別業(yè)廣，曾言,2，楊張永,2，成純富,2，歐藝文,2(. 湖北工業(yè)大學(xué)理學(xué)院， 湖北 武漢 430068;2. 太陽能高效利用湖北省協(xié)同創(chuàng)新中心(湖北工業(yè)大學(xué))，湖北 武漢 430068)

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高相干度中紅外超連續(xù)譜光源的研究

別業(yè)廣1，曾言1,2，楊張永1,2，成純富1,2，歐藝文1,2
(1. 湖北工業(yè)大學(xué)理學(xué)院， 湖北 武漢 430068;2. 太陽能高效利用湖北省協(xié)同創(chuàng)新中心(湖北工業(yè)大學(xué))，湖北 武漢 430068)

選用全波段正常色散As2S3光子晶體光纖作為非線性介質(zhì)來消除反常色散區(qū)中孤子分裂引起的調(diào)制不穩(wěn)定性所造成的超連續(xù)譜相干特性的惡化問題.利用分步傅里葉法數(shù)值模擬超短激光脈沖在全波段正常色散As2S3光子晶體光纖中的非線性傳輸和中紅外超連續(xù)譜的產(chǎn)生.分析脈寬、傳輸距離、入射峰值功率和初始啁啾對中紅外超連續(xù)譜光源的帶寬、相干特性和平坦度的影響.通過優(yōu)化泵浦激光參數(shù)和光纖參量，在最佳負(fù)啁啾Cp=-4、脈寬為50 fs、中心波長為2 800 nm、入射峰值功率為100 W和光纖長度為20 cm時，獲得3 dB帶寬高達(dá)2 484 nm的中紅外超連續(xù)譜，且具有良好相干度和平坦度.關(guān)鍵詞：光纖光學(xué)；As2S3光子晶體光纖；中紅外超連續(xù)譜光源；相干特性

0 引言

1 理論模型

為研究全波段正常色散As2S3光子晶體光纖中超連續(xù)譜光源的產(chǎn)生及其相干特性，本文中采用分步傅里葉法數(shù)值求解廣義非線性薛定諤方程[17].

(1)

圖1 As2S3光子晶體光纖色散曲線

式中，A表示脈沖慢變包絡(luò)振幅，z是沿光纖方向的傳輸距離，βm表示光纖的色散效應(yīng)(m表示色散階數(shù))，τ=t-vg是以群速率為vg參考系的時間參量，τ表示時延，α和γ分別為光纖的傳輸損耗和非線性系數(shù)，R(t)=(1-fR)δ(t)+fRhR(t)為拉曼響應(yīng)函數(shù)，fR表示延時拉曼響應(yīng)對非線性極化的貢獻(xiàn)，約為0.18，hR(t)為拉曼響應(yīng)函數(shù)，其表達(dá)式為[17]：

(2)

式中，參量τ1和τ2是2個可調(diào)節(jié)的參量，其值分別為15.5fs和230.5fs[14].本文中采用的高非線性光纖為全波段正常色散的As2S3光子晶體光纖，其色散曲線如圖1所示[ 16].由圖1可以看出，該光纖在2 800 nm處色散值趨于零，表明2 800 nm處色散效應(yīng)較弱.研究表明，色散效應(yīng)越弱越有利于高相干度超連續(xù)譜的產(chǎn)生[18]，故本文中的泵浦波長選為2 800 nm.由于2 800 nm處色散效應(yīng)較弱，本文中只需考慮到六階，更高階的色散效應(yīng)可忽略，在2 800 nm處，色散系數(shù)分別為β2=6.927 6×10-5ps2m-1，β3=-3.598 04×10-6ps3m-1，β4=6.577 56×10-7ps4m-1，β5=2.828 96×10-9ps5m-1，β6=2.828 96×10-13ps6m-1，非線性系數(shù)為γ=1 642 W-1km-1.由于所用光纖長度較短，光纖的傳輸損耗可以忽略不計.研究表明，當(dāng)泵浦脈沖的譜寬大于6 nm時，高斯白噪聲模型較量子噪聲模型更好[19]，故本文中采用高斯白噪聲模型，即在入射的高斯脈沖中引入高斯白噪聲，因此泵浦脈沖的表達(dá)式為：

(3)

(4)

圖4 傳輸距離對超連續(xù)譜(a)及其相干特性(b)的影

圖5 λ射峰值功率對超連續(xù)譜(a)及其相干特性(b)的影

圖6 初始啁啾對超連續(xù)譜(a)及其相干特性(b)的影

2 模擬結(jié)果與分析

為了進(jìn)一步改善超連續(xù)譜的平坦度和相干特性，我們研究入射峰值功率為100 W及其他參數(shù)與圖5相同條件下初始啁啾對超連續(xù)譜平坦度和相干性的影響，研究結(jié)果如圖6所示.由圖6(b)可以看出，正啁啾可以改善超連續(xù)譜的相干特性，但無法改善超連續(xù)譜的平坦度(見圖6(a))，而負(fù)啁啾不但可以改善超連續(xù)譜的相干性，還可改善其平坦度.在最佳負(fù)啁啾Cp=-4處，3 dB帶寬達(dá)2 484 nm，超連續(xù)譜的平坦度小于11 dB，與無啁啾時的平坦度(小于14.9 dB)相比，改善3.9 dB.這主要是由于負(fù)啁啾可以抵消自相位調(diào)制產(chǎn)生的正啁啾[21-23]，從而使超連續(xù)譜逐漸壓縮(見圖7(a))，隨著傳輸距離的增大，初始負(fù)啁啾不足以抵消自相位調(diào)制產(chǎn)生的正啁啾，從而使超連續(xù)譜逐漸展寬(見圖7(a)).即初始負(fù)啁啾對自相位調(diào)制效應(yīng)有一定的抑制作用，從而使超連續(xù)譜的平坦度得到一定的改善.

圖7 負(fù)啁啾對超連續(xù)譜的影響(a) 頻譜演變圖;(b) 時域演變圖

3 結(jié)論

采用分步傅里葉算法數(shù)值模擬超短激光脈沖在全波段正常色散.光子晶體光纖中的非線性傳輸和中紅外超連續(xù)譜的產(chǎn)生，并利用一階相干因子分析脈寬、傳輸距離、入射峰值功率和初始啁啾對中紅外超連續(xù)譜相干特性的影響.研究表明，脈寬越短，越有利于高相干度高平坦度中紅外超連續(xù)譜的產(chǎn)生；傳輸距離越短，相干特性和平坦度越好，但帶寬受限.增加峰值功率可顯著改善超連續(xù)譜的帶寬，但相干特性和平坦度因受色散效應(yīng)和自變陡效應(yīng)的影響而急劇退化；負(fù)啁啾可改善超連續(xù)譜的平坦度和相干特性，而正啁啾只能改善超連續(xù)譜的相干特性.在最佳負(fù)啁啾Cp=-4、脈寬為50 fs、入射峰值功率為100 W和光纖長度為20 cm時，獲得3 dB帶寬高達(dá)2 484 nm、平坦度小于11 dB的高相干度的超連續(xù)譜.研究結(jié)果對于如何優(yōu)化光纖參數(shù)和泵浦激光參數(shù)以獲得高質(zhì)量的中紅外超連續(xù)譜具有重要意義.

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(責(zé)任編輯 郭定和)

Study on highly coherent mid-infrared supercontinuum source

BIE Yeguang1, ZENG Yan1,2, YANG Zhangyong1,2, CHENG Chunfu1,2, OU Yiwen1,2

(1.School of Science, Hubei University of Technology, Wuhan 430068, China; 2.Hubei Collaborative Innovation Center for High-efficient Utilization of Solar Energy(Hubei University of Technology), Wuhan 430068, China)

An all-normal dispersion As2S3photonic crystal fiber is selected as the nonlinear media to eliminate the degradation of coherence characteristics of supercontinuum in the anomalous dispersion region which is caused by the modulation instability induced by the fission of higher-order soliton. The nonlinear propagation of an ultrashort pulse and mid-infrared supercontinuum generation in an all-normal dispersion As2S3photonic crystal fiber were simulated with the standard split-step Fourier algorithm. The impact of pulse width, propagation distance, input peak power, initial frequency chirp on the bandwidth, coherence properties and flatness of supercontinuum was simulated and analyzed. By optimizing the parameters of the pump pulse and parameters of the fiber, a highly coherent and flat supercontinuum with 3 dB bandwidth of 2 484 nm is obtained when the optimal chip is -4, pulse width is 50 fs, pump wavelength is 2 800 nm, input peak power is 100 W and fiber length is 20 cm. Key words: fiber optics; As2S3photonic crystal fiber; mid-infrared supercontinuum source; coherence characteristics

2016-11-14)

國家自然科學(xué)基金(61475044、41301372、51405143)、太陽能高效利用湖北省協(xié)同創(chuàng)新中心開放基金(HBSKFMS2014019、HBSKFZD2014007) 和博士啟動金(BSQD13047、 BSQD13048)資助)

別業(yè)廣(1964-)，男，副教授，E-mail:bieyygg@126.com；成純富，通信作者，副教授，E-mail：chengchunfu@126.com

1000-2375(2017)03-0258-06

TN249

A

10.3969/j.issn.1000-2375.2017.03.009