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Abstract
Lithium niobate (LN) is a versatile material for applications in integrated nonlinear optics; however, due to its stable physical and chemical properties, efficient nonlinear conversion with nanostructured LN is not easy to implement. Here, we propose a resonant nanostructure composed of a SiO2 grating and a lithium niobate on insulator (LNOI) layer, which has been proven to support bound states in the continuum (BIC) modes through simulations. By experimentally measuring the angle-resolved transmittance spectra of the fabricated sample, we confirm that our proposed nanostructure exhibits quasi-BIC modes transitioning from BIC modes, resulting in strong localized field confinement. In the nonlinear experiment, our results show the significant potential of the nanostructure in enhancing second harmonic generation (SHG). By pumping at the resonant wavelength, we achieve a SHG enhancement factor of 6400, compared to a flat LNOI thin film under a fundamental wave (FW) peak intensity of 460 MW/cm2. The SHG conversion efficiency reaches up to 1.741 × 10−7, leading to a normalized conversion efficiency of 3.785 × 10−7 cm2/GW. Although the experimental results are two orders of magnitude lower than the theoretical maximum SHG conversion efficiency of approximately 10−5, we believe that our proposed etchless LNOI nanostructure highlights the tremendous potential for applications in nonlinear resonant nanophotonics.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Second harmonic generation (SHG) is a common and influential second-order nonlinear optical effect. It occurs when two photons interact with nonlinear materials, generating a new photon with twice the energy and half the wavelength of the incident light [1]. Since its experimental discovery in 1961 by Franken et al. [2], SHG has found numerous applications, including nonlinear holographic imaging [3], materials encryption [4], and biomedical imaging system [5]. However, the intrinsic weak nonlinearity of optical materials hinders the efficient nonlinear response necessary for high integration and compatibility of optical devices [6]. In the last decade, advances in nanostructures have been used to enhance optical nonlinear processes by increasing the coherence length of photon-material interaction. Plasmonic nanostructures have shown potential in increasing nonlinear response through resonant field enhancement. However, the ohmic loss of the metal itself leads to heat generation and damage, resulting in low conversion efficiency even at high pump intensities [7]. Therefore, all-dielectric nanostructures have been proposed to address these challenges and improve nonlinear response [6]. In recent years, the study of bound states in the continuum (BIC) has garnered great interest in nanophotonics, as it provides a novel platform for achieving ultra-high-quality factor (Q) modes and large tunability for enhancing light-matter interactions in applications such as narrow-band transmission filtering and nanolayers [8–11], as well as efficient nonlinear processes like SHG and third harmonic generation [12–15]. Furthermore, BIC has been realized in various optical structures, such as photonic crystals [16–18], arrays of nanorods and nanosphere [19,20], and even high-contrast dielectric gratings [21–24], offering platforms for harvesting light from the ambient medium.
Lithium niobate (LiNbO3, LN) is a crystal with excellent characteristics. One of its outstanding properties is a large second-order nonlinear susceptibility d33 = 27 pm/V (at λ = 1064 nm). LN also has a wide transparency window from near-ultraviolet to mid-infrared and extremely low optical loss [25,26]. Recently, the “Lithium Niobate on insulator” (LNOI) platform has gained great interest due to its high-index contrast [27,28]. This platform has already found many applications in nonlinear optics, including broadband optical frequency combs [29] and efficient SHG-based on traveling-wave waveguide structure [30–34]. However, the increase in coherence length has limited the development of compactness and miniaturization in these applications. To overcome this challenge, micro-nano structures of lithium niobate have been proposed. Some theoretical studies have suggested using resonant nanostructures based on LNOI to enhance SHG through Mie-resonances [35–37] and Fano resonances [38]. Moreover, experimental demonstrations of SHG have been achieved in LNOI nanopyramids and nano gratings by etching LNOI directly using reactive-ion etching (IBE) and focused-ion-beam (FIB) technologies [39,40]. Additionally, the SHG of single LN nanoparticles prepared by chemical synthesis has also been observed [41,42]. However, the fabrication of accurate micro-nanostructured LN with steep sidewalls, large etching depths, and low optical losses using commercial process methods is challenging, limiting their applications in nonlinear nanophotonics. Therefore, it is essential to find alternative approaches to achieve relatively high-Q resonances and efficient SHG without directly etching the LN.
Here, we report on an unstructured LNOI nanostructure for greatly efficient second harmonic generation (SHG) by exploiting the quasi-BIC mode transition from BIC. By designing one-dimensional SiO2 nanogratings on the top surface of the LN thin film, we observe the generation of a Fabry-Perot-like BIC, which originates from the interference between waveguide modes and grating diffractions, offering strong local field confinement inside the LN thin film. We fabricated large-scale samples for experiments and achieved a quasi-BIC resonance with a Q factor of 315, enhancing the interaction between the fundamental excitation source and the nonlinear material. This allows us to achieve a SHG enhancement of 6400 when normalized to a flat LNOI film of the same thickness under an illumination intensity of 460 MW/cm2, contributing to an absolute conversion efficiency of 1.741 × 10−7 and a normalized conversion efficiency of 3.785 × 10−7 cm2/GW. Additionally, we theoretically calculate the maximum SHG conversion efficiency of ∼10−5 at an incident angle of 0.5°, which is about two orders of magnitude higher than the experimental value. Therefore, we demonstrate that this etchless LNOI nanostructure can support quasi-BIC resonances for generating efficient SHG at low fundamental pump intensity.
2. Structure design and principle
The schematic of the proposed high-Q resonant etchless LNOI nanostructures is shown in Fig. 1(a). The structure is built on the LNOI platform, where the 700 nm-thick LN thin film is bonded on a 2 µm-thick SiO2 buffer layer and a 500 µm-thick LN substrate, while one-dimensional SiO2 gratings are patterned on the top surface of the 700 nm-thick LN thin film. It should be noted that there are two main reasons why we choose SiO2 material as gratings: i) the preparation process of SiO2 is very mature, and it is easy to process grating with a high precision linewidth; ii) the refractive index difference Δn between SiO2 and LN can reach 0.75, resulting in the optical field mainly localized in the LN layer. In order to better take advantage of the interaction between the localized electric field and the largest second-order optical nonlinear susceptibility d33, we choose a commercially available x-cut LNOI thin film (NANOLN) with the crystalline axis along the x-axis in the Cartesian coordinate system. The x-z cross-section of the structure is shown in Fig. 1(b). The geometrical parameters of the SiO2 grating are as follows: the height is H = 600 nm, the periodicity is P = 685 nm, and the width is W = 355 nm, respectively.
Fig. 1. Schematic of an unstructured x-cut LNOI nanostructured device. (a) Three-dimensional view. The extraordinary refractive index ne is along the x-axis, while the ordinary refractive index no is along the y- and z-axis. (b) Cross-section view.
To reveal the principle of the BIC supported by the etchless LNOI nanostructure, we carried out the bandstructures calculations using the Eigenfrequency module of Multiphysics COMSOL. A two-dimensional model with periodic boundary conditions (PBC) along the x-axis was used, while a perfect matched layer (PML) was applied in the z-axis to avoid unphysical reflections. The optical constants of SiO2 were determined using an ellipsometer (see Section 1 in Supplement 1), and the refractive indexes ne and no of LN were obtained from the Sellmeier equation. The simulation results, shown in Fig. 2 (extracted from the bandstructures analysis, see Section 2 in Supplement 1), reveal that the nanostructure sustains bandstructures in pairs, with the paired bands approaching each other very closely at the Γ point in the Brillouin zone. The Q-factor was calculated using, where f is the complex eigenfrequency. The Q-factor of band A at the Γ point approaches infinity, indicating that this mode is a BIC mode, while the Q-factor of band B is less than 103, indicating that this mode is a superradiant mode. However, when deviating from the Γ point (kx = 0) case, the Q-factors of the BIC and superradiant modes drop dramatically, while the Q-factor of the alternative mode only rises slightly to the same value of 103. This phenomenon indicates that the optical BIC hosted by the high-contrast dielectric grating-waveguide can be attributed to the symmetry-protected standing wave BIC previously reported [23,43–45]. By varying the excitation wavevector, we can transform the BIC mode into a quasi-BIC mode with a large but finite Q-factor, maintaining a value of 103 over a wide range of wavevectors. Moreover, we captured the eigen mode field distribution in Fig. 2(a) at kx = 0 and kx = 0.0087, corresponding to incident angles of 0° and 0.5°, respectively. The Fig. 2(b) shows that both the quasi-BIC mode and the superradiant mode can confine the strong optical field inside the LN thin film, even though their Q-factors are on the order of 103. Therefore, our proposed etchless LNOI nanostructure provides a way to enhance optical nonlinear phenomena, such as SHG, by trapping the strong local field in the LNOI via the quasi-BIC mode.
Fig. 2. (a) Calculated band structures (left) and measured angle-resolved transmittance spectra (right) around 1000 to 1200 nm for the unstructured LNOI nanostructured device, respectively. The color represents the logarithm of Q factors. (b) Electric field distributions for BIC mode and superradiant mode at kx = 0 (marked by red arrows), corresponding to an incident angle of 0°. The right parts are for Mode A and B at kx = 0.0087 (marked by blue arrows), corresponding to an incident angle of 0.5.
To confirm the behavior of the nanostructure, we measured the dispersion of the sample under investigation via angular resolved transmittance spectroscopy, and found the results to be consistent with the properties predicted by numerical calculations
3. Results and discussion
3.1 Optical spectrum measurement and fitting
From the analysis above, the SiO2 nanostructured gratings are then fabricated using widely-used commercial processing technology (see Section 3 in Supplement 1). The scanning electron microscopy (SEM) image is shown in Fig. 3(a). To investigate the behavior of the etchless LNOI nanostructure, we calculate the transmission spectra for normal incidence (θ = 0°) and oblique incidence (θ = 0.5°) using Lumerical FDTD Solution Software. The results in Fig. 3(b) show that the transmission spectra exhibit an asymmetric Fano lineshape due to the constructive interference and destructive interference among different modes [23,46], forming superradiant resonance and quasi-BIC resonance. However, the resonance has a calculated Q factor of 445, indicating that it originates from the superradiant mode (a leaky mode) rather than the BIC mode under normal illuminated source. When the incidence angle deviates slightly from 0°, the BIC separates into two quasi-BIC resonances labeled Mode-A and Mode-B. According to the analysis of band structures in Fig. 2(a), the mode-A has a calculated Q factor of 1065 when the incident angle is changed to θ = 0.5°, corresponding to kx = 0.0087, while the Q factor of the mode-B increases to 760. Furthermore, we find that the mode-A is derived from the BIC mode, while mode-B is derived from the superradiant mode as shown in Fig. 3(b). Therefore, we characterized the transmission spectra of the nanostructure using a homemade optical experimental setup (see Section 4 in Supplement 1). The incident angle is adjusted to θ = 0° and θ = 0.5°, and the transmission intensity is recorded as shown in Fig. 3(c). The Q factor of the Fano resonance is described by the formula defined as [47,48].
Fig. 3. (a) Scanning electron microscopy (SEM) image with a scale bar of 4µm. (b) the calculated transmission spectra of incident angle θ = 0° and θ = 0.5°, respectively. (c) the measured transmission spectra illuminated by x-polarized incident light with incident angle θ = 0° and θ = 0.5°, respectively. The orange circles represent the measured data; the solid line is Fano lineshape.
Here, ω0 is the center frequency of resonance; T0 is the basic transmission at ω0; q is the asymmetry factor of the Fano resonance; γ is the damping rate of resonance, defined by $\gamma = {\omega _0}/2Q$.
The Fano resonance single dip occurs at λ = 1043.15 nm with a Q factor of 225 when the incident angle θ = 0° (Fig. 3(b)). For an oblique incidence θ = 0.5°, two resonant dips can be observed at λ1 = 1039.8 nm and λ2 = 1045.45 nm with fitting Q factors of 285 and 315, respectively, as shown in Fig. 3(c). The electromagnetic field distribution for this case (Fig. 2(b)) reveals that they respond to leaky modes with different propagating directions, but are still confined inside the LNOI device. The Q factors of Fano resonances supported by our proposed structure are not as better as those resonances with ultrahigh Q factors, which can reach several thousand [49,50]. However, an important condition to achieve efficient SHG is that the linewidths of the resonances are approximately the same as that of the pump laser, so that the external optical energy can be injected into the cavity as much as possible [51,52].
3.2 Second harmonic generation measurement
We aimed to achieve Second Harmonic Generation (SHG) by utilizing the near-field enhancement from quasi-BIC resonances trapped inside LNOI nanostructured devices. The schematic diagram of the measurement setup system is shown in Fig. 4(a). The infrared objective (×10, NA = 0.27) was used to focus the femtosecond laser beam orthogonally onto the LNOI device, creating a spot with an area of 400 × 400 µm2. The Forward-Generated (FWG) pump source, generated by an optical parametric oscillator (OPO) with a seed light source centered at 800 nm and a pulse duration of 140 fs, was employed. The OPO had tunable wavelengths ranging from 1000 nm to 1600 nm and a repetition rate of 80 MHz. The SHG signal generated in the forward direction was collimated with a lens in air, filtered by a short-pass filter, and then sent to a spectrometer (Ocean Optics, USB 4000) with an exposure time of 0.1 ms.
Fig. 4. (a) Experimental setup for SHG measurement and detailed Materials of optical elements. The incident light is orthogonal to the sample. (b) Overall view for unstructured LNOI nanostructured device with a size of 1500 × 1500 µm2. The scale bar is 500 µm. The circles with different colors represent the regions where SHG measurements were performed. (c) SHG intensity of region 1 to 5 marked with various colors, respectively. The average pump power of the FW is 13 mW.
Based on the eigenmode analysis in Sec. 2, the wavelength at which the quasi-BIC resonance appears is related to the period constant of the SiO2 gratings, which is slightly modified during the sample fabrication process, particularly for the sidewall of the gratings. For a large-scale sample, we scanned the SHG intensity response in five regions marked by various colors in Fig. 4(b). The wavelength of the OPO was centered at 1045 nm (see Section 5 in Supplement 1), and the average pump power was 10 mW, corresponding to a peak intensity of 220 MW/cm2. The results are shown in Fig. 4(c) and indicate that Region 2 exhibits the strongest SHG response among the selected regions when illuminated by the 1045 nm pump source. Therefore, we chose Region 2 for the nonlinear measurements of the LNOI device. To quantify the nonlinear enhancement, we compared the SHG intensity of the unstructured LNOI nanostructured device with that of an unpatterned LNOI film illuminated by the same FWG pump source, which had an average power of 20 mW and a peak intensity of 460 MW/cm2. The result is shown in Fig. 4(a), indicating an SHG enhancement factor of approximately 6400. Such a significant enhancement arises from the strong electric field trapped inside the LNOI due to the quasi-BIC resonances
To quantitatively determine the relationship between SHG and FW, we measured the SHG power using an optical power meter (OPHIR, RM9-PD) operating in the visible regime. The experimental results are shown in Fig. 5(b), where the SHG power and the averaged power of the FW are plotted using a double logarithmic plot. By fitting the curves with Eq. (2), we obtained a linear coefficient of 1.996, indicating the approximately quadratic dependence expected from SHG. When the FW pump intensity is 460 MW/cm2, we achieve an absolute SHG conversion efficiency of 1.741 × 10−7, as calculated using Eq. (3). To theoretically quantify the SHG process from the intensity of pulses with fundamental frequency, we calculated the normalized conversion efficiency of 3.785 × 10−7 cm2 /GW using Eq. (4).
Fig. 5. (a) SHG intensity enhancement of the LNOI device compared with a LNOI thin film with same thickness. The average pump power of the FW is 20 mW. (b)Log-log plot of the SHG power as a function of FW averaged pump power and peak intensity. The black circles represent the measured data and the vertical red short lines represent the y-axis error bars. The blue line is the numerical fit to the data with a slope of 1.996.
Here, ${P_{SH}}$ and ${P_{FW}}$ represent the averaged power of SHG and FW pump source, respectively. $I_{FW}^{peak}$ is the peak intensity of FW pump source.
Furthermore, we also perform nonlinear simulation utilizing COMSOL Multiphysics to determine the theoretical value of SHG conversion efficiency, which can exceed 10−5 when the incident angle is 0.5° at a peak pump intensity of 460 MW/cm2 (see Section 6 - 7 in Supplement 1). However, the quasi-bound states in the continuum resonance transition from the standing wave symmetry-protected BIC, which is highly sensitive to the incident angle as shown in Fig. 1(a). By decreasing the incident angle very close to 0°, we theoretically predict a higher conversion efficiency of up to 10−3 with the quasi-bound states in the continuum resonance.
Furthermore, LNOI is an anisotropic material with the largest second-order susceptibility d33 = 27 pm/V (at λ = 1064 nm) along the crystal axis (as demonstrated in Fig. 1(a)). This means that we can obtain a strong nonlinear response when the excited electric field is parallel to the crystal axis. By fabricating SiO2 nanogratings on top of the LNOI, we can control the polarization states of the FW pump light through rotations of 0° to 360° with a step of 20°. This allowed us to generate a localized field polarized along the optical axis of LNOI, allowing us to verify the origin of the SHG enhancement. The results, indicated in Fig. 6(a), reveal that the SHG emission signal is polarization sensitive, and there are significant differences in x- and y-directions (see Section 8 in Supplement 1) due to the combination of the localized electric field and largest second-order optical nonlinear susceptibility. The backward and forward photographs of SHG emission for the LNOI device under 20 mW averaged pump power are shown in Fig. 6(b), which obviously display the second harmonic green light emission. To significantly increase the conversion efficiency, a laser with higher power can be utilized.
Fig. 6. (a) Dependence of the SHG intensity on the polarization states of the FW pump source with an averaged power of 20 mW. (b) Backward (left) and forward (right) photographs for SHG emission, respectively.
4. Conclusion
In summary, we have theoretically and experimentally investigated the nonlinear optical characteristics of etchless LNOI nanostructured devices. By fabricating a one-dimensional SiO2 nanogratings on top of the LNOI, we have realized the symmetry protected BIC, which effectively traps the strong localized electromagnetic field inside the LNOI. This breakthrough offers the potential for significantly boosting the efficiency of second harmonic generation (SHG). When the laser beam is focused on the device, the quasi-BIC resonance, which transitions from the symmetry-protected BIC, is utilized to couple power into the proposed device. This results in an SHG enhancement factor of 6400 compared to the unpatterned LNOI thin film, at the FW pump peak intensity of 460 MW/cm2. As a result, we achieve an absolute conversion efficiency of 1.741 × 10−7 and a normalized conversion efficiency of 3.785 × 10−7 cm2/GW. Although our structure is not as efficient as the LNOI traveling-wave waveguides structure, which achieves highly efficient SHG by increasing the coherence length [32–35], it accommodates the development trend of compactness and miniaturization through quasi-BIC resonance, making it suitable for nonlinear resonant nanophotonic applications.
Funding
Key project of Guangdong Mechanical & Electrical Polytechnic (YJZD2022-02); High-level Talents Project of Guangdong Mechanical & Electrical Polytechnic (Gccrcxm-202208); Outstanding Innovative Talents Cultivation Funded Programs for Doctoral Students of Jinan University (2022CXB011); Fundamental Research Funds for the Central Universities (21622107, 21622403); Fundamental and application foundation project of Guangzhou (202201010654); Natural Science Foundation of Guangdong Province (2020A1515010791, 2021A0505030036, 2022A1515110970); NSAF Joint Fund (U2030103, U2230111); National Natural Science Foundation of China (61775084, 62075088).
Acknowledgments
We all would like to express our sincere thanks for the help from Dr. Leyong Hu (Institute of Physics, Chinese Academy of Sciences) in sample fabrication and Liling Liu (Institute of Photonics Technology, Jinan University) in SEM characterization of samples.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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