# High-contrast grating resonator supported quasi-BIC lasing and gas sensing

Haoran Zhang1,2, Tao<EMAIL_ADDRESS>Jiacheng Sun1,3, Shaoxian
Li1,2, Israel De Leon4, Remo Proietti Zaccaria5, Liang Peng1,2, Fei Gao6, Xiao
Lin6, Hongsheng<EMAIL_ADDRESS>GaoFeng
<EMAIL_ADDRESS>1Engineering Research Center of Smart
Microsensors and Microsystems of MOE, Hangzhou Dianzi University, Hangzhou,
310018, China  2School of Electronics and Information, Hangzhou Dianzi
University, Hangzhou, 310018, China  3School of Zhuoyue Honors, Hangzhou
Dianzi University, Hangzhou, 310018, China  4School of Engineering and
Sciences, Tecnológico de Monterrey, Monterrey, Nuevo León 64849, Mexico  5Cixi
Institute of Biomedical Engineering, Ningbo Institute of Materials Technology
and Engineering, Chinese Academy of Sciences; Italian Institute of Technology
via Morego 30, 16163 Genova, Italy  6Interdisciplinary Center for Quantum
Information, College of Information Science and Electronic Engineering,
Zhejiang University, Hangzhou 310027, China

###### Abstract

In this work, we propose and numerically investigate a new kind of two-
dimensional microcavity resonator, consisting of an organic Rhodamine 6G doped
SiO2 thin layer sandwiched between two symmetric high-contrast-grating (HCG)
layers. The larger periodic-index-contrast from the grating enables an ultra-
high (99$\%$) reflectivity over a broad spectrum. Meanwhile, the so called
bound states in continuum (BIC) are supported when the light in the guided
modes interfere destructively with Fabry-Perot modes. Upon a proper choice of
topological parameters, a quasi-BIC lasing with emission wavelength at 570 nm
is realized. The ultracompact laser exhibits very low threshold (pump fluence
of 17 $\mu$J/cm2), and very narrow optical spectrum linewidth. Moreover, it
displays distinguished sensing performance for gas detection. The emission
wavelength sensitively shifts to the longer wavelength with the changing of
environment refractive index (in order of $5\times 10^{-4}$). The achieved
bulk sensitivity is 221 nm/RIU with a high signal to noise ratio, and a
record-high figure of merit (FOM) reaches to 4420 RIU-1. This ultracompact and
low threshold characteristics of quasi-BIC laser facilitated by the ultra-
narrow resonance can serve as formidable candidate for on-chip gas sensor.

##  I Introduction

In recent years, the investigation of bound states in the continuum (BICs) has
attracted substantial attention due to the interesting physics and practical
applications Joseph2021 . The BIC theory originated from quantum mechanics and
was firstly proposed by von Neumann and Wigner in 1929 Neumann1929 ; Han2019 .
Since then, it has been used to explain the important physical concept of
destructive interference in various physical systems, such as photonics
Marinica2008 ; Hsu2013 ; Dong2021 ; Tang2021 , acoustics Lyapina2015 ;
Xiao2017  and water waves Linton2007 . According to Neumann and Wigner’s
seminal work Neumann1929 , when two resonances pass each other as a function
of a continuous parameter, the two channels will interfere, and give rise to
an avoided crossing for their resonances. Theoretically, at a given value of
the continuous parameter, one of the channels vanishes entirely and hence
becomes a dark mode (BIC mode) with an infinite quality $Q$ factor Azzam2018 .
In practice, BICs are limited by a finite structure size, material absorption,
and structural imperfection Koshelev2020 , they manifest themselves and
collapse to Fano resonant states with long lifetime, also known as quasi-BICs
Hsu2016 ; Sadrieva2017 . Recently, high-$Q$ quasi-BICs have been observed in
many passive systems, and it has been recognized that practical systems
supporting such resonances are well suited for lasing and sensing applications
Kodigala2017 ; Ha2018 .

Sub-wavelength high-contrast gratings (HCGs) possess distinct features, such
as broadband high reflectivity ($>99\%$) and high $Q$ resonances ($>10^{7}$)
Karagodsky2012 . In particular, In particular, it has been shown that HCG
systems can support symmetry-protected BICs with improved spectral performance
Joseph2021 ; Lee2020 . The narrow spectral linewidths ($\gamma$) featured by
these structures are quite sensitive to changes in refractive index around
them Maksimov2020 , making them promising candidates for engineering optical
sensors with high sensitivity ($S$) and excellent figure of merit, FOM=
$S/\gamma$ Romano2018 . Thus, photonic structures supporting high-$Q$ quasi-
BICs are of great interest in sensing applications, as they could offer
possibilities of achieving a sensing performance beyond that of more
conventional photonic sensors Yesilkoy2019 ; Liu2017 .

In this work, we propose an innovative resonator composed of highly reflecting
HCG layers surrounding a thin organic-dye-doped SiO2 layer working as gain
material for laser emission. This ultracompact resonator design not only opens
an alternative route to generate symmetry-protected resonance modes, but also
provides a platform to demonstrate a quasi-BIC laser by combining organic dye
molecules with inorganic grating. Finite difference-time-domain (FDTD)
numerical simulations have been performed to evaluate the performance of the
aforementioned system with the results suggesting that a high-$Q$ quasi-BIC
mode ($Q>10^{4}$) can be established by carefully optimizing the HCG
structural parameters. Then, when the quasi-BIC mode spectrum overlaps with
that of the gain material, a pronounced lasing action is obtained. This
lasing, resulting from the high-$Q$ quasi-BIC resonance generated within the
structure, allows for a highly precise environment change detection through
the reading of the emission wavelength shift. The achieved narrow linewidth (
0.05 nm) combined with a large bulk sensitivity of 221 nm/RIU, results in a
FOM of 4420 RIU-1, which is approximately 20 times larger than typical passive
sensors Maleki2020 . Our results indicate that the proposed quasi-BIC active
sensor offer great potential for optical sensing of gases in low-
concentrations.

##  II Resonator design and numerical model

###  II.1 Structure design

The schematic diagram of proposed HCG resonant structure is shown in Fig. 1.
The structure is designed to support a resonance at a wavelength of 570 nm.
The active region consists of 215 nm thick SiO2 layer doped with Rhodamine 6G
(R6G), as shown in Fig. 1(a). A similar gain medium has been reported in a
previous work Anedda2005 . The R6G layer is surrounded by Si3N4 stripes with a
symmetric arrangement along $z$ direction, and its refractive index is 2.0.
The HCG parameters are described by the thickness of grating layer is $T$,
filling factor (the grating width divided by the period) $F$ and the period
$\Lambda$. For the whole device, as exhibited in Fig. 1(b), we consider the
dimension in $x$\- and $y$-direction are infinite. The detail parameters are
shown in Table 1.

Figure 1: The schematic of proposed resonator based on HCGs: (a) single unit
cell of two dimensional resonator; (b) whole structure with the organic R6G
thin layer. The green downward arrow represents optical pump, the reseda
arrows on both sides of resonator are emitted light from the resonator. GMR
indicates the guided mode resonance, and FPR means Fabry-Perot resonance.

###  II.2 Theory and simulation

A semi quantum framework is adopted to simulate the interaction between the
electromagnetic fields and gain medium. The organic dye molecules in this work
are well described as a four-energy-level system, and the population inversion
is generated between the electronic level of $L_{2}$ state and $L_{1}$ state.
As shown in Fig. 2, which presents the population dynamics of the four
relevant electronic levels of the molecule, such as the ground state, $L_{0}$,
and the three excited states, $L_{1}$, $L_{2}$, and $L_{3}$. The molecular
polarization given by spontaneous and stimulated transitions are described
through the following equation Zhong2013 :

Figure 2: Energy level diagram and parameters used for modelling the dye
molecules in FDTD simulations. The transition energies are
$E_{30}=E_{3}-E_{0}$ and $E_{21}=E_{2}-E_{1}$. Since the transition from
$L_{3}$ to $L_{2}$ is much faster than the transition from $L_{3}$ to $L_{0}$,
the excitation quickly decay to $L_{2}$, leading to a population inversion for
the transition from $L_{2}$ to $L_{1}$.

$\displaystyle\frac{d^{2}\overrightarrow{P}_{i,j}}{dt^{2}}+\Delta\omega_{i,j}\frac{d\overrightarrow{P}_{i,j}}{dt}+\omega^{2}_{i,j}\overrightarrow{P}_{i,j}=\kappa_{(i,j)}\Delta
N_{i,j}(t)\overrightarrow{E}(t)$ (1)

where $\Delta\omega_{i,j}$ and $\omega_{i,j}$ are the bandwidth and frequency
of the transition between states $i$ and $j$,
$\kappa_{i,j}=6\pi\varepsilon_{0}c^{3}/(\omega^{2}_{i,j}\cdot\tau_{i,j})$,
$\tau_{i,j}$ represents the lifetime of the spontaneous emission. $\Delta
N_{i,j}(t)$ is the difference of population density between two energy states
of the interest. $\overrightarrow{E}(t)$ is the total electric field, and can
be calculated by solving the curl Maxwell equations Dridi2013 :

$\displaystyle\nabla\times\overrightarrow{E}(t)=-\mu_{0}\frac{\partial\overrightarrow{H}(t)}{dt}\,,$
(2)
$\displaystyle\nabla\times\overrightarrow{H}(t)=\varepsilon\frac{\partial\overrightarrow{E}(t)}{\partial
t}+\frac{\partial(\overrightarrow{P}_{30}(t)+\overrightarrow{P}_{21}(t))}{\partial
t}$ (3)

In order to solve for the fields in a self-consistent fashion, it is necessary
to couple the molecular polarization $\overrightarrow{P}_{i,j}$ to the
electromagnetic fields via the rate equations of the four-level system
describing the gain medium Trivedi2017 . Such rate equations describe the time
evolution of the energy states’ population densities, and are give by Ref.
Zhou2013 . The time evolution of each energy state density is described by
their respective spontaneous decay processes $N_{i}/(\tau_{i,j})$ and
stimulated processes ($\overrightarrow{E}(t)\cdot
d\overrightarrow{P}_{i,j}/dt$). The field involved in the rate equations is
the total field and accounts for the effects of any local optical intensity on
the dynamics of the population densities.

The FDTD technique is adopted to solve the coupled equations. For the case of
R6G-doped SiO2, we set that the absorption transition: $\lambda_{a}$ = 512 nm
and $\Delta\lambda_{a}=35$ nm; the emission transition: $\lambda_{e}=570$ nm
and $\Delta\lambda_{e}=50$ nm; the concentration of dye molecule: $C=1\times
10^{19}$ cm-3, which is comparable to the concentrations previously reported
in the same material host Anedda2005 ; and the lifetimes:
$\tau_{32}=\tau_{10}=5\times 10^{-14}$s, $\tau_{30}=1\times 10^{-9}$ s,
$\tau_{21}=1.8\times 10^{-9}$ s. Finally, the calculated emission cross
section is around 3 $\times$ 10-16 cm2, which is also consistent with the
experimental report Grossmann2010 .

##  III Bound states in the continuum and quasi-BIC lasing

###  III.1 BIC modes supported by the passive structure

First, we analyze the optical properties of the single HCG layer. For this, we
carry out FDTD simulations and calculate the structure’s reflectance, for a
normally incident planewave polarized along the y-direction. Fig. 3(a)
illustrates the results of our simulations as a function of the wavelength and
of the grating thickness, taking a grating filling fraction F = 0.5. We
observe two regions, which we refer to as the dual/multi-mode region (from
$\lambda$ = 530 nm to 700 nm) and the single-mode region ($\lambda>700$ nm),
as suggested by previous nomenclature Hasnain2012 . For the single mode
region, the grating operates in a longer wavelength regime, behaving like a
quasi-uniform layer Karagodsky2012 , so only Fabry-Perot modes are supported
in this wavelength range. On the other hand, in the dual/multi-modes region,
the pattern is quite different, describing contrasting regions with high
($>99\%$) and low reflectance. In addition, we find the localized patterns
don’t change in an obvious manner when modify the filling factor $F$, instead,
just a wholly shifting to the longer wavelength. The reflectance spectrum
shown in Fig. 3(a) reveals that with a proper selection of the grating
parameters (e.g. the thickness $T$, filling factor $F$ and period $\Lambda$),
an ultra-high ($>99\%$) reflectivity over a spectral range can be achievable
(as shown by the double arrow line). Fig. 3(b) shows the corresponding
reflection spectrum calculated by setting $F$ = 0.50, $\Lambda$ = 530 nm, and
$T$ = 230 nm.

Figure 3: (a) Reflectance spectra mapping as a function of grating thickness
when the filling factor $F$ = 0.50; (b) calculated reflectance spectrum of
single grating layer by using $F$ = 0.50, $\Lambda$ = 530 nm, and $T$ = 230
nm.

The optical characteristics of the structure composed of two HCGs sandwiched
by a thin SiO2 layer is investigated by varying the angle of incidence
($\theta$, from -25∘ to 25∘) with respect to the $z$-axis. As shown in Fig.
4(a), we observe symmetric patterns relative to the axis of $\theta$ = 0∘
(also $\Gamma$ point) and the disappearance of resonance features at discrete
points of $\theta$ = 0∘ (positions marked by ‘1’, ‘2’, and ‘3’) and 14.8∘
(marked by ‘4’). Those vanishing linewidths suggest a non-leaky bound state
within the continuous spectrum of radiating waves Marinica2008 . Fig. 4(b)
presents the field distribution profiles in ($x$, $z$)-plane at discrete
points (incident angle $\theta$ = 0∘), which indicate the dark mode feature of
BICs. For instance, the $E_{y}$ distribution of mode 2 over the
($x$,$z$)-plane shows two radiators with equal amplitude but opposite phase at
the top interface, canceling the upward out-of-plane radiation. Similarly, the
two radiators at the bottom interface cancel the downward out-of-plane
radiation. Hence, mode 2 is a symmetry-protected BIC, as the out of plane
radiation vanishes due to the intrinsic symmetry Hsu2016 . By using the same
analysis, we can recognize the mode 1 and mode 3 also as symmetry-protected
BICs. The mode 4 located off the $\Gamma$ point (also above the light line) is
classified as Friedrich-Wintgen BIC Azzam2018 , which is caused by the
destructive interference of resonances at the correct phase-matching
conditions Friedrich1985 .

To confirm the existence of BICs, we investigate the reflectance spectra
properties of the structure with illumination at 0∘ and 14.8∘ (black curves in
Fig. 4(c) and (d)), respectively. No modes are observed at the marked spectral
positions, except the mode 2 around $\sim$ 566 nm. Then, when the incident
angle is tilted by 2∘, distinct narrow peaks appears at the positions of mode
1, mode 3 and mode 4 (see red curves). Meanwhile, we find mode 2 shows an
enhancement by using this oblique illumination. The large difference obtained
by a small angle shifting indicates the unique feature of BIC — resonance
singularity above light line, thus the BIC with infinite $Q$ factor cannot be
directly observed at the correct incidence wavevector. However, sharp spectral
feature with narrow linewidth can distinctly appear near the BIC (shift the
incidence by a small angle). Indeed near the BIC, the resonance spectrum
exhibits a asymmetric Fano line shape, but is collapses at the breaking point.
Therefore, the distinct spectral features offer another confirmation for the
BICs of mode 1, mode 3 and mode 4.

BICs have been found in various photonic structures Marinica2008 ; Hsu2013 ;
Joseph2021 ; Bulgakov2008 ; Timofeev2018 ; Plotnik2011 ; Molina2012 , and the
mechanisms leading to BICs have been extensively discussed. Here, the
formation of BICs at $\Gamma$ point can refer to a destructive interference
between two radiating channels with different optical behaviour — the FP modes
and guided modes within this specific spectral domain, which contribute to the
generation of dark modes. For the Friedrich-Wintgen BIC at off-$\Gamma$ point,
we consider that it is mainly caused by the destructive interference between
higher order FP mode and guided resonance mode. In principle, two HCG layers
are considered as a pair of perfect mirrors, the transmission and resonant
radiation in $z$-direction can destructively interfere when the spacing
between HCG layers is satisfied a certain condition, making the round-trip
phase shifts add up to an integer multiple of 2$\pi$ Fan2003 . Consequently,
Fano resonance collapses to a Friedrich-Wintgen BIC state.

Figure 4: (a) Resultant reflectance contour distribution of the architecture
by sweeping the incident angle from -25∘ to 25∘; (b) electric field
distribution profiles corresponding to the places marked by ‘1’, ‘2’, ‘3’ and
‘4’, respectively; (c) reflection spectra of resonator when the incident angle
is 0∘ and 2∘; (d) reflection spectra of resonator when the incident angle is
14.8∘ and 16.8∘; (e) evolution of the quasi-BIC mode with incident angles; (f)
angular dependence of $Q$-factor of the quasi-BIC mode.

Closer investigation of mode 2 reveals that there is a broad frequency
dispersion over the range of momentum around 566 nm, which indicates the
quasi-BIC feature and strong resonance in individual unit cell Taghizadeh2017
. Fig. 4(e) presents the evolution of quasi-BIC mode with incident angle, it
is clear to find that the spectrum reaches a minimum intensity value at 0∘,
then the Fano resonance featured spectrum becomes broader and larger at
off-$\Gamma$ positions. To evaluate the performance of observed the quasi-BIC
at 566 nm, we calculated the quality factor of the resonance mode at $\lambda$
position by using the formula $Q=\lambda/\Delta\lambda$, where $\Delta\lambda$
is the full width at half maximum (FWHM) of the spectrum. Fig. 4(f) shows the
calculated $Q$-factor of the quasi-BIC mode obtained by sweeping the incidence
angle. It is evident from the figure that the $Q$-factor of the mode reaches
to 2 $\times$ 104 at $\Gamma$ point, and this finite number further presents
the property of quasi-BIC. The high-$Q$ resonance enables the compact
resonator to realize lasing over a large area in a single mode.

To further investigate the influences of structural parameters on the
formation of BICs with normal incidence, we plot the reflectance spectra for
the resonator with varied HCGs ($T$, Fig. 5(a)) and SiO2 layer thicknesses
($T_{S}$, Fig. 5(b)), respectively. We find both of these two parameters play
significant impact on the formation of BICs, and they only can be created when
some certain conditions are satisfied. In detail, when we set the thickness of
SiO2 layer to be 215 nm and change HCGs’ thicknesses (Fig. 5(a)), the
corresponding BIC around 566 nm is observed when $T=230$ nm, which appears on
the boundary between two high-transmission channels. Additional BICs around
612 and 660 nm are also recognized when $T=$ 170 and 410 nm, respectively.
These BICs exhibit similar formation mechanism, but locate at different
frequency positions. Then, when $T$ is kept at 230 nm and $T_{S}$ is variable
(Fig. 5(b)), the discussed BIC around 566 nm is confirmed when $T_{S}=215$ nm.
It is worthy to note that such BIC presents periodical repetition (period
thickness $T_{P}=195$ nm) through increasing $T_{S}$, favoring the BIC
engineering and device fabrication. Another BIC around 750 nm is observed when
$T_{S}=565$ nm. Therefore, we conclude that the refractive index symmetry
environment support the generation of SP-BIC, different BICs can appear by
changing the thicknesses of HCGs; Changing the thickness of central SiO2 layer
leads to the modification of the phase shift between two radiation channels,
thus favoring the periodical appearance of the supported BIC.

Figure 5: Reflectance spectra as a function of the thickness of HCGs and SiO2,
respectively: (a) with varied HCGs thickness; (b) with varied SiO2 thickness.

###  III.2 Quasi-BIC lasing and characterization

To realize quasi-BIC lasing, we selected the grating parameters ($T$ = 230 nm,
$F$ = 0.50, and $\Lambda$ = 530 nm) which can provide the highest possible
reflectivity (as marked in Fig. 3), and the SiO2 thickness is 215 nm. Then,
R6G dye molecules are doped into SiO2 thin layer to compensated the internal
losses of resonator. As shown in Fig. 1(b), the proposed sandwiched structure
recalls conventional VCSELs, however our design significantly reduces the
cavity length. Fig. 6(a) shows the gain spectrum of R6G (black curve), the
spectrum of the cavity mode (blue curve) and typical lasing spectrum of
resonator (red curve). Clearly, the R6G gain spectrum has a broad linewidth
with its central region overlapping with the cavity mode peak, a feature
guaranteeing a proper compensation of the cavity losses. Interestingly, the
cavity mode shows the typical asymmetric line shape of a Fano resonance. This
Fano resonance is caused by the interference of radiative (bright) and non-
radiative (dark) modes Limonov2017 ; Heo2019 . For Si3N4-based HCG resonator,
dark mode is associated with the Bragg scattering induced by HCG in the
lateral direction, which results in a resonant mode with narrow bandwidth. On
the other hand, the bright mode is associated with the weak Fabry-Perot mode
induced by the index difference in the vertical direction, which results in a
mode with nearly flat-band spectrum. The interference of these two modes
result in an asymmetric line shape of the spectrum Zhou2009 ; Wu2013 .
Moreover, this phenomenon could confine the optical mode in the structure well
and result in a high Q factor, which is beneficial for the BIC laser operation
with very narrow linewidth (red curve).

Fig. 6(b) shows the detail characterizations of lasing behaviour. The black
curve is the conventional plot of output power as a function of pump energy
density, so we can estimate the threshold is around 17 $\mu$J/cm2. The blue
curve represents the corresponding optical spectrum linewidth changing, The
sharp narrowing of spectrum also indicates a coherence emission is achieved
when the laser is operated above threshold. Both of two kinds of
characterizations indicate the BIC laser has been successfully demonstrated.

Fig. 6(c) and (d) are the electric field intensity distributions of resonator
in ($x$, $y$) and ($x$, $z$) planes, respectively. When the resonator is
operated above threshold, a large mode overlaps with the input pump
contributing to a simple and efficient coupling of the input light, as
suggested by the high intensity interfere fringes. From the side view (Fig.
6(d)), it is clear how the light is confined predominantly within the grating
bars and there is exactly one intensity lobe within the interval of
neighbouring bars. In the middle, higher intensity stripe indicates the gain
medium region, where we can find the vertical confinement of this device is
much stronger than the confinement typically found in conventional DBRs-based
vertical cavity emitting lasers. Since the double gratings provide the largest
power reflectance, all diffraction orders disappear except the 0th order. In
addition, the HCGs bring a higher effective refraction index and much higher
than the surrounding environment, leading to strong lateral confinement for
the lateral modes.

Figure 6: (a) Gain spectrum of R6G (black curve), cavity mode spectrum (blue
curve), and typical emission spectrum of laser (red curve) operated above
threshold; (b) input-out function curve (black) and spectrum linewidth
changing as a function of input energy (blue); (c) electric field intensity
distribution of laser emission in ($x$, $y$) plane; (d) electric field
intensity distribution in ($x$, $z$) plane.

##  IV Sensing function for gas detection

High-$Q$ resonators with narrow resonance line widths and long photon storage
time, have been considered as ideal candidates for sensors with enhanced
detection sensitivity Armani2003 ; Zhu2010 . Therefore, we carry out
quantitative calculations of the quasi-BIC laser intrinsic sensitivity upon
changes of the surrounding refractive index. We first reproduced a gas
environment and immersed the resonator in a atmosphere of known refractive
index value, performing then a refractive index change from 1.0000 to 1.0020.
Fig. 7(a) displays the full lasing spectra of the device vs. variation of
refractive index, where it is easily observe a shift of the emission
wavelength towards a longer wavelengths, even though the refractive index
increase step was just of the order of 5 $\times$ 10-4. The inset exhibits the
laser spectra upon change of the gas environment, where we notice a single
wavelength shifting without any other obvious changing. This also can be found
from Fig. 7(b), which presents the linear dependence of emission peaks on the
refractive index (black curve), and the linewidth variation (dash curve). It
is further confirmed that the change of refractive index results in only the
shift of lasing wavelength without affecting the lasing state. This simple
linear relationship between lasing wavelength shift and the variation of
environment confirms the sensing capability of the proposed microlaser
structure.

Specifically, the sensing performance of the device was evaluated by
estimating the sensitivity ($S_{\lambda}$) and figure of merit
($FOM_{\lambda}$), which can be calculated through using the following
formulas:

$\displaystyle S_{\lambda}=\frac{\Delta\lambda}{\Delta n}\,,$ (4)
$\displaystyle FOM_{\lambda}=\frac{S_{\lambda}}{\gamma}\,$ (5)

where $\Delta\lambda$ represents the emission wavelength shifting, and
$\Delta$n is the change of refractive index. $\gamma$ is the emission spectrum
linewidth measured at it full width at half maximum. FOM parameter is another
important and more comprehensive benchmark to evaluate sensing performance
Zhou2019 ; Huang2016 . From the results in Fig. 7(b), we calculated the
$S_{\lambda}$ and $FOM_{\lambda}$, which are 221 nm/RIU and 4420 RIU-1,
respectively. Very importantly, the achieved FOM value resulted much higher
than the theoretical result for localized surface plasmon resonance (LSPR)
sensors ($\sim$ 20) Bingham2010 , photonic crystal (PhC) cavity Liu2017 ,
microring Yen2006  and fiber Bragg grating (FBG) sensors Li2019 . It is also
comparable with that of state-of-the-art symmetry guided-mode resonance based
sensors Zhou2019 . In addition, the organic gain enabled laser design leads to
a coherent light source, which can either be detected at optical far field, or
be easily coupled into fiber system. Thus, this flexible operation will
facilitate the experimental measurements. In addition, the simple structure
design will effectively reduce the cost of fabrication, making the sensor more
appealing.

Figure 7: (a) Mapping of emission wavelength shift with the variation of
environment refractive index, inset: full lasing spectra for different
refractive indexes; (b) linear relationship between emission wavelength shift
and environment refractive index (black curve), and the corresponding spectrum
linewidth changing with refractive index.

##  V Conclusion

In conclusion, we have presented the design and numerical characterization of
a compact quasi-BIC-laser based sensor for detecting of gas environment
changing. The sensor is designed by using double Si3N4 HCG grating layers and
organic R6G dye molecule doped SiO2 layer located between the grating layers.
The proposed unique hybrid design enables stimulated vertical emission from
the organic gain medium embedded in the HCG stripes. Optimizations concerning
HCGs and microcavity configuration designed for a 570 nm resonant wavelength
have been performed. Our design features a high-Q resonance, which enables a
narrow-linewidth laser emission of 0.05 nm. Therefore, a pronounced lasing
behaviour with narrow spectrum linewidth have been realized. The emitted light
is close to the plane wave in air, which indicates a single lobe far field
pattern for laser beam distribution. The sensing mechanism can be reasonably
explained through the guided-mode resonance effect originated by constructive
interference between the guided modes of the slab grating and the strong
reflection modes. Finally, we also investigated the bulk sensing performance
by inserting the device in some specific environment with different refractive
index values, demonstrating remarkable sensitivity and figure of merit
estimated equal to 221 nm/RIU and 4420 RIU-1, respectively. Especially the
figure of merit value outperforms recently reported GRM devices Wan2017 ;
Zhou2019  and other state-of-the-art passive sensors Liu2017 . In view of
these achievements, it is believed that this new platform could improve the
current technology in remote gas sensing, e.g. warning from dangerous chemical
gas.

## Acknowledgment

We are grateful to Prof. Yang Li from Tsinghua University for useful
discussions. T. Wang acknowledges financial support from the National Natural
Science Foundation of China (Grant No. 61804036) and Zhejiang Province
Commonweal Project (Grant No. LGJ20A040001). I. De Leon acknowledges the
support of the Federico Baur Endowed Chair in Nanotechnology. L. Peng thank
the support from the Natural Science Foundation of China (Grant No. 61875051)
and Zhejiang Province Natural Science Foundation (LR21F010002). F. Gao thank
the support from the Natural Science Foundation of China (Grant No. 61801426)
and Zhejiang Provincial Natural Science Foundation (Grant No. Z20F010018). X.
Lin thank the support from the Fundamental Research Funds for the Central
Universities and Zhejiang University Global Partnership Fund.

## Conflict of Interest

The authors declare no conflict of interest.

## References

  * (1) S. Joseph, S. Sarkar, S. Khan, and J. Joseph, “Exploring the optical bound state in the continuum in a dielectric grating coupled plasmonic hybrid system”, Adv. Opt. Mater., DOI: 10.1002/adom.202001895. (2021).
  * (2) J. von Neumann and E. Wigner, “On the behavior of eigenvalues in adiabatic processes,” Phys. Z., 30, 467 (1929).
  * (3) S. Han, L. Cong, Y. K. Srivastava, B. Qiang, M. V. Rybin, A. Kumar, R. Jain, W. X. Lim, V. G. Achanta, S. S. Prabhu, Q. J. Wang, Y. S. Kivshar, R. Singh, “All dielectric active terahertz photonics driven by bound states in the continuum”, Adv. Mater., 31, 1901921 (2019).
  * (4) C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound States in the continuum in photonics”, Phys. Rev. Lett., 100, 183902 (2008).
  * (5) C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljac̆ić, “Observation of trapped light within the radiation continuum”, Nature, 499, 188-191 (2013).
  * (6) T. Dong, J. Liang, S. Camayd-Munoz, Y. Liu, H. Tang, S. Kita, P. Chen, X. Wu, W. Chu, E. Mazur, and Y. Li, “Ultra-low-loss on-chip zero-index materials”,  Light: Science $\&$ Applications, 10, 10 (2021).
  * (7) H. Tang, C. DeVault, S. A. Camayd-Munoz, Y. Liu, D. Jia, F. Du, O. Mello, D. I. Vulis, Y. Li, and E. Mazur, “Low-loss zero-index materials”, Nano. Lett., 21, 914-920 (2021).
  * (8) A. A. Lyapina, D. N. Maksimov, A. S. Pilipchuk, and A. F. Sadreev, “Bound states in the continuum in open acoustic resonators,” J. Fluid Mech., 780, 370-387 (2015).
  * (9) Y. X. Xiao, G. Ma, Z. Q. Zhang, and C. T. Chan, “Topological Subspace-Induced Bound State in the Continuum”, Phys. Rev. Lett., 118, 166803 (2017).
  * (10) C. M. Linton and P. McIver, “Embedded trapped modes in water waves and acoustics”, Wave Motion, 45, 16-29 (2007).
  * (11) C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, M. Soljacic, “Bound states in the continuum”, Nat. Rev. Mater., 1, 16048 (2016).
  * (12) S. I. Azzam, V. M. Shalaev, A. Boltasseva, and A. V. Kildishev, “Formation of bound states in the continuum in hybrid plasmonic-photonic systems”, Phys. Rew. Lett., 121, 253901 (2018).
  * (13) E. N. Bulgakov and A. F. Sadreev, “Bloch bound states in the radiation continuum in a periodic array of dielectric rods”, Phys. Rev. A, 90, 053801 (2014).
  * (14) I. V. Timofeev, D. N. Maksimov, and A. F. Sadreev, “Optical defect mode with tunable Q factor in a one-dimensional anisotropic photonic crystal”, Phys. Rev. B, 97, 024308 (2018).
  * (15) Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observation of optical bound states in the continuum”, Phys. Rev. Lett., 107, 183901 (2011).
  * (16) M. I. Molina, A. E. Miroshnichenko, and Y. S. Kivshar, “Surface bound states in the continuum”, Phys. Rev. Lett., 108, 070401 (2012).
  * (17) S. Fan and W. Suh, “Temporal coupled-mode theory for the Fano resonance in optical resonators”, J. Opt. Soc. Am. A, 20, 569-572 (2003).
  * (18) A. Taghizadeh and II. Chung, “Quasi bound states in the continuum with few unit cells of photonic crystal slab”, Appl. Phys. Lett., 111, 031114 (2017);
  * (19) H. Friedrich and D. Wintgen, “Interfering resonances and bound states in the continuum,” Phys. Rev. A, 32, 3231 (1985).
  * (20) K. Koshelev, S. Kruk, E. Melik-Gaykazyan, J. H. Choi, A. Bogdanov, H. G. Park, and Y. Kivshar, “Subwavelength dielectric resonators for nonlinear nanophotonics”, Science, 367, 288-292 (2020).
  * (21) Z. F. Sadrieva, I. S. Sinev, K. L. Koshelev, A. Samusev, I. V. Iorsh, O. Takayama, R. Malureanu, A. A. Bogdanov, and A. V. Lavrinenko, “Transition from optical bound states in the continuum to leaky resonances: role of substrate and roughness”, ACS Photonics, 4, 723-727 (2017).
  * (22) A. Kodigala, T. Lepetit, Q. Gu, B. Bahari, Y. Fainman, and B. Kanté, “Lasing action from photonic bound states in continuum”, Nature, 541, 196-199 (2017).
  * (23) S. T. Ha, Y. H. Fu, N. K. Emani, Z. Pan, R. M. Bakker, R. Paniagua-Domínguez, and A. I. Kuznetsov, “Directional lasing in resonant semiconductor nanoantenna arrays”, Nat. Nanotech., 13, 1042-1047 (2018).
  * (24) S. G. Lee, S. H. Kim and C. S. Kee, “Bound states in the continuum (BIC) accompanied by avoided crossings in leaky-mode photonic lattices”, Nanophotonics, 9, 4373-4380 (2020).
  * (25) D. N. Maksimov, V. S. Gerasimov, S. Romano, and S. P. Polyutov, “Refractive index sensing with optical bound states in the continuum”, Opt. Express, 28, 38907-38916 (2020).
  * (26) S. Romano, G. Zito, S. Torino, G. Calafiore, E. Penzo, G. Coppola, S. Cabrini, I. Rendina, and V. Mocella, “Label-free sensing of ultralow-weight molecules with all-dielectric metasurfaces supporting bound states in the continuum”, Photonics Res., 6(7), 726-733 (2018).
  * (27) F. Yesilkoy, E. R. Arvelo, Y. Jahani, M. Liu, A. Tittl, V. Cevher, Y. Kivshar, and H. Altug, “Ultrasensitive hyperspectral imaging and biodetection enabled by dielectric metasurfaces”, Nat. Photonics, 13(6), 390-396 (2019).
  * (28) Y. Liu, S. Wang, D. Zhao, W. Zhou, and Y. Sun, “High quality factor photonic crystal filter at k $\approx$ 0 and its application for refractive index sensing”, Opt. Express, 25, 10536-10545 (2017).
  * (29) A. Anedda, C.M. Carbonaro, F. Clemente, R. Corpino, S. Grandi, A. Magistris, and P.C. Mustarelli. “Rhodamine 6G-SiO2 hybrids: A photoluminescence study”, Journal of Non-Crystalline Solids, 351, 1850-1854 (2005).
  * (30) X.L. Zhong and Z.Y. Li. “All-analytical semiclassical theory of spaser performance in a plasmonic nanocavity”, Phys. Rew. B., 88, 085101 (2013).
  * (31) M. Dridi and G. C. Schatz, “Model for describing plasmon-enhanced lasers that combines rate equations with finite-difference time-domain”, J. Opt. Soc. Am. B, 30, 2791-2797 (2013).
  * (32) D. J. Trivedi, D. Wang, T. W. Odom, and G. C. Schatz, “Model for describing plasmonic nanolasers using Maxwell-Liouville equations with finite-difference time-domain calculations”, Phys. Rev. A, 96, 053825 (2017).
  * (33) W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C.Schatz and T. W. Odom, “Lasing action in strongly coupled plasmonic nanocavity arrays”, Nat. Nanotech., 8, 1-6 (2013).
  * (34) T. Grossmann, S. Schleede, M. Hauser, M. B. Christiansen, C. Vannahme, C. Eschenbaum, S. Klinkhammer, T. Beck, J. Fuchs, G. U. Nienhaus, U. Lemmer, A. Kristensen, T. Mappes, and H. Kalt. “Low-threshold conical microcavity dye lasers”, Appl. Phys. Lett., 97, 063304 (2010).
  * (35) T. T. Wu, S. H. Wu, T. C. Lu, and S. C. Wang, “GaN-based high contrast grating surface-emitting lasers”, Appl. Phy. Lett., 102, 081111 (2013).
  * (36) M. Maleki, M. Mehran, and A. Mokhtari, “Design of a near-infrared plasmonic gas sensor based on graphene nanogratings”, Journal of the Optical Society of America B, 37, 3478-3486 (2020).
  * (37) C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics”, Advances in Optics and Photonics, 37, 379-440 (2012).
  * (38) V. Karagodsky and C. J. Chang-Hasnain, “Physics of near-wavelength high contrast gratings”, Opt. Express, 20, 10888-10895 (2012).
  * (39) R. F. Ndangali and S. V. Shabanov, “Electromagnetic bound states in the radiation continuum for periodic double arrays of subwavelength dielectric cylinders”, J. Math. Phys. 51, 102901 (2010).
  * (40) T. Sun, S. Kan, G. Marriott, and C. Chang-Hasnain, “High-contrast grating resonators for label-free detection of disease biomarkers”, Sci. Rep., 6, 27482 (2015).
  * (41) M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics”, Nat. Photon., 11, 543-554 (2017).
  * (42) H. Heo , S. Lee, and S. Kim, “Tailoring Fano resonance for flat-top broadband reflectors based on single guided-mode resonance”, J. Lightwave Technol., 37, 4244-4250 (2019).
  * (43) Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-index-contrast grating (HCG) and its applications in optoelectronic devices”, IEEE J. Sel. Top. Quantum Electron., 15, 1485-1499 (2009).
  * (44) D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-q toroid microcavity on a chip”, Nature, 421, 925-928 (2003).
  * (45) J. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator”, Nat. Photon., 4, 46-49 (2010).
  * (46) Y. Zhou, X. Li, S. Li, Z. Guo, P. Zeng, J. He, D. Wang, R. Zhang, M. Lu, S. Zhang, and X. Wu,“Symmetric guided-mode resonance sensors in aqueous media with ultrahigh figure of merit,” Opt. Express, vol. 27, pp. 34788-34802, 2019.
  * (47) Q. L. Huang, J. Peh, P. J. Hergenrother, and B. T. Cunningham, “Porous photonic crystal external cavity laser biosensor”, Appl. Phys. Lett., 109, 071103 (2016).
  * (48) J. M. Bingham, J. N. Anker, L. E. Kreno, and R. P. Van Duyne, “Gas sensing with high-resolution localized surface plasmon resonance spectroscopy”, J. AM. CHEM. SOC., 132, 17358-17359 (2010).
  * (49) C. Chung-Yen, W. Fung, and L. J. Guo, “Polymer microring resonators for biochemical sensing applications”, IEEE J. Sel. Top. Quantum Electron., 12, 134-142 (2006).
  * (50) X. Li, S. Liang, Y. Zhang, Q. Yu, X. Sheng, S. Lou, X. Wang, W. Zhang, M. Dong, and L. Zhu, “Novel refractive index sensor based on fiber bragg grating in nano-bore optical fiber”, Opt. Quant. Electron, 51, 117 (2019).
  * (51) Y. H. Wan, N. A. Krueger, C. R. Ocier, P. Su, P. V. Braun, and B. T. Cunningham, “Resonant mode engineering of photonic crystal sensors clad with ultralow refractive index porous silicon dioxide”, Adv. Opt. Mater., 5, 1700605 (2017).