evanescently coupled to the guided mode. (b)
Real and imaginary part of the $n_{eff}$ obtained from the FEM simulation for
the waveguide with water cladding. (c) Loss coefficient of the water with the
zoom-in view which demonstrates subtle changes on a smaller scale. (d)
Comparison between the sensitivity of the single-pass approach with respect to
MRR enhancing cavity. Only substantial material losses (close to 10$\%$ ) can
be resolved with a single-pass approach with reasonable contrast (i.e. ¿ few
percent) (dark blue curve), while cavity-enhancement (orange) reveals even the
minute changes on the scale less than 0.1$\%$. Blue curve represents the
change of 1$\%$ in water losses which mimics the scenario for biomedical
sensing in liquid medium. (e) Complex $D_{int}$ extracted from the simulation,
where $\mu=0$ corresponds to 1559 nm (same as in our experiment). Much higher
concavity is expected with respect to the data obtained from the in Fig, 3.
Inset shows the dependence of the transmission on the coupling coefficient,
for two cases of loss in the MRRs cladding, which defines the resulting signal
(d) contrast.

MRR cavity transmission can be mathematically represented by the following
equation[43]:

$H(\omega)=|(r-ae^{i\phi})/(1-rae^{i\phi})|^{2},$ (2)

where $r$ is the self-coupling coefficient, $a$ designates cavity losses,
$\phi=n_{eff}(\omega)kL$ is the phase of the waveguide mode with the
wavenumber $k$ and effective refractive index $n_{eff}$ propagating along the
cavity of length $L$. We calculated the $n_{eff}$ for the waveguide dimensions
used in the experiment, but this time the SiO2 cladding was substituted with
the water as is depicted in Fig.4(a). Complex $n_{eff}=n_{r}+in_{i}$ obtained
from the simulation is shown in Fig.4(b). From the imaginary part of $n_{eff}$
we calculated a loss coefficient as $a=\exp(2\pi n_{i}Lf/c)$ that is shown in
Fig.4(b), the inset demonstrates a zoom-in view to emphasize the features
presented at a small scale. Cavity transmission calculated with the Eq.2 using
the losses coefficient obtained from the numerical calculation is shown in
Fig.4(c): orange plot demonstrates the transmission with the initial water
$n_{eff}$ data, while the blue one shows the effect of the $0.1\%$ change in
the absorption coefficient $a$. Induced absorption change in the simulation
mimics the scenario when liquid is used as a mediator between the biological
measurands like for example biomolecules, DNA or RNA and light. This became
especially important in the context of the recent COVID-19 pandemic to develop
a reliable and compact sensor for the virus signature detection [44]. We want
to emphasize that for the presented simulation, we used a fixed value of
$r=0.993$, which, due to the frequency-dependent nature of the loss
coefficient, resulted in critical coupling (zero transmission value) only for
a specific portion of the transmission spectrum. This suggests that bus-ring
coupling can be used as an additional degree of freedom during the design of a
specific sensing device. To show the sensitivity enhancement of the absorption
spectroscopy we also plot the transmission spectrum of the straight waveguide
with length L equal to the MRR’s circumference as a conventional spectroscopy
approach reference. It is clearly seen that the use of cavity allows to
distinguish minute features of the water absorption spectrum, while a single-
pass approach is sensitive only to a huge variations of losses. We also note
that the information about the change in the real part of the refractive index
is merely absent for the case of the waveguide sensing, such a setup should be
supplemented with a form of interferometric subsystem [45, 46] in order to get
an access to it. Quantitatively, we define cavity-enhancement as the ratio
between absorption per unit length in the straight waveguide with respect to
the effective absorption per unit length in MRR, which is a frequency
dependent quantity. Based on the simulation we evaluated the effective
enhancement to be 39 at 150.7 THz (1.99 $\mu$m) and 9200 at 230.6 THz (1.3
$\mu$m) for the two typical cases of a high and small losses. These results
suggest that in case of a small change in the losses the effective enhancement
can reach nearly 4 orders of magnitude, exploiting the high finesse of our
cavity. Fig.4(d) shows the complex $D_{int}$ obtained from the simulation for
the same mode numbers $\mu$ that were used in the experiment. In the presence
of water, the concavity of the second-order dispersion is significantly
increased with respect to the oxide cladding target MRR cavity (Fig.3(a)), but
the measurement can still be easily realized with a temperature scan of
approximately 10${}^{\circ}C$ . To highlight the importance of the coupling
the inset of Fig.4(d) shows the cavity transmission as a function of coupling
coefficient $r$. The mismatch between losses and coupling is the discriminator
mechanism responsible for the contrast change in response to the change in the
losses. We also note that our simulation does not account for a frequency-
dependent coupling coefficient , which can compensated by using pulley
coupling [42]. Consequently, broadening of the resonances presented in
Fig.4(d) and change in the contrast are a direct consequence of the losses.

##  IV Discussion

Our demonstration marks a significant advancement towards both lab-based and
out-of-the lab applications. However, in our current setup, the acquisition
and characterization of broadband optical signals was obtained by using of a
table-top, large, and non-integrated OSA, hindering the realization of a fully
integrated sensor. While chip-scale spectrometers are a prominent filed of
research, the coherence of our microcomb suggests the adoption of a dual-comb
approach. This method facilitates the conversion of the spectrum and
spectroscopic information from the optical to radio-frequency domain, enabling
rapid measurement of the entire spectrum. Dual-comb setups with microcombs
have been successfully implemented [19], offering a scalable and integrable
solution for broadband detection. Alternatively, a viable, albeit more complex
solution, involves using wavelength-division-multiplexer (WDM) filters
combined with an array of photodetectors to split the comb signal into
separate lines and track them simultaneously.

In our experiment, we utilize identically designed THz-rate MRRs for both comb
generation and cavity analysis, facilitating broadband microcomb-MRR coupling
with a modest thermo-optic scan range. However, certain sensing scenarios or
photonic dispersion characterizations may necessitate finer resolution.
Therefore, a more general approach for MRRs of larger radii would be
advantageous. Lower FSRs and repetition rates at the GHz rate could
potentially enable continuous and simultaneous scanning of our target MRR and
microcomb, allowing for gap-less scanning of the entire microcomb spectrum.
Achieving this would require establishing the capability to scan the
microcomb’s frequency offset whilst maintaining a known measurable repetition
rate. Additionally, it would be intriguing to explore the possibility of using
two MRRs with different radii. In such a scenario, for example, we can
leverage the established extreme broadband nature of THz-rate microcombs to
measure the dispersion of microcavities with much smaller FSRs (tens and
hundreds of GHz), up to the possibility of directly observing zero $D_{int}$
points responsible for dispersion wave generation. Even a relatively sparse
THz microcomb frequency grid should be enough to reliably extract smoothly
varying dispersion of a GHz-rate microcavities.

Finally, we note that our demonstrated experiment implemented with two
separate photonic chips can be straightforwardly integrated onto a single
chip, offering a fully integrated solution for microcomb-based cavity-enhanced
spectroscopy. Such an integration can also provide a wider characterization
bandwidth, eliminating the influence of fiber chip-to-chip interconnects.

##  V Conclusion

In conclusion, we have proposed and demonstrated the universal photonically-
integrated platform based on the microcomb-microcavity coupling, which enables
simultaneous investigation of microcavity dispersion and on-chip cavity-
enhanced direct frequency comb spectroscopy of molecules. Both comb source and
target cavity were implemented using identically designed SiN MRRs. We
performed a detailed MRR dispersion characterization by a single-shot
temperature scan that outperformed conventional tunable laser source
approaches providing a wide bandwidth of 250 nm. Numerical simulations as well
as measurement by aid of a wavelength meter (albeit, smaller bandwidth)
confirmed the reliability of the proposed method. Our measurements provided
access to information not only about the cavity resonance positions but also
about their lineshapes. Thus, we termed the resulting data representation as
complex integrated dispersion. Combination of the comb source and a high-Q
cavity along with the complex integrated dispersion representation naturally
suggests to use such a system for a cavity-enhanced evanescent spectroscopy.
We performed a numerical simulation to demonstrate the expected enhancement of
our system, which we evaluated to be at least few dozens in case of a severe
losses of the order of 10$\%$ and up to $10^{4}$ for small losses of the order
of 0.01$\%$. Finally, we discussed the apparent limitations of the proposed
system and strategies to overcome them. Our study provides a valuable basis
for the design and investigation of the MRRs for nonlinear optics applications
like soliton or OPO generation, as well as offers a clear path for the
implementation of an ultra-compact chip-scale cavity-enhanced spectrometer for
biomedical, food-safety [47] and environmental sensing applications.

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