楊帥帥 滕浩 何鵬 黃杭東 王兆華 董全力 魏志義

1)(魯東大學(xué)物理與光電工程學(xué)院,煙臺(tái) 260405)

2)(中國(guó)科學(xué)院物理研究所,北京凝聚態(tài)物理國(guó)家實(shí)驗(yàn)室,北京 100190)

3)(西安電子科技大學(xué)物理與光電工程學(xué)院,西安 710126)

4)(中國(guó)科學(xué)院大學(xué)物理學(xué)院,北京 100049)

基于大基模體積的10 mJ飛秒鈦寶石激光再生放大器?

楊帥帥1)2)滕浩2)?何鵬3)黃杭東3)王兆華2)董全力1)?魏志義2)4)?

1)(魯東大學(xué)物理與光電工程學(xué)院,煙臺(tái) 260405)

2)(中國(guó)科學(xué)院物理研究所,北京凝聚態(tài)物理國(guó)家實(shí)驗(yàn)室,北京 100190)

3)(西安電子科技大學(xué)物理與光電工程學(xué)院,西安 710126)

4)(中國(guó)科學(xué)院大學(xué)物理學(xué)院,北京 100049)

(2017年1月25日收到;2017年4月20日收到修改稿)

文章報(bào)導(dǎo)了基于大基模體積的高能量飛秒鈦寶石激光再生放大器的設(shè)計(jì)與實(shí)驗(yàn)研究,在重復(fù)頻率10 Hz、抽運(yùn)能量60 mJ的激勵(lì)下,得到了單脈沖能量17.4 mJ的種子脈沖放大結(jié)果,壓縮后的脈沖寬度為40.6 fs,能量為13.9 mJ.借助于此大基模體積再生腔,僅增加一級(jí)多通放大,實(shí)現(xiàn)了峰值功率達(dá)1.9 TW飛秒激光脈沖輸出.結(jié)果表明,大模體積再生放大不僅降低了后續(xù)放大對(duì)抽運(yùn)能量的要求,也可以單獨(dú)壓縮實(shí)現(xiàn)再生腔直接輸出10 mJ量級(jí)的飛秒激光脈沖,是大能量高峰值功率飛秒激光系統(tǒng)的優(yōu)質(zhì)前端.

∶飛秒激光,啁啾脈沖放大,再生放大器,太瓦

PACS∶42.60.—v,42.60.By,42.60.Da,42.65.ReDOI∶10.7498/aps.66.104209

1 引 言

隨著克爾透鏡鎖模飛秒鈦寶石激光的實(shí)現(xiàn)[1]以及啁啾脈沖放大(chirped-pulse amplification,CPA)技術(shù)[2]的發(fā)明,飛秒激光在脈沖寬度不斷變窄的同時(shí),峰值功率也在不斷的提高,峰值功率超過(guò)拍瓦(PW)的超強(qiáng)激光已經(jīng)在一些實(shí)驗(yàn)室實(shí)現(xiàn)[3?5].

在常規(guī)的CPA方案中,飛秒振蕩器輸出的種子脈沖能量只有納焦耳量級(jí),其放大過(guò)程要經(jīng)歷指數(shù)增長(zhǎng)和線性增長(zhǎng)兩個(gè)階段[6,7].指數(shù)增長(zhǎng)階段是將種子脈沖從納焦耳提升到幾百微焦耳或毫焦耳量級(jí),其增長(zhǎng)約106倍.為了實(shí)現(xiàn)指數(shù)增長(zhǎng),必須將鈦寶石晶體中的激光光斑控制得非常小,激光在晶體中的能流密度非常高;線性增長(zhǎng)階段是將能量從毫焦放大到焦耳甚至更高,該階段采用大能量抽運(yùn),晶體上的光斑也較大,放大倍數(shù)為幾倍到幾十倍.指數(shù)增長(zhǎng)階段通常在激光放大中被稱為預(yù)放大,線性增長(zhǎng)階段被稱為大能量放大.

預(yù)放大又分為多通預(yù)放大和再生放大[8].再生放大由于是振蕩腔結(jié)構(gòu),其輸出的光束質(zhì)量高,穩(wěn)定性和指向性好,而且還可以隔離振蕩器和后續(xù)放大器,壓縮后輸出的光束質(zhì)量與振蕩器種子光無(wú)關(guān);多通預(yù)放大的光束質(zhì)量依賴種子光源,由于放大程數(shù)少,在晶體上的光斑控制得非常小,容易損傷晶體,但多通放大結(jié)構(gòu)簡(jiǎn)單,易于操作,更適合用于后面的線性增長(zhǎng)大能量放大.

預(yù)放大是種子脈沖與后續(xù)大能量放大的橋梁,其輸出激光品質(zhì)的好壞直接影響整體放大效率和光束質(zhì)量.大能量輸出的預(yù)放大脈沖可以大大降低線性放大器對(duì)抽運(yùn)能量的要求,特別是雙CPA放大方案中高對(duì)比度交叉偏振濾波(cross-polarized wave generation,XPW)技術(shù)[9,10]的轉(zhuǎn)換效率約百分之十,只有提高壓縮脈沖的能量才能夠輸出更高能量的高對(duì)比度種子脈沖.多通預(yù)放大由于放大程數(shù)少,放大后脈沖能量通常較低,而再生放大可以控制腔模來(lái)獲得大能量的輸出,所以研究大基模體積高能量再生放大是非常有意義的.

圖1 已報(bào)道的不同重復(fù)頻率的鈦寶石飛秒再生腔輸出能量,本文結(jié)果用紅色星號(hào)表示Fig.1.Overview of the state of art of output energy from regenerative amplifier at different repetition rate,the results in this letter is highlighted in red star.

鈦寶石晶體的飛秒再生放大器,根據(jù)不同的應(yīng)用和不同重復(fù)頻率來(lái)進(jìn)行設(shè)計(jì),大多數(shù)再生放大器一般都工作在幾個(gè)毫焦耳.我們將已發(fā)表的再生放大器的輸出能量按照不同重復(fù)頻率整理在圖1中,可以看出高重復(fù)頻率(1—10 kHz)的再生放大器由于晶體熱透鏡效應(yīng)的影響,輸出脈沖能量普遍比較低,基本維持在1—3 mJ,在特殊冷卻方式和補(bǔ)償熱透鏡情況下,最高能量為6.5 mJ[11?19].低重頻再生放大器由于每發(fā)之間持續(xù)時(shí)間長(zhǎng),熱量有足夠長(zhǎng)的時(shí)間被帶走,不會(huì)出現(xiàn)高重復(fù)頻率工作時(shí)形成熱堆積,所以可以不考慮熱效應(yīng),其輸出能量相對(duì)較高,但大多輸出能量也不足10 mJ[20?29].文獻(xiàn)[30]報(bào)道了重復(fù)頻率為5 Hz的再生放大能量為13 mJ.在文獻(xiàn)[31,32]中分別報(bào)道了重復(fù)頻率10 Hz的再生放大輸出能量為20 mJ,其中文獻(xiàn)[31]中采用雙晶體結(jié)構(gòu)的再生放大器,腔長(zhǎng)非常長(zhǎng),結(jié)構(gòu)復(fù)雜,調(diào)節(jié)難度也較大,且抽運(yùn)能量為150 mJ,光-光轉(zhuǎn)換效率較低;文獻(xiàn)[32]中報(bào)道的再生腔放大結(jié)果是雙波段放大的能量,而單一波段輸出也只有10 mJ.對(duì)于50 Hz再生放大也報(bào)道過(guò)輸出能量為19 mJ的放大結(jié)果[33],但其輸出脈沖的光譜較窄,加入光譜整形后也只有12 mJ的激光輸出.相比于前述已經(jīng)報(bào)道的這些再生放大器,我們?cè)O(shè)計(jì)的再生放大器采用了增大腔內(nèi)模場(chǎng)體積的方法來(lái)提高能量輸出,僅一塊鈦寶石晶體,腔長(zhǎng)短、結(jié)構(gòu)簡(jiǎn)單易于維護(hù),在60 mJ抽運(yùn)能量下放大后的脈沖能量為17.4 mJ,其光譜半高寬為35 nm,壓縮后的能量輸出為13.9 mJ,脈沖寬度為40.6 fs,是大能量太瓦級(jí)飛秒系統(tǒng)的優(yōu)質(zhì)前端.

2 大基模體積再生放大的設(shè)計(jì)和實(shí)驗(yàn)結(jié)果

大基模體積再生腔型的設(shè)計(jì)中首先要考慮的是腔模光斑尺寸是否支持高能量激光脈沖的放大,以及抽運(yùn)激光和種子光光斑與腔內(nèi)模式的匹配[34].根據(jù)需要放大的能量,腔內(nèi)鈦寶石晶體中光斑大小的控制既要保證其能流密度大于鈦寶石晶體飽和能流密度(～0.8 J/cm2),又要確保其小于晶體的損傷閾值(10 J/cm2),只有合適的光斑才能保證再生腔內(nèi)放大后的能量既處于過(guò)飽和狀態(tài)又不至于損傷晶體.再生腔內(nèi)的其他光學(xué)元件則只需要考慮光斑盡可能大,能流密度相對(duì)低,讓其工作在安全區(qū)域.

高重復(fù)頻率比如kHz再生放大器[17,18],抽運(yùn)激光通常采用YLF調(diào)Q倍頻激光,由于該激光脈沖寬度寬(～200 ns)而且能量低,耦合到鈦寶石晶體上采用緊聚焦方式,所以再生腔內(nèi)的腔模較小,放大后的能量較低.對(duì)于低重復(fù)頻率如10 Hz的再生放大器[29],抽運(yùn)激光采用燈泵532 nm激光,由于其能量高、脈沖寬度窄(～10 ns),所以聚焦在鈦寶石晶體上的光斑較大,適合大腔模體積的高能量再生放大器.

如圖2(b)所示為大基模體積再生腔結(jié)構(gòu)圖,其腔型為線性穩(wěn)定腔,由兩端鏡M1和M4,以及腔內(nèi)鈦寶石晶體(Ti∶S)和一個(gè)普克爾盒(PC)組成,其中M1為凹面反射鏡,曲率半徑為10 m,M4為平面反射鏡.鈦寶石距離M4為30 cm,PC距離M1為20 cm.總腔長(zhǎng)為1.9 m,激光脈沖往返一次的時(shí)間間隔為12.7 ns.由于激光器運(yùn)行在低重復(fù)頻率,鈦寶石晶體上的熱透鏡效應(yīng)可以不考慮,所以整個(gè)腔內(nèi)光斑的分布如圖2(a)所示,腔內(nèi)光斑大小從M1到M4是逐漸下降的,但最小的光斑(M4)半徑約1 mm,M1上的光斑半徑則為1.1 mm,其腔內(nèi)光斑明顯大于常規(guī)的高重復(fù)頻率再生腔,所以可以支持大能量激光脈沖的放大.

在前述腔型計(jì)算的基礎(chǔ)上,實(shí)驗(yàn)室搭建的實(shí)際光路圖如圖3所示,包括飛秒振蕩器、展寬器、大基模體積的再生放大器和壓縮器.

圖2 (網(wǎng)刊彩色)大基模體積再生腔腔內(nèi)模式分布(a)和結(jié)構(gòu)圖(b)(M1,M4為腔鏡;PC為普克爾盒;Ti:S為鈦寶石晶體)Fig.2.(color online)Radius of TEM00mode in large mode size cavity(a)and scheme of corresponding cavity(M1,M4 are end mirrors,PC is pockels cell,Ti:S is Ti:sapphire crystal).

圖3 (網(wǎng)刊彩色)大基模體積再生放大系統(tǒng)光路圖(ISO代表隔離器;G代表光柵;C代表?xiàng)l形鏡;P代表格蘭棱鏡;FR代表旋光器;Ti:Sa代表鈦寶石;PC代表普克爾盒;M代表腔鏡;L代表透鏡)Fig.3.(color online)Optical layout of the regenerative amplifier with large mode size.

種子激光采用啁啾鏡色散補(bǔ)償?shù)拟亴毷袷幤鱗35](型號(hào)FlashWave-30,鹽城物科光電有限公司),該振蕩器輸出功率為350 mW,重復(fù)頻率為83 MHz,光譜半高全寬85 nm,脈沖寬度小于20 fs.經(jīng)過(guò)Martinez展寬器[36]后脈沖寬度為185 ps,光譜寬度為60 nm.展寬后的脈沖通過(guò)格蘭棱鏡(P1)、法拉第旋光器(FR)和半波片,偏振態(tài)由P偏振變?yōu)镾偏振,經(jīng)過(guò)格蘭棱鏡(P2)注入到再生腔中.再生腔中普克爾盒晶體處于靜態(tài)1/4波片狀態(tài),工作時(shí)再加1/4波片高壓實(shí)現(xiàn)單脈沖選擇,單脈沖被鎖在再生腔內(nèi)振蕩并放大,直到去掉高壓電源后放大脈沖的偏振態(tài)又變回S偏振,由格蘭棱鏡(P2)從腔內(nèi)導(dǎo)出.再生腔的抽運(yùn)激光采用的是燈泵Nd∶YAG電光調(diào)Q納秒脈沖激光的倍頻激光(532 nm),其輸出總能量為450 mJ,脈沖寬度約為8 ns.用一片半波片和一片薄膜偏振片控制再生腔抽運(yùn)激光的能量.抽運(yùn)激光通過(guò)一焦距為600 mm的凸透鏡聚焦在鈦寶石晶體上,鈦寶石晶體尺寸為6 mm×6 mm×20 mm,品質(zhì)因數(shù)(figure of merit,FOM)＞150,對(duì)532 nm激光的吸收大于90%,端面布儒斯特角度切割.為了避免抽運(yùn)激光聚焦后損傷鈦寶石晶體,晶體放置在焦點(diǎn)之前,抽運(yùn)激光聚焦在晶體中的光斑控制在2 mm,抽運(yùn)激光能流密度為1.5 J/cm2,遠(yuǎn)低于鈦寶石的損傷閾值.由于抽運(yùn)能量比較低,鈦寶石晶體采用自然冷卻.

圖4 (網(wǎng)刊彩色)再生腔中種子脈沖注入后的建立時(shí)間和倒空脈沖Fig.4.(color online)Built-up time of amplified seed in the cavity(red)and dumped pulse(black).

展寬后的種子激光注入再生腔后,種子脈沖在再生腔內(nèi)的建立時(shí)間過(guò)程見(jiàn)圖4.經(jīng)過(guò)優(yōu)化腔內(nèi)激光建立時(shí)間,將PC的倒出時(shí)間選擇在放大峰值的第二個(gè)脈沖處,獲得了穩(wěn)定的放大脈沖輸出.我們首先研究了再生腔放大輸出能量與抽運(yùn)激光能量的關(guān)系,如圖5所示,放大能量隨抽運(yùn)激光能量是線性增長(zhǎng)的,但增長(zhǎng)曲線在高能量抽運(yùn)下低于模擬結(jié)果,其原因是高能量抽運(yùn)下會(huì)有一定的熱積累效應(yīng),導(dǎo)致放大效率降低.在實(shí)驗(yàn)中經(jīng)過(guò)優(yōu)化,在能量為60 mJ抽運(yùn)激光激勵(lì)下,再生腔放大后的單脈沖能量為17.4 mJ,光光轉(zhuǎn)換效率為29.0%.

用光譜儀測(cè)量放大后脈沖光譜,中心波長(zhǎng)為790 nm,光譜寬度為35 nm,如圖6所示,不同輸出能量下,脈沖的光譜分布幾乎沒(méi)變化.相對(duì)于種子脈沖,再生放大激光脈沖光譜由于增益窄化效應(yīng)而變窄[37],但35 nm的譜寬也足夠支持小于40 fs的激光脈沖輸出.

圖5 (網(wǎng)刊彩色)大基模體積再生腔能量輸出曲線Fig.5.(color online)Output energy as a function of pump energy.

圖6 (網(wǎng)刊彩色)種子光和再生腔有種子注入的光譜曲線Fig.6.(color online)Spectrum of seeding laser pulses and amplified laser pulses.

再生放大后的激光脈沖經(jīng)過(guò)擴(kuò)束準(zhǔn)直后進(jìn)入壓縮器進(jìn)行壓縮.壓縮器由兩塊光柵常數(shù)為1500 lp/mm的光柵和爬低鏡組成,經(jīng)過(guò)優(yōu)化入射角和光柵對(duì)之間的距離,壓縮后的脈沖寬度采用商品化自參考光譜干涉的自相關(guān)儀(Wizzler-800,Fastlite公司)進(jìn)行測(cè)量,其脈沖寬度為40.6 fs,如圖7(a)所示.圖7(b)為反演出的脈沖光譜相位分布曲線,可以看出相位分布接近直線,壓縮后的能量為13.9 mJ.

壓縮后的脈沖還未能完全達(dá)到變換極限脈寬,主要原因是由于壓縮器沒(méi)能完全補(bǔ)償展寬器和再生腔內(nèi)材料引入的高階色散.展寬器和壓縮器引入的色散可通過(guò)光線追跡法模擬計(jì)算,再生腔內(nèi)材料的二階色散和三階色散可根據(jù)以下公式給出∶

其中(1)和(2)式中?為光頻相位,ω為光頻,λ為波長(zhǎng),l為材料長(zhǎng)度,c為光速,n(λ)為材料的折射率可由賽爾邁耶(Sellmeier)公式給出.在最優(yōu)壓縮角度下得到模擬計(jì)算結(jié)果如表1所列,追跡波長(zhǎng)選取中心波長(zhǎng)790 nm.可見(jiàn)通過(guò)優(yōu)化壓縮器光柵入射角和光柵間距,在完全補(bǔ)償二階色散基礎(chǔ)上,還有一部分三階色散未能完全補(bǔ)償,故未實(shí)現(xiàn)壓縮至變換極限脈寬,后續(xù)可在展寬器前加入色散補(bǔ)償?shù)穆暪庹{(diào)制器(Dazzler)補(bǔ)償色散,可實(shí)現(xiàn)更短脈寬的輸出.

圖7 (網(wǎng)刊彩色)再生腔輸出脈沖壓縮后的脈沖寬度(a),光譜相位分布曲線(b)Fig.7.(color online)(a)The pulse duration of compressed pulses directly from regenerative amplifier and(b)corresponding distribution of spectral phase.

表1 系統(tǒng)中各部分色散列表Table 1.Lists of dispersion in the CPA laser system.

圖8所示為壓縮后的激光脈沖光束質(zhì)量,采用M2因子儀器測(cè)量結(jié)果為1.28.這表明我們?cè)O(shè)計(jì)的大基模體積再生放大器輸出的激光具有較好的光束質(zhì)量.

圖8 (網(wǎng)刊彩色)壓縮后光束質(zhì)量Fig.8.(color online)The beam quality(M2)of laser beam from the regenerative amplifier and compressor

3 基于大基模體積再生放大的TW激光輸出

以上述大能量再生放大器為基礎(chǔ),將再生放大器輸出的激光經(jīng)過(guò)擴(kuò)束準(zhǔn)直后注入到六通放大器進(jìn)一步放大.六通放大器是采用Bowtie對(duì)稱結(jié)構(gòu),將532 nm抽運(yùn)激光抽運(yùn)再生放大器的剩余能量分成兩路,分別通過(guò)真空像傳遞管縮束后從兩端對(duì)稱抽運(yùn)鈦寶石晶體,經(jīng)過(guò)優(yōu)化后,脈沖能量放大到110 mJ.放大后的脈沖再次注入上述的壓縮器中進(jìn)行壓縮,經(jīng)過(guò)測(cè)量脈沖寬度為43 fs,壓縮后的能量為81.4 mJ,對(duì)應(yīng)的峰值功率為1.9 TW.能量穩(wěn)定性經(jīng)過(guò)測(cè)量為2.15%(RMS),光束質(zhì)量(M2)為1.5.

4 結(jié) 論

本文報(bào)道了一種具有輸出能量大于10 mJ的大基模體積飛秒鈦寶石激光再生放大方案,在60 mJ抽運(yùn)能量下,得到了放大能量為17.4 mJ的結(jié)果,光光轉(zhuǎn)換效率為29%,壓縮后實(shí)現(xiàn)了能量為13.9 mJ、脈沖寬度為40.6 fs的飛秒激光輸出.在此基礎(chǔ)上,通過(guò)增加一級(jí)多通放大器,建成一臺(tái)緊湊型太瓦級(jí)飛秒鈦寶石激光裝置,壓縮后的輸出能量為81.4 mJ,脈沖寬度為43 fs,對(duì)應(yīng)的峰值功率為1.9 TW,能量穩(wěn)定性為2.15%.該結(jié)果表明大基模體積的高能量再生放大器不僅可以有效降低后續(xù)放大級(jí)對(duì)抽運(yùn)能量的要求,而且具有光束質(zhì)量好,結(jié)構(gòu)緊湊、穩(wěn)定等優(yōu)點(diǎn),是開(kāi)展強(qiáng)場(chǎng)物理實(shí)驗(yàn)、超快科學(xué)特別是戶外飛秒激光大氣傳輸?shù)入x子體通道等研究工作[38?41]的優(yōu)質(zhì)光源.

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PACS∶42.60.—v,42.60.By,42.60.Da,42.65.ReDOI∶10.7498/aps.66.104209

*Project supported by the Special Foundation of State Major Scientific Instrument and Equipment Development of China(Grant No.2012YQ12004701),the State Key Development Program for Basic Research of China(Grant No.2013CB922401),and the National Natural Science Foundation of China(Grant Nos.11474002,11674386).

?Corresponding author.E-mail:hteng@iphy.ac.cn;qldong@iphy.ac.cn;zywei@iphy.ac.cn

10 mJ femtosecond Ti∶Sapphire regenerative amplifier with large mode size?

Yang Shuai-Shuai1)2)Teng Hao2)?He Peng3)Huang Hang-Dong3)Wang Zhao-Hua2)Dong Quan-Li1)?Wei Zhi-Yi2)4)?
1)(Schoolof Physics and Optoelectronic Engineering,Ludong University,Yantai 260405,China)
2)(Beijing National Laboratory for Condensed Matter Physics,Institute of Physics,Chinese Academy of Sciences,Beijing 100190,China)
3)(Schoolof Physics and Optoelectronic Engineering,Xidian University,Xi’an 710126,China)
4)(Schoolof Physical Sciences,University of Chinese Academy Sciences,Beijing 100049,China)

25 January 2017;revised manuscript

20 April 2017)

With advent of chirped-pulse amplification,the peak power of femtosecond laser pulse was reached to petawatt(PW)or hundreds of terawatt(TW).Many progresses of high- field physics and ultrafast dynamics in matter are achieved using TW or PW laser.Pre-amplifier is an exponential growth amplifier which is also a bridge between oscillator and power amplifier.The best choice of pre-amplifier is amplification in regenerative cavity,due to its high stability and beam quality.The quality of pre-amplified laser pulse is significant to efficiency and beam quality of the successive power amplifier.High energy pre-amplifier with high beam quality will reduce the requirement of pump laser infinal power amplifier.But typical regenerative amplifier only support low output energy of few millijoule.Higher energy from only one regenerative amplifier is crucial to whole laser system.

High energy regenerative amplifier can be achieved by increasing the size of TEM00in cavity.A new femtosecond Ti∶sapphire regenerative amplifier with large mode size was demonstrated in this letter.The regenerative cavity is designed as stable linear resonator in which end mirrors are planar,the diameter of beam waist in Ti∶sapphire crystal is larger than 2 mm,which can support high energy pulse amplified in cavity.By matching the focal spot of pump laser with the size of mode and optimization of cavity,the output laser energy up to 17.4 mJ was achieved under the pump energy of 60 mJ at repetition rate of 10 Hz,which corresponds to the efficiency of 29%.The amplified laser pulse from regenerative amplifier was compressed in a grating-pair compressor.By carefully alignment of incident angle and distance between the two gratings of compressor,the shortest pulses duration of 40.6 fs and energy of 13.9 mJ are obtained,which is a little bit longer than Fourier-transform limit based on spectrum of laser.The dispersion in the CPA laser system was also analyzed,after optimization of compressor,there are still high order dispersions uncompensated,which results in the duration of compressed pulses longer than Fourier-transform limit.

Based on this large mode size regenerative amplifier,peak power of 1.9 TW laser pulses which compressed pulse energy of 81.4 mJ in 43 fs were also further realized by following only one stage of multipass amplifier.The beam quality(M2)was measured to be 1.6 and 1.5 in X and Y directions respectively,and the energy stability is 2.15%(rms).The results show that this large mode size regenerative amplifier is an ideal choice of pre-amplifier in TW laser system.

∶femtosecond laser,chirped-pulse amplification,regenerative amplifier,terawatt

?國(guó)家重大科學(xué)儀器設(shè)備開(kāi)發(fā)專項(xiàng)基金(批準(zhǔn)號(hào):2012YQ12004701)、國(guó)家重點(diǎn)基礎(chǔ)研究發(fā)展計(jì)劃(批準(zhǔn)號(hào):2013CB922401)和國(guó)家自然科學(xué)基金(批準(zhǔn)號(hào):11474002,11674386)資助的課題.

?通信作者.E-mail:hteng@iphy.ac.cn;qldong@iphy.ac.cn;zywei@iphy.ac.cn

?2017中國(guó)物理學(xué)會(huì)Chinese Physical Society