李 晨,張海洋*,趙長明,張立偉,2,楊蘇輝,楊宏志
(1.北京理工大學(xué) 光電學(xué)院 電子科學(xué)與技術(shù)系, 北京 100081; 2.中電科海洋信息技術(shù)研究院有限公司, 北京 100041)
近年來,移頻反饋激光器(frequency shifted feedback, FSF)以其獨(dú)特的時(shí)頻特性,被研究應(yīng)用在鎖模激光[1-2]、激光線寬測(cè)量[3]、泰伯效應(yīng)[4]、實(shí)時(shí)光域傅里葉變換[5]、啁啾[6]等諸多方向。移頻反饋激光通常是在常規(guī)F-P腔[7-9]或者環(huán)形腔[10-12]內(nèi)加入移頻器(如聲光調(diào)制器),激光每次通過其都會(huì)發(fā)生頻率的改變。通過控制反饋環(huán)路的增益,該激光可以輸出多次移頻后的拍頻信號(hào),其頻率間隔由移頻器的調(diào)制頻率決定。當(dāng)移頻器的調(diào)制頻率與反饋腔長滿足一定關(guān)系時(shí)可以產(chǎn)生類似鎖模體制的超短脈沖[13-20]。
作者通過在光纖環(huán)路中插入光纖放大器與聲光調(diào)制器,設(shè)計(jì)出一種基于聲光移頻和光纖放大的頻移反饋激光。通過注入1064nm波長的單頻激光,在環(huán)路中實(shí)現(xiàn)了基頻的拓展,通過控制光纖放大器(或增益),研究了增益對(duì)各階次諧波相對(duì)強(qiáng)度的影響。同時(shí),建立了激光外差相干理論模型,通過耦合器傳輸效率矩陣對(duì)實(shí)驗(yàn)進(jìn)行理論分析,推導(dǎo)出受放大增益系數(shù)影響的輸出電場(chǎng)公式。最后,實(shí)驗(yàn)驗(yàn)證了放大增益系數(shù)對(duì)頻譜中各階次諧波相對(duì)強(qiáng)度的影響。
采用聲光調(diào)制-光纖放大的光纖環(huán)路移頻反饋激光器實(shí)驗(yàn)裝置如圖1所示。該裝置由連續(xù)激光器、聲光調(diào)制器(acousto-optic modulation,AOM)、光纖放大器(ytterbium-doped fiber amplifier,YDFA)、光探測(cè)器、2×2光纖耦合器組成。波長為1064nm連續(xù)激光由輸入端1注入2×2光纖耦合器,經(jīng)由輸出端口2輸入聲光調(diào)制器,聲光調(diào)制器調(diào)制頻率fAO,入射的激光經(jīng)由聲光調(diào)制器發(fā)生+1級(jí)衍射,衍射光由光纖放大器放大后,再經(jīng)由輸入端口2進(jìn)入耦合器,部分光由輸出端口2輸出,端口2接探測(cè)器進(jìn)行探測(cè)。輸出端口1與輸入端口2間形成環(huán)路,激光不斷在環(huán)路中發(fā)生頻移調(diào)制,由端口2輸出頻率間隔一致(fAO)的移頻反饋激光,即實(shí)現(xiàn)了光學(xué)頻率梳。
Fig.1 Experiment device of fiber loop frequency-shifted feedback lasers of acousto-optic modulate and fiber amplification(CW laser—continuous wave laser; AOFS—acousto-optic shifter)
設(shè)矩陣[tij]是耦合器的分光比,tij為其矩陣元,Ein是輸入的電場(chǎng),Eout是輸出的電場(chǎng),則輸入的電場(chǎng)Ein與輸出的電場(chǎng)Eout之間滿足公式:
(1)
因?yàn)楣饫w組成一個(gè)閉合環(huán)路,則環(huán)路入射到耦合器的光場(chǎng)滿足公式:
Ein,2(t)=γEout,2(t-τ)exp[i2πfAO(t-τ)](2)
由(1)式可以得到:
Eout,2(t)=t12Ein,1(t)+t22Ein,2(t)(3)
將(2)式代入(3)式,則可得:
Eout,2(t)=t21Ein,1(t)+
t22γEout,2(t-τ)exp[i2πfAO(t-τ)](4)
公式展開如下:
將(5)式代入(4)式,可得:
Eout,2(t)=t21Ein,1(t)+
t21t22γEin,1(t-τ)exp[i2πfAO(t-τ)]+
t21(t22γ)2Ein,1(t-2τ)exp[i2πfAO(t-2τ)]+
t21(t22γ)3Ein,1(t-3τ)exp[i2πfAO(t-3τ)]+
…(6)
(6)式整理可得:
exp[i2πfAOp(t-τ)]exp[-iπfAOp2t](7)
實(shí)驗(yàn)中需要對(duì)輸出端1的輸出電場(chǎng)進(jìn)行探測(cè),即Eout,1,且由于輸入端1的輸入電場(chǎng)Ein,1易于測(cè)量。根據(jù)(2)式和(7)式,Eout,1(t)可寫為:
Eout,1(t)=t11Ein,1(t)+t12Ein,2(t)=t11Ein,1(t)+
t12γEout,2(t-τ)exp[i2πfAO(t-τ)](8)
如果入射電場(chǎng)Ein,1為連續(xù)波,其能量為Pin,則滿足:
exp[i2πfAO(p+1)(t-τ)]×
當(dāng)入射激光器功率為40mW、聲光調(diào)制器調(diào)制頻率為200MHz、光纖環(huán)路光程約為27.90m、光纖放大器的輸出功率為30mW時(shí),移頻反饋激光的拍頻功率譜分別如圖2a所示,其頻譜由一串頻率間隔相同的諧波組成,相鄰諧波的頻率間隔為200MHz,最高階諧波頻率為2.4GHz。
為了研究不同增益系數(shù)(即參量G)對(duì)頻譜中各諧波強(qiáng)度和最高階諧波的影響,調(diào)節(jié)光纖放大器的輸出功率分別為50mW,70mW,80mW,其功率譜如圖2b~圖2d所示。隨著輸出功率的增大,最高階諧波的頻率也隨著提高。同時(shí)可以發(fā)現(xiàn),部分諧波存在著明顯的抑制現(xiàn)象,即均低于左右兩邊的諧波,這是由于反饋腔內(nèi)激光干涉時(shí)的相互抵消導(dǎo)致。
Fig.2 Relationship between power spectral density and frequency under different powers
a—30mW b—50mW c—70mW d—80mW
由于實(shí)驗(yàn)中采用光纖放大器的輸出功率為控制參量,為了更加深入的研究頻移反饋激光的相關(guān)特性,理論中采用更為普遍的增益系數(shù)G作為控制變量,數(shù)值仿真增益系數(shù)G對(duì)拍頻頻譜的影響。當(dāng)G分別取值G=1.6,G=2.4,G=2.6,G=2.8時(shí),功率頻譜密度如圖3a~圖3d所示。通過對(duì)比可以發(fā)現(xiàn),實(shí)驗(yàn)與仿真結(jié)果相吻合,具有較高一致性。同時(shí)由圖3a~圖3d對(duì)比可以觀察,隨著G的不斷增大,各階次諧波的強(qiáng)度也發(fā)生了較大的變化;增益系數(shù)越大,最高階的諧波階次也越高。因此,光纖放大器的引入有效地實(shí)現(xiàn)了基頻的拓展,為實(shí)現(xiàn)信號(hào)的頻譜上變換提供了一種有效的方法。除此之外,各階次頻率的相對(duì)強(qiáng)度也具有一定規(guī)律。以1GHz拍頻為例,從圖中可以明顯發(fā)現(xiàn)其強(qiáng)度明顯低于左右兩邊諧波的高度,這是由于激光在反饋腔內(nèi)外差干涉時(shí)的相互抵消作用,尤其表現(xiàn)在當(dāng)G=4時(shí),1GHz整數(shù)倍的諧波明顯低于左右兩邊。同時(shí),受探測(cè)器的最大帶寬3.5GHz的限制,實(shí)驗(yàn)中無法觀察到更高階次的諧波。
Fig.3 Relationship between power spectral density and frequency under different power gainG
a—G=1.6 b—G=2.4 c—G=2.6 d—G=2.8 e—G=4
通過聲光調(diào)制-光纖放大的光纖環(huán)路,得到了一個(gè)不斷移頻放大的頻率梳式激光器,并對(duì)其理論進(jìn)行了研究。吻合較好的實(shí)驗(yàn)及仿真結(jié)果說明,光纖放大器的增益對(duì)頻譜圖的波形具有一定的影響。后續(xù)的實(shí)驗(yàn)若能通過選擇性能更優(yōu)越的探測(cè)器或在實(shí)驗(yàn)裝置中添加衰減元件來解決探測(cè)器峰值功率及其增益帶寬的問題,對(duì)移頻反饋激光器的選頻問題則具有一定的意義。
[1] RYU H Y, MOON H S, SUH H S. Optical frequency comb generator based on actively mode-locked fiber ring laser using an acousto-optic modulator with injection-seeding [J]. Optics Express, 2007, 15(18): 11396-11401.
[2] YOSHIDA M, FUJIMOTO M, NAKAZAWA M,etal. A mode-locked frequency-shifted feedback fiber lasers[C]//Coference on Lasers and Electro-Optics,2001. New York,USA: IEEE,2001:299-300.
[3] HALE P D, KOWALSKI F V. Output characterization of a frequency shifted laser: Theory and experiment[J]. Journal of Quantum Electronics,1990,10(10):1845-1851.
[4] BERRY M V, KLEIN S. Integer, fractional and fractal Talbot effects[J].Journal of Modern Optics,1996,43(10): 2139-2164.
[5] de CHATELLUS H G, PIQUE J P. Statistical properties of frequency shifted feedback lasers[J].Optics Communications, 2010, 283(1): 71-77.
[6] YATSENKO L P, SHORE B W, BERGMANN K. Theory of a frequency-shifted feedback laser[J].Optics Communications,2004,236(1/3): 183-202
[7] ZHANG H Y, BRUNEL M, ROMANELLI M,etal. Green pulsed lidar-radar emitter based on a multipass frequency-shifting external cavity[J]. Applied Optics,2016,55(10):2467-2473.
[8] VALLET M, BARREAUX J, ROMANELLI M,etal. Lidar-radar velocimetry using a pulse-to-pulse coherent RF-modulatedQ-switched laser[J]. Applied Optics,2013, 52(22):5402-5410.
[9] HEIDT V, BURGER J P, MARAN J N.High power and high energy ultrashort pulse generation with a frequency shifted feedback fiber laser[J]. Optics Express,2007, 15(24):15892-15897.
[10] SABERT H, BRINKMEYER E. Pulse generation in fiber lasers with frequency shifted feedback[J]. Journal of Lightwave Technology, 1994,12(8):1360-1368.
[11] NIKODEM M P, KLUZNIAK E, ABRAMASKI K. Wavelength tenability and pulse duration control in frequency shifted feedback re-doped fiber lasers[J]. Optics Express, 2009,17(5):3299-3304.
[12] NAKAMURA K, HARA T, YOSHIDA M,etal. Optical frequency domain ranging by a frequencyshifted feedback laser[J]. IEEE Journal of Quantum Electronics, 2000, 36(3): 305-316 .
[13] KOWALSKI F V, NDIAYE C, NAKAMURA K. Noise waveforms with repetitive phase and nonrepetitive amplitude[J].Optics Letters, 2002, 27(22): 1965-1967.
[14] YATSENKO L P, SHORE B W, BERGMANN K. Coherence in the output spectrum of frequency shifted feedback lasers[J].Optics Communications, 2009, 282(2): 300-309 .
[15] KOWALSKI F V, SQUIER J A, PINCKNEY J T. Pulse generation with an acousto-optic frequency shifter in a passive cavity[J]. Applied Physics Letters, 1987, 50(12): 711-713.
[16] de CHATELLUS H G, JACQUIN O, HUGON O,etal. Generation of ultrahigh and tunable repetition rates in CW injection-seeded frequency-shifted feedback lasers[J].Optics Express,2003, 21(13):15065-15074.
[17] KOWALSKI F V, NDIAYE C, NAKAMURA K. Noise waveforms generated by frequency shifted feedback lasers: application to multiple access communications[J].Optics Communications, 2016,231(1/6): 149-164.
[18] NIKODEM M, ABRAMSKI K. Controlling the frequency of the frequency shifted feedback fiber laser using injection-seeding technique[J].Optics Communications, 2010, 283(10): 2202-2205.
[19] PHILLIPS M W, LIANG G Y, BARR J R M. Frequency comb generation and pulsed operation in a Nd∶YAG laser with frequency-shifted feedback[J]. Optics Communications,1993,100(5/6):473-478.
[20] COPPIN P, HODGKINSON T G. Novel optical frequency comb synthesis using optical feedback[J]. Electronics Letters, 1990,26(1): 28-30.