Mid-infrared to ultraviolet efficient multiphoton frequency upconversion in NbOI_2 crystals

Domain: chemistry
Published: 2026-03-14
Editorial outcome: minor_revision

Abstract
Nonlinear frequency upconversion of mid-infrared (MIR) light is of particular importance for infrared imaging, detection and spectroscopy. However, achieving efficient and broadband MIR upconversion is hindered by phase-matching constraints and limited nonlinear coefficients of optical materials. Here, we demonstrate phase-matching-free, broadband and efficient multiphoton frequency upconversion in NbOI . We observe generation of harmonics from the second to the 11th order, with upconverted signals spanning from the MIR to the ultraviolet. We also achieve nonlinear frequency mixing in the broad spectral window of 1500-5000 nm, including degenerate four-wave mixing, sum-frequency mixing and sum-frequency generation with an efficiency up to 6×10-⁴ W-¹, surpassing those of leading metasurface-based platforms. Finally, we demonstrate broadband MIR upconversion imaging by direct detection from a conventional silicon camera. Our results establish NbOI as a promising platform for MIR nanophotonics, enabling advanced applications in ultrabroadband imaging, sensing and spectral conversion.

Introduction
Mid-infrared nonlinear optics is crucial for developing next-generation infrared light sources1, enabling ultrasensitive molecular detection2, and advancing on-chip photonic integration3. In particular, multiphoton nonlinear frequency upconversion manifested as second-harmonic generation (SHG)4, third-harmonic generation (THG)5,6, sum-frequency generation (SFG)7,8, difference-frequency generation (DFG)9,10, four-wave mixing (FWM)11,12, and high-order harmonic generation (HHG)13-15, offers an essential route to convert invisible MIR signals into the visible and ultraviolet (UV) ranges for cost-effective and efficient detection and imaging16-18.

Conventional bulk nonlinear materials such as silicon (Si), silicon nitride (Si N ), silicon dioxide (SiO ), and lithium niobate face intrinsic limitations in MIR upconversion due to weak nonlinear susceptibilities, stringent phase-matching requirements, and processing constraints. In contrast, Van der Waals two dimensional (2D) materials, such as graphene and transition metal dichalcogenides (TMDCs), exhibit strong optical nonlinearities19,20 that make them attractive for on-chip nonlinear optical devices21,22. However, the nonlinear conversion efficiency (e.g., SHG) in many 2D layered materials is constrained by the layer number, owing to strong interlayer coupling or changes in crystal symmetry, as observed in 2H-TMDCs23, rhombohedral boron nitride (rBN)24,25, SnP Se 16, and 3R-MoS 26,27.

Recently, ferroelectric van der Waals materials such as NbOX (X=I, Cl, Br) have emerged as promising nonlinear platforms due to their intrinsic inversion symmetry breaking and robust optical anisotropy28-33. In particular, NbOI demonstrates exceptionally strong SHG in the visible and near-infrared regions, enhanced by excitonic resonances, and the density functional theory (DFT) predicts an large second-order susceptibilities (𝜒(2)) in the infrared region28. Yet, its potential for broadband multiphoton frequency conversion and parametric processes in the MIR and UV has remained largely unexplored.

Here, we present a comprehensive demonstration of broadband, efficient, and phase-matching-free MIR multiphoton harmonic generation in nanoscale NbOI crystals. We report high-order harmonic generation up to the 11th order, encompassing both even and odd harmonics, with harmonic signals extending deep into UV, enabled by the material’s large 𝜒(2) and 𝜒(3) values (𝜒(2)≈147 pm/V at 1300 nm, ≈121 pm/V at 1700 nm, ≈60 pm/V at 2500 nm, and 𝜒(3)≈3×10-¹⁹ m²/V² at 1550 nm). Beyond harmonic generation, we achieve broadband nonlinear frequency mixing including SFG, degenerate four-wave mixing (DFWM), sum-frequency mixing (SFM), covering a wide input range (1500-5000 nm) with a SFG efficiency up to 6×10-⁴ W-¹ at 2600 nm, surpassing those reported for the state-of-the-art metasurfaces. Particularly, we demonstrate the broadband MIR upconversion imaging (2700-4000 nm) using the visible silicon camera based on phase-matching-free SFG in a single NbOI flake at room temperature. Our findings pave the way for a new paradigm in MIR nonlinear photonics, combining broadband response, large optical nonlinearity, and structural scalability to enable unprecedented capabilities in broadband upconversion, optical imaging, and long-wavelength infrared detection.

Results
Figure 1a illustrates a schematic diagram of MIR upconversion processes in the NbOI flake. Bulk NbOI crystals belong to the monoclinic space group C2 and feature a characteristic van der Waals layered structure along the a-axis (Fig. 1b)28. Figure 1c presents an optical image and an atomic force microscopic image (AFM) of the NbOI flake with a typical thickness of ~8 nm. Atomic-resolved annular dark field-scanning transmission electron microscopy (ADF-STEM) technique confirms the b-axis of the NbOI crystal, consistent with the simulated image (Supplementary Fig. S1c). While NbOI crystals exhibit anisotropic absorption along the two in-plane axes28, no experimental data on absorption in the MIR region was previously available. We measured the absorption spectra of a 20-nm NbOI flake, revealing smooth absorption across a 1000 to 2600 nm spectral range. Notably, the absorption exhibits strong anisotropy in the infrared region (Fig. 1d), attributed to excitonic-absorption-induced decay differences along the two in-plane axes in the visible spectral region28. The difference in the Raman spectra along the b- and c-axes also indicates the anisotropic phonon response derived from different crystal orientations between the two axes (Supplementary Fig. S2).

Strong SHG and THG processes with polarization anisotropy in asymmetric NbOI crystals

We investigate the second- and third-order nonlinear effects of the NbOI crystal in the infrared region through SHG and THG processes (Fig. 2a). The second- and third-order nonlinear susceptibilities of NbOI are quantitatively determined to characterize its nonlinear optical properties. The 𝜒(2) values of the NbOI crystal are calculated to be 147 pm/V at 1300 nm and 121 pm/V at 1700 nm by comparing with quartz (Supplementary Fig. S3). The 𝜒(2) value at 2500 nm is estimated to be ~60 pm/V. The 𝜒(3) values of the NbOI crystal are calculated to be 3×10-19 m2/V2 and 5.5×10-19 m2/V2 at 1550 nm by comparing with the silica substrate and monolayer WS , respectively (Supplementary Fig. S4). The difference in 𝜒(3) is mainly derived from the discrepancies in experimentally reported 𝜒(3) values for TEMDC monolayers. In addition, 𝜒(3) is also independent on the excitation intensity, indicating that extracted 𝜒(3) is not affected by thermal nonlinear optical effects (Supplementary Fig. S5). The SHG (𝜂 = 𝐼 ⁄𝐼 ) and THG (𝜂 = 𝐼 ⁄𝐼 ) conversion efficiencies as a function of the excitation intensity are shown in Fig. 2b. The SHG conversion efficiency under 2500-nm excitation is calculated to be 4.3×10-6 under an excitation intensity of 70 GW/cm2, corresponding to a normalized conversion efficiency (𝜂 ) of 8.6×10-4 W-1 based on the equation34,35: 𝜂 = 𝐼 ⁄𝐼 2. This value is comparable to that of Weyl Te in the MIR region35 and is an order of magnitude higher than that achieved in lithium niobate waveguides34.

The NbOI crystal also exhibits polarization-dependent SHG and THG responses, arising from its intrinsically asymmetric in-plane crystal structure. We introduce the anisotropic ratio (𝜌) to characterize the anisotropic nonlinear optical response of the NbOI crystal. The SHG anisotropic ratio of the NbOI crystal is defined as: 𝜌 = 𝐼 ⁄𝐼 ∝(𝜒 (2) ⁄𝜒 (2) )2 , where 𝐼 is the SHG intensity with the excitation polarization along the (c) x-axis, 𝐼 is the SHG intensity with the excitation polarization along the (b) y-axis. Figure 2c demonstrates polar plot of the SHG intensity under 2500-nm excitation with both parallel and perpendicular configurations. The SHG response demonstrates distinct in-plane anisotropy, with the maximum intensity observed along the b-axis. This observation is well explained and fitted through crystal symmetry analysis of the NbOI crystal (Fig. 2c, Supplementary Note S2). The 𝜌 value at 2500 nm is ~14, corresponding to 𝜒 :𝜒 =3.7. The differences in 𝜌 across different wavelengths arise from the dispersion of the nonlinear optical susceptibility in the NbOI crystal (Fig. 2e, Supplementary Fig. 6b, c, Fig. S9)28. Supplementary Fig. S8a-c show SHG mappings of the NbOI flake at 1400 nm along the b- and c-axes, respectively. Notably, a strong SHG signal is observed when the excitation polarization is along the b-axis, whereas the SHG signal is negligible when the excitation polarization is along the c-axis.

The THG anisotropic ratio is defined as: 𝜌 = 𝐼 ⁄ 𝐼 ∝(𝜒 (3) ⁄𝜒 (3) )2 . Figure 2d demonstrates x- and y- components of the THG intensity under 2500-nm excitation. It can be found that THG intensity is the largest when the excitation polarization is along the b-axis. The extracted relative magnitudes of the 𝜒(3) tensor components are 𝜒 (3) :𝜒 (3) :𝜒 (3) :𝜒 (3) =1:1.6:0.05:0.2, corresponding to 𝜌 =2.56. THG shows different polar-plot patterns under 1300-nm and 1550-nm excitations due to the 𝜒(3) dispersion (Supplementary Fig. S7). The extracted relative magnitudes of the 𝜒(3) tensor components are 𝜒 (3) :𝜒 (3) :𝜒 (3) :𝜒 (3) =1:3.2:0.9:0.1 at 1300 nm corresponding to 𝜌 =10 and 𝜒 (3) :𝜒 (3) :𝜒 (3) :𝜒 (3) =1:0.8:0.9:0.1 at 1550 nm corresponding to 𝜌 =0.64. The anisotropic ratios of SHG and THG as a function of the excitation wavelength in the NbOI crystal are also studied. Figure 2e presents the 𝜌 value depending on the excitation wavelength across a range of 850 to 3200 nm. We find that a 20-nm NbOI flake exhibits a high 𝜌 value of ~10 across a broad spectral range (1300-3200 nm), reaching a value of ~33 under 1400-nm excitation. This behavior correlates well with anisotropic SHG spectra shown in Supplementary Fig. S9a-e. The broad spectral range is larger than those in all the 2D layered materials (Supplementary Table S1). It is worth noting that the 𝜌 value starts to decrease from 10 at ~850 nm to the minimum value of 1 at ~1070 nm, which corresponds to the exciton peaks P /P at ~530 nm along the c-axis. Exciton peaks P /P enhance the SHG intensity along c-axis, while reducing the SHG anisotropy at ~1070 nm.

Figure 2f illustrates the 𝜌 value as a function of the excitation wavelength ranging from 1250 to 2600 nm, corresponding to anisotropic THG spectra in Fig. S9f-j. NbOI exhibits a high 𝜌 value of ~17, which gradually decreases at wavelengths beyond 1250 nm. Strikingly, the 𝜌 value exhibits a transition (𝜌 < 1 ) and reaches a minimum value of ~0.38 when the excitation wavelength approaches 1590 nm. The corresponding THG wavelength aligns with the P /P exciton peaks at ~530 nm along the c-axis28, where three-photon enhancement along the c-axis contributes to wavelength-dependent changes in THG anisotropy. Furthermore, THG mappings of the NbOI flake at 1300 nm are also performed for linear polarization parallel to the b- and c-axes, respectively (Supplementary Fig. S8d-f). The mapping intensity in Fig. S8e is larger than that in Fig. S8f, confirming strong THG anisotropy at 1300 nm. This mapping technique enables effective identification of the crystal axes in large-area NbOI flakes. The 𝜌 value of ~17 is higher than that observed in most reported 2D layered materials (Supplementary Table S2).

High-order harmonic processes

Due to the inversion symmetry breaking caused by spontaneous ferroelectric polarization in the bulk state, even-order harmonic processes (such as SHG, SFG, 4th-, and 6th-harmonic processes in the MIR region) can be potentially realized in the NbOI flake28,36. The high-order multiphoton optical processes in NbOI flakes are investigated based on a home-built optical system (Fig. 1e). A ~200-nm NbOI flake is excited at normal incidence, and the generated SHG, THG, fourth (FOHG, 4th), fifth (FIHG, 5th), sixth (SIHG, 6th), seventh (SEHG, 7th), eighth (EIHG, 8th), nineth (NIHG, 9th), tenth (TEHG, 10th), and eleventh (ELHG, 11th) harmonic signals are collected in the transmission direction. Figure 3b presents THG, FOHG, and FIHG spectra under 2500-nm excitation, while Fig. 3c, d display SIHG, SEHG, EIHG, NIHG, TEHG, and ELHG spectra under 3500-nm excitation. Remarkably, the NbOI flake generates SEHG, EIHG, NIHG, TEHG, and ELHG signals that extend beyond its optical bandgap into the UV regime, highlighting its exceptional capability for upconversion photodetection and UV light source.

It is well known that harmonic signals generated in the perturbative regime of nonlinear polarization follow the intensity scaling law15: 𝐼 ∝𝐼𝑛, where 𝐼 and 𝐼 are the intensities of Nth-harmonic signals and excitation laser, N is the harmonic order. We performed power-law fits to the experimental results (Fig. 3e, f, Supplementary Fig. S6a). The generated SHG, THG, FOHG, FIHG, SIHG, SEHG, EIHG, and NIHG intensities follow relations of 𝐼2.1, 𝐼3, 𝐼4.2, 𝐼4.8, 𝐼5.3, 𝐼7.1, 𝐼8.1, and 𝐼8.8 , respectively, indicating multiphoton harmonic processes in the perturbative regime (Fig. 3a)15,37. For the high-order harmonic processes, minor differences between the experimental and theoretical results are attributed to measurement uncertainties and signal instability, primarily arising from additive and shot noise15. Owing to the spectral range limitations of the spectrometer, we employ a 3500 nm laser to excite the high-order harmonic signals. It is noted that the 11th-harmonic signal is close to the noise signal, thus we perform the wavelength-dependent 11th-harmonic process with excitation wavelengths at 3530 nm, 3895 nm, and 4125 nm. The corresponding signals at 320 nm, 354 nm, and 375 nm verify the 11th-harmonic process (Supplementary Fig. S10). The similar phenomenon to THG in Fig. 2f is also found in the 6th-harmonic process, which shows the wavelength-dependent anisotropy (Supplementary Fig. S11).

The conversion efficiency (𝜂 = 𝑃 ⁄𝑃 ) is measured using a calibrated spectrometer (Methods). It is evident that high-order harmonic signals exhibit the lower conversion efficiency, as high-order multiphoton optical processes require the higher excitation intensity38-40 (Fig. 3g). Typically, the EIHG conversion efficiency is as high as 3.5×10-10 at an excitation intensity of 120 GW/cm2 in the perturbative regime, same order to that generated in the CuInP S flake (Supplementary Table S3)15. The FIHG conversion efficiency is in the order of 4×10-8, one order higher than that at the same order in the Si metasurface (Supplementary Table S3)41.

Frequency-mixing for MIR frequency upconversion

Multiphoton high-order harmonic generation driven by a single-beam pump requires high pump intensities due to the intrinsically weak high-order nonlinear susceptibilities, e.g., GaP metamaterial requires an excitation intensity of 0.6 TW/cm2 to generate NIHG signals14. In contrast, nonlinear frequency mixing driven by a two-beam pump can generate multiple colors within the spectral range of HHG signals, benefiting from lower excitation intensities due to the large 𝜒(2) and 𝜒(3) values of NbOI . As illustrated in Fig. 1e, we demonstrate nonlinear frequency mixing via a two-beam excitation scheme (𝜔 at 1030 nm, 𝜔 at 1500-5000 nm). The collinearly propagating pump beams are focused on the sample by a lens (Methods). When two beams (𝜔 at 1030 nm, 𝜔 at 2500 nm) are focused onto a ~100-nm NbOI flake with temporal overlapping, four distinct spectral peaks emerge across the entire visible range. As shown in Fig. 4a, b, the signals are categorized into SFG (𝜔 +𝜔 ) at 730 nm, DFWM (2𝜔 −𝜔 ) at 650 nm, SFM1 (𝜔 +2𝜔 ) at 565 nm, and SFM2 (2𝜔 +𝜔 ) at 430 nm. Notably, the FWM peak exhibits the lower amplitude compared to the sum-frequency generation (SFG) peak, reflecting the higher efficiency of 𝜒(2) mediated frequency mixing process42. Furthermore, we systematically verified the physical origins of these frequency-mixing processes through wavelength- and power-dependent measurements, showing that the output wavelengths scale with the input pump wavelengths, while the corresponding intensities follow the expected nonlinear power dependences. For example, the signal peak at 730 nm shows the linear dependence on the 𝜔 and 𝜔 powers (Supplementary Fig. S12a, b). In a similar manner, 𝜔 power dependent SFM (SFM1 and SFM2) spectra are also measurement (Supplementary Fig. S12c). The blue curve shows the nearly quadratic dependence of the SFM2 (2𝜔 +𝜔 ) intensity on the 𝜔 power. In contrast, the red curve shows the linear dependence of the SFM1 (𝜔 +2𝜔 ) intensity on the 𝜔 power. To further confirm the SFG process in the broadband MIR spectral range, the wavelength dependent SFG is also performed, as shown in Fig. 4c. The SFG wavelength is tuned accordingly by varying the 𝜔 wavelength in the range from 1500 to 5000 nm, confirming the high frequency-mixing performance in the broadband MIR spectral range due to large 𝜒(2) values in the infrared region. It is worth noting that the spectrum with 𝜔 =5000 nm is not symmetric due to the asymmetric pump spectrum, which is derived from frequency chirp from the OPA system (including periodically poled lithium niobate (PPLN), mirror, and lens)43 and absorption effect of PPLN44.

Typically, the SFG efficiency at the signal wavelength of 2600 nm is calculated (Fig. 4d). The conversion efficiency (𝜂 = 𝑃 ⁄𝑃 ) reaches the maximum value of 6×10-8 at the signal intensity of 663 MW/cm2, where 𝑃 and 𝑃 are SFG power and MIR signal power, respectively. Considering the power ratio between the SFM2 and SFG processes, the conversion efficiency for SFM2 at 430 nm is estimated to be 8×10-9 at the same signal intensity, nearly one order higher than the signal for SIHG at a pump intensity of 110 GW/cm2, confirming the higher efficiency for frequency mixing11. Correspondingly, the maximum normalized SFG conversion efficiency (𝜂 =𝑃 ⁄(𝑃 𝑃 )) is 6×10-4 W-1, where 𝑃 is the pump power. Polarization angle-dependent SFG and SFM processes are also measured by tuning the polarization of the 𝜔 beam (Supplementary Fig. S12d, e). The two beams are co-polarized parallel to the b-axis of NbOI when the angle is 0°. It can be found that both SFG and SFM peaks show the maximum values, and the signals are negligible when the polarizations of the two beams are perpendicular. This demonstrates the frequency mixing process by two beams and the anisotropic response in NbOI . It is worthing noting that nonlinear conversion efficiencies (such as SHG, THG, and SFG) increase monotonically with the thickness smaller than 200 nm, since the thicknesses used in this work is within the coherence lengths (Supplementary Note S4, Fig. S13, S14). The anisotropies of SHG and THG are nearly independent on the flake thickness as both harmonic intensities increase monotonically for thicknesses up to 200 nm as the excitation polarization is aligned along the b- and c-axes, respectively (Supplementary Fig. S15). In addition, the nonlinear response (e.g., SHG) of NbOI deviates from the expected 𝑁2 scaling with layer number due to interference between surface and bulk contributions29,45,46. In order to provide a comprehensive comparison for different nonlinear optical processes, we measured efficiencies of SHG, SFG, THG, 4th-, 5th-, 6th-, 7th-, and 8th-harmonic processes in the same NbOI flake (~200 nm). The results indicate that the conversion efficiency decreases with increasing harmonic order (Supplementary Fig. S16), as high-order processes require higher excitation intensities15,47.

Broadband MIR upconversion imaging

Given the inferior performance of MIR cameras compared to their NIR and visible counterparts, the development of upconversion imaging techniques has become increasingly essential. A promising approach to upconversion imaging involves leveraging strong light-matter interactions in subwavelength resonators arranged into resonant metasurfaces12,48,49. Although metasurface platforms offer exciting opportunities for miniaturized frequency conversion devices without the phase-matching constraints of bulk crystals, they still face limitations, which include reduced power conversion efficiency due to high-order diffraction effects, angle-dependent resonance characteristics across the imaging field of view49. Consequently, there is a pressing need to explore alternative miniature upconversion devices that are simpler to implement and offer imaging performance comparable to their counterparts.

With the broadband and efficient upconversion capability of NbOI established, we demonstrate its application for room-temperature MIR upconversion imaging in Fig. 5. For the SFG process, 1030 nm and MIR light are used as the pump and signal, respectively. In the imaging setup (Fig. 5a), the beam sizes of the pump and signal are controlled by lens groups to approximately 105 μm and 70 μm (Supplementary Note S3, Fig. S17). The 1030 nm light passes through two lenses with different focal lengths (𝑓 = 200 mm and 𝑓 = 30 mm) and directly illuminates the surface of the NbOI flake. For the MIR light, the test target is positioned at the front focal plane of the first lens. The separation between the two lenses is set equal to the sum of their focal lengths, ensuring a conjugate imaging configuration. This configuration allows the MIR beam to be focused onto the same spot on the sample surface, thereby achieving optimal spatial overlap between the laser beams. An objective is placed behind the sample to collect the signals generated by the interaction. To isolate the SFG signal and remove other unwanted signals, two filters (FELH0700 and FESH0875, Thorlabs) are positioned in the signal collection path. Finally, the converted images of the test target are captured by a visible silicon camera (CS135MUM, Thorlabs) at the collection side.

We successfully realized and demonstrated broadband MIR upconversion imaging based on the SFG process in the NbOI crystal. Under white light illumination, the target image is shown in Fig. 5b. Figure 5c displays the SFG converted images captured by the camera for excitation light pairs of 1030 nm+2700 nm, 1030 nm+3500 nm, and 1030 nm+4000 nm, respectively. Notably, the demonstrated SFG imaging technique can, in principle, be extended to arbitrary objects. It is worth noting that upconversion images from different wavelength combinations do not spatially overlap but show vertical offsets. The offsets mainly come from optical misalignments, which arise from the operation mechanism of the OPA system and the external collimation optics. Leveraging the polarization-dependent properties of the SHG process in NbOI , we further demonstrate SHG imaging with different polarizations of the incident beam (1550 nm in this work), as shown in Fig. 5e. Figure 5d shows the target image (the letter "i") under white light illumination. The converted images at polarization angles of 0º, 30º, 50º, and 90º are shown in Fig. 5e. It is evident that the SHG imaging performance deteriorates as the polarization angle of the incident shifts from 0º to 90º. This is because when the polarization aligns with the b-axis of NbOI (0º in our experiment), the SHG efficiency is maximized, resulting in the clearest converted image. As the polarization angle continues to rotate, the misalignment between the excitation beam and the sample's b-axis increases, resulting in reduced conversion efficiency and degraded imaging performance.

Methods
Synthesis of NbOI crystals and sample preparation

High-quality NbOI bulk crystals were synthesized by the chemical vapor transport method. The reaction precursors Nb, Nb O and I powders with a molar mass ration of 3:1:6 was mixed and sealed in an evacuated quartz tube with pressure less than 10 mbar. The tube was then slowly heated up to 700 °C and maintained at this temperature for 5 days, followed by naturally cooling to room temperature. Finally, the synthesized NbOI crystals were soaked in alcohol to remove the excess I . The NbOI flakes were obtained by mechanical exfoliation from the bulk NbOI .

Electron and phonon characterization

High resolution transmission electron microscope (HRTEM) imaging was carried out on an JEOL 2200FS transmission electron microscope operated at 200 keV. Raman spectra were acquired using a micro-Raman spectrometer (WITec) with a confocal backscattering geometry. A continuous wave 532 nm laser was focused on the samples by an objective lens (×100, NA=0.9) with a spot size of ~1 μm. The generated Raman signals were collected by the same objective and analyzed by a spectrometer equipped with a thermoelectric cooling (TEC) detector. To reveal the phonon anisotropy, the polarization-resolved Raman spectra were measured with the excitation polarization along b- and c-axes, respectively.

Absorbance measurement

The micro-absorption measurement was performed using a Fourier-transform infrared spectrometer (FTIR) with a microscope, in which the NbOI samples were placed between aligned objective lenses for light focusing and collecting. A broadband light source was focused on the sample by an objective lens. The transmitted light was collected by the other one objective lens and then sent to the FTIR. The absorption spectra could be obtained by comparing the transmitted spectra between the sample and the substrate. For measurements of anisotropic absorption spectra in the infrared region, a linear polarizer was set in front of the first objective to realize linearly polarized incidence. Polarized absorption spectra were obtained by making the polarizer along b- and c-axes, respectively.

Nonlinear optical response measurements

The nonlinear optical response of the NbOI flake was measured in the home-built optical system (Fig. 1e). An optical parametric amplifier (OPA) pumped by a mode-locked laser (1030 nm, 400 fs, 100 kHz) was used as the tunable laser source for the nonlinear optical experiments. The excitation beam was focused by an objective lens onto the sample. The transmitted nonlinear signals were collected by another objective lens and analyzed by a spectrometer. To measure the efficiencies, wavelength-dependent and broadband nonlinear optical processes, we used a single or broadband light source to calibrate the collecting path by characterizing the wavelength-dependent losses of the optical setup, including the absorption of the objective, the lens, the fiber, the grating efficiency, and the CCD quantum efficiency. To perform the multiphoton harmonic generations, the MIR incident light was focused by a 40× reflective objective onto the sample, and the generated signals were collected by a 20× objective. To carried out frequency mixing experiments, a near-infrared laser at 1030 nm and another infrared laser (1500-5000 nm) from OPA were spatially combined by a dichroic mirror (DM) and then collinearly propagate into a lens. The temporal overlap between the pulses was controlled by a variable delay line. The generated signals were collected by a 20× objective and then analyzed by a spectrometer.

To measure SHG with parallel and perpendicular configurations, a half waveplate (HWP) and a polarizer were rotated simultaneously to detect SHG signal with the polarization components parallel or perpendicular to the excitation polarization. For anisotropic THG measurement, we rotated a HWP to tune the excitation polarization while keeping the polarizer along c- or b-axes of the NbOI crystal, and thus x- or y-components of the THG signal could be measured. For SHG/THG imaging of the NbOI flake, 1400 nm/1300 nm lasers were used as excitation sources. The samples were scanned with an area of 80 μm×80 μm through a high-resolution X-Y stage, and the SHG/THG signals were detected by a photomultiplier (PMT). We used HWP to tune the excitation polarization. All the measurements were performed in ambient condition, which proves its good stability in the ambient. Long-term stability measurement under 1550-nm excitation indicates that the NbOI crystal can maintain a relatively good quality over a period of 24 h (Supplementary Fig. S18).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "I find the paper to include a range of important and novel results with significant impact to the field. This includes the manufacturing of a novel nonlinear material and a range of detailed and fundamental investigations of the basic material and optical properties. This is basic investigations that can benefit much future work on this and other materials. Furthermore the main results in the paper beautifully investigate and document the nonlinear properties over a broad range of processes. Everything is described in details and conclusions are well supported by results and scientific based arguments. The supplementary materials should also be mentioned as thorough and detailed. In the end a more practical application is tested and included as possible use of this novel material. Again the method and documentation is sound and the application show a relevant choice that points towards future possibilities.\nA few minor suggestions and questions came to mind while reading the paper:\nFigure 1e - From the description of the experimental setup in the paper and the methods it is clear how the experiment overall is conducted. It is however still unclear what is the purpose of the CCD next to the white light source. A clarification of this would improve the interpretation of figure 1e.\nDiscussion - It is discussed how to enhance the nonlinear interactions further and several devices is suggested. It is however a little unclear how the technology can be moved from a flake with to practical implementations of detection and imaging devices. I understand most of this is out of scope for this paper, but it could be relevant to include more on the relevant parameters in the discussion. Is this material possible to machine or grow in different shapes or thicknesses? How does it work with other materials and environments. Most important could be how to reach high performance at less extreme intensities and more product relevant quantum efficiencies.\nFigure S6 - Double check the y-axis values on the plot a. Compared to the other plots it looks strange, maybe a brief comment why it does not baseline at 0.", "reviewer_2": "This manuscript reports the use of NbOI2 as a nonlinear optical material for mid-infrared upconversion, including two-photon, three-photon, and higher-order multiphoton processes. The material exhibits excellent anisotropy and conversion efficiency. The study is clearly written, logically structured, and the data generally support the authors’ conclusions. The manuscript presents valuable and innovative results, but clarification and further discussion of the following points would substantially enhance the rigor and impact of the work, and ensure its suitability for publication in Nature Communications.\nBefore publication, however, the following issues should be carefully addressed:\n1. It is not clear whether the conversion efficiency and anisotropy of SHG, THG, and other multiphoton processes depend on sample thickness. If thickness dependence exists, the underlying mechanism should be discussed.\n2. In Fig. 2e, ρSHG shows a pronounced minimum around 1000 nm, attributed to an excitonic resonance along the c-axis. The authors should clarify whether similar features occur in ρTHG or other multiphoton processes.\n3. In Fig. 3c, the 11th-order signal intensity is very close to the noise level, making it difficult to confirm whether an actual harmonic was observed. Stronger evidence is required to substantiate this result.\n4. Fig. 4c shows a shoulder on the long-wavelength side of the SFG peak, especially when w2 = 5000 nm. The authors should provide a physical explanation for this feature.\n5. In Fig. S8, SHG and THG spectra under long-wavelength pumping display multiple peaks in the harmonic line shapes. The origin of this behavior should be further clarified.\n6. In Fig. 5c, upconversion images from different wavelength combinations do not spatially overlap but show vertical offsets. The possible causes, such as phase-matching, optical alignment, or material anisotropy, should be discussed.\n7. The long-term stability of the material is not addressed. Can it retain its high upconversion efficiency after repeated measurements? Experimental data on stability would significantly strengthen the manuscript.\n8. The sensitivity of this material to strain or other external perturbations should be considered. The authors should discuss whether such sensitivity might pose limitations for practical applications.\n9. What is the role of ferroelectricity in this mid-infrared upconversion process?", "reviewer_3": "I have co-reviewed this manuscript in collaboration with another reviewer.\nThis manuscript reports the use of NbOI₂ as a nonlinear optical material for mid-infrared upconversion, including two-photon, three-photon, and higher-order multiphoton processes. The material exhibits excellent anisotropy and conversion efficiency. The study is clearly written, logically structured, and the data generally support the authors’ conclusions. The manuscript presents valuable and innovative results, but clarification and further discussion of the following points would substantially enhance the rigor and impact of the work, and ensure its suitability for publication in Nature Communications.\nBefore publication, however, the following issues should be carefully addressed:\n1. It is not clear whether the conversion efficiency and anisotropy of SHG, THG, and other multiphoton processes depend on sample thickness. If thickness dependence exists, the underlying mechanism should be discussed.\n2. In Fig. 2e, ρSHG shows a pronounced minimum around 1000 nm, attributed to an excitonic resonance along the c-axis. The authors should clarify whether similar features occur in ρTHG or other multiphoton processes.\n3. In Fig. 3c, the 11th-order signal intensity is very close to the noise level, making it difficult to confirm whether an actual harmonic was observed. Stronger evidence is required to substantiate this result.\n4. Fig. 4c shows a shoulder on the long-wavelength side of the SFG peak, especially when w₂ = 5000 nm. The authors should provide a physical explanation for this feature.\n5. In Fig. S8, SHG and THG spectra under long-wavelength pumping display multiple peaks in the harmonic line shapes. The origin of this behavior should be further clarified.\n6. In Fig. 5c, upconversion images from different wavelength combinations do not spatially overlap but show vertical offsets. The possible causes, such as phase-matching, optical alignment, or material anisotropy, should be discussed.\n7. The long-term stability of the material is not addressed. Can it retain its high upconversion efficiency after repeated measurements? Experimental data on stability would significantly strengthen the manuscript.\n8. The sensitivity of this material to strain or other external perturbations should be considered. The authors should discuss whether such sensitivity might pose limitations for practical applications.\n9. What is the role of ferroelectricity in this mid-infrared upconversion process?", "reviewer_4": "The authors systematically investigated various nonlinear optical processes—including second-harmonic generation (SHG), third-harmonic generation (THG), high-harmonic generation (HHG), sum-frequency generation (SFG), degenerate four-wave mixing (DFWM), and sum-frequency mixing (SFM)—in NbOI₂ nanosheets, employing pump wavelengths spanning from 800 to 5000 nm. They demonstrated broadband and substantial optical nonlinearities, which depend sensitively on the excitation laser’s wavelength, polarization, and power. Additionally, the authors achieved mid-infrared (MIR) upconversion imaging in the 2500–4200 nm range, with direct detection using a conventional silicon camera. This study may be suitable for publication in Nature Communications, pending satisfactory revisions:\n1- “However, the nonlinear conversion efficiency (e.g., SHG) in many 2D layered materials is constrained by the layer number, owing to strong interlayer coupling or changes in crystal symmetry, as observed in 2H-TMDCs,…” (Page 3 Line 62)\nI would like to note that while AA-stacked NbOI₂ with a C₂ space group exhibits broken inversion symmetry regardless of thickness, its nonlinear response—such as SHG—does not scale quadratically with the number of layers (N), as one might expect for ideal, lossless media. This deviation from the expected N² dependence primarily arises from interference between surface and bulk SHG contributions, leading to pronounced oscillations in the overall nonlinear signal, as reported in [Nature 613, 53 (2023); Science 367, 903 (2020); Scientific Reports 6, 22620 (2016)]. Therefore, making direct comparisons between different nonlinear optical processes using NbOI₂ flakes of varying thicknesses (e.g., 20 nm for SHG/THG, 200 nm for higher-order harmonics, and 100 nm for frequency upconversion) may not provide a fully comprehensive or consistent evaluation.\n2- The authors report a value of χ_SHG(2) ≈ 147 pm/V at 1300 nm. Is this the highest value observed to date? In a previous study on NbOI₂ flakes of comparable thickness (Nat. Photon. 16, 644 (2022)), the authors reported a maximum χ_SHG(2) at a pump wavelength of approximately 1000 nm (see their Fig. 3F), with the value decreasing as the pump wavelength was shifted to longer wavelengths.\n3- The reported value of χ^(3) in this work is ≈ 5.5 × 10⁻¹⁹ m²/V² at 1550 nm. This is surprisingly high compared to the findings in Advanced Optical Materials 11, 2202833 (2023), where the authors measured negligible third-order susceptibility for NbOCl₂ flakes at various pump wavelengths (850–1600 nm) under pump intensities of kW/cm² and a repetition rate of 100 kHz. In contrast, the present study calculates nonlinear efficiencies at much higher pump intensities, on the order of GW/cm². I therefore suspect that the reported nonlinear responses may be significantly influenced by thermal nonlinear optical effects rather than being purely due to the material’s intrinsic (electronic) optical nonlinearity.\n4- The caption for Figure S1 is incomplete. Does Fig. S1c show STEM images taken along the [100] zone axis? Please clarify this in the caption, and indicate the polar and nonpolar axes directly on the images.\n5- “The anisotropic in-plane structure can be directly observed by atomic-resolved annular dark field-scanning transmission electron microscopy (ADF-STEM) technique, which confirms the 1D Peierls distortion of Nb atoms, inducing polarization along the b-axis…” (Page 4 Line 96)\nPlease note that the second-order Peierls distortion and the associated periodic modulations along the polar axis cannot be visualized in STEM images taken exactly along a perfect zone axis, due to the staggered AA packing structure of NbOI₂ (see Nature 613, 53 (2023) and Adv. Optical Mater. 11, 2202833 (2023)).\n6- “Notably, the absorption exhibits strong anisotropy, attributed to excitonic absorption differences along the two in-plane axes in the visible spectral region (Figure 1d)24…” (Page 4 Line 104)\nThe absorption data presented in Fig. 1d were collected in the near- and mid-infrared regions, not in the visible spectral region.\n7- Why is the χ(3) value calculated relative to monolayer WS₂, rather than quartz? There are significant discrepancies in experimentally reported χ(3) values for TMD monolayers, owing to the variety of formalisms used in the literature. Using quartz as a reference could provide a more consistent and widely accepted benchmark.\n8- It is confusing to interpret the data, as figures and subfigures were collected using different excitation wavelengths. For example, THG imaging was performed under 1300 nm excitation, the THG polar plot under 1550 nm, and the THG spectrum under 2500 nm. For clarity and consistency, please use the same excitation wavelength across related measurements or clearly indicate the differences in each figure.\n9- What excitation wavelength was used in Fig. 2b? Please specify this information in the figure or its caption.\n10- “Remarkably, the NbOI₂ flake generates SEHG, EIHG, NIHG, TEHG, and ELHG signals that extend beyond its bandgap into the UV regime,…” (Page 8 Line 199)\nPlease note that although the electronic bandgap (E₉) of NbOI₂ is approximately 2.24 eV, the material also exhibits optical bandgaps in the UV region along both the polar and nonpolar axes (Nat. Photon. 16, 644 (2022)).\n11- The Raman spectrum presented in Fig. S2 is not referenced or discussed in the main text. Please include an appropriate reference to Fig. S2 and discuss its relevance.\n12- What is the scale bar for the maps shown in Figure S7? I assume they correspond to 80 μm × 80 μm areas—please confirm and indicate this clearly in the figure or its caption.\n13- What pump power or intensity was used in Figure S6b? Please specify this information in the figure or its caption.\n14- Please rearrange the figures in the Supplementary Information to match the order in which they are first cited in the main text, to ensure a smoother flow for the reader."}, "author_response": "Thanks for the reviewer’s comments and suggestions.\nResponse to “The supplementary materials should also be mentioned as thorough and detailed”\nWe have carefully addressed this point and ensured that all the contents of the supplementary materials are clearly mentioned and discussed in the revised manuscript.\n1- Figure 1e - From the description of the experimental setup in the paper and the methods it is clear how the experiment overall is conducted. It is however still unclear what is the purpose of the CCD next to the white light source. A clarification of this would improve the interpretation of figure 1e.\nResponse:\nTo locate samples and focus the pump light on a micrometer-scale area, a CCD camera and a white light source are used for imaging, thus enabling precise determination of the pump position.\nWe also provided the related descriptions in the revised manuscript.\nline 132-line 133:\nCCD: charge coupled device (the CCD camera and white light source are used for imaging, enabling precise determination of the pump position).\n2- Discussion - It is discussed how to enhance the nonlinear interactions further and several devices is suggested. It is however a little unclear how the technology can be moved from a flake with to practical implementations of detection and imaging devices. I understand most of this is out of scope for this paper, but it could be relevant to include more on the relevant parameters in the discussion. Is this material possible to machine or grow in different shapes or thicknesses? How does it work with other materials and environments. Most important could be how to reach high performance at less extreme intensities and more product relevant quantum efficiencies.\nResponse:\nWe appreciate the reviewer’s constructive suggestions.\nResponse to “It is discussed how to enhance the nonlinear interactions further and several devices is suggested”\nThere are several ways to enhance the nonlinear interactions in the NbOI crystals. First, the nonlinear optical interactions can be further enhanced by patterning the NbOI crystals into resonance structures such as metasurfaces1,2, flat-band photonic crystals3,4, and nanodisks5,6. Second, we can also enhance the nonlinear optical interactions by introducing quasi-phase-matching by stacking the NbOI flakes with periodically poling7.\nWe also provided discussions in the revised manuscript.\nline 404-line 408:\nThe nonlinear optical interactions can be further enhanced by patterning the NbOI flakes into resonance structures such as metasurfaces51, flat-band photonic crystals52, and nanodisks53,54. It is also possible to enhance the nonlinear optical interactions by introducing quasi-phase-matching by stacking the NbOI flakes with periodically poling55.\nResponse to “It is however a little unclear how the technology can be moved from a flake with to practical implementations of detection and imaging devices. I understand most of this is out of scope for this paper, but it could be relevant to include more on the relevant parameters in the discussion”\nThanks for reviewer’s suggestions.\nThe NbOI flakes used in this work have relatively small sizes since they are from the mechanical exfoliation process. In order to achieve practical implementations of detection and imaging devices, it is necessary to synthesize large-area NbOI films through the chemical vapor deposition (CVD) method in the future8.\nWe also provided this discussion in the revised manuscript.\nline 411-line 413:\nIn order to achieve practical implementations of detection and imaging devices, it is necessary to synthesize large-area NbOI films through the chemical vapor deposition (CVD) method in the future57.\nResponse to “Is this material possible to machine or grow in different shapes or thicknesses? How does it work with other materials and environments”\nNbOI bulk crystals can be synthesized by the chemical vapor transport (CVT) method. The mechanical exfoliation process is the most mature method to get high-quality NbOI flakes with different shapes or thicknesses9-11. NbOI belongs to a group of transition metal oxide halide compounds with chemical formula MOX (M = V, Nb, Mo and Ta, and X = Cl, Br and I)12-14. It has been reported that several 2D transition metal oxide halides films (e.g., MoO Cl ) can be synthesized through the chemical vapor deposition (CVD) method8. It is possible to grow 2D NbOI film through CVD by optimizing the synthesizing process.\nNbOI can also interact with other 2D materials to generate heterostructures, such as MoSe /NbOI heterojunction15, NbOI /WSe heterojunction16, NbOI /WS heterojunction16, possessing potential applications in photodetectors.\nWe also provided this discussion in the revised manuscript.\nline 411-line 413:\nIn order to achieve practical implementations of detection and imaging devices, it is necessary to synthesize large-area NbOI films through the chemical vapor deposition (CVD) method in the future57.\nResponse to “Most important could be how to reach high performance at less extreme intensities and more product relevant quantum efficiencies”\nThere are several ways to enhance the nonlinear interactions (high imaging performances) at less extreme intensities in the NbOI crystals. First, the nonlinear optical interactions can be further enhanced by patterning the NbOI crystals into resonance structures such as metasurfaces1,2, flat-band photonic crystals3,4, and nanodisks5,6. Second, we can also enhance the nonlinear optical interactions by introducing quasi-phase matching by stacking the NbOI flakes with periodically poling7. The two methods can produce higher quantum efficiencies and higher imaging performance\nWe also provided discussions in the revised manuscript.\nline 404-line 408:\nThe nonlinear optical interactions can be further enhanced by patterning the NbOI flakes into resonance structures such as metasurfaces51, flat-band photonic crystals52, and nanodisks53,54. It is also possible to enhance the nonlinear optical interactions by introducing quasi-phase-matching by stacking the NbOI flakes with periodically poling55.\n3- Figure S6 - Double check the y-axis values on the plot a. Compared to the other plots it looks strange, maybe a brief comment why it does not baseline at 0.\nResponse:\nThanks for the reviewer’s suggestion.\nWe have repeated the measurements, removed the background of the spectra and updated the results in the revised supplementary information.\nFigure S4:\nFig. S4. a) THG spectra of the NbOI flake (157 μW) and fused silica (7000 μW) under 1550-nm excitation. b) THG spectra of the NbOI flake and monolayer WS (15 μW) under 1550-nm excitation (15 μW).\nWe sincerely appreciate the reviewer’s valuable comments and suggestions.\nReviewer #2 (Remarks to the Author):\nThis manuscript reports the use of NbOI as a nonlinear optical material for mid-infrared upconversion, including two-photon, three-photon, and higher-order multiphoton processes. The material exhibits excellent anisotropy and conversion efficiency. The study is clearly written, logically structured, and the data generally supports the authors’ conclusions. The manuscript presents valuable and innovative results, but clarification and further discussion of the following points would substantially enhance the rigor and impact of the work, and ensure its suitability for publication in Nature Communications.\nBefore publication, however, the following issues should be carefully addressed:\n1- It is not clear whether the conversion efficiency and anisotropy of SHG, THG, and other multiphoton processes depend on sample thickness. If thickness dependence exists, the underlying mechanism should be discussed.\nResponse:\nWe appreciate the reviewer for the constructive comments.\nWe have performed more tests to confirm the relations between the SHG, THG, and SFG conversion efficiencies and the sample thicknesses. Since the sample is normally excited by the fundamental light, there exist phase-mismatching for SHG, THG and SFG processes due to the natural dispersion of the refractive index in NbOI . Therefore, we theoretically calculated the corresponding coherence lengths and thickness-dependent SHG, THG, and SFG processes.\n(1) The conversion efficiency of SHG, THG, and SFG processes depending on the sample thickness\nThere exists phase-mismatching for SHG, SFG, and THG processes in the NbOI crystal when the light is normally excited. Here, we studied the phase-mismatching for SHG, SFG, and THG processes with an excitation wavelength of 1500 nm. As shown in Fig. R1a, refractive indexes of NbOI crystals along the three axes are measured by the ellipsometer. When the fundamental wavelength is 1500 nm, the coherence lengths between the fundamental and the forward propagating harmonic signals for SHG, SFG, and THG processes are calculated to be 3.8 μm, 3.9 μm, and 1 μm, respectively17,18. The existence of coherence lengths causes the harmonic intensity to oscillate periodically with the propagation distance, as shown in Fig. R1b-d. Since the flake thicknesses ( ≤ 200 nm) used in this work are smaller than the coherence length, the harmonic intensity will not be affected by the coherence length.\nAs shown in Fig. R2, we measured the SHG, SFG, and THG efficiencies as a function of flake thickness in the range of 1–600 nm. The SHG efficiency increases with thickness up to approximately 200 nm. Both the SFG and THG efficiencies also increase monotonically with increasing thickness. Therefore, within the thickness range investigated in this work, the conversion efficiencies of the SHG, SFG, and THG processes all exhibit a monotonic dependence on flake thickness.\nFig. R1. a) Refractive indexes (RIs) of NbOI crystals along the three axes measured by the ellipsometer. b) Normalized SHG intensity as a function of the thickness. c) Normalized SFG intensity as a function of the thickness. d) Normalized THG intensity as a function of the thickness.\nFig. R2. a) Measured SHG efficiency as a function of the thickness. b) Measured SFG efficiency as a function of the thickness. c) Measured THG efficiency as a function of the thickness.\nWe also provided these discussions in the revised manuscript and supplementary information.\nFigure S13:\nFig. S13. RIs of NbOI crystals along the three axes measured by the ellipsometer.\nFigure S14:\nFig. S14. a) Measured SHG efficiency as a function of the thickness. b) Measured SFG efficiency as a function of the thickness. c) Measured THG efficiency as a function of the thickness.\n(2) The anisotropies of SHG and THG processes depending on the sample thickness\nWe also experimentally studied the anisotropies of SHG and THG depending on the flake thickness (Fig. R3). The results indicate that both the anisotropies of SHG and THG almost keep unchanged with the flake thickness within 200 nm. This is because both harmonic intensities increase monotonically when the excitation polarization is aligned along the b- and c-axes, respectively.\nFig. R3. Anisotropic ratios of SHG and THG processes as a function of the flake thickness.\nWe also provided these parts in the revised manuscript and supplementary information.\nline 316-line 322 in the revised manuscript:\nIt is worthing noting that nonlinear conversion efficiencies (such as SHG, THG, and SFG) increase monotonically with the thickness smaller than 200 nm, since the thicknesses used in this work is within the coherence lengths (Note S4, Fig. S13, S14). The anisotropies of SHG and THG are nearly independent on the flake thickness as both harmonic intensities increase monotonically for thicknesses up to 200 nm as the excitation polarization is aligned along the b- and c-axes, respectively (Fig. S15).\nNote S4 in the revised supplementary information:\nNote S4. Conversion efficiencies and anisotropies versus the flake thickness\nThere exists phase mismatching for SHG, SFG, and THG processes in the NbOI crystals when fundamental light is normally excited. We studied phase mismatching for SHG, SFG, and THG processes with an excitation wavelength of 1500 nm. As shown in Fig. S13, RIs of NbOI crystals along the three axes are measured by the ellipsometer. At a fundamental wavelength of 1500 nm, the coherence lengths between the fundamental wave and the forward-propagating harmonic signals for the SHG, SFG, and THG processes are calculated to be 3.8 μm, 3.9 μm, and 1.0 μm, respectively7,8. The existence of coherence lengths causes the harmonic intensity to oscillate periodically with the propagation distance5. Since the flake thicknesses (≤ 200 nm) used in this work are much smaller than the coherence length, the harmonic intensities are not limited by coherence-length effects.\nAs shown in Fig. S14, we measured SHG, SFG, and THG efficiencies as a function of the flake thickness (1-600 nm). The SHG efficiency increases continuously with increasing flake thickness from 0 to 200 nm. Similarly, the SFG and THG efficiencies also exhibit a monotonic increase with the flake thickness. Consequently, the conversion efficiencies of the SHG, SFG, and THG processes all increase monotonically with the thickness range investigated in this work.\nWe also experimentally investigated the thickness-dependent anisotropies of SHG and THG (Fig. S15). The results show that the anisotropies of both SHG and THG remain nearly unchanged for flake thicknesses up to 200 nm. This behavior arises because the harmonic intensities increase monotonically when the excitation polarization is aligned along the b- and c-axes, respectively.\nFigures S13-S15:\nFig. S13. RIs of NbOI crystals along the three axes measured by the ellipsometer.\nFig. S14. a) Measured SHG efficiency as a function of the thickness. b) Measured SFG efficiency as a function of the thickness. c) Measured THG efficiency as a function of the thickness.\nFig. S15. Anisotropic ratios of SHG and THG processes as a function of the flake thickness.\n2- In Fig. 2e, 𝜌 shows a pronounced minimum around 1000 nm, attributed to an excitonic resonance along the c-axis. The authors should clarify whether similar features occur in 𝜌 or other multiphoton processes.\nResponse:\nFor THG process, 𝜌 is also affected by the excitonic resonance, which was discussed in the original version of the manuscript.\n“Strikingly, the 𝜌 value exhibits a transition (𝜌 < 1) and reaches a minimum value of ~0.25 when the excitation wavelength approaches 1590 nm. The corresponding THG wavelength aligns with the P1/P2 exciton peaks at ~530 nm along the c-axis28, where three-photon enhancement along the c-axis contributes to wavelength-dependent changes in THG anisotropy”\nBased on the reviewer’s suggestion, we also studied the dependance of 6th-harmonic process on the fundamental wavelength. The anisotropy of the 6th-harmonic process is defined as: 𝜌 = , where 𝐼 and 𝐼 represent the 6th-harmonic intensities when the excitation polarization is along the c- (non-polar) and b- (polar) axes, respectively. The fundamental wavelength is tuned from 2800 nm to 3400 nm, corresponding to the 6th-harmonic wavelength ranging from 466 nm to 566 nm, in which the exciton peaks P1/P2 contribute the resonance enhancement along the c-axis (Fig. R4a). As shown in Fig. R4b, the anisotropy ratio of the 6th-harmonic process decreases from the 2800 nm, reaching to the minimum value around 3000 nm and keeps increasing as the wavelength increases. The dip around 3000 nm is due to resonance enhancement of the exciton peaks P1/P2 (along c-axis).\nFig. R4. a) The imaginary dielectric function 𝜀 of NbOI along the polar (red) and non-polar (blue) directions10. b) Anisotropic ratio of the 6th-harmonic process as a function of the wavelength.\nWe also provided discussions in the revised manuscript and supplementary information.\nline 243-line 244 in the revised manuscript:\nThe similar phenomenon to THG in Fig. 2f is also found in the 6th-harmonic process, which shows the wavelength-dependent anisotropy (Fig. S11).\nFigure S11 in the revised supplementary information:\nFig. S11. Anisotropic ratio (𝐼 ⁄𝐼 ) of the 6th-harmonic process as a function of the excitation wavelength. 𝐼 and 𝐼 are the 6th-harmonic intensities with the excitation polarization along the b- and c-axes, respectively.\n3- In Fig. 3c, the 11th-order signal intensity is very close to the noise level, making it difficult to confirm whether an actual harmonic was observed. Stronger evidence is required to substantiate this result.\nResponse:\nThanks to the reviewer for the suggestion.\nTo precisely confirm the existence of the 11th-harmonic signal, we repeated the measurements and used an UV-grating inside the spectrometer to analyze the spectrum. Since the 11th-order signal intensity is not stable, we carried out the wavelength dependent 11th-harmonic process by tuning the excitation wavelength ranging from 3530 to 4125 nm. The results indicate that the 11th-harmonic wavelength corresponds to the excitation wavelength well.\nFig. R5. The 11th-harmonic process versus the excitation wavelength.\nWe also provided related descriptions in the revised manuscript and supplementary information.\nline 239-line 243 in the revised manuscript:\nIt is noted that the 11th-harmonic signal is close to the noise signal, thus we perform the wavelength-dependent 11th-harmonic process with excitation wavelengths at 3530 nm, 3895 nm, and 4125 nm. The corresponding signals at 320 nm, 354 nm, and 375 nm verify the 11th-harmonic process (Fig. S10).\nFigure S10 in the revised supplementary information:\nFig. S10. The 11th-harmonic process versus the excitation wavelength. The wavelength-dependent spectra confirm the 11th-harmonic process.\n4- Fig. 4c shows a shoulder on the long-wavelength side of the SFG peak, especially when 𝜔 = 5000 nm. The authors should provide a physical explanation for this feature.\nResponse:\nAs shown in Fig. 4c in the manuscript, there is a shoulder on the long-wavelength side of the SFG peak when 𝜔 is 5000 nm, resulting in the asymmetric spectrum. Two reasons lead to this kind of phenomenon: (1) Frequency chirp in the OPA (including PPLN, mirror, and lens) causes different frequency components of the pump or seed to interact with varying intensities at different times, leading to uneven amplification across the spectrum. Combined with wavelength-dependent phase-matching, this results in an asymmetric and sometimes multi-peaked output spectrum19-24, as shown in Fig. R6a-b. In addition, we also measured the signal spectrum from the OPA system at 1550 nm, which shows the asymmetric spectrum due to frequency chirp (Fig. R6c). It is difficult for us to measure MIR idler spectra as there is no suitable MIR spectrometer in our lab. (2) The pump light in the MIR is generated from the periodically poled lithium niobate (PPLN) crystal. There exists absorption edge when the wavelength is longer than 4 μm in lithium niobate25 (Fig. R6d). The absorption will lead to asymmetric spectrum in the OPA system.\nFig. R6. a) Idler spectra obtained from the OPA22. b) Idler spectra obtained from the OPA24. c) The signal spectrum from our home built OPA. d) Absorption spectra of RTA, KPT, and LiNbO 26.\nWe also provided physical explanations in the revised manuscript.\nline 290-line 293:\nIt is worth noting that the spectrum with 𝜔 =5000 nm is not symmetric due to the asymmetric pump spectrum, which is derived from frequency chirp from the OPA system (including PPLN, mirror, and lens)43 and absorption effect of PPLN44.\n5- In Fig. S8, SHG and THG spectra under long-wavelength pumping display multiple peaks in the harmonic line shapes. The origin of this behavior needs further clarification.\nResponse:\nAs shown in Fig. S9e, j in the supplementary information, the SHG and THG spectra display multiple peaks, which are derived from the pump spectra. The pump laser around 2500 nm used in this test is from the OPA with the KTA crystal. The multiple peaks mainly come from the frequency chirp in the KTA crystal27-29, like the spectra in Fig. R6b.\nWe also provided explanations in the revised supplementary information.\nCaption of Fig. S9:\nThe SHG and THG spectra exhibit multiple peaks that originate from the pump laser spectrum. The pump laser around 2500 nm used in this experiment is generated by the OPA based on a KTA crystal. The multiple spectral peaks mainly arise from the frequency chirp introduced in the KTA crystal9-11.\n6- In Fig. 5c, upconversion images from different wavelength combinations do not spatially overlap but show vertical offsets. The possible causes, such as phase-matching, optical alignment, or material anisotropy, should be discussed.\nResponse:\nWe thank the reviewer for this keen observation and the opportunity to clarify the physical mechanisms governing the spatial stability of the excitation beam. We agree that the slight spatial displacement of the MIR beam during wavelength tuning is a critical factor for imaging registration. We have carefully analyzed this phenomenon based on the three suggested aspects: (1) Optical alignment & Beam pointing, (2) Phase-matching conditions, and (3) Material anisotropy.\nOur analysis reveals that the shift is primarily attributed to the inherent beam pointing characteristics of the OPA system and chromatic aberration in the external optics, while material-induced effects are present but secondary due to the ultrathin nature of the sample.\n(1) Optical alignment and beam pointing stability: The primary source of the observed spatial shift originates from the operation mechanism of the OPA system and the external collimation optics:\nPPLN period switching: To cover the broad mid-infrared spectral range, our OPA system requires switching between different poling periods of the PPLN crystal. This mechanical translation of the crystal, combined with minor wedge angles or non-parallelism relative to the optical axis, introduces a minute but detectable change in the beam’s propagation vector.\nChromatic aberration: The refractive index of the collimating and focusing lenses (e.g., CaF ) is wavelength-dependent. As the MIR wavelength is tuned (e.g., from 3 μm to 4 μm), the effective focal length changes slightly. Residual chromatic aberration results in a slight variation of the focal spot position on the sample plane for non-normal incidence rays.\n(2) Phase-matching considerations: In bulk nonlinear crystals, phase-matching imposes a strict angular selection. However, for the ultra-thin NbOI flakes used in our work (thickness L<<coherence length), the longitudinal phase-matching condition is significantly relaxed.\nSpatial overlap sensitivity: While the thin film allows for broadband up-conversion without strict angle tuning, the conversion efficiency is strictly confined to the spatial overlap region between the pump and the signal beams. The \"shift\" observed in the up-converted image is, therefore, a direct mapping of the MIR probe beam's displacement (discussed in point 1) relative to the fixed pump beam. The relaxed phase-matching ensures that the signal is still generated despite these small angular deviations, but it does not correct the spatial position.\n(3) Material anisotropy and dispersion: We also considered the intrinsic properties of the NbOI material:\nDispersion & Birefringence: NbOI exhibits strong optical anisotropy. According to Snell’s Law, the refraction angle inside the material changes with wavelength due to dispersion. Additionally, the birefringence leads to a walk-off effect where the Poynting vector deviates from the wave vector. However, given the atomic-scale thickness of our samples (typically tens of nanometers), the lateral beam displacement caused by refraction and walk-off within the material is negligible (sub-nanometer scale) compared to the micron-scale shift induced by the external optical path. Therefore, while anisotropy is a fundamental property of NbOI , it is not the dominant cause of the macroscopic spot shift observed in the experiment.\nWe also provided related descriptions in the revised manuscript.\nline 363-line 366:\nIt is worth noting that upconversion images from different wavelength combinations do not spatially overlap but show vertical offsets. The offsets mainly come from optical misalignments, which arise from the operation mechanism of the OPA system and the external collimation optics.\n7- The long-term stability of the material is not addressed. Can it retain its high upconversion efficiency after repeated measurements? Experimental data on stability would significantly strengthen the manuscript.\nResponse:\nTo verify the stability of the NbOI crystal under ultrafast laser excitation, we repeated THG measurements under 1550-nm excitation during the period of 24 h, as shown in Fig. R7. The result indicates that the THG intensity only degrades 20% under ultrafast laser excitation, which verifies the relatively good long-term stability of the material, especially in high-intensity excitation.\nFig. R7. Long-term stability measurement under ultrafast laser excitation.\nWe also provided discussions in the revised manuscript and supplementary information.\nline 481-line 483 in the revised manuscript:\nLong-term stability measurement under 1550-nm excitation indicates that the NbOI crystal can maintain a relatively good quality over a period of 24 h (Fig. S18).\nFigure S18 in the revised supplementary information:\nFig. S18. Long-term stability measurement under 1550-nm excitation. To evaluate the stability of NbOI under ultrafast laser irradiation, we performed repeated THG measurements under 1550-nm excitation over a period of 24 h. The results show a relatively good long-term stability of the material even under high-intensity excitation.\n8- The sensitivity of this material to strain or other external perturbations should be considered. The authors should discuss whether such sensitivity might pose limitations for practical applications.\nResponse:\nThanks for the reviewer’s suggestions.\nNbOX (X=I, Cl, Br) crystal is one kind of ferroelectric material, its physical properties especially nonlinear activities are sensitive to external perturbations including strain10,30,31, temperature10,14, and electric field10,14. Since the NbOI flakes are measured in the room temperature environment (25±1 ℃) and there is no applied electric field on the samples, the nonlinear performances of the flakes are not affected by the temperature and electric field. To avoid any strain in the NbOI flakes, we used the standard exfoliation and dry transferring process in the fabrication process32. As shown in Fig. R8, the exfoliated and transferred NbOI flakes on the clean silica substrate do not display any strain on the surface, confirming that strain or other external perturbations will not pose limitations for practical applications, such as imaging.\nFig. R8. Exfoliated NbOI flakes on the silica substrate.\nWe also provided discussions in the revised manuscript.\nline 408-line 411:\nWe used the standard exfoliation and dry transferring process in the fabrication process56, avoiding strain on the sample surface. Strain and other external perturbations such as temperature will not pose limitations for nonlinear activities and imaging.\n9- What is the role of ferroelectricity in this mid-infrared upconversion process?\nResponse:\nFerroelectricity in NbOI is a kind of optical property arising from spontaneous electric polarization, which leads to inversion symmetry breaking10. This behavior enables the NbOI to have intrinsic even-order harmonic processes, such as SHG, SFG, 4th-, and 6th-harmonic processes.\nWe have highlighted the role of ferroelectricity in the revised manuscript.\nline 214-line 216:\nDue to the inversion symmetry breaking caused by spontaneous ferroelectric polarization in the bulk state, even-order harmonic processes (such as SHG, SFG, 4th-, and 6th-harmonic processes in the MIR region) can be potentially realized in the NbOI flake28,36.\nWe sincerely appreciate the reviewer’s valuable comments and suggestions.\nReviewer #3 (Remarks to the Author):\nI have co-reviewed this manuscript in collaboration with reviewer #2.\nReviewer #4 (Remarks to the Author):\nThe authors systematically investigated various nonlinear optical processes—including second-harmonic generation (SHG), third-harmonic generation (THG), high-harmonic generation (HHG), sum-frequency generation (SFG), degenerate four-wave mixing (DFWM), and sum-frequency mixing (SFM)—in NbOI₂ nanosheets, employing pump wavelengths spanning from 800 to 5000 nm. They demonstrated broadband and substantial optical nonlinearities, which depend sensitively on the excitation laser’s wavelength, polarization, and power. Additionally, the authors achieved mid-infrared (MIR) upconversion imaging in the 2500–4200 nm range, with direct detection using a conventional silicon camera. This study may be suitable for publication in Nature Communications, pending satisfactory revisions:\n1- “However, the nonlinear conversion efficiency (e.g., SHG) in many 2D layered materials is constrained by the layer number, owing to strong interlayer coupling or changes in crystal symmetry, as observed in 2H-TMDCs,…” (Page 3 Line 62)\nI would like to note that while AA-stacked NbOI₂ with a C₂ space group exhibits broken inversion symmetry regardless of thickness, its nonlinear response—such as SHG—does not scale quadratically with the number of layers (N), as one might expect for ideal, lossless media. This deviation from the expected N² dependence primarily arises from interference between surface and bulk SHG contributions, leading to pronounced oscillations in the overall nonlinear signal, as reported in [Nature 613, 53 (2023); Science 367, 903 (2020); Scientific Reports 6, 22620 (2016)]. Therefore, making direct comparisons between different nonlinear optical processes using NbOI₂ flakes of varying thicknesses (e.g., 20 nm for SHG/THG, 200 nm for higher-order harmonics, and 100 nm for frequency upconversion) may not provide a fully comprehensive or consistent evaluation.\nResponse:\nThanks for the reviewer’s constructive suggestions.\nWe agree the reviewer’s comment that “making direct comparisons between different nonlinear optical processes using NbOI₂ flakes of varying thicknesses (e.g., 20 nm for SHG/THG, 200 nm for higher-order harmonics, and 100 nm for frequency upconversion) may not provide a fully comprehensive or consistent evaluation”.\nThus, we performed more experiments to make sure different nonlinear optical processes are studied at the same thickness, as shown in Fig. R9. We measured efficiencies of SHG, THG, 4th-, 5th-, 6th-, 7th-, 8th-, and SFG harmonic processes in the same NbOI flake (~200 nm). SHG shows the highest conversion efficiency and THG efficiency is smaller. The high-order harmonic processes display the lower efficiencies compared to SHG, SFG and THG. the conversion efficiency decreases with increasing harmonic order, as the high-order processes require the higher excitation intensities33,34.\nFig. R9. Conversion efficiencies of a) SHG, b) THG, c) 4th-, d) 5th-, e) 6th-, f) 7th-, g) 8th-, and h) SFG harmonic processes in the 200-nm NbOI flake.\nWe also provided discussions in the revised manuscript and supplementary information.\nline 321-line 328 in the revised manuscript:\nIn addition, the nonlinear response (e.g., SHG) of NbOI deviates from the expected 𝑁2 scaling with layer number due to interference between surface and bulk contributions29,45,46. In order to provide a comprehensive comparison for different nonlinear optical processes, we measured efficiencies of SHG, SFG, THG, 4th-, 5th-, 6th-, 7th-, and 8th-harmonic processes in the same NbOI flake (~200 nm). The results indicate that the conversion efficiency decreases with increasing harmonic order (Fig. S16), as high-order processes require higher excitation intensities15,47.\nFigure S16:\nFig. S16. Conversion efficiencies of a) SHG, b) THG, c) 4th-, d) 5th-, e) 6th-, f) 7th-, g) 8th-, and h) SFG harmonic processes in the 200-nm NbOI flake. SHG, THG, SFG, 4th-, and 5th-harmonic processes are excited at 3000 nm. However, the 6th-, 7th-, and 8th-harmonic processes are excited at 4000 nm due to limitation of the detector in the spectrometer. SHG exhibits the highest conversion efficiency, while the THG efficiency is comparatively lower. High-order harmonic processes show even lower efficiencies than SHG, THG, and SFG, and the conversion efficiency decreases with increasing harmonic order because high-order processes require higher excitation intensities12,13.\nWe also cited related papers in the references:\n45. Liu, F. et al. Disassembling 2D van der Waals crystals into macroscopic monolayers and reassembling into artificial lattices. Science 367, 903-906 (2020).\n46. Deckoff-Jones, S. et al. Observing the interplay between surface and bulk optical nonlinearities in thin van der Waals crystals. Sci. Rep. 6, 22620 (2016).\n2- The authors report a value of χ ≈ 147 pm/V at 1300 nm. Is this the highest value SHG(2) observed to date? In a previous study on NbOI₂ flakes of comparable thickness (Nat. Photon. 16, 644 (2022)), the authors reported a maximum χ at a pump wavelength of approximately SHG(2) 1000 nm (see their Fig. 3F), with the value decreasing as the pump wavelength was shifted to longer wavelengths.\nResponse:\nIn a previous study on NbOI flakes of comparable thickness (Nat. Photon. 16, 644 (2022)), the author found the 𝜒(2) value of NbOI (unstrained) is 190 pm/V under 1050-nm excitation, with the value decreasing as the pump wavelength was shifted to longer wavelengths. We found that the 𝜒(2) value of NbOI is about 147 pm/V at 1300 nm, smaller than that at 1050 nm. The value matches well with the calculated dispersion curve of 𝜒(2), as shown in Fig. R1010.\n(2)\nFig. R10. Calculated single particle SHG susceptibility (𝜒 ) for unstrained monolayer 𝑦𝑦𝑦 NbOI .\n3- The reported value of χ(3) in this work is ≈ 5.5 × 10⁻¹⁹ m²/V² at 1550 nm. This is surprisingly high compared to the findings in Advanced Optical Materials 11, 2202833 (2023), where the authors measured negligible third-order susceptibility for NbOCl₂ flakes at various pump wavelengths (850–1600 nm) under pump intensities of kW/cm² and a repetition rate of 100 kHz. In contrast, the present study calculates nonlinear efficiencies at much higher pump intensities, on the order of GW/cm². I therefore suspect that the reported nonlinear responses may be significantly influenced by thermal nonlinear optical effects rather than being purely due to the material’s intrinsic (electronic) optical nonlinearity.\nResponse:\nThanks for the reviewer’s comment.\nIn the previous findings in Advanced Optical Materials 11, 2202833 (2023)35, the author used the average power intensities of kW/cm², but not pulse peak power intensities. According to the laser parameters (pulse duration of 180 fs, repetition rate of 200 kHz) in Advanced Optical Materials 11, 2202833 (2023), the peak power intensity is at least tens of GW/cm2. This pump intensity is comparable to that used in our work. To exclude the influence of thermal nonlinear optical effects, we extracted 𝜒(3) values of NbOI under different excitation intensities (40 GW/cm2-240 GW/cm2), as shown in Fig. R11. The results indicate that extracted 𝜒(3) values are not affected by the excitation intensities, which means that there is no influence of thermal nonlinear optical effects.\nFig. R11. Extracted 𝜒(3) values of NbOI versus the excitation intensity. The extracted 𝜒(3) values are independent on the excitation intensity.\nWe also provided discussions in the revised manuscript and supplementary information.\nline 145-line 147 in the revised manuscript:\nIn addition, 𝜒(3) is also independent on the excitation intensity, indicating that extracted 𝜒(3) is not affected by thermal nonlinear optical effects (Fig. S5).\nFigure S5:\nFig. S7. Extracted 𝜒(3) values of NbOI versus the excitation intensity. The extracted 𝜒(3) values are independent on the excitation intensity.\n4- The caption for Figure S1 is incomplete. Does Fig. S1c show STEM images taken along the [100] zone axis? Please clarify this in the caption, and indicate the polar and nonpolar axes directly on the images.\nResponse:\nThanks for the reviewer’s suggestion.\nThe SEM is taken along the [201] zone axis, as shown in Fig. S1c. we also clarifies this in the caption, and indicate the polar (b) axis on the images.\nWe also revised Fig. S1 in the revised supplementary information.\nFigure S1:\nFig. S1. a-b) Energy dispersive analytical X-ray spectroscopy (EDX) spectra of the NbOI crystal. c) Upper: NbOI crystal structure; Bottom: Cross-sectional atomic-resolution ADF-STEM images (left: experiment, right: simulation) of the crystal viewed along the [201] zone axis. The b-axis is in the vertical direction of the image.\n5- “The anisotropic in-plane structure can be directly observed by atomic-resolved annular dark field-scanning transmission electron microscopy (ADF-STEM) technique, which confirms the 1D Peierls distortion of Nb atoms, inducing polarization along the b-axis…” (Page 4 Line 96)\nPlease note that the second-order Peierls distortion and the associated periodic modulations along the polar axis cannot be visualized in STEM images taken exactly along a perfect zone axis, due to the staggered AA packing structure of NbOI₂ (see Nature 613, 53 (2023) and Adv. Optical Mater. 11, 2202833 (2023)).\nResponse:\nWe agree with the reviewer’s comment and we have revised this description in the revised manuscript.\nline 112-line 114 in the revised manuscript:\nAtomic-resolved annular dark field-scanning transmission electron microscopy (ADF-STEM) technique confirms the b-axis of the NbOI crystal, consistent with the simulated image (Fig. S1c).\n6- “Notably, the absorption exhibits strong anisotropy, attributed to excitonic absorption differences along the two in-plane axes in the visible spectral region (Figure 1d)24…” (Page 4 Line 104)\nThe absorption data presented in Fig. 1d were collected in the near- and mid-infrared regions, not in the visible spectral region.\nResponse:\nIn this work, we mainly focus on the infrared spectral range and the absorbance in the infrared region shows strong anisotropy. Since the difference in excitonic absorption between b- and c-axes of NbOI is in the visible region, which has been confirmed in Ref.10, as shown in Fig. R2a. The resonance decays in the two axes lead to the anisotropic absorption the infrared region. To avoid any confusion to readers, we revised expressions the revised manuscript.\nline 118-line 120:\nNotably, the absorption exhibits strong anisotropy in the infrared region (Fig. 1d), attributed to excitonic-absorption-induced decay differences along the two in-plane axes in the visible spectral region28.\n7- Why is the χ(3) value calculated relative to monolayer WS₂, rather than quartz? There are significant discrepancies in experimentally reported χ(3) values for TMD monolayers, owing to the variety of formalisms used in the literature. Using quartz as a reference could provide a more consistent and widely accepted benchmark.\nResponse:\nThanks for the reviewer’s suggestion.\nWe agree with a fact that there are some discrepancies in experimentally reported 𝜒(3) values for TMD monolayers. Therefore, we extracted 𝜒(3) values of NbOI by comparing with both monolayer WS and silica substrate (quartz). Monolayer WS is reported to possess a 𝜒(3) value of 2.4×10-19 m2/V2 36. The 𝜒(3) value of NbOI is estimated to be 5.5×10-19 m2/V2 by comparing with WS . We also extracted 𝜒(3) values by comparing with silica substrate with different excitation intensities, as shown in Fig. R11.\nWe also provided contents in the revised manuscript and supplementary information.\nline 94-line 96 in the revised manuscript:\nenabled by the material’s large 𝜒(2) and 𝜒(3) values (𝜒(2) ≈147 pm/V at 1300 nm, ≈121 pm/V at 1700 nm, ≈60 pm/V at 2500 nm, and 𝜒(3)≈3×10-¹⁹ m²/V² at 1550 nm).\nline 141-line 145 in the revised manuscript:\nThe 𝜒(3) values of the NbOI crystal are calculated to be 3×10-19 m2/V2 and 5.5×10-19 m2/V2 at 1550 nm by comparing with the silica substrate and monolayer WS , respectively (Fig. S4). The difference is mainly derived from the discrepancies in experimentally reported 𝜒(3) values for TMDC monolayers.\nline 391-line 392 in the revised manuscript:\nAdditionally, the 𝜒(3) value of the NbOI crystal was estimated to be 3×10-19 m2/V2 at 1550 nm.\nFigure S12:\nFig. S5. Extracted 𝜒(3) values of NbOI versus the excitation intensity. The extracted 𝜒(3) values are independent on the excitation intensity.\n8- It is confusing to interpret the data, as figures and subfigures were collected using different excitation wavelengths. For example, THG imaging was performed under 1300 nm excitation, the THG polar plot under 1550 nm, and the THG spectrum under 2500 nm. For clarity and consistency, please use the same excitation wavelength across related measurements or clearly indicate the differences in each figure.\nResponse:\nIn this work, we measured nonlinear activities in the NbOI flakes across the broadband spectra, thus we showed the SHG and THG performances with different excitation wavelengths. To avoid any confusion, we put result of polar-plot of the THG process under 2500-nm excitation in Fig. 2e, so that all the nonlinear processes in Fig. 2 is measured in the MIR region.\nFigure 2 in the revised manuscript:\nFig. 2. Anisotropic SHG and THG processes with NbOI flakes. a, Schematic description of SHG and THG processes. b, SHG and THG efficiencies versus excitation intensity under 2500-nm excitation. c, Polar plots of the SHG intensity versus the polarization angle (θ) with parallel (red) and perpendicular (blue) configurations under 2500-nm excitation. d, Polar plots of angle-dependent THG intensity under 2500-nm excitation. 0° corresponds to the x-axis. e, The 𝜌 value versus the fundamental wavelength. f, The 𝜌 value versus the fundamental wavelength. Inset represents SHG and THG spectra under 2500-nm excitation with excitation polarization along the b- and c-axes.\nWe also moved result of polar-plot of the THG process under 1300-nm excitation to Fig. S7.\nFig. S7. Polar plots of angular dependent THG intensity under a) 1300-nm excitation and b) 1550-nm excitation. 0° corresponds to the x-axis. The differences in the patterns are derived from the dispersion of the 𝜒(3) elements.\nWe also modified descriptions in the revised manuscript.\nline 180-line 186:\nThe THG anisotropic ratio is defined as: 𝜌 = 𝐼 ⁄𝐼 ∝(𝜒 (3) ⁄𝜒 (3) )2. Figure 2d demonstrates x- and y- components of the THG intensity under 2500-nm excitation. It can be found that THG intensity is the largest when the excitation polarization is along the b-axis. The extracted relative magnitudes of the 𝜒(3) tensor components are (3) (3) (3) (3) 𝜒 :𝜒 :𝜒 :𝜒 =1:1.6:0.05:0.2, corresponding to 𝜌 =2.56. THG shows different polar-plot patterns under 1300-nm and 1550-nm excitations due to the 𝜒(3) dispersion (Fig. S7).\nAs shown in Fig. S8 of the Supplementary Information, THG mapping was performed under 1300-nm excitation. This choice was made because the THG response of NbOI at 1300 nm exhibits pronounced anisotropy, allowing the mapping to clearly reveal the spatial distribution of THG activity. The corresponding polarization-resolved THG polar plot under 1300-nm excitation is shown in Fig. S7a.\n9- What excitation wavelength was used in Fig. 2b? Please specify this information in the figure or its caption.\nResponse:\nThanks for the reviewer’s suggestion.\nWe have provided excitation wavelength information in the revised manuscript.\nline 148-line 150:\nThe SHG conversion efficiency under 2500-nm excitation is calculated to be 4.3×10-6 under an excitation intensity of 70 GW/cm2\nline 156-line 159:\nb SHG and THG efficiencies versus the excitation intensity under 2500-nm excitation. c Polar plots of the SHG intensity versus the polarization angle (θ) with parallel (red) and perpendicular (blue) configurations under 2500-nm excitation. d Polar plots of angle-dependent THG intensity under 2500-nm excitation.\n10- “Remarkably, the NbOI₂ flake generates SEHG, EIHG, NIHG, TEHG, and ELHG signals that extend beyond its bandgap into the UV regime,…” (Page 8 Line 199)\nPlease note that although the electronic bandgap (E ) of NbOI₂ is approximately 2.24 eV, the material also exhibits optical bandgaps in the UV region along both the polar and nonpolar axes (Nat. Photon. 16, 644 (2022)).\nResponse:\nWe agree with the reviewer’s expression that although the electronic bandgap (E ) of NbOI₂ is approximately 2.24 eV, the material also exhibits optical bandgaps in the UV region along both the polar and nonpolar axes. As shown in Fig. R2 (Nat. Photon. 16, 644 (2022)), there is an absorption peak (P at 300 nm) along nonpolar (c) axis and an absorption peak (P at 350 nm) along polar (b) axis. The two peak wavelengths are shorter than the electronic bandgap (2.24 eV) of NbOI .\nTherefore, we revised the relevant expressions in the revised manuscript:\nline 225-line 227:\nRemarkably, the NbOI flake generates SEHG, EIHG, NIHG, TEHG, and ELHG signals that extend beyond its optical bandgap into the UV regime\n11- The Raman spectrum presented in Fig. S2 is not referenced or discussed in the main text. Please include an appropriate reference to Fig. S2 and discuss its relevance.\nResponse:\nThanks for the reviewer’s suggestion.\nWe have provided appropriate reference to Fig. S2 in the revised manuscript.\nline 120-line 122:\nThe difference in the Raman spectra along the b- and c-axes also indicates the anisotropic phonon response derived from different crystal orientations between the two axes (Fig. S2).\n12- What is the scale bar for the maps shown in Figure S7? I assume they correspond to 80 μm × 80 μm areas—please confirm and indicate this clearly in the figure or its caption.\nResponse:\nWe have provided scale bar information in the caption of Fig. S8 in the revised supplementary information.\nFig. S8. a) Optical microscopic image of the NbOI flake for SHG imaging (scale bar: 10 μm). SHG intensity imaging under 1400-nm excitation by setting the excitation polarization parallel to b) b- and c) c- axes of the NbOI flake (scale bar: 10 μm). d) Optical microscopic image of the NbOI flake for THG imaging (scale bar: 10 μm). THG intensity imaging under 1300-nm excitation by setting the excitation polarization parallel to e) b- and f) c-axes of the NbOI flake (scale bar: 10 μm).\n13- What pump power or intensity was used in Figure S6b? Please specify this information in the figure or its caption.\nResponse:\nThanks for the reviewer’s suggestion.\nWe have repeated measurements and provided pump information in the caption.\nFigure S4:\nFig. S6. a) THG spectra of the NbOI flake (157 μW) and fused silica (7000 μW) under 1550-nm excitation. b) THG spectra of the NbOI flake and monolayer WS (15 μW) under 1550-nm excitation (15 μW).\n14- Please rearrange the figures in the Supplementary Information to match the order in which they are first cited in the main text, to ensure a smoother flow for the reader.\nResponse:\nThanks for the reviewer’s suggestion.\nWe have rearranged the figures in the supplementary information.\nWe sincerely appreciate the reviewer’s valuable comments and suggestions."}, {"round": 2, "reviewer_comments": {"reviewer_2": "The author has already addressed most of the questions effectively. I believe the paper is ready for publication in Nature Communications. I have only one minor suggestion: it would be preferable to include error bars for each data point measured on every sample.", "reviewer_3": "I have co-reviewed this manuscript in collaboration with another reviewer.The authors have already addressed most of the questions effectively. I believe the paper is ready for publication in Nature Communications. I have only one minor suggestion: it would be preferable to include error bars for each data point measured on every samples.", "reviewer_4": "For me, this revised version is suitable for publication in Nature Communications. The authors have satisfactorily addressed the various questions and concerns I raised in my previous review."}, "author_response": "Response to Reviewer #2 and 3:\nWe sincerely appreciate the reviewer’s constructive suggestion on adding error bars for all data presented in the manuscript.\nHowever, due to the large amount of experimental data involved and the extremely heavy workload required for repeated measurements under identical conditions, it is currently difficult to add statistical error bars for every data point within the revision timeline. All experimental data shown in this work were obtained under consistent and well-controlled experimental conditions, and the key results and trends are highly reproducible and reliable.\nFor example, the SHG and THG efficiencies in Fig. 2b are comparable to those in Fig. S14a and S14c; The SHG anisotropy and THG anisotropy in Fig. 2e and 2f also have comparable values to those in Fig. S15. Therefore, we conclude that the conclusions drawn in this study are not affected by the absence of error bars.\nWe will carefully consider adding error bars in our future follow-up work when conducting more systematic statistical analysis.\nWe hope the reviewer can understand the situation and kindly approve this revision. We would like to express our sincere gratitude to the reviewers for your time and professional comments.\nReviewer #4 (Remarks to the Author):\nFor me, this revised version is suitable for publication in Nature Communications. The authors have satisfactorily addressed the various questions and concerns I raised in my previous review.\nResponse:\nWe would like to express our sincere gratitude to the reviewers for their valuable comments and suggestions."}]

Decision letter