www.advopticalmat.deQuantization of Mode Shifts in Nanocavities Integrated
with Atomically Thin Sheets
Nan Fang,* Daiki Yamashita,* Shun Fujii, Keigo Otsuka, Takashi Taniguchi,
Kenji Watanabe, Kosuke Nagashio, and Yuichiro K. Kato*

The unique optical properties of 2D layered materials are attractive for achieving
increased functionality in integrated photonics. Owing to the van der Waals
nature, these materials are ideal for integrating with nanoscale photonic structures. Here a carefully designed air-mode silicon photonic crystal nanobeam
cavity for efficient control through 2D materials is reported. By systematicallyinvestigating various types and thicknesses of 2D materials, the authors are able
to show that enhanced responsivity allows for giant shifts of the resonant wavelength. With atomically precise thickness over a macroscopic area, few-layer
flakes give rise to quantization of the mode shifts. The dielectric constant of theflakes is extracted and found to be independent of the layer number down to amonolayer. Flexible reconfiguration of a cavity is demonstrated by stacking andremoving ultrathin flakes. With an unconventional cavity design, these results
open up new possibilities for photonic devices integrated with 2D materials.

N. Fang, K. Otsuka, Y. K. Kato
Nanoscale Quantum Photonics Laboratory
RIKEN Cluster for Pioneering Research
Saitama 351-0198, Japan
E-mail: nan.fang@riken.jp; yuichiro.kato@riken.jp
D. Yamashita, S. Fujii, Y. K. Kato
Quantum Optoelectronics Research TeamRIKEN Center for Advanced Photonics
Saitama 351-0198, Japan
E-mail: daiki.yamashita@riken.jp
K. Otsuka
Department of Mechanical Engineering
The University of Tokyo
Tokyo 113-8656, Japan
T. TaniguchiInternational Center for Materials Nanoarchitectonics
National Institute for Materials Science
Ibaraki 305-0044, JapanK. Watanabe
Research Center for Functional Materials
National Institute for Materials Science
Ibaraki 305-0044, JapanK. Nagashio
Department of Materials Engineering
The University of Tokyo
Tokyo 113-8656, JapanThe ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/adom.202200538.
© 2022 The Authors. Advanced Optical Materials published by WileyVCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution andreproduction in any medium, provided the original work is properly cited.

DOI: 10.1002/adom.202200538

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1. Introduction

2D layered materials such as graphene,transition metal dichalcogenides (TMDs),and hexagonal boron nitride (h-BN) haveattracted considerable attention due totheir exotic physical properties and potential for diverse applications. Monolayer
graphene exhibits the quantum Hall effecteven at room temperature,[1] while ultrathin TMD based field-effect transistors arepromising for continuation of the Moore's
Law.[2] Moiré patterns can be created bylayers with twisted angles, which has led
to the observations of superconductivity
in bilayer graphene[3] and ferroelectricity
in bilayer h-BN.[4] Many TMDs are foundto become direct bandgap semiconductors at the monolayer limit, making them the thinnest opticalemitters.[5] Furthermore, rich optical phenomena exist in theseatomically thin flakes, such as spin-valley coupling,[6] Moiré
excitons,[7] and layer number dependent nonlinearity.[8]To further utilize the optical properties of TMDs, microcavities can be used to enhance the light– matter interaction. By forming TMD/cavity hybrids, nanolasers have been
demonstrated[9–11] and second-order nonlinear response hassignificantly improved.[12,13] Evidence for strong coupling andformation of microcavity polaritons have also been reported.[14]Compared to the successful use of TMDs as an active material within microcavities, it is a challenge to control the cavity
modes with 2D materials. Because of the atomically thin nature,cavity modes are barely affected and the resonant wavelength
can only be tuned slightly.[15–20] With atomically precise thickness over macroscopic areas and extensive compatibility offeredby van der Waals interface, photonic devices controlled throughsingle atomic layers would present a new direction in nanotechnology. Cavity structures designed specifically for enhanced
sensitivity to ultra-thin materials is required to unravel the fullfunctionality and capability of the TMD/cavity hybrids.
Here we substantially boost the responsiveness of microcavities to 2D materials by using specially designed photonic crystal
nanobeam structures. Various 2D material types and thickness
dependence are investigated, and we find that it is possible toachieve giant wavelength shifts of the cavity mode. By precisely
controlling tungsten diselenide (WSe2) thickness down to amonolayer, we observe quantized mode shifts of the 2D/cavity
hybrids. The dielectric constant in the atomically thin limit canbe extracted by comparing to finite-difference time-domain© 2022 The Authors. Advanced Optical Materials published by Wiley-VCH GmbH

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Research Article

www.advopticalmat.de(FDTD) calculations. Stacking and removal of WSe2 flakes arealso performed, demonstrating the flexible reconfiguration
capability of the 2D/cavity hybrids.

2. Results and Discussion
2.1. Design of 2D/Cavity Hybrids
We begin by designing cavities suited for interaction with
2D materials. Most microcavities, such as microsphere resonators,[21,22] are designed based on refractive index contrast
between two media, and the modes are confined in the highindex medium using total internal reflection. The evanescentfields are typically small outside of the cavity, and coupling to
2D materials would be weak. Reducing the size of the cavity
would force the mode to extend outside, and therefore smaller
mode volumes are in general favorable for enhanced evanescent fields. For example, toroidal microcavities having small
diameters show more of the modes occupying the spaceexternal to the cavity.[23]We propose to use photonic crystal (PC) nanobeam cavities
with ultra-small mode volumes,[24] consisting of an array of airholes on a silicon waveguide as shown in Figure 1a,b. Braggreflectors are formed by periodic arrays of holes, and localized
modes are formed by modulating the periodicity at the cavity

center to break the Bragg condition. The nanobeam cavities feature ultra-small mode volumes on the order of 10−2λ3 where λis the cavity wavelength. In addition, the air holes act to reduce
the average refractive index, weakening the confinement andincreasing the evanescent fields.
We further utilize the characteristics of the photonic bands
to engineer the cavity modes for enhancing the interaction with
2D materials. The periodic modulation of the refractive index
gives rise to a photonic bandgap, separating the lower frequency dielectric band from the higher frequency air band.[25]The dielectric bands are characterized by field amplitudes
maximized within the dielectric material, while the air bands
exhibit large fields in the air holes. The dielectric-band modes
can be confined by locally reducing the lattice constant, as thefrequency of the modes will become higher and the photons
will be surrounded by the photonic bandgap.[25] Similarly, airband modes can be confined by introducing a larger lattice
constant region.[26,27] We expect that the air mode would haveincreased coupling with 2D materials because of stronger fields
in air. Furthermore, the air band is closer to the light line thanthe dielectric band, corresponding to a lower effective refractive
index with stronger evanescent fields.
The mode profiles in the two different cavity designs are
mapped out by performing FDTD calculations. The y-component of the electric field Ey for the fundamental transverse-electric mode in the dielectric-mode cavity is shown in Figure 1c,

Figure 1. Design of PC nanobeam cavities. a) A schematic of a 2D/cavity hybrid. b) A top-view SEM image of a bare nanobeam cavity. Spatial distribution of Ey for the fundamental cavity modes of c) dielectric-mode and d) air-mode structures with top views (top) and cross-section views (bottom). PL
spectra of the fundamental mode for e) a dielectric-mode nanobeam and f) an air-mode nanobeam with (red) and without (black) a 9.0-nm-thick WSe2
flake on top. The excitation power is 300 µW and the excitation wavelength is 780 nm. Spectra are plotted with respect to the resonant wavelengths
before the transfer of WSe2 flakes, which are 1405.6 and 1477.4 nm for (e) and (f), respectively. We note that the initial resonant wavelength in thepresent range barely affects the shift values in the FDTD simulation. Dots are data and solid lines are Lorentzian peak fits. Arrows indicate the shift
directions. Scale bars in (b–d) are 1 µm.

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www.advopticalmat.deand higher field amplitudes within silicon are confirmed as
illustrated in the top view. In the air-mode cavity, the fields
are mostly distributed within the holes as shown in Figure 1d.
The mode profiles are distinctly different not only in the x–yplane but also for the evanescent fields in the z-direction as
can be seen in the cross sectional views. The dielectric-mode
cavity does show some evanescent fields, but the air-mode
cavity exhibits even larger evanescent fields that extend farther out into free space as expected (see Figure S1, Supporting
Information).
We experimentally compare the dielectric mode and the airmode cavities by transferring WSe2 flakes onto the devices. The
cavities are designed to have the fundamental mode in the telecommunication band based on the FDTD calculations, andwe fabricate the nanobeams from a silicon-on-insulator substrate using electron beam lithography and inductively-coupledplasma etching. WSe2 flakes with the same thickness of 9.0 nm
are transferred on the two types of cavities using a conventional polydimethylsiloxane (PDMS) stamp method.[28] Theinteraction with the 2D material is evaluated with a home-built
confocal photoluminescence (PL) microscopy system at room
temperature by comparing the fundamental mode before andafter the transfer of WSe2. All measurements are performed in
dry nitrogen to avoid environmental effects (see Figure S2, Supporting Information).
PL spectra for the dielectric-mode and the air-mode cavities
are shown in Figure 1e,f, respectively. A single sharp peak isobserved in each spectrum and is identified as the fundamental
mode. The dielectric-mode cavity shows a redshift of 13.5 nm
after the transfer, which is attributed to a change in the average
dielectric constant. In comparison, the air-mode cavity has anincreased shift value by almost twofold. The larger shift indicates the enhanced responsivity, consistent with the simulations
showing stronger fields for the air mode cavities. We note thathigher-order modes show even more wavelength shifts becauseof the larger fraction of the mode volumes in free space (seeFigure S3, Supporting Information).
We now survey the interaction of various 2D materials withthe air-mode cavities. Four typical 2D materials are studied
including insulating h-BN and semiconducting TMDs ranging
from molybdenum disulfide (MoS2), WSe2, to molybdenum
ditelluride (MoTe2). We select flakes with thickness close to
11 nm, and compare PL spectra before and after the transfer.

As shown in Figure 2, various 2D materials show distinct
shift values because of the different dielectric constants. The
smallest redshift of only 7.6 nm is observed for h-BN, which isa widely studied 2D material for photonics.[29,30] For the TMDs,
the redshifts increase in the order of MoS2, WSe2, and MoTe2.
The tail of the MoTe2 emission spectrum shows some overlap
with the cavity mode, which is expected to lead to considerable cavity loss by absorption and exciton-cavity coupling.[31]In the following study, we make use of WSe2 which exhibits
large shifts with negligible emission in the present wavelength
range.[32]2.2. Giant Wavelength Tuning in WSe2/Cavity Hybrids
To explore the capability of the enhanced responsiveness in
WSe2/cavity hybrids, modifications of the cavity mode by thick
WSe2 flakes are investigated. We transfer flakes with different
thickness t onto the cavities and mode shifts are measured by
PL spectroscopy. As shown in Figure 3a, the redshifts becomelarger with increasing t owing to a larger mode overlap. The
largest value of 201.8 nm is achieved for t = 40.3 nm, where
the mode wavelength is close to the detection limit of ourdetector. We note that the tuning range covers a wide spectrum
corresponding to the telecommunication E-band to L-band.
We are able to extract the dielectric constant e from thethickness dependent shifts by comparing to FDTD simulations(Figure 3b). The calculated shifts are almost linearly dependent
on the thickness when t < 10.0 nm, and become superlinear
in the thicker region which may be due to changes in themode profile. The experimental data is reproduced well whene = 19 ± 1, whose value corresponds to the dielectric constantof bulk WSe2. We note that in-plane e is important for determining the redshifts because the fundamental mode is transverse electric (see Figure S5, Supporting Information).
We also study the quality factor Q in our WSe2/cavity
hybrids since large wavelength shifts are often accompanied
by increased optical losses.[16,19,20] As the spectral resolutionof the present PL spectroscopy system is insufficient, transmittance measurements are performed to determine the
Q factor.[33,34] For t = 22.0 nm sample, the resonant wavelengthis shifted by over 110 nm while the Q-factor remains almost
unaltered at 2.2 × 104 (see Figure S6, Supporting Information).

Figure 2. Resonant wavelength shifts by different types of 2D materials. PL spectra of an air-mode nanobeam before (black) and after (red) transfer ofa) a 12.5-nm-thick h-BN flake, b) a 11.0-nm-thick MoS2 flake, c) a 10.8 nm-thick WSe2 flake, and d) a 11.9 nm-thick MoTe2 flake on top. The excitation
power is 300 µW and the excitation wavelength is 780 nm. Arrows indicate the shift directions. Insets are optical images for the samples, and the scalebars are 20 µm. Dots are data and solid lines are Lorentzian peak fits.

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2.3. Quantized Wavelength Shifts by Atomically Thin WSe2

Figure 3. Thickness dependence of resonant wavelength shifts. a) Normalized PL spectra of the fundamental mode for air-mode nanobeams
before (red) and after (black) transfer of WSe2 flakes. The data from top tobottom correspond to thickness of 40.3, 35.7, 22.0, and 15.5 nm. Spectra
are plotted with respect to the resonant wavelengths before the transfer,which are 1378.1, 1420.0, 1460.4, and 1439.7 nm, respectively. The excitation power is 300 µW and the excitation wavelength is 780 nm. Arrows
indicate the shift directions. Dots are data and solid lines are Lorentzianpeak fits. b) Resonant wavelength shifts as a function of WSe2 thickness.
Dots are data and lines are FDTD simulations with e of 18.0 (purple),
19.0 (green), and 20.0 (orange). We note that several samples with thethin WSe2 flakes deviate from the simulations, which could be due to theformation of an air space between the 2D material and the nanobeam(see Figure S4, Supporting Information).

The negligible effect on the Q factor could be attributed to ahomogeneous interface with suppressed scattering loss aswell as the absence of absorption from the WSe2 flake at thecavity wavelength.

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With the enhanced interaction, even a minor perturbation by
2D materials would influence the cavity mode and become
detectable. By controlling the thickness of WSe2 flakes withatomic precision, we demonstrate extreme sensitivity down
to the monolayer limit. Since ultra-thin 2D materials are too
fragile for sustaining the strain induced by PMDS stamps,
deformation including rupture often occurs in the suspended
region.[19,35] Here we utilize the anthracene-assisted transfer
method,[36] where the organic molecule single crystal supports
and protects 2D flakes during the process (see Figures S7–S9,
Supporting Information). Figure 4a shows a scanning electron
microscopy (SEM) image of the prepared monolayer WSe2/
cavity hybrid, where a uniform morphology over the nanobeam
can be observed.
The typical PL spectra of nanobeam cavities that are integrated with quad- (4L), tri- (3L), bi- (2L), and mono-layer (1L)
WSe2 flakes are shown in Figure 4b. The wavelength shift
decreases by ≈3 nm as the thickness is reduced layer by layer. It
is notable that the 1L WSe2, the limit of the scaling, still tunes
the mode of the nanobeam cavity effectively. The observed shifts
are almost two orders of magnitude larger than the linewidth,
assuming Q ≈ 104.
The roughly constant spacings between the cavity resonancessuggest that the mode shifts are quantized due to the discrete
thickness of atomically thin layers. To verify that the mode
shifts are indeed governed by the layer number, we have prepared three sets of samples for each thickness and repeated themeasurements (Figure 4c). Clearly resolved steps are observed,
confirming the quantization of the mode shifts. It is remarkable that the resonant shifts show relatively small deviations
that are comparable with conventional PC nanocavities,[37] benefitting from atomically precise thickness of the 2D material
over the entire cavity.
The observed discrete wavelength shifts offer an opportunity
to study the dielectric constant even in the ultra-thin limit. We
compare experimental results with FDTD simulation to extracte for 1L to 4L WSe2. Since calculated wavelength shifts are linearly dependent on t in the thin limit (Figure 3b), we fit theexperimental results with a simple linear model (Figure 4d).
We observe a small intercept of 0.7 nm, which may come fromanthracene residues as well as adsorption of other moleculeson the surface of the 2D material. We have also performed
FDTD simulations for various e, and find that wavelength shift
Δλ is also linearly dependent on e (see Figure S5, Supporting
Information). The data can therefore be described by∆λ = α (ε − 1)t + λ0(1)where α = 0.21, is the coefficient determined by the FDTD calculations and λ0 is the intercept. Considering that anthracene
residue or surface adsorption should occur similarly in all thesamples, we take λ0 = 0.7 nm. The values of e are extracted
from data using Equation (1), and the results are shown in
Figure 4e. The obtained values are comparable with the bulk
value, revealing that the dielectric screening in the atomicallythin limit is as effective.

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www.advopticalmat.deFigure 4. Quantized wavelength shifts induced by atomically thin WSe2 flakes. a) A top-view SEM image of a nanobeam cavity with a monolayer WSe2
flake transferred above. Scale bar is 2 µm. b) Normalized PL spectra of the fundamental modes for air-mode nanobeams with a monolayer (blue),bilayer (green), trilayer (orange), and quadlayer WSe2 flake (red) on top. The horizontal axis is the shift with respect to the resonant wavelength before
the transfer, which are 1461.6, 1454.9, 1464.2, and 1468.4 nm, respectively. The excitation power is 300 µW and the excitation wavelength is 780 nm. Dotsare data and solid lines are Lorentzian plus linear fits. c) Resonant wavelength shifts for all the measured samples. d) Resonant wavelength shifts as afunction of layer number. Dots are data and the broken line is a linear fit. e) Extracted dielectric constant as a function of the layer number. Thicknessof each layer is taken to be 0.65 nm in the analysis.

Since the cavity resonances arise from transverse-electricmodes, the extracted values correspond to the in-plane e. It
is reported that in-plane e measured by spectroscopic ellipsometry decreases with increasing the layer number for ultrathin TMDs.[38,39] In comparison, first-principle calculations
show that in-plane e is insensitive to the layer number since
the main contribution comes from in-plane atomic displacements.[40] Our results show no apparent thickness dependence down to the monolayer limit, which is consistent withthe calculations. The behavior of in-plane e is important for2D materials based electronic devices, for example, the tunneling length through Schottky barriers in metal/2D contacts
is strongly affected by in-plane e.[41] We note that extrinsic
effects from processing and adsorption have been taken into
account through λ0 in our analysis, and the extracted values
should therefore represent the intrinsic dielectric properties ofatomically thin WSe2.

the quantized values shown in Figure 4c. We note that the
linewidth increases slightly, suggesting additional loss fromscattering induced by 2D–2D interfacial bubbles. By picking
up the stack using an anthracene stamp (see Figure S8, Supporting Information), the Q factor is recovered and the modeis shifted back.

2.4. Flexible Reconfiguration of 2D/Cavity Hybrids
One of the advantages of using 2D materials comes from theirversatile manipulation capabilities, where flakes can be placedin the desired order without the restriction of lattice matching.
In addition, the removal of transferred flakes is possible owing
to the weak van der Waals force. In Figure 5, we demonstrate
additive and reversible control with a WSe2/cavity hybrid. A
2L WSe2 flake is first transferred on top of a nanobeam, andwe observe a mode shift by 6.5 nm (blue curve). Next, anothertransfer of a 3L flake is performed, which further shifts themode by 9.5 nm (purple curve). The shifts are consistent with

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Figure 5. Reconfiguration of a cavity by stacking and removing of WSe2
flakes. PL spectra of the fundamental mode of the as-fabricated cavity(gray), after the first transfer of a 2L WSe2 flake (blue), after the second
transfer of a 3L flake (purple), and after the removal of the stacked flakes(green). The excitation power is 300 µW and the excitation wavelengthis 780 nm. Dots are data and solid lines are Lorentzian plus linear fits.
Insets illustrate the configuration of the device during the measurements.

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The high compatibility between 2D materials and cavities
demonstrated here opens up various applications in integrated
photonics. The integration with 2D materials could be used
as a post-fabrication tuning technology, where the giant wavelength tunable range of over 200 nm can cover the telecommunication E-band through L-band. By using ultra-thin flakes,
fine tuning can be done with high predictability and reproducibility because of the quantized shifts arising from the atomically precise thickness. This is in contrast to continuous mode
shifts obtained in conventional methods such as chemical
etching,[42] coating of photochromic films,[43] and condensationof gases.[44] In addition, the stackable and removable 2D materials offer a new degree of freedom for reconfigurable cavities.
Finally, as demonstrated in the measurement of e, 2D/cavity
hybrids are an ideal platform for investigating the optical properties of atomically thin structures due to the high sensitivity of
the air-mode cavities. Sensing of a small number of molecules
could become possible by monitoring a high-Q cavity resonance, which would extend the limits of the 2D materials based
sensing technologies.[45]3. Conclusion
In conclusion, we have developed an air-mode cavity for integration with 2D materials. By investigating various 2D material
types and thickness dependence, we show that the fabricated
2D/cavity hybrids have a giant wavelength tunable range ofover 200 nm. We observe a clear quantization behavior of the
wavelength shift for WSe2 where each step represents an effectfrom an additional monolayer. The in-plane dielectric constantof WSe2 can be extracted because of the high surface sensitivityof the air-mode cavity, and shows a thickness independent characteristic down to the monolayer. By stacking and removing
the transferred flakes, we demonstrate that the hybrids benefit
from the versatile manipulation capabilities of the 2D materials. These findings reveal fascinating features of the cavity
that is efficiently controlled by 2D materials, and provide a universal design strategy for enhancing the light–matter interaction with nanomaterials.

4. Experimental Section
Nanobeam Cavity Fabrication: The nanobeam cavities were fabricatedon a silicon-on-insulator substrate with a 260-nm-thick top siliconlayer and a 1-µm-thick buried-oxide (BOX) layer. After defining the PC
pattern on a resist mask by electron beam lithography, the pattern wastransferred to the top silicon slab through an inductively coupled plasma
process using C4F8 and SF6 gases. Following resist removal, the BOX
layer was etched with 20% hydrofluoric acid to form an air-suspended
nanobeam structure.
PL Measurements: A homebuilt confocal microscopy system was used
to perform PL measurements at room temperature in dry nitrogen gas.
A wavelength-tunable Ti:sapphire laser was used for excitation with
its power controlled by neutral density filters. Polarization angle wasadjusted to match the cavity mode by a half-wave plate. The laser beam
was focused on the samples using an objective lens with a numericalaperture of 0.65 and a working distance of 4.5 mm. The 1/e2 beam
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were ≈1.2 and 5.4 µm, respectively. PL was collected through the same
objective lens and detected using a liquid-nitrogen-cooled 1024 pixel
InGaAs diode array attached to a spectrometer. PL was dispersed by a
150 lines per mm grating and the dispersion was 0.52 nm per pixel at thecenter wavelength of 1340 nm.
Transfer of 2D Materials by PDMS Stamps: Thick flakes of 2D materials
with t > 5 nm were transferred on the cavities by a conventional PDMS
stamp method to form 2D/cavity hybrids.[28] 2D material flakes wereprepared on a PDMS sheet (Gelfilm by Gelpak) by mechanical exfoliationand then transferred on the target nanobeam cavity at 120 °C by using a
micromanipulator system. The thickness of the transferred 2D material
flakes was determined by atomic force microscopy. h-BN crystals were
supplied by NIMS and other 2D material crystals were purchased from
HQ graphene.
Transfer of 2D Materials by Anthracene Crystals: Anthracene crystals
were grown with the same method as in ref. [36]. 2D flakes wereprepared on a standard 90-nm-thick SiO2/Si substrates by mechanicalexfoliation and the layer number was determined by optical contrast. An
anthracene single crystal was picked up with a glass-supported PDMS
sheet to form an anthracene/PDMS stamp. 2D flakes were picked up
by pressing the anthracene/PDMS stamp against a substrate with thetarget 2D flakes, followed by quick separation (>10 mm s−1) so that theanthracene crystal remained attached to the PDMS sheet. The stamp
was then pressed on a receiving substrate with the cavity. By slowly
peeling off the PDMS (<0.2~µm s−1), the anthracene crystal with thetarget 2D flake was released. Sublimation of anthracene in air at 110 °C
for 10 min left behind clean 2D flakes because contamination fromsolvents was absent in the all-dry process.

Supporting Information
Supporting Information is available from the Wiley Online Library orfrom the author.

Acknowledgements
N.F. and D.Y. contributed equally to this work. Parts of this study aresupported by JSPS (KAKENHI JP20H02558, JP20K15199, JP20J00817,
JP20K15137, JP20K15120, JP19K23593, JP18H03864, JP19H00755,
JP21H05237, JP21H05232), MIC (SCOPE 191503001), and MEXT
(Nanotechnology Platform JPMXP09F19UT0075). The growth of hBN
crystals was supported by the Elemental Strategy Initiative conductedby the MEXT, Japan (Grant Number JPMXP0112101001) and JSPS
KAKENHI (Grant Numbers JP19H05790, JP20H00354 and JP21H05233).
D.Y. is supported by JSPS (Research Fellowship for Young Scientists).
N.F. and S.F. are supported by RIKEN Special Postdoctoral Researcher
Program. The FDTD calculations were performed using the HOKUSAI
BigWaterfall supercomputer at RIKEN. The authors thank the Advanced
Manufacturing Support Team at RIKEN for technical assistance. The
authors also thank H. Kumazaki for helpful discussion of the dimpled
fiber fabrication.

Conflict of Interest
The authors declare no conflict of interest.

Data Availability Statement
The data that support the findings of this study are available from thecorresponding author upon reasonable request.

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Keywords
2D materials, cavity mode modification, nanocavities, quantization
Received: March 8, 2022
Revised: May 13, 2022
Published online: July 10, 2022

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