1. Introduction

Optical clocks based on petahertz (10¹⁵ Hz) transitions have much higher Q values in comparison with that of microwave atomic clocks, can provide better stability and accuracy, and are promising candidates for the next generation frequency standards [1,2]. Optical clocks based on ²⁷Al⁺ ion, ¹⁷¹Yb⁺ ion, ¹⁷¹Yb atom, and ⁸⁷Sr atom have demonstrated fractional uncertainties of 10⁻¹⁸ [3–6]. In particular, ²⁷Al⁺ ion has the smallest sensitivity to blackbody radiation at room temperature among all atomic species currently under consideration [7]. Therefore, it is a very promising optical frequency standard candidate and has been actively investigated in recent years [8–10].

Due to the absence of the suitable ultraviolet (UV) laser at the time of the proposal, Al⁺ ions cannot be Doppler-cooled directly, so a method of sympathetic cooling together with quantum logic spectroscopy (QLS) [11] is proposed to solve this difficulty, resulting in a system that is very complicated, and the systematic uncertainty is still limited by the second order Doppler effects [12]. Recently a direct laser cooling scheme of Al⁺ ion optical clocks is proposed [13]. A pulsed 234 nm laser with a high repetition rate, corresponding to the Al⁺ ion ¹S₀-¹D₂ two-photon transition [14,15], can be used to directly cooled the Al⁺ ions, and the total systematic uncertainty can be reduced to less than 1×10⁻¹⁸, which is expected to be able to improve over the current QLS-based type to achieve a better uncertainty. In addition, for the researches on optical clocks, the mutual verification between different technical solutions can greatly promote the fundamental physics research and expand the related laser technology. Hence, it is worthwhile to study this direct laser cooling scheme and develop a 234 nm deep-UV pulse laser source.

Excimer lasers and diode lasers can operate at the UV spectral region, but they cannot directly generate 234 nm radiations up until now [16,17]. Nonlinear frequency-conversion, such as second-harmonic generation (SHG) and sum-frequency generation (SFG), is normally considered to be the most effective approach [18], but so far no reports about 234 nm pulsed laser sources have appeared in the literature, which are mainly due to the lack of suitable input wave for the χ⁽²⁾ nonlinear crystal and are limited by low frequency-conversion efficiency. For example, as to conventional mode-locked lasers like Nd:YAG solid-state laser [19], mode-locked erbium-doped fiber amplifier [20], and more recently Yb-fiber lasers [21], their operating wavelengths cannot meet the 234 nm requirement through quadruple frequency conversion. While using a direct SFG technique, the process usually needs another high-energy UV laser in a specific wavelength to participate, which is not practical and costly. The recently reported quasi-three level neodymium (Nd) doped fiber laser is an interesting option, and can operate at 936 nm for the subsequent frequency quadrupling. However, either the pulse laser oscillation or the amplification at that wavelength has to compete with four-level transition (⁴F_3⁄2- ⁴I_11/2) at 1060 nm, resulting in a lower gain at 910-940 nm even if some filter elements are used [22,23]. If a longer Nd-doped fiber length is adopted for a pulse laser system to improve the power, additional nonlinear effect will be introduced, which will deteriorate the pulse parameters such as the contrast ratio in time and the noise characteristics. As a consequence, such pulses will reduce the nonlinear conversion efficiency and are not conducive in the generation of deep-UV lasers. Moreover, the lower gain also indicates a smaller nonlinear phase shift for single pulse mode-locking so that it is difficult to achieve a higher repetition rate (i.e. a shorter cavity length for the oscillator).

Kerr-lens-mode-locked Ti:Sapphire laser can easily reach hundreds of megahertz, and it can be tuned to cover the wavelength of 702 nm (3 × 234 nm), which could be a potential option. But it has the disadvantages of limited power scalability, high cost and difficulties in maintenance. On the other hand, in recent reports, several methods have been developed for generating ultraviolet pulses, using a synchronously pumped optical parametric oscillators (OPO). Due to its ability to emit multiple wavelength coherent pulses at the same time, as well as its wider power scalability and broader spectral coverage, it has become a very promising potential option [24–28]. However, there are no reports in the literature about 234 nm deep-UV wavelength pulse lasers based on the synchronously pumped OPO. Furthermore, a detail design for the strict requirements on the input wave and as the selection of the nonlinear crystals in practical realization requires further investigation [29].

To this end, in this paper, we propose a flexible wavelength-conversion scheme to generate a 250-MHz 234 nm deep-ultraviolet pulse source. The scheme is based on a bifocal cavity frequency-doubled optical parametric oscillator (FD-OPO) together with a cascaded frequency conversion process. We employ the recently developed χ⁽²⁾ nonlinear envelope equation (NEE) model [30] to understand the pulse evolution of FD-OPO and to design the OPO crystal. A high conversion efficiency FD-OPO is constructed to convert a 1041 nm pump pulse to a 850 nm frequency doubling signal light, and the obtained output power is up to 1.16 W. This 850 nm light is further mixed with an additional 1041 nm pump laser for a 468 nm laser generation with a 229-mW average power, and finally we use a subsequent single-pass SHG stage to generate the 234 nm UV laser. Its average power is as high as 3.0 mW with a fluctuation less than 1% rms over 20 minutes, and no degradation in the UV power over time is observed. The developed UV laser is envisioned to be also used in many other quantum optics experiments.

2. Experimental setup

 Figure 1 shows the schematic of the 234 nm deep UV pulse laser generation. For the FD-OPO, a high power pump laser with an average power of 8 W at 1041 nm is used. Its pulse width is 120 fs with a 250 MHz repetition rate. A large nonlinearity multi-grating periodically poled LiNbO₃ (PPLN) is used for high conversion efficiency over a wide wavelength tuning range. The OPO cavity is singly resonant for the signal beam and is a compact six-mirror bifocal ring, comprised of two plane mirrors (M5-M6), and four plano-concave mirrors (M1-M4) with a radius of curvature 100 mm. The total optical length of FD-OPO cavity is ∼1.2 m, corresponding to a repetition rate of 250 MHz for meeting the synchronously pumping condition. Another nonlinear crystal is used in the cavity for frequency doubling of the signal wave. The two intra-cavity foci have beam radii of about 50 μm to minimize the risk of surface damage to the nonlinear crystals. All mirrors have high reflectivity for wavelength from 1600 to 1900 nm (signal), and high transmission for wavelength from 820 to 1070 nm (pump) and 2100 to 5000 nm (idler).

 

Fig. 1. Schematic of the experimental setup. ISO, Faraday isolator; H, half-wave plate; PBS, polarizing beam splitter; L1-L5, lenses; M1-M6, mirrors; DM, dichroic mirror; F, filter.

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The design of the PPLN crystal is very critical. One can estimate the temporal overlap length of the pump and signal pulse in the nonlinear crystal according to the coupled wave theory, from which a path length of 1 mm is chosen [31,32]. Similarly, poling periods of the PPLN are roughly determined first using the calculated phase matching bandwidth profile, and the matching efficiency map using the Sellmeier equations for PPLN [33] is shown in Fig. 2. We can see that the bandwidth increases as the poling approaches degeneracy (i.e., signal and idler wavelengths are both equal to twice of the pump wavelength), and favorable poling periods of the crystal mainly distributes from 30.7 to 31.7 µm on the quasi-phase matched diagram so that the matching signal wave can cover around 1700 nm, as required in our scheme. However, since other components in the FD-OPO, such as frequency doubling crystal for the signal beam and the intra-cavity mirrors, also affect the balance among dispersion, nonlinearity and loss in the cavity, which directly determine the actual gain dynamics of the output pulse spectrum, the above phase matching profile estimation for poling periods of the crystal is not good enough. Therefore, as a further theoretical prediction, we use the recently developed NEE model to simulate the FD-OPO gain characteristics, as well as controlling the influence of the phase mismatch, and finally design the optimal working crystal period, as will be described in the next section.

 

Fig. 2. PPLN phase matching efficiency map for a pump wavelength of 1041 nm with a bulk temperature of 60 °C, and a crystal length of 1000 µm. The white shaded area corresponds to a matching broad-signal wave centered around 1700 nm.

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On the other hand, since the generated frequency-doubled signal beam is quickly filtered out by the intra-cavity mirror (M3), so it is only treated as a single-pass process on one round trip in the simulation. Hence, the path length of this crystal can also be determined using the above mentioned coupled wave theory [31,32]. Considering BBO has good resistance to be damaged at high average power and low dispersion in the near infrared region, it is suitable to be used for the SHG of the signal wave operating at 1700 nm. Its path length adopted here is 2 mm, cut with θ=20.2° for type I phase matching.

For the cascaded frequency conversion process, second harmonic (SH) of the signal wave is coupled out through mirror M3, and then aligned with an additional pump laser to subsequently single-pass sum-frequency generate into 468 nm. We are aware of PPLN and PPKTP that are most often used for blue light generation. A 2 mm-long single grating period PPLN is used for its higher second-order nonlinear coefficient. Due to dispersion, we use a variable delay to control the temporal overlap of the above two-color pulses interacting in the SFG crystal. We focus both beams at the center of the SFG crystal using two different focal length lenses, L3 and L4, and select their focal lengths to access the optimum beam size of the interacting beams for maximum conversion efficiency. Another BBO crystal is employed to convert the SHG into 234 nm UV radiation. The BBO crystal is 3 mm long, 5 mm × 5 mm cross section, cut at θ=58.6° for type-I phase matching, and anti-reflection-coated for 468 nm and 234 nm wavelength. We can also change the focal length of lens L5 to ensure an optimal focusing spot at the center of the BBO crystal as required by the Boyd-Kleinman condition [31]. Finally, we separate the UV radiation from the residual blue beam using a dichroic mirror and a band-pass filter F, respectively. The 2 mm thick filter has a transmission of 85% at 234 nm. Moreover, the cascaded single-pass SFG and SHG apparatus are both housed in a temperature-controlled box made of temperature-insensitive Teflon plates and thermally conductive copper boards with a temperature adjustable range of 22 ± 2 °C with an accuracy of ± 0.1 °C.

3. Results and discussion

As mentioned above, in order to choose an optimal poling period of PPLN, we present in Fig. 3(a) simulation of the FD-OPO intra-cavity pulse intensity using the NEE model. Note that NEE provides a rigorous means of analyzing ultra-broadband pulse evolution in a χ⁽²⁾ medium like PPLN [34], but for the BBO section, it is required to use a coupled model to describe the dynamics and interactions of the ordinary and extraordinary field polarizations [35,36]. The detailed simulation process is described in Appendix A. The simulation reaches steady state after approximately 200 round trips as shown in Fig. 3(a), the evolution of the fields as they propagate through two crystals of the FD-OPO for the steady-state condition is shown in Fig. 3(b). This simulation reveals that the signal and idler light are strongly generated in the OPO section (the first 1000 μm for PPLN), and after passing through M2-M5-M4 mirrors, in-cavity retained signal interacts inside the BBO (the last 2000 μm) for a strong SHG at 850 nm, as shown in the top plot of Fig. 3(b).

 

Fig. 3. Simulated intra-cavity pulse evolution in the FD-OPO for PPLN with a grating period of 31.1 µm and a bulk temperature of 60°C. (a) The power contains in the FD-OPO field as it builds up from a weak noise pulse to the steady state, evaluated in the range of 1400-2100 nm. (b) The evolution of the FD-OPO pulse spectrum going through the two crystals once after the steady state is reached. The top plot shows the output pulse spectrum for the PPLN (blue curves) and the BBO (red curves).

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Further, with different crystal grating periods ranging from 30.7 to 31.7 μm, in steps of 0.1 μm, we have separately simulated the pulse evolution of the FD-OPO and understood the gain dynamics of the SH-signal from a weak pulse to the steady state. The pump chosen is a Gaussian pulse with a width of 120 fs, centered at 1041 nm, with 0.7 GW/cm² and 1 GW/cm² peak intensity, respectively. Figure 4 shows the relative power of the final frequency-doubled signal output centered at 850 nm with a minimum value as a reference level once the FD-OPO reaches the steady state by adjusting a suitable cavity delay in the simulation. The red and blue curves have approximately parabolic shapes, and an optimal poling period is found to be around 31.1 μm.

 

Fig. 4. The relative power of the SH-signal centered at 850 nm output from the FD-OPO with seven PPLN grating periods at a pump intensity of 0.7 GW/cm² (red curve) and 1 GW/cm² (blue curve), respectively, using the NEE model simulation.

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We then verify the theoretical prediction in experiments. A PPLN crystal adopted in our experimental scheme has dimensions of 1 mm high, 10.7 mm wide, and 1 mm long, consisting of seven different grating periods (i.e. 30.7, 30.9, 31.1, 31.3, 31.4, 31.6, 31.7 µm). Both end-faces are antireflection-coated for the signal beam as well as for the pump beam to reduce reflection losses and decrease the lasing threshold. To avoid the photorefractive effect, the crystal is located in a copper housing, whose temperature is maintained at 60 °C with an accuracy of ± 0.1 °C. Using seven grating periods with varying cavity delay to ensure the phase-matching of the interacting waves, a flexible wavelength-conversion of resonant pulses in the FD-OPO is allowed. Figure 5(a) shows the measured center wavelength changes of the output pulses when the system operates at seven different poled periods of PPLN. The result is obtained by a continuous increment of the cavity length with a 2.6 W pump laser. It can be seen that the SH output can cover from 790 to 980 nm, and the inset of Fig. 5(a) is the sampling result of these spectrum measurements. Furthermore, by setting the pump intensity at about 0.7 GW/cm² and 1 GW/cm², respectively, we measure the maximum output power of the SH-signal centered at 850 nm with different poling periods, and present the results in Fig. 5(b). To be noticed that the SH-signal is split by a 99:1 beam splitter, and the spectrum and the average power are synchronously monitored. We measure and record its power when the center wavelength is tuned to 850 nm measured with an optical spectrum analyzer. As can be seen, the distribution of the power data are in good agreement with theoretical predictions. The grating with a poling period of 31.1 µm is the optimal one and achieve a highest conversion efficiency.

 

Fig. 5. (a) The measured center wavelength changes of the output pulses when the system operates at seven different poled periods of PPLN with a continuous increment of the FD-OPO cavity length. The inset is the sampling result of these spectrum measurements. (b) SH (at 850 nm) power with seven PPLN grating periods at a pump intensity of 0.7 GW/cm² (red curve) and 1 GW/cm² (blue curve), respectively.

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Based on the above results, we focus on the grating of 31.1 μm in the experiment and further investigate the power scaling property of the SH-signal at 850 nm as displayed in Fig. 6(a). The OPO lases at a pump threshold of 0.8 W and the SH-signal average output power increases almost linearly, achieving a maximum power of 1.16 W at 5.74 W pump power. While the conversion efficiency exhibits saturation, the maximum conversion efficiency is ∼20.2% when the pump power is higher than 5 W. The high-power 850 nm pulse provides a suitable input wave, thereby, mode-matched with the additional pump laser at the frequency summing process for the blue light generation. The focused beam waist radii of the two-color pulse lasers in the crystal are maintained at about 18 μm. The overlap between the two-color pulses in the time domain is optimized by adjusting the delay line. Then the power scaling property of the 468 nm laser is also studied, and shown in Fig. 6(b). The maximum average power is about 229 mw corresponding to a conversion efficiency from 850 nm as much as 19.74%.

 

Fig. 6. (a) The output power scaling property (red) and the corresponding conversion efficiency (black) at 850 nm. The inset is the pulse spectrum with a 1.16 W output power. (b) The output power scaling property and the corresponding spectrum at 468 nm. The inset is the blue light pulse spectrum at 229 mW.

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Finally, by fine tuning the incident angle of the blue light and choosing an optimal focused beam waist of about 15 μm in the BBO crystal, UV radiation at 234 nm is obtained with a full width half maximum bandwidth of about 0.6 nm, shown in Fig. 7(a). The measured maximum power is around 3.0 mW. In the experiment, a smaller focused spot size does not generate a higher UV laser power. It can be understood that in the SHG process, when the input beam spot becomes smaller, which leads to an increase in the light intensity, it also shortens the length of the spatial walk-off, causing a non-optimal frequency doubling efficiency. An optimum focused spot size shall be carefully selected. And inferring from the measured narrower spectrum, one possible reason for power limitation is that the blue pulse is stretched in time due to the influence of material dispersion in the sum-frequency generation system. A suitable dispersion compensation is worthy of future consideration. In addition, another possible effective way to improve the conversion efficiency is to use a cavity-enhanced optical frequency doubler [37,38], which can greatly increase the peak intensity of the 468 nm blue pulse, and will be considered in the future for the generation of higher-power deep-UV lasers. Furthermore, we also measure the power stability of the deep-UV pulse laser, which exhibits an rms stability better than 1% over 20 min, shown in Fig. 7(b). We have not observed any power degradation with time. The instability in the UV power is attributed to mechanical vibrations and air currents in the laboratory, which can be further suppressed by vibration isolation and active feedback control. In addition, because the FD-OPO provides high average power across broad spectral region, the actual UV spectrum in our scheme can also be continuously tuned and covers from 232.0 to 234.5 nm, as shown in Fig. 7(a). The data is recorded with an optical spectrum analyzer (Ocean Insight, HR4000CG-UV-NIR) up to UV range, with a resolution of 0.75 nm. The spectrum analyzer is calibrated with a 280 nm frequency stabilized laser for Mg⁺ ion cooling [39].

 

Fig. 7. (a) Normalized output spectrum from 232.0 to 234.5 nm. Note that the spectral bandwidth measured here is limited by the resolution of the spectrum analyzer. (b) The power stability of the generated 234 nm UV laser.

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4. Conclusion

In summary, we have demonstrated a flexible wavelength-conversion scheme to generate a 250-MHz 234 nm deep-UV laser source. The simulation in the FD-OPO using χ⁽²⁾ NEE model provides an effective means to analyze ultra-broadband pulse evolution and guides the experimental design of the OPO nonlinear crystal and results in an optimized power output as much as 1.16 W at the desired 850 nm wavelength, which is suitable as an input wave for the cascaded frequency conversion process. An average output power of 3.0 mW at 234 nm is obtained. Such deep-ultraviolet pulse laser source is expected to be useful for direct laser cooling of ²⁷Al⁺ ion and can also be used in many applications in quantum optics. Further work in this aspect is underway. Additionally, owing to the robust fiber-based pump source and the electronic lock, this scheme can also provide a stable optical comb with wide spectral region from IR to UV, which is essential for real-world spectroscopy experiments.

Appendix A

The NEE model can be found in the literature [34], the equation is a scalar form, which can be used for the simulation in a PPLN crystal. The expression can be written as

(1)$$\frac{{\partial A}}{{\partial z}} + iDA ={-} i\frac{{{\mathrm{\chi }^{(2 )}}\omega _0^2}}{{4{\beta _0}{c^2}}}\left( {1 - \frac{i}{{{\omega_0}}}\frac{\partial }{{\partial \tau }}} \right)[{A^2}{e^{i{\omega _0}\tau - i({{\beta_0} - {\beta_1}{\omega_0}} )z}} + 2{|A |^2}{e^{ - i{\omega _0}\tau + i({{\beta_0} - {\beta_1}{\omega_0}} )z}}],$$

where A is the complex electric field envelope, ${\omega _0}$ is an arbitrary reference frequency, and ${\beta _0}$ is the wavevector measured at ${\omega _0}$. The linear part of the equation describes the effect of dispersion, which is $D = \Sigma _{m \ge 2}^\infty \frac{{{i^{m + 1}}}}{{m!}}{\beta _m}\frac{{{\partial ^m}}}{{\partial {t^m}}}$, ${\beta _m} = \frac{{{\partial ^m}k}}{{\partial {\omega ^m}}}{|_{{\omega _0}}}$. $\tau = t - {\beta _1}z$ represents a coordinate transformation into a co-moving frame at the reference group velocity ${\beta _1}^{ - 1}$. ${\mathrm{\chi }^{(2 )}}$ represents the position-dependent susceptibility, and its detailed expression can be found in Ref. [34].

For the BBO crystal, in order to describe the dynamics and interactions of the ordinary and extraordinary field polarizations, it is required to use a coupled model [35,36] as

(2)$$\begin{array}{{c}} {\frac{{\partial {A_x}}}{{\partial z}} + i{k_x}(\omega ){A_x} ={-} i\frac{\omega }{{c{n_x}(\omega )}}{\bf {\cal F}}[{2{d_1}{A_x}{A_y} + {d_2}A_y^2} ],}\\ {\frac{{\partial {A_y}}}{{\partial z}} + i{k_y}(\omega ){A_y} ={-} i\frac{\omega }{{c{n_y}(\omega )}}{\bf {\cal F}}[{2{d_2}{A_x}{A_y} + {d_1}A_x^2} ],} \end{array}$$

where ${A_x}$ and ${A_y}$ describe an extraordinary polarized wave and an ordinary polarized wave in an uniaxial second-order nonlinear material, ${k_x}$ and ${k_y}$ are the corresponding propagation wavenumbers, ${n_x}$ and ${n_y}$ are the corresponding refractive indices.${\; }{d_1}$ is the effective nonlinearity for eoe, oee, and eeo interactions, whereas ${d_2}$ is the effective nonlinearity for eoo, oeo, and ooe interactions. The detailed definitions of these parameters can be found in Refs. [35,36]. It is noted that in our FD-OPO, the pump pulse laser is linearly polarized and directly incident into the PPLN crystal. For phase-matching in SHG, we rotate the BBO crystal to ensure that the input light polarization satisfies the ordinary light direction. Therefore, in the simulation process, the electric field function in the FD-OPO can be unified. That means that A can always be assigned to be${\; }{A_y}$.

Here we give a detailed simulation process description in the FD-OPO. Figure 8 shows the diagram of simulation process, which includes the following steps:

• (a) Parameters setting. Such as setting the electric field functions of the pump pulse and the noise signal pulse, Gaussian shape can be used here; then set the time domain and the frequency domain windows;
• (b) The optical parametric generation process in the PPLN. The electric field functions of the noise signal pulse and the pump pulse are superimposed as a unified form and substituted into the NEE model, the numerical solution to NEE model [Eq. (1)] can be implemented by a split step Fourier method, in which the linear part of the equation (the left-hand side) is solved in the frequency domain and the nonlinear part (the right-hand side) was integrated by using a Runge-Kutta scheme;
• (c) Firstly filtering by the cavity mirrors M2-M5-M4. The mathematical form of the filter function is a super Gaussian function $H(\omega )= \sqrt R \textrm{exp}\left( { - \textrm{ln}2{{\left[ {\frac{{2({\omega - {\omega_0}} )}}{{\Delta \omega }}} \right]}^{10}}} \right)$, where${\; }R$ is the peak cavity reflectivity, $\Delta \omega $ represents the filter bandwidth. In the frequency domain, the electric field function is multiplied by the super Gaussian function to simulate the filtering process;
• (d) The SHG process in the BBO crystal. The new electric field function is substituted into the comprehensive coupled model [Eq. (2)]; like (b), the numerical solution can be obtained by using the above mentioned split step Fourier method and the Runge-Kutta scheme;
• (e) Secondly filtering by the cavity mirrors M3-M6-M1 with an additional cavity delay effect. Note that the filter function still uses the super Gaussian function, the cavity delay mathematically corresponds to a delay phase term T, which is written into the super Gaussian function to form a new one $H(\omega )= \sqrt R \textrm{exp}\left( { - \textrm{ln}2{{\left[ {\frac{{2({\omega - {\omega_0}} )}}{{\Delta \omega }}} \right]}^{10}} - i({\omega - {\omega_0}} )T} \right)$. The pulse electric field function is multiplied by this super Gaussian function to simulate the interaction process; Since the generated e-light (frequency doubled light) is filtered out by M3, the remained field is still o-light, so the electric field function can always be assigned again;
• (f) The signal laser (o-light) electric field re-arrives to the PPLN crystal, and superimposes a new pump pulsed electric field function for the next round-trip;
• (g) Determine whether the FD-OPO is stable, that is, the relative error of the single pulse intensity in two consecutive round-trips should be below a small value, such as ∼10⁻⁸. If the intensity of the signal laser is not stable, repeat steps (b)-(f). Otherwise, stop the loop and output the steady state electric field results.

 

Fig. 8. Diagram of simulation process in the FD-OPO. M1-M6, mirrors.

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Funding

Key-Area Research and Development Program of GuangDong Province (2019B030330001); National Key R&D Program of China (2017YFA0304400); National Natural Science Foundation of China (11904112, 61875065, 11774108, 11274133); Key Project of Basic Research and Applied Basic Research in Ordinary Universities of Guangdong Province (2018KZDXM067); China Postdoctoral Science Foundation (2019M652613).

Disclosures

The authors declare no conflicts of interest.

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