Yun
Zhao
^{a},
Zhaoxi
Chen
^{b},
Cheng
Wang
*^{b},
Yuanmu
Yang
*^{a} and
Hong-Bo
Sun
*^{a}
^{a}State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, Beijing 100084, China. E-mail: ymyang@tsinghua.edu.cn; hbsun@tsinghua.edu.cn
^{b}Department of Electronical Engineering and State Key Laboratory of Terahertz and Millimeter Waves, City University of Hong Kong, Hong Kong 999077, China. E-mail: cwang257@cityu.edu.hk

Received
26th May 2023
, Accepted 9th July 2023

First published on 10th July 2023

Lithium niobate (LiNbO_{3}) is a material that has drawn great interest in nonlinear optics because of its large nonlinear susceptibility and wide transparency window. However, for complex nonlinear processes such as high-harmonic generation (HHG), which involves frequency conversion over a wide frequency range, it can be extremely challenging for a bulk LiNbO_{3} crystal to fulfill the phase-matching conditions. LiNbO_{3} metasurfaces with resonantly enhanced nonlinear light–matter interaction at the nanoscale may circumvent such an issue. Here, we experimentally demonstrate efficient second-harmonic generation (SHG) and HHG from a LiNbO_{3} metasurface enhanced by guided-mode resonance. We observe a high normalized SHG efficiency of 5.1 × 10^{−5} cm^{2} GW^{−1}. Moreover, with the alleviated above-gap absorption of the material, we demonstrate HHG up to the 7^{th} order with the shortest generated wavelength of 226 nm. This work may provide a pathway towards compact coherent white-light sources with frequency spanning into the deep ultraviolet region for applications in spectroscopy and imaging.

To allow efficient nonlinear light–matter interaction in a bulk LiNbO_{3} crystal or a LiNbO_{3} waveguide, the phase-matching conditions must be met.^{10} Nonetheless, conventional phase-matching techniques, including birefringent phase-matching and quasi-phase-matching, typically only work for a limited bandwidth and do not perform well for nonlinear processes such as high-harmonic generation (HHG), which involves frequency conversion over many octaves. To tackle this challenge, it was recently shown that a stringently engineered chirped periodically poled LiNbO_{3} (CPPLN) crystal can allow HHG up to the 10^{th} order,^{11–13} generating a supercontinuum white light source spanning an extremely wide wavelength range from 350 nm to 2500 nm. However, HHG into the deep ultraviolet (DUV) spectral range is yet to be observed due to the strong absorption of the above-gap harmonics when propagating inside such a bulk LiNbO_{3} crystal.

The abovementioned issues of phase mismatch and above-gap absorption may be partly addressed using LiNbO_{3} metasurfaces with a subwavelength thickness. With the rapid development of lithium niobate on insulator (LNOI)^{14} technology over the last few years, LiNbO_{3} thin films can now be patterned into metasurfaces^{15} that support a variety of Mie resonances, including electric- or magnetic-dipole resonance,^{16–18} Fano resonance,^{19,20} anapole resonance,^{21,22} bound states in the continuum (BIC) resonance,^{23–27} and guided-mode resonance.^{28–30} For SHG, LiNbO_{3} metasurfaces with resonantly enhanced nonlinear light–matter interaction have been demonstrated, yet with relatively low conversion efficiency, which may be due to the relatively low Q-factors limited by design or fabrication constraints. For HHG, reports from LiNbO_{3} metasurfaces remain elusive. HHG from the Si metasurface,^{31,32} GaP metasurface,^{33} and sub-wavelength-thick epsilon-near-zero thin film^{34} has been demonstrated, yet the relatively strong above-gap absorption loss in the UV region still poses an issue.

In this work, we demonstrate efficient SHG and HHG up to the 7^{th} order, with the shortest generated wavelength of 226 nm in the DUV regime, from a LiNbO_{3} metasurface that supports a guided-mode resonance. When the metasurface is resonantly driven by a transverse electric (TE) polarized femtosecond laser, we observed a high SHG conversion efficiency of 8.6 × 10^{−3} at a peak pump intensity of 0.17 TW cm^{−2}. We further observed the 7^{th} harmonic generation in the DUV region.

Fig. 2a depicts the geometry of the grating which is designed to support high-Q guided-mode resonance. We calculate the eigenmodes and the transmission spectrum of the metasurface for TE polarization using the commercial software Lumerical FDTD (see Numerical simulations in the Methods section for more details). The photonic band structure of the 1D subwavelength grating is shown in Fig. 2b, which reveals two strong resonances in the first Brillouin zone, corresponding to a guided-mode resonance and a BIC resonance, respectively. Though the BIC resonance can have an extremely large Q-factor approaching infinity, it is prohibited to couple with normally incident light due to symmetry constraints.^{35} In contrast, the guided-mode resonance can be excited under normal incidence, occurring at a wavelength of 1580 nm. The simulated normal-incident transmittance spectrum of the metasurface, as shown in Fig. 2c, also indicates that only the guided-mode resonance is excited. The electric field distribution at the resonant wavelength is given in Fig. 2d, which shows about 9-fold enhancement of the local electric field confined inside the LiNbO_{3} structure. The optical photo and scanning electron microscopy (SEM) images of the fabricated metasurface, patterned by electron beam lithography (EBL) followed by reactive ion etching (RIE), are shown in Fig. 2e and f (see Sample fabrication in the Methods section for more details). Subsequently, the linear transmittance spectrum of the fabricated metasurface is experimentally measured under TE-polarized normal incident light. As shown in Fig. 2c, the experimental result qualitatively agrees with the simulation. The lower extinction ratio and larger resonance linewidth may originate from the imperfection of fabrication as well as the finite angular range of the incident white light. To further experimentally characterize the nonlinear responses of the metasurface, we set up the nonlinear optical measurement system (see Optical characterization in the Methods section for more details) as schematically shown in Fig. 3a. The pump laser with a pulse duration of 290 fs and a repetition rate of 75 kHz is focused on the sample via a lens with a focal length of 50 mm. The polarization of the pump laser is controlled by a linear polarizer and a half-wave plate. The generated harmonic signals are collected with a high numerical aperture lens (NA = 0.69) and then spatially dispersed with a CaF_{2} prism before being coupled into the grating spectrometer.

By tuning the pump wavelength from 1550 nm to 1630 nm with a step of 10 nm at a constant peak pump intensity of 1.8 GW cm^{−2}, we observed a SHG signal peak at a pump wavelength of 1580 nm, as shown in Fig. 3b. The peak in the signal confirms the resonance enhancement of the SHG as a result of the guided-mode resonance. As the pump power increases, the SHG intensity exhibits a quadratic relationship with the excitation intensity, as depicted in Fig. 3c. The SHG intensity starts to drop at a peak pump intensity of 0.21 TW cm^{−2}, which corresponds to the damage threshold of the metasurface. Compared with an unpatterned LiNbO_{3} film at an identical excitation intensity of 1.8 GW cm^{−2}, the SHG intensity of the LiNbO_{3} metasurface is enhanced 7 times, as shown in Fig. 3d. Because of the polarization-sensitive nature of the GMR metasurface and the substantial difference in χ^{(2)} tensor components along the z- and y-crystal directions, the SHG intensity of LiNbO_{3} gratings is strongly dependent on the polarization of the pump light, as shown in Fig. 3e. The intensity shows 80-fold enhancement in the resonant pump with TE polarization compared to the non-resonant pump with transverse magnetic (TM) polarization. At a peak pump intensity I^{FH}_{peak} of 0.17 TW cm^{−2}, we measured a high absolute conversion efficiency η = P^{SH}_{avg}/P^{FH}_{avg} of 8.6 × 10^{−3}, where P^{SH}_{avg} is the average power of the second harmonic. Since the SHG efficiency is proportional to the peak pump intensity, we use the normalized SHG efficiency, defined as η_{norm} = η/I^{FH}_{peak}, as the criterion to benchmark the SHG efficiency of various metasurface platforms. The normalized efficiency of our LiNbO_{3} metasurface is 5.1 × 10^{−5} cm^{2} GW^{−1}. We compare this value with other dielectric metasurfaces^{36–41} including Si,^{24,42,43} III–V semiconductors,^{17,20,27,44–49} and other LiNbO_{3} platforms^{50–54} and summarize the results in Fig. 4. The high efficiency of our LiNbO_{3} metasurface supporting guided-mode resonance may result from the large intrinsic second-order nonlinear coefficient of LiNbO_{3} as well as the high Q-factor of the metasurface with fine fabrication process control and is comparable to some III–V semiconductor metasurfaces which have a larger second-order susceptibility.

Subsequently, we measured the higher-order nonlinear optical responses of the metasurface. As shown in Fig. 5a, harmonic signals from the 3^{rd} to 7^{th} order are observed when pumping the metasurface at a resonant wavelength of 1580 nm. Due to the non-centrosymmetric crystal structure of LiNbO_{3}, both even- and odd-order harmonics have been observed. Fig. 5b–d show the dependence of the n^{th} harmonic intensity on the excitation intensity. The harmonic intensity of the 3^{rd}–5^{th} order as (I^{FH}_{peak})^{3,4,5}, respectively, which indicates that the harmonic generations are in the perturbative regime. As the pump power increases further, the intensity of the 6^{th} and 7^{th} harmonics reaches the non-perturbative regime, which indicates that the strength of the laser field approaches the atomic bonding strength of the material.^{55} We finally characterized the polarization states of the output even- and odd-order harmonics respectively when pumping with a TE-polarized beam at the resonant wavelength. As shown in Fig. 5e and f, both the 3^{rd} and 4^{th} harmonics have good linear polarizations with the same direction as the pump light which illustrates the dominant role of the nonlinear optical tensor d_{33}.

For the nonlinear harmonic generation measurement, the excitation laser beam with a 290 fs pulse duration and a 75 kHz repetition rate is generated by an optical parametric amplifier (Light Conversion Orpheus-ONE-HP) pumped by a Yb: KGW laser amplifier (Light Conversion Pharos). A linear polarizer and a half-wave plate are used to adjust the polarization of the pump laser. The laser is focused onto the sample with a spot radius of 18 μm, using a lens with a focal length of 50 mm. The generated high-harmonic signals are collected by a high numerical aperture aspheric lens with an NA of 0.69 and further spatially dispersed by a CaF_{2} prism (Thorlabs, PS863). The harmonic signals are finally coupled into a visible-UV grating spectrometer (Ideaoptics, PG2000-pro) for spectrum analysis through a multimode fiber.

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