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Title Extraordinary Enhancement of Nonlinear Optical Interaction in NbOBr2 Microcavities
Wenduo Chen†, Song Zhu†, Ruihuan Duan†, Chongwu Wang, Fakun Wang, Yao Wu, Mingjin Dai,
Jieyuan Cui, Sang Hoon Chae, Zhipeng Li, Xuezhi Ma, Qian Wang, Zheng Liu*, Qi Jie Wang*
Wenduo Chen, Song Zhu, Chongwu Wang, Fakun Wang, Mingjin Dai, Jieyuan Cui, Sang Hoon Chae,
Zheng Liu, Qi Jie Wang
School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore
Ruihuan Duan, Yao Wu, Zheng Liu
School of Materials Science and Engineering, Nanyang Technological University, 639798, Singapore
Zhipeng Li, Xuezhi Ma, Qian Wang
Institute of Materials Research and Engineering (IMRE), Agency for Science, Technology and
Research (A*STAR), 2 Fusionopolis Way, Innovis, #08-03, Singapore 138634, Singapore
†These authors contributed equally to this work
E-mail: qjwang@ntu.edu.sg and z.liu@ntu.edu.sg
Keywords: niobium oxide dibromide, nonlinear optics, harmonic generation, Fabry-Pérot microcavity,
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optical anisotropy
Abstract
Two-dimensional (2D) materials are burgeoning as promising candidates for investigating nonlinear
optical effects due to high nonlinear susceptibilities, broadband optical response, and tunable
nonlinearity. However, most 2D materials suffer from poor nonlinear conversion efficiencies, resulting
from the reduced light-matter interactions and lack of phase matching at atomic thicknesses. Herein,
we report a new 2D nonlinear material, niobium oxide dibromide (NbOBr2), featuring strong and
anisotropic optical nonlinearities with scalable nonlinear intensity. Furthermore, Fabry-Pérot (F-P)
microcavities are constructed by coupling NbOBr2 with air holes in silicon. Remarkable enhancement
factors of approximately 630 times in second harmonic generation (SHG) and 210 times in third
harmonic generation (THG) are achieved on cavity at the resonance wavelength of 1500 nm. Notably,
the cavity enhancement effect exhibits strong anisotropic feature tunable with pump wavelength,
owing to the robust optical birefringence of NbOBr2. The ratio of the enhancement factor along the b-
and c-axis of NbOBr2 reaches 2.43 and 5.27 for SHG and THG at 1500 nm pump, respectively, which
leads to an extraordinarily high SHG anisotropic ratio of 17.82 and a 10° rotation of THG polarization.
Our research presents a feasible and practical strategy for developing high-efficiency and low-power-
pumped on-chip nonlinear optical devices with tunable anisotropy.
1. Introduction
Harmonic generation, a resplendent pearl on the crown of nonlinear optics, has long captivated
tremendous research attention due to its promising applications across various fields including
biomedical imaging[1, 2], frequency conversion[3, 4] and laser sources[5, 6]. Different orders of harmonic
generation have been extensively explored, ranging from SHG, THG to high-order harmonic
generation (HHG), among which the SHG and THG processes are more prevalent. The advent of 2D
materials, such as graphene and transition metal dichalcogenides (TMDs), provides a promising
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platform for these nonlinear optical researches[7-13] attributed to their unique physical properties such
as the large nonlinear susceptibilities[13-15], broadband optical response[16-18], tunable nonlinearity[19-
24], and favorable on-chip integration compatibility[25-27]. However, the nanoscale thickness of 2D
materials imposes limitations on the light-matter interaction length, thereby severely restricting the
nonlinear conversion efficiency and harmonic generation power density. Consequently, enhancing the
nonlinear conversion efficiency is of paramount importance for practical applications.
So far, particular attention has been directed towards the integration of 2D materials with
photonic cavities. Photonic cavities, with their tight spatial and temporal confinement of light, can be
an efficient means to achieve amplified nonlinear generation in 2D materials. [28-34] Among various
cavity structures, the Fabry-Pérot (F-P) cavity[31, 32, 35] stands out due to the low divergence angle and
small mode volume. Moreover, it can be easily constructed with 2D materials. For instance, by
transferring a monolayer WS2 onto a silicon hole matrix, F-P cavities are formed between the top
monolayer and the hole bottoms, showcasing high SHG enhancement.[31] A similar structure has also
been proven effective for SHG enhancement in TMD heterostructures.[32] However, the cavity
confinement is limited by the low reflectivity of the monolayer flake and silicon substrate, resulting in
reduced enhancement factors. Besides, the spectral range of enhancement is constrained around the
exciton resonance wavelength of TMDs in the reported structures.
Recently, an emerging class of layered 2D materials, MOX2 (M = V, Nb, Ta, Mo; X = Cl, Br, I) has
garnered growing attention for the anisotropic crystal structure and unique physical properties. [36-44]
The weak interlayer electronic coupling in MOX2 is favorable for strong optical nonlinearities. For
example, NbOI2 has been reported as a stable ferroelectric material with high SHG response.[40] In
contrast to TMDs where SHG is only observable in odd layers[45, 46], NbOI2 exhibits scalable SHG
intensity with increasing thickness, attributable to the noncentrosymmetric stacking characteristic.
Similarly, strong second-order nonlinear responses have also been observed in 2D NbOCl2 for ultrathin
quantum light sources.[41] Furthermore, the Perierls-distorted crystal structure[36, 47] imparts
anisotropic properties to 2D NbOX2 flakes, indicating a polarization-sensitive nonlinear response.
In this work, we report a novel transition metal oxide dihalide, NbOBr2, which features intense and
scalable nonlinear response with strong anisotropy. Strongly anisotropic SHG and THG emissions are
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observed in the exfoliated flakes. Furthermore, F-P cavities are constructed by integrating few-layer
NbOBr2 flakes with air holes in the silicon substrate to bolster SHG and THG intensities concurrently.
Giant enhancement factors of approximately 630 and 210 times are observed for SHG and THG
processes, respectively, at a pump wavelength of 1500 nm, away from the exciton resonance state.
The enhancement effect spans a broad spectral range and peaks at the cavity resonance wavelengths.
In addition, strongly anisotropic enhancement is observed in both SHG and THG processes, attributed
to the birefringence feature of NbOBr2 crystal. At the pump wavelength of 1500 nm, the ratio of the
cavity enhancement factor between the crystal b-axis and c-axis reaches 2.43 and 5.27, for SHG and
THG, respectively. Consequently, the anisotropic SHG ratio increases from 7.34 to 17.82, while a 10°
rotation is observed for the THG polarization direction. Our findings provide a feasible method for
obtaining strong harmonic generation emission with broadband response and anisotropic properties,
opening the door to innovative 2D nonlinear optical devices for on-chip applications.
2. Results and discussion
The F-P cavity has been demonstrated as a straightforward and effective technique for achieving giant
enhancement of optical nonlinearity within a relatively compact footprint. Hence, an F-P cavity
structure is designed as depicted in Figure 1a. Air holes are etched into a silicon substrate with a 180
nm Si3N4 layer on top. A thin layer of gold is evaporated onto the bottom of the holes to enhance the
cavity reflectance. The depth of the holes is 10 μm and the diameter is 8 μm, verified by the cross-
section scanning electron microscope (SEM) image in Figure 1h. The holes exhibit steep sidewalls and
a smooth bottom. Subsequently, NbOBr2 flakes with a thickness of around 10 nm are transferred onto
the holes, serving as the second mirror of the F-P cavity. The Si3N4 layer functions as an isolation layer
to suppress charge transfer between the NbOBr2 flake and the Si substrate, which may quench the
nonlinear signal.
NbOBr2 is chosen as the top mirror due to its large nonlinearity, stemming from the unique
noncentrosymmetric crystal structure as shown in Figure 1b,c. NbOBr2 crystal belongs to the
monoclinic C2 space group[36, 47] with a = 13.83 Å, b = 3.91 Å and c = 7.02 Å. The atoms in NbOBr2 are
arranged in the form of [NbO2Br4] octahedra, reminiscent of the typical perovskite structure[48]. The
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octahedra are connected by I atoms along the c-axis and by O atoms along the b-axis, while van der
Waals stacking is found along the a-axis. Different from the common TMDs, the layers in NbOBr2 are
stacked in a noncentrosymmetric way, with each layer shifting a constant distance along the c-axis.
The Nb atoms exhibit a 1D Peierls distortion.[36, 47] Nb atoms are displaced from the center of the
[NbO2Br4] octahedra, leading to a polarization along the b-axis, while the distance between the
adjacent Nb atoms is alternating unequal along the c-axis. The high single-crystalline nature of NbOBr2
is further verified by scanning transmission electron microscopy (STEM, Figure 1d), selected-area
electron diffraction (SAED, Figure 1d) and X-ray diffraction (XRD, Figure S1d).
The NbOBr2 crystal can be easily exfoliated into monolayer or few-layer flakes due to the weak
interlayer interaction. Figure S2a shows the optical microscopy (OM) image of the exfoliated NbOBr2
flakes on a silicon wafer with a 285 nm oxidation layer. Distinct optical contrast is observed between
flakes with different thicknesses. The Raman spectra of NbOBr2 flakes with different thicknesses are
investigated in Figure 1e. Five peaks are resolved in the spectral range, denoted as P1 to P5 from low
to high Raman shift. All the peak positions remain almost constant when the thickness increases,
indicating the weak interlayer coupling nature in NbOBr2. The angle-resolved polarized Raman
spectroscopy is further performed to study the anisotropic phonon vibration features in NbOBr2. As
shown in Figure 1f,g, the angle-resolved polarized Raman signals of P2 mode are collected parallel or
perpendicular to the incident polarization respectively. A two-lobed shape is exhibited in the parallel
configuration, demonstrating the A-symmetry vibration nature of Raman mode P2 (see Supporting
Information S3). For the other four modes shown in Figure S3, they are all confirmed as the A-
symmetry modes as well due to the two-lobe-shaped plot in the parallel configuration. All the Raman
modes exhibit strong anisotropy, indicating the strong anisotropy of NbOBr2 crystal.
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Figure 1. F-P cavity with NbOBr2. a) Illustration of the hole cavity structure covered by a few-layer
NbOBr2 flake, with the crystal structure of NbOBr2 from the b) b-axis, and c) a-axis. The monolayer
thickness of NbOBr2 is about 7.0 Å. In b), Nb atoms show a 1D Peierls distortion (two alternating
unequal Nb-Nb distances L1≠L2). d) STEM image of NbOBr2 crystal. Scale bar: 5 nm. Inset: SAED pattern
of the NbOBr2 crystal. e) Thickness dependent Raman spectra of NbOBr2 flakes. The arrows above
indicate the positions of the Raman peaks. The polar plots show the measured and fitted Raman
intensities in f) perpendicular and g) parallel polarization configurations at the peak position near 236
cm-1. h) OM image of NbOBr2 on Si substrate with holes. The scale bar is 10 μm. The spots labeled “On
cavity” and “Off cavity” are the positions to excite and collect the signals on the hole and on the
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substrate. Inset: SEM image of the cross-section of the F-P cavity. The scale bar is 10 μm. i) Angle-
resolved reflectance spectra of the NbOBr2-covered cavity in the visible region. j) The cavity absorption
spectra in the near-infrared range. Blue: simulated spectra; Purple: experimental results. The diamond
markers show the absorption peaks, well consistent with the simulation data.
The Raman intensities of these A-symmetry modes reach the maximum along the c-axis, providing a
convenient tool to determine the direction of the crystal axis. The NbOBr2 flakes are relatively stable
in air and the Raman signals are still strong after heating for several hours (see Supporting Information
S4).
After transferring NbOBr2 flakes onto the hole spots, distinct color contrast can be observed
between the covered and bare holes, and between the covered holes with different NbOBr2
thicknesses (Figure 1h), indicating that the flakes are successfully suspended on the holes. To further
confirm the formation of the F-P cavity, angle-resolved reflection spectra of the holes covered with
NbOBr2 are measured. As shown in Figure 1i, parabola-like mode dispersion can be clearly resolved.
In contrast, no resonance modes are observed on bare holes (Figure S5). Therefore, a vertical F-P
cavity is confirmed to be formed between the bottom Au substrate and the top NbOBr2 flake. The
resonance periodicity ΔE in Figure 1e is measured to be 64 meV. Considering the theoretical mode
periodicity
[49] and taking the hole depth L as 10 μm, the mode periodicity ΔE is calculated to
be 62 meV in theory, well consistent with the experimental result. The cavity absorptance spectra are
also measured in the near-infrared range as shown in Figure 1j, where the cavity resonance
wavelengths exactly match the simulation results. All the consistency further confirms the existence
of an F-P cavity between the two optical reflectors formed by NbOBr2 and Au. F-P cavity is also formed
beyond the hole region, where light can be confined inside the middle Si3N4 layer. However, the
enhancement from the NbOBr2/Si3N4/Si cavity can be excluded, as discussed in Supporting
Information S6.
The nonlinear optical properties of NbOBr2 crystal are investigated using a home-built microscopic
system[8] under transmission configuration (Figure 2a). Figure 2b illustrates the power-dependent SHG
spectra of a 20-nm-thick NbOBr2 nanoflake excited by a 1600 nm laser. The SHG peak is detected near
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800 nm, where the emission linewidth is almost two times smaller compared to that of the incident
light (Figure S7a). The SHG intensity undergoes a quadratic increase with increasing pump power, and
the fitted slope of 1.96 confirms a typical SHG process. Strong SHG response can be observed under
broadband excitation with the wavelength ranging from 1150 nm to 1600 nm, establishing NbOBr2 as
a promising infrared nonlinear material without phase-matching requirement (Figure 2c). Especially,
the SHG intensity is observed to increase when approaching a shorter pump wavelength around 1250
nm, which should be attributed to the interband transition absorption. Due to the
noncentrosymmetric character of the NbOBr2 crystal, the layer-number-dependent SHG intensity is
measured, under a fixed pump power of around 37 μW (Figure 2d). As expected, the SHG intensity
scales quadratically[41] with the increasing layer number in the measured
Figure 2. SHG response in layered NbOBr2. a) Schematic of the measurement geometry. The NbOBr2
flakes are exfoliated on fused silica substrate for measurements. Inset shows the principle of the SHG
process. b) Power-dependent SHG intensity pumped at 1600 nm. A linear fitting with a slope of 1.96
confirms the quadratic nature of the second-order nonlinear process. c) SHG spectra excited by
different wavelengths. Higher SHG signal is observed near 1200 nm pump due to the interband
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transition absorption. d) Thickness-dependent SHG intensity spectra. The scaling SHG intensity with
increasing thickness is attributed to the noncentrosymmetric crystal structure as shown inside the
figure. e) SHG spectra from a ~ 9 nm NbOBr2 flake and a monolayer (ML) MoS2. f) Highly anisotropic
polarization-dependent SHG response. Blue: total SHG intensity; purple: SHG component parallel to
the incident polarization direction; orange: SHG component perpendicular to the incident polarization
direction.
thickness range below the coherence length. Superior to TMDs where SHG is only observable in odd
layers, the SHG intensity in NbOBr2 keeps scaling due to the noncentrosymmetric crystal structure and
weak interlayer electronic coupling. Figure 2e compares the SHG intensity of a NbOBr2 of around 9 nm
with a monolayer MoS2, where both materials can generate SHG power on almost the same order of
magnitude. However, NbOBr2 possesses a larger tunable range of SHG intensity by altering the flake
thickness, which is advantageous for practical device applications. The second-order nonlinear
susceptibility of NbOBr2 is calculated to be about 9.16×10-11 m V-1 at the incident wavelength of 1500
nm[50] (Supporting Information S8), competitive with TMDs.
As shown in Figure 2f, the SHG response in NbOBr2 features highly in-plane anisotropic behavior.
The polarization-angle-dependent SHG indicates that the total SHG intensity strongly
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Figure 3. THG response in layered NbOBr2. a) Power-dependent THG intensity pumped at 1600 nm. A
linear fitting with a slope of 2.96 confirms the cubic nature of the third-order nonlinear process. b)
Thickness-dependent THG spectra. c) THG spectra from a ~ 9 nm NbOBr2 flake and a monolayer MoS2.
d) Anisotropic polarization-dependent THG response. Blue: total THG intensity; purple: THG
component parallel to the direction of crystal c-axis; orange: THG component parallel to the direction
of crystal b-axis. e) Linearly polarized THG signal. The THG intensity is measured by rotating a polarizer.
The purple arrow indicates the polarization state of the pump source, aligning with the crystal c-axis.
f) THG intensity depending on the pump ellipsometry. An ellipticity of 0 or ±1 corresponds to linear
polarization or circular polarization respectively.
relies on the azimuthal angle of the pump light, with the maximum SHG response along the b-axis
(polar axis). The azimuthal dependence originates from the low crystal symmetry of NbOBr2,
significantly distinguished from the high crystal symmetry in TMDs. Furthermore, the polarization
properties of the emitted SHG signal are examined and fitted in Figure 2f. The largest signal is also
observed along the b-axis, consistent with the crystallographic symmetry analysis (Supporting
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Information S9). The highly anisotropic SHG signal of NbOBr2 offers a feasible way to identify the
crystal orientation and a novel choice for various polarization-dependent nonlinear applications.
NbOBr2 can also generate higher-order nonlinear signals, such as THG in Figure 3. As shown in
Figure 3a, the power-dependent THG spectra demonstrate a cubic dependence with the pump power.
Figure 3b shows the THG power as a function of the NbOBr2 thickness, which can be fitted by the
simplified formula
, where L is the flake thickness, and κ is the extinction
coefficient at the THG emission wavelength λ3.[51] The formula of the thickness-dependent intensity
can be interpreted from two mechanisms. Firstly, the rising THG intensity is mainly attributed to the
cumulative contribution from the increasing layer number. Secondly, stronger optical absorption
occurs in thicker flakes, leading to an exponential depletion of the THG power. Monolayer MoS2 is
used as a reference to calculate the third-order nonlinear susceptibility χ(3) of NbOBr2 (Figure 3c).[52]
The χ(3) is estimated to be 8.1×10-19 m2 V-2 at 1500 nm incidence from the analysis in Supporting
information S8.
Strongly anisotropic properties are also observed in the THG response of NbOBr2. From the
polarization-angle-dependent THG shown in Figure 3d, the strongest THG response is observed when
the polarization of the pump light is along the c-axis, opposite to the SHG process. In SHG, the
noncentrosymmetric crystal structure of NbOBr2 leads to strong spontaneous polarization along the
polar b-axis, which is the main contribution of the SHG signal. Therefore, the strongest SHG response
is fixed along the b-axis as the broken crystal symmetry is independent of the excitation wavelength.
In contrast, THG process does not rely on breaking the crystal symmetry, but depents more on the
crystal structure and band structure. Consequently, the direction of the maximum THG response
depends on the incident wavelength (see Supporting Information 9). Besides, the polarization of the
emitted THG signal is measured in Figure 3e. The polarization of the incident light is fixed at a certain
direction and a rotating polarizer is added right before the spectrometer. The THG intensity reaches
the maximum only when the polarizer is parallel to the polarization of the fundamental light, indicating
that the emitted THG signal is linearly polarized, parallel to the pump polarization. Furthermore,
polarization-dependent THG is studied using an elliptically polarized pump source, as shown in Figure
3f. The pump beam is linearly or circularly polarized when the ellipticity equals 0 or ±1, respectively.
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The THG intensity is observed to reach the maximum with a linearly polarized pump, while it reduces
to almost zero under the circular pump condition. The experimental results agree well with the
theoretical fitting in Supporting Information S9.
Although NbOBr2 flakes can generate stronger nonlinear signals compared to TMDs, the limited
light-matter interaction length due to the nanoscale thickness remains an imperfection from high
power density and nonlinear conversion efficiency. Therefore, the F-P cavity is demonstrated here as
an effective amplifier for optical nonlinearity. The cavity is first excited at the resonance wavelength
of 1500 nm. Figure 4a compares the SHG spectra of the NbOBr2 flake on the hole (labeled as “On
cavity” in purple) and on the Si3N4 substrate (labeled as “Off cavity” in blue). Strong enhancement of
around 630 times is observed on the F-P cavity compared with the off-cavity spot. SHG mapping is
performed around two covered holes as
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Figure 4. SHG and THG enhancement of NbOBr2 on the F-P cavity. a) SHG spectra of NbOBr2 collected
on cavity (purple) and off cavity (blue) with the same pump power at 1500 nm. b) SHG enhancement
factors on ten different F-P cavities. The dashed line indicates the simulated enhancement factor.
Inset: SHG mapping (above) of two neighbouring holes (below, OM image, diameter 8 μm) covered
with NbOBr2. Scale bar: 8 μm. c) THG spectra of NbOBr2 collected on cavity (purple) and off cavity
(blue) pumped at 1500 nm with the same incident power. d) THG enhancement factors on seven
different F-P cavities. Simulated electric field distribution () inside the NbOBr2 flake e) on cavity
and f) off cavity at the excitation wavelength of 1500 nm. The position of the hole is indicated by the
white dashed circle. g) Wavelength-dependent SHG enhancement factors from 1480 nm to 1640 nm.
Five types of cavities with cavity depth of 5 μm, 8 μm, 10 μm, 12 μm and 15 μm are measured. The
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black diamonds indicate the positions of the local maximum enhancement factors. h) The simulated
cavity absorption spectra of the five types of cavities in g).
shown in the inset of Figure 4b. Uniform and particularly intense SHG signal is observed from the on-
cavity region, compared with which the SHG intensity from the NbOBr2 flake on the substrate is
negligible. The large amplification effect is further examined and verified in several more samples in
Figure 4b. The SHG signals from all ten on-cavity samples are strongly amplified with the enhancement
factor ranging from 520 to 670 times, affirming the reliability of the F-P cavity design. The small
fluctuation of the enhancement factor may be attributed to the fabrication deviation, the
inhomogeneity of the flakes, and the inhomogeneity induced by the transfer process. THG
enhancement is also observed on F-P cavities as shown in Figure 4c,where an enhancement factor of
about 210 is obtained. We confirm the repeatability of THG enhancement likewise in Figure 4d, where
the SHG intensities of the seven on-cavity NbOBr2 flakes are enhanced from 179 to 226 times. The
enhancement of higher-order nonlinear processes can also be realized theoretically, but are not
studied due to the wavelength limitation of our spectrometer.
To interpret the origin of the nonlinear enhancement, finite-difference time-domain (FDTD)
simulation is applied to calculate the enhancement factor. Both the pump light and emission light can
resonate between the NbOBr2 flake and the bottom substrate, which leads to the giant enhancement
of the electric field. As the SHG intensity is proportional to the fourth order of the incident electric
field and second order of the emission field, the F-P cavity would result in an SHG enhancement factor
(EF) as
, where and are the electric field amplitudes of the region on the
cavity and substrate, respectively.[53] Figures 4e and 4f show the simulated electric field distribution
of the on-cavity and off-cavity NbOBr2 flakes at 1500 nm pump, showing an enhancement of the
electric field () by ~ 8.53 times. The distribution of the emission electric field is also shown in Figure
S12, where the electric field is enhanced by ~ 8.73 times on the cavity. Therefore, the total SHG
enhancement factor induced by the F-P cavity is ~ 636 times, which is in good agreement with the
experiment results. Similarly, for the THG process, the enhancement factor is calculated by
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, indicating a stronger enhancement reaching ~ 1063 times at the same pump
wavelength. However, the observed cavity enhancement is far below the theoretical estimation. The
low enhancement factor should be ascribed to the strong absorption of the gold substrate and the
NbOBr2 flake at the emission wavelength.
An outstanding advantage of the F-P cavity is the ability to provide enhancement across a broad
spectral range. Herein, the wavelength-dependent SHG enhancement is measured with the pump
wavelength ranging from 1480 nm to 1640 nm. SHG enhancement can be observed throughout the
measurement range as shown in Figure 4g. In the case of the F-P cavities with a 10 μm hole depth, the
variation tendency of the enhancement factor with pump wavelength is consistent with the cavity
absorption spectra in Figure 1j. Notably, the incident wavelengths of
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Figure 5. a) Schematic of the experiment setup for measuring overall b) SHG and c) THG intensities
under different polarization excitation angles. Purple: on cavity; blue: off cavity. The incident
polarization angle is changed by rotating a halfwave plate (HWP). d) Schematic of the experiment
setup for measuring e) SHG and f) THG intensities versus the rotation angle of the polarizer. Purple:
on cavity; blue: off cavity. The excitation polarization is fixed 45° to the b-axis of NbOBr2 crystal, while
the output polarization is analyzed with a rotating polarizer. g) Calculated anisotropic enhancement
factor of SHG and THG processes. h) Measured anisotropic enhancement factor ranging from 1485 nm
to 1602 nm, consistent with the calculation curve in g).
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17
the maximum enhancement factors locate near 1500 nm and 1625 nm, which conform with the
positions of the cavity resonance modes. The wavelength-dependent SHG enhancement is further
performed on F-P cavities with different cavity depths, where all the cavities show SHG enhancement
with the similar trend corresponding to the simulated absorption spectra in Figure 4h. By tuning the
cavity depth, we can change the cavity resonance wavelength, consequently achieving strong
enhancement at any expected wavelength.
Furthermore, the anisotropy of the nonlinear signal can be controlled by the F-P cavity. Although
the F-P cavity is constructed in an isotropic manner, the enhancement factor still exhibits an intriguing
anisotropic characteristic. Comparing the on-cavity and off-cavity polarization-angle-dependent SHG
intensities in Figure 5b, the cavity enhancement factor is strongly dependent on the incident
polarization direction. SHG enhancement on cavity is much more prominent when the pump
polarization aligns with the b-axis of the NbOBr2 crystal. Hence, the SHG anisotropy increases from
7.34 (off cavity) to 17.82 (on cavity) between the b- and c-axis. Similarly, for THG process in Figure 5c,
the cavity enhancement is also much stronger along the b-axis, thus leading to the THG anisotropy
reduced from 6.22 to 1.18 between the b- and c-axis. Both SHG and THG processes obtain the
maximum enhancement when the pump polarization aligns with the b-axis of the NbOBr2 crystal,
which originates from the anisotropic nature of NbOBr2. For F-P cavities, the quality factor at the
wavelength λ is approximately given by , where n is the refractive index of
the cavity medium (air for our cavity), L is the cavity depth, and and are the reflectivities of the
two mirrors.[35] For the NbOBr2 mirror, the reflectivity can be calculated by the Fresnel equation
, where is the complex refractive index. Due to the birefringence feature of NbOBr2,
the reflectance of the NbOBr2 flake will be different when the cavity is pumped with orthogonal
polarizations. Hence, at the pump wavelength of 1500 nm, the ratio of the quality factor between the
b- and c-axis is calculated to be 1.27, while the ratio is 1.36 and 2.55 at the SHG and THG output
wavelengths respectively. Accordingly, the total anisotropic ratio of the enhancement factor along the
b- and c-axis is estimated to be 2.19 and 5.22 for the SHG and THG process respectively, consistent
with the experimental results (2.43 for SHG and 5.27 for THG). The anisotropic enhancement feature
also exerts an influence on the polarization of the nonlinear signal. In Figure 5e,f, the incident
polarization is fixed to 45° to both b- and c-axis, while a polarizer is rotated before the spectrometer
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18
to study the polarization of the emitted signal. For THG process, the stronger amplification along the
b-axis reduces the THG anisotropy and increases the THG component along the b-axis, thus rotating
the polarization of the total THG signal towards the b-axis. Consequently, a 10° rotation is observed
on cavity for the linear polarization orientation of the THG signal. On the contrary, the polarization
direction of the SHG signal remains almost unchanged due to the enhanced anisotropy.
The anisotropy of the nonlinear processes can be further tuned by altering the incident
wavelength. As shown in Figure 5h, we measure the wavelength-dependent anisotropic factor from
1486 nm to 1602 nm, which is defined as the ratio of the cavity enhancement factors when the
incident polarization is along the b- and c-axis. The measured anisotropic factors are consistent with
the calculation results in Figure 5g. Considering that the refractive index of NbOBr2 can be controlled
by various factors such as temperature, pressure and external fields[40], the F-P cavity design further
provides a wonderful platform to enhance nonlinear signals with tunable anisotropy, which is
promising for various potential photonic devices.
3. Conclusion
We report a novel van der Waals crystal, NbOBr2, and delve into its anisotropic nonlinear properties.
The NbOBr2 crystal features a highly anisotropic structure with weak interlayer coupling, resulting in
strong and anisotropic SHG and THG signals. The second-order and third-order nonlinear
susceptibilities of NbOBr2 flakes are measured to be ~ 3.59×10-11 m V-1 and 8.10×10-19 m2 V-2 at 1500
nm pump, comparable to TMDs. Due to the noncentrosymmetric crystal structure, the SHG and THG
intensities in few-layer NbOBr2 flakes are scalable with thickness and can easily surpass that of
monolayer MoS2.
To further enhance the nonlinear conversion efficiency and power density in NbOBr2, F-P cavities
are successfully constructed by coupling a few-layer NbOBr2 with holes on a silicon substrate. The
enhancement effect covers a broad spectral range, yielding maximum enhancement factors of around
630 times and 210 times for SHG and THG, respectively, near the cavity resonance wavelength of 1500
nm. The strong enhancement originates from the cavity-induced electric field enhancement inside
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19
NbOBr2, which is corroborated by the numerical simulation, angle-resolved reflection spectra and
absorption spectra.
Additionally, the enhancement factor of the F-P cavity is strongly anisotropic, exhibiting the largest
amplification along the b-axis of NbOBr2 flakes, which is ascribed to the birefringence nature of NbOBr2
crystal. At the incident wavelength of 1500 nm, the ratio of the enhancement factor reaches 2.43 and
5.27 between the b- and c-axis for SHG and THG, respectively. Accordingly, a high anisotropic ratio of
17.82 is obtained for the total SHG signal, while the THG signal tends to be isotropic. Meanwhile, the
direction of the THG polarization is observed to rotate around 10°. Furthermore, the anisotropic ratios
of SHG and THG are also proven tunable with the pump wavelength. Our proposed F-P cavity suggests
an exciting avenue to generate strong and anisotropic nonlinear signals, promoting nonlinear optical
applications with 2D materials.
4. Methods
Sample Synthesis and Characterization Bulk NbOBr2 crystals were synthesized via a chemical vapor
transport (CVT) method. The raw materials of Nb, Nb2O5, and Br2 with the element ratio of Nb: O: Br
= 1: 1: 2 were loaded into a silica tube, which was vacuumed and sealed with the end of tube immersed
in liquid nitrogen. Then, the tube was transferred to a two-zone furnace which was heated to 700
within 1 day and held for 7 days. Subsequently, the reaction and growth zones of the furnace were
cooled down to room temperature with different cooling rates within 15 days. At last, NbOBr2 crystals
with large size were obtained in the cool zone of the furnace. The crystal structure of the exfoliated
flakes was studied by HRTEM (JEOL-2100F). The XRD patterns of NbOBr2 crystal were measured by an
XRD Bruker D8 Advance Powder with Cu−Kα target with the angle ranging from 5° to 60°. The Raman
spectra were collected by a confocal Raman spectrometer (WITec alpha 300 RAS) equipped with a 532
nm laser. The optical absorption spectra were measured using a Fourier-transform infrared
spectrometer (FTIR) equipped with a silicon detector and an InGaAs detector.
Cavity Design and Fabrication FDTD simulation was performed to study the cavity enhancement effect.
In the simulation, the diameter of the holes was set as 8 μm, and the depth was 10 μm. The NbOBr2
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20
with a thickness of 10 nm was placed on top of the substrate. A Gaussian source with a waist radius
of 2.5 μm was chosen to excite the cavity. All the boundary conditions were set as perfectly matched
layers (PML).
A Si3N4 layer of 180 nm was deposited on a Si substrate by low-pressure chemical vapor deposition
(LPCVD). The hole array was patterned on ZEP 520A ebeam resist by electron beam lithography (EBL,
JEOL 6300FS). Then the pattern was transformed to the substrate by reactive-ion etching (RIE) which
removed the Si3N4 layer, and subsequently by deep reactive-ion etching (DRIE) which etched the silicon
holes. The resist was stripped in hot N-methyl-2-pyrrolidone after a layer of 10 nm Ti/ 100 nm Au was
evaporated on the sample. The sample was finally cleaned in oxygen plasma to remove the residues.
The NbOBr2 flakes were exfoliated mechanically onto polydimethylsiloxane (PDMS) stamps. After the
thickness of the flakes was checked through an optical microscope, the flakes with a thickness of
around 10 nm were transferred onto the hole region.
Experimental Setup Optical harmonic generation in NbOBr2 flakes was measured using a home-built
optical setup.[7, 8] The sample was excited by an optical parametric amplifier (OPA) system (pulse
width 150 fs, repetition rate 100 kHz). The femtosecond laser beam transmitting through a half
wavelength plate (HWP) was focused by an objective lens (50×, NA 0.45) to a spot of 2 μm in
diameter. For the transmission measurement setup, the generated signals were collected by another
objective lens (20×, NA 0.45), filtered by a short-pass filter, and analyzed by a spectrometer. To
check the polarization of the emission signal, a polarizer was added before the spectrometer. For
spatial SHG imaging, the sample was scanned within an area of 15 μm × 40 μm using a high-
resolution X-Y translation stage, and the signals were collected by a photomultiplier.
Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.
Acknowledgements
This research was supported by National Research Foundation Singapore program (NRF-CRP22-2019-
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21
0007 and NRF-CRP23-2019-0007) and Ministry of Education Tier 2 program (MOE-T2EP50120-0009),
Singapore A*STAR funding (A2090b0144, R22I0IR122, and M22K2c0080), and National Medical
Research Council (NMRC) (MOH-000927).
Conflict of Interest
The authors declare no conflict of interest.
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Table of Contents
Wenduo Chen†, Song Zhu†, Ruihuan Duan†, Chongwu Wang, Fakun Wang, Yao Wu, Mingjin Dai,
Jieyuan Cui, Sang Hoon Chae, Zhipeng Li, Xuezhi Ma, Qian Wang, Zheng Liu*, Qi Jie Wang*
Title Extraordinary Enhancement of Nonlinear Optical Interaction in NbOBr2 Microcavities
ToC figure (55 mm broad × 50 mm high)
Strong and anisotropic second- and third-harmonic generation (SHG and THG) processes are observed
in a novel two-dimensional material, niobium oxide dibromide (NbOBr2). Both SHG and THG processes
in NbOBr2 are significantly enhanced up to hundreds of times by coupling with a Fabry-Pérot (F-P)
microcavity. The enhancement factor is anisotropic and reaches maximum along the crystal b-axis.
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