Single-Mode Characteristic of a Supermode Microcavity Raman Laser

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Downloaded by guest on September 24, 2021 PNAS a Xiao Yun-Feng and Zhang Pei-Ji laser Raman microcavity supermode a of characteristic Single-mode edi eosrtd ofimn h igemd aueo the of nature pump single-mode the the on confirming demonstrated, effect ultrahigh- Q is clamping an field in the laser Raman Experimentally, supermode In investigat- microcavity. a 41). by of paradox 9, dynamics spectral the (8, these lasing ing lasers this that lasing super- elucidate dual-mode we so in single-mode as work, this observed scanning, regarded a generally widely pump to are are during lasers notes leading output beat microlaser 40), thresh- However, mode 39, lasing 23). the (24, 6, once value (2, reached fixed is pump a the at old in clamped and energy be burning Hence, should hole (35–38). field spatial gain homogeneous the a bosonic from holds immune only inherently involving is scattering modes stimulated a transitions, featuring tronic (34), reader rotation splitting. the Earth gyro- to corresponding an nanoparticle optical note and beat for exceptional-point-enhanced 33), merit an (11, stimu- scope unique 9), the shown (8, 32), detection also supermode (31, in lasers has perturbation Brillouin or microcavities, Raman external as such the scattering, lated supermodes to of fre- sensitive splitting operation energy require- is in the limitation a that a Given for neither (26–30). nor advantageous as quencies materials is gain well latter specific as of the (23–25), ment particular, linewidths scat- In low stimulated 11). recording 9, e.g., 7, 8, effects, (3, (2, optical materials tering nonlinear gain have also intrinsic microcavities but only 12–14), WGM not waves in with by lasers demonstrated counterpropagating been supermode formed far, degenerate are So which between (20–22). supermodes, coupling nat- studying a the for as high-Q novel found platform supporting are and ural (17–19) microcavities (WGMs) (7–11), Single modes measurement whispering-gallery (12–16). precise sources excep- (3–6), light 2), (1, points breaking symmetry tional spontaneous as such advances M laser modes near-degenerate the and microcavity dB optical 15 by improved Hz. further 100 below is is supermodes, linewidth lasing SMSR the the manipulate where to lasers. exploited supermode is two the Self-injection between process interference switching transient the the as during recognized supermodes is signal near-degenerate beating to More- the over, waves. of up counterpropagating between emergence (SMSR) backscattering the the ratio by suppression despite side-mode dB, a 37 with las- whispering-gallery behavior single-mode its a ing experimentally in demonstrate laser and Raman microcavity contradicts we supermode Here, field. however, the pump clamped investigate which, the to due lasing, nature single-mode their scat- dual-mode phenomena, stimulated as and beating the reported interpreted sources, microcavities of supermode light experiments in novel tering Recent physics, sensors. non-Hermitian 2021) advanced 27, cornerstone of January review the studies for lay (received 2021 for supermodes 29, near-degenerate April approved in and CA, Microlasers Berkeley, California, of University Bell, T. Alexis by Edited and China; China; Beijing, 100871 University, Peking Nano-optoelectronics, tt e aoaoyfrMssoi hsc,Sho fPyis eigUiest,107 ejn,China; Beijing, 100871 University, Peking Physics, of School Physics, Mesoscopic for Laboratory Key State ifrn rmtecnetoa neso aesbsdo elec- on based lasers inversion conventional the from Different 01Vl 1 o 2e2101605118 22 No. 118 Vol. 2021 uhatnini h atdcds rmtn various promoting decades, drawn past the have in supermodes attention near-degenerate much in icrolasers d agz et nttt fOteetois eigUiest,Nnog261,China 226010, Nantong University, Peking Optoelectronics, of Institute Delta Yangtze a,b,1 | igXnJi Qing-Xin , tmltdRmnscattering Raman stimulated a,b,c,d,2 | microlasers a,1 iToCao Qi-Tao , | a,2 eigWang Heming , c olbrtv noainCne fEteeOtc,Sax nvriy aya 030006, Taiyuan University, Shanxi Optics, Extreme of Center Innovation Collaborative a,3 ulse a 5 2021. 25, May Published 3 2 1 under distributed BY).y is (CC article access open This Submission.y Direct PNAS a is article This interest.y competing no supervised Y.-F.X. declare authors and The Q.G. and idea; Y.-F.X. the and conceived Q.G., Y.-F.X. project.y W.L., the and H.W., H.W., Q.-T.C. Q.-T.C., Q.-T.C., paper; P.-J.Z., Q.-X.J., Q.-X.J., the P.-J.Z., P.-J.Z., experiments; wrote data; model; analyzed Y.-F.X. the theoretical and the performed Q.G., proposed W.L., Q.-T.C. H.W. and and Q.-T.C., Q.-X.J., Q.-X.J., P.-J.Z., contributions: Author cascaded or (46) effect oscillation clamping parametric the reach of of can assistance observation loss the pump previous with clamped smaller the the the with Despite compe- accompanied with field. mode (45), mode condition the lasing the to the stimulated only According different theory, Methods). symmet- the tition and the to (Materials (43, in directions due 44) counterpropagating gains the smaller in Raman rates slightly scattering decay the Raman are larger here and mode at addition, frequency ric particle In resonance dielectric higher) (31). a (or rate supermode lower symmetric is the a scatterer defect), has vacancy-like the the a and (or If surface distribution the 1B). mode the (Fig. between scatterer position standing-wave of relative pair the a by forms which symmetric 42), the 21, supermodes, 9, scatterer (8, The a surface 26). by the coupled (2, at are 1A) waves (CW) (Fig. counterpropagating clockwise directions intracavity the (CCW) both counterclockwise in and propagates and microcavity WGM supermodes. the the during between interference switching are transient lasing phenomena the beating as pro- recognized laser, and and Raman introduced observed the is of reflection self-injection tiny vides a When laser. supermode rsn drs:T .Wto aoaoyo ple hsc,Clfri nttt of Institute California Physics, Applied of Laboratory 91125.y Watson CA Pasadena, J. Technology, T. address: Present owo orsodnemyb drse.Eal fiopueuc or [email protected] Email: addressed. be may correspondence [email protected]. whom To work.y this to equally contributed Q.-X.J. and P.-J.Z. ehiu.Ti okpoie nisgtu udnefor guidance sources. way insightful light the reconfigurable to paves an and self-injection provides measurements the precision microlaser-based work of help This the technique. with supermodes switching lasing the the between recog- during lasing interference been transient has single-mode the signal as dynamics beating nized The the lasing and microlasers. confirmed, the is behavior Raman investigating supermode las- by the of paradox elucidate experimentally spectral stimu- we ing the article, this of characteristic In lasing nature dilemma. the generating single-mode been have beat- the scattering lated observed and widely phenomena the However, ing sources, pivotal light sensors. novel advanced a physics, and non-Hermitian play of studies supermodes for role near-degenerate in Microlasers Significance h aa irlsri eeae yotclypmiga pumping optically by generated is microlaser Raman The ejn Liu Wenjing , y a,b b rnir cec etrfor Center Science Frontiers iun Gong Qihuang , https://doi.org/10.1073/pnas.2101605118 a + n antisymmetric and raieCmosAtiuinLcne4.0 License Attribution Commons Creative a,b,c,d , a − defined , | f6 of 1

APPLIED PHYSICAL SCIENCES A B Symmetric mode C LasLaLaseerr LasLaseerr Pump Gain aCW a+ Pumpp g a a Anti-symmetric mode CW CCW a - Low loss Mode spectrum

Laser power High loss Scanning time aCCW g a+ a-

Wavelength

Fig. 1. Schematic of supermode laser in a microcavity. (A) Counterpropagating waves in a WGM cavity are coupled by a defect with strength g, forming a pair of supermodes. (Inset) Schematic of the beating phenomenon during pump scanning. (B) Formation of the symmetric a+ and antisymmetric a− supermodes. (Right) Field distribution of the two supermodes. (C, Upper) The cavity modes (gray lines) in the frequency domain and the optical gain (orange curve) from the pump (black line). (C, Lower) The zoomed-in spectrum of the black dashed box in C, Upper.

stimulated scattering (24, 47), the clamped input pump char- the mode at lower frequency features smaller loss indicates that acterizing the single-mode lasing has not been directly demon- the scatterer is a vacancy-like defect. By tuning the pump laser strated in the supermode microlasers so far, while beating (∼1,490 nm) into the resonance of the cavity mode, the first- phenomena (Fig. 1A) were widely observed and generally order Raman laser is observed as a single line at 1,610 nm interpreted as a dual-mode signature. (Fig. 2C) with the threshold of 213 µW, where the cascaded To investigate the supermode Raman lasing, a silica micro- Raman laser is absent (39, 48). Note that multiline Raman lasers sphere cavity with intrinsic Q factor over 4 × 107 is applied, as were also reported previously with the presence of Kerr para- illustrated in Fig. 2A. A tapered fiber is evanescently coupled to metric gain (49, 50) or cascaded scattering gain (51), which are the cavity, and the transmission of the Stokes supermodes is mea- avoided in the present work by carefully controlling the pump sured, as shown in Fig. 2B (Materials and Methods). The doublet power as well as the coupling condition. The clamping of the indicates a coupling strength of g = 5.49 ± 0.01 MHz between pump field is then examined by monitoring the intracavity pump the counterpropagating waves. The decay rates of the symmetric power via an add–drop coupling scheme (22, 52). As the pump and antisymmetric modes are fitted to be κ+0/2π = 4.05 ± 0.05 laser with a constant power scans from the blue-detuned region MHz and κ−0/2π = 3.93 ± 0.05 MHz, respectively. The fact that toward the resonance, the intracavity pump power increases and

A B PC OSA @1610 nm a a Probe laser 1.0 - + PC @1490 nm Pump laser OSC

OSC Pump+Raman Transmission ESA LPF 0.6 Raman 2g LPF > 1500 nm > 1500 nm -25 052 Frequency (MHz) C D 2 E Threshold RBW: 1 kHz f Pump - power Pump Raman Raman 150 250 1 37 dB Pump power ( W)

Power (a.u.) f f + Power (20 dB/div) Power (30 dB/div) Raman 0 1500 16001700 1800 024 0 30 60 Frequency (MHz) Scanning time (ms) Frequency (MHz)

Fig. 2. Experimental characterizations of the microcavity Raman laser. (A) Experimental setup. PC, polarization controller; OSA, optical spectrum analyzer; OSC, oscilloscope; ESA, electrical spectrum analyzer; LPF, long-pass filter. (B) Transmission spectrum of the supermodes and the theoretical fitting. (C) Optical spectrum of the Raman laser. (Inset) Threshold curve of the Raman laser. (D) Experimental observation of the clamping effect on the pump field. (E) Frequency spectrum of the combined probe light and Raman emission, in which the wavelength of the pump beam is unchanged.

2 of 6 | PNAS Zhang et al. https://doi.org/10.1073/pnas.2101605118 Single-mode characteristic of a supermode microcavity Raman laser Downloaded by guest on September 24, 2021 Downloaded by guest on September 24, 2021 nebtenterijce aeadteoiia ae fields. laser original the and wave reinjected the between ence the laser. resulting supermode rate, tuning the coupling of by switching the the and reversed in reflectivity, and two the the phase, compensated between injection be difference loss can intrinsic supermodes The reflector. the and phase index refractive injection the with as by Methods), obtained and approximately (Materials coupling be analysis can eigenvalue the supermodes the system, of i.e., realistic rates enough, decay a large In is facet. strength end the the at and reflectance phase optical-path–related the for accounting and reflectivity rate, coupling external the represents and respectively, loss, Here ewe h w uemds ee h etn frequency beating the signal Here, the supermodes. two and the tiny laser between the while at probe located supermode, the peak (antisymmetric) of symmetric between 2E. the frequency Fig. interference from out- center in the the presented the with is to with spectrum interfere peak frequency to the The introduced and laser, is put supermode the than be regime. single-mode cannot the supermode in other operates laser the the of and that compensated, loss higher-Q indicating the the 2D), Hence, of (Fig. Raman loss unchanged. value the the constant matching gain, a of the at power clamped pump is the intracavity power the which Simultaneously, monotonically. after grows laser threshold, the reaches igemd hrceitco uemd ircvt aa laser Raman microcavity supermode a of characteristic Single-mode al. et Zhang Hamiltonian system dynamics, the basis write traveling-wave we injection, shift frequency Kerr the deviates of slightly result Methods). frequency a and beating as (Materials splitting This passive 3B). spike-like the frequency (Fig. from center the a MHz as with 9.7 oscillations featured of fast periodically, of consisting appears envelopes note beat the into the laser 3 output with partial reflector (Fig. a reinjects as cavity 0.033, serving only fiber, intracavity of output Experimen- reflectance the the of a (54–56). face regulate effect end flat to interference a tally, the utilized supermodes. through widely field two is the laser the which modulate to of loss, introduced difference is mode technique loss dynam- self-injection lasing the the the Thus, on study 2E), we (8, dependent (Fig. physics, previously underlying ics SMSR reported the large notes reveal To beat the 9). strong to the due contradicts observed which be cannot to output due linewidth narrowed ampli- the a compensation. as gain with inferred Raman is emission, mode spontaneous symmetric the fied in effect, signal clamping weak observed the the laser considering single-mode a Additionally, indicates as 53). hence operates (12, criterion, laser Raman adopted supermode widely the a that as magnitude. SMSR, of large orders three The over (SMSR) ratio the the suppression of mode of that mode intensity than effect-induced higher The much (22). Kerr is Methods) the and to (Materials due shift supermodes Raman sive to equal h ouaino h aigsau eut rmteinterfer- the from results status lasing the of modulation The uniaiey rb ae ihtefeunysihl higher slightly frequency the with laser probe a Quantitatively, osdrn h neato fC-C aeswt self- with lasers CW-CCW of interaction the Considering of presence the Despite ω and f − − κ κ A, r h netre eoatfeunyadmode and frequency resonant unperturbed the are f ± + H n δ = ssihl agrta h pitn ftepas- the of splitting the than larger slightly is , .Drn h upwvlnt scanning, wavelength pump the During Inset). f = n brlength fiber and κ 12.5 =   ± g γ (a γ + | ∓ stedsiaieculn strength. coupling dissipative the is cw ω H orsod oteinterference the to corresponds MHz i ϕ δ , r ˜ γ 2 + f 2 = |κ eprloclain ntelaser the in oscillations temporal , − a i in |g f ccw + κ 2 n i | | r ˜ o (ϕ cos ω ek aietn ag side- large a manifesting peak, κ ) L L/c in ewe h opigpoint coupling the between oivsiaetelasing the investigate to 2|, γ/ ω g ± eae otematerial the to related + + r 2ngL/c ˜ f i i + eoe h complex the denotes uemd,remains supermode, | γ 2 κ 2 r ˜ κ   (f in − . | sattributed is ) ), H n hsthe thus and , ne the under f − peak [1] [2] δ κ f in , edaklnt.Tehpigpro ftesproelasers supermode the of the period of hopping function (T a The as the length. period hopping feedback under the study clamped experimentally not we is field pump 4 (Fig. the modulation self-injection. that loss the indicating to B), due fluctuation exhibits power periodic las- pump a a intracavity the the between scanning, provides switch temporal During actively modes. also ing and the pump method selectively Besides self-injection to strategy obtained. the be generation, stable beating cannot and decaying evolution, lasing a nonequilibrium super- dual-mode and under both from only laser lasing dur- occurs simultaneous emerging interference result, modes a transient an As 4B). the between (Fig. laser from switching arises the note the ing beat extracting the by that calculation, the in In derived a Methods. calculation and theoretical 3A the als notes Figs. by in beat predicted scanning The also pump detuning. the pump thermo- during the and emerge controlling Kerr by the via effects wavelength optic laser Raman the tune cally two the same. which the at exactly points are rates switching supermodes decay the two with the alternatively, difference, lase loss can initial by the induced exceeds super- shift injection two slight the a of term with mode the losses oppositely, one net nearly while oscillate the of Consequently, modes phase, other. injection field the the CCW with increasing interfere the Hence destructively respectively. with will phase, CCW of interfering out and and constructively CW phase in the the are For supermodes, fields field. antisymmetric CCW intracavity and the symmetric to coherently contribute will wave reinjected The at point switching mode lasing phase. the injection denote particular circles the black The regime. lasing in shift area phase gray tion the (C of observed. Zoom-in (Inset laser. (B) Raman laser. the of output Real-time 3. Fig. rqec hf pe fteRmnlsr xeietly the Experimentally, laser. Raman the of speed shift frequency A B − ofrhrpoeteetbihdter flsn dynamics, lasing of theory established the prove further To phase injection the regulate to Experimentally, 1 opnnso h opn uemd ae,i sfound is it laser, supermode hopping the of components reads 4A) Fig. in etntso h uemd aa ae ihsl-neto.(A) self-injection. with laser Raman supermode the of notes Beat ±2ngL/c hoeia ispto ftetosproe essinjec- versus supermodes two the of dissipation Theoretical ) le(rne hdn:Smerc(niymti)mode (antisymmetric) Symmetric shading: (orange) Blue ϕ. .Oc h osvrainb h self- the by variation loss the Once 3C). (Fig. a in,ccw T 1 2 = rmterflce Wotu laser output CW reflected the from π/ C https://doi.org/10.1073/pnas.2101605118 ϕ ˙ = hr yia etnt is note beat typical a where A, c ceai fteself-injected the of Schematic ) (nL π/ ω ˙ where ), hc is which 4A, and edynami- we ϕ, PNAS ω ˙ a Materi- a | + A sthe is in,ccw f6 of 3 and and

APPLIED PHYSICAL SCIENCES A 1.0 1.0 B 1.0 1.0 C a Intracavity pump Pump + 40 a-

T Raman T 1 0.5 2 0.5 0.5 0.5 30 (1/ms) 1 T 1/ Exp.

Pump power (a.u.) Pump power (a.u.) 20 Raman power (a.u.) Raman power (a.u.) 0.0 a- a+ 0.0 0.0 0.0 Theory 02040 02040 0.7 1.1 1.5 Scanning time ( s) Scanning time ( s) L (m)

Fig. 4. Switchable supermode laser with self-injection. (A) Measured intracavity pump power (gray) and Raman laser output (blue) versus scanning time with self-injection. T1 ∼ 20.6 µs is the hopping period, and T2 ∼ 11.3 µs is the duration of the antisymmetric mode lasing in one period. (B) Simulated dynamics of lasing mode switching with self-injection. (C) Dependence of hopping frequency on optical length L. The error bars denote standard deviation of 10 measurements.

fiber length L between the coupling point and the reflector is ing mode is tracked. With the pump laser fully tuned out of resonance, changed by cutting the fiber sequentially, and the measured hop- transmission of the Raman lasing mode is recorded, as shown in Fig. 2B. ping period exhibits a linear dependence on L, consistent with The pump clamping effect in Fig. 2D is observed by including a drop cou- pler, so that the intracavity pump and Raman laser power are measured the theoretical result. In each period, the occupation time T2 of the antisymmetric mode lasing is longer than that of the other without the influence of the direct-transmitted pump light. The Raman laser mode, also predicted by the theory (Fig. 4B). The SMSR of the supermode laser is characterized depending on the self-injection condition. In absence of the self-injection, the SMSR is proportional to the output Raman power (Fig. 5A), A as predicted by the Langevin analysis (Materials and Methods). With the injection feedback, it deviates from the linear power dependence due to the loss difference modulation along the variation of the laser power. Particularly, the SMSR increases 15 dB at a certain laser power, corresponding to an increase of the loss difference of 7.5 dB. The linewidths of the supermode lasers are measured by a Mach–Zender interferometer with a free spectral range of 5.591 MHz (57). As shown in Fig. 5B, the frequency noise reaches a similar level of tens of Hz2/Hz with and without self-injection, demonstrating that the laser linewidth is narrower than 100 Hz. Besides, the peaks with respect to the Kerr-shifted mode splitting are observed on the noise spectrum. Considering the relation- ship between the Kerr-modulated mode splitting and the laser power (Materials and Methods), the dependence of the measured laser linewidth on the mode splitting δf (Fig. 5 B, Inset) demon- strates that the linewidth will be broadened as the laser power declines (58). B In summary, we have clarified the controversy between the single-mode nature of stimulated scattering lasers and the previous observed “dual-mode” beat note in near-degenerate supermodes. Experimentally, the pump field is clamped to the mode with lower loss, while the laser is single mode with a SMSR up to 37 dB. The beating phenomenon is retrieved by introducing a self-injection feedback to the microcavity and identified as the transient interference when the lasing mode switches between the supermodes. In this regard, the elusive phenomenon of the temporal beat notes in previous works (8, 9) can be well understood as the interference induced by the existence of a slight reflection in the fiber loops. This work provides an insightful guidance for microlaser-based precision measurements (11) and paves the way to reconfigurable light sources (2) and low-power-consumption optical memories (59).

Materials and Methods Experimental Details. The transmission spectrum of the supermode for gen- Fig. 5. Characterization of the supermode Raman lasers with injection. erating the Raman laser is characterized with the following protocol. First, (A) Measurement of side-mode suppression ratio. The gray dashed line the pump laser is tuned into the mode resonance to excite the Raman laser. indicates theoretical ﬁtting of SMSR in the case without self-injection. (B) Second, a weak probe laser is injected (∼ 10 µW) into the cavity, whose Spectral density of single-sideband (SSB) frequency noise at different lasing frequency is in the vicinity of the generated Raman laser. When the scan- states with and without injection feedback. Values of corresponding white ning range of the probe laser covers the lasing mode, an evident beat signal frequency noise are marked with dashed lines. Inset shows values of the between the Raman laser and the probe laser is observed. Third, the pump white frequency noise versus the mode splitting δf. The dashed-dotted line laser is gradually tuned away from the resonance, while the Raman las- indicates ﬁtting results assuming inverse linear power dependence.

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P (a |a | − 4 ai,the basis, cw ξ δ p ± + = 2 | , 2 , ,the g), g)L/c a = |a |g sthe is g ccw − ω > [6] [5] [3] [4] ) | − T 2 ), 0 . , oeequations, mode Laser. the under Raman laser, Supermode the of power SMSR different 3B the Fig. of supermodes. because in two splitting, frequency the mode in beating changing passive The the modes. from lasing deviates the of switching otnosysicigfrom switching continuously oeblwtrsod ihu oso eeaiy easm htthe that reads assume density spectral we generality, of tion mode loss is mode without lasing threshold, below mode and factor emission aa aigi uemdsae(39) are supermodes in lasing Raman with force text, main where 0.Cntnsaetem-pi coefficient thermo-optic are index refractive Constants 1/500. as frequency frequency pump 225 Raman are of parameters threshold experimental lasing Other the Hz. length addition, In fiber same. output the the and MHz index tive κ scattering side strength coupling the loss 3, mode Fig. unperturbed In below. given are tion linear of denotes capacity term heat Hz. third a 330 the give simulations and element (62), scattering absorption. phonon inelastic of Here, and detuning cavity (δ amplitude Dynamics. Lasing field Supermode varying the of 5. Calculations Fig. Numerical in used is Hz 100 of bandwidth resolution a experiment, where with reads peak SMSR central calculated the the of (61), power mode total nearest the the of of power ratio peak the the as defined is SMSR As t detuning. laser-cavity respectively. supermodes, where = in t oeaut h oe fapie pnaeu msin(S)o the of (ASE) emission spontaneous amplified of power the evaluate To h aaeesue ntetertclmdladtenmrclsimula- numerical the and model theoretical the in used parameters The laser- the correct to utilized is equation thermal-diffusion simplified A /2π ± 2nL/c δ κ stefeunyo uemds respectively. supermodes, of frequency the is g) t + κ eoe hra rqec shift, frequency thermal denotes |c = f κ t /2 BW p ± stetemldfuinrt,tescn etn emi result a is term heating second the rate, diffusion thermal the is 0 dt H,adteotu brlength fiber output the and MHz, 2 | d 2 = steadtoa rvln ieo h enetdwv and wave reinjected the of time traveling additional the is Ω n

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± p κ ~ω ± κ 9Mz h diinldcyrt nue by induced rate decay additional the MHz, 3.99 = p = 9 H,pm oe mW. 1 power pump THz, 190 p + 2 δ C ) ± = ∗ p = n n sdsiainrt ftepm mode. pump the of rate dissipation is p κ δ a |a i

APPLIED PHYSICAL SCIENCES Data Availability. All study data are included in this article. 11654003, 61435001, 11527901, and 62035017), the National Key R&D Program of China (Grants 2018YFB2200401 and 2016YFA0301302), ACKNOWLEDGMENTS. We thank X.-C. Yu, J.-H. Chen, Q.-F. Yang, and the Key R&D Program of Guangdong Province (2018B030329001), Y.-Z. Gu for helpful discussions, as well as S.-J. Tang and Y. Zhi for the National Postdoctoral Program for Innovative Talents (Grant comments on the manuscript. This project is supported by the National BX20200014), and the China Postdoctoral Science Foundation (Grant Natural Science Foundation of China (Grants 12041602, 11825402, 2020M680185).

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