王永勝趙彤王安幫張明江王云才

1)(太原理工大學(xué),新型傳感器與智能控制教育部重點(diǎn)實(shí)驗(yàn)室,太原 030024)

2)(太原理工大學(xué)物理與光電工程學(xué)院,光電工程研究所,太原 030024)

大幅度增加弛豫振蕩頻率來(lái)實(shí)現(xiàn)毫米級(jí)外腔半導(dǎo)體激光器的外腔機(jī)制轉(zhuǎn)換?

王永勝1)2)趙彤1)2)王安幫1)2)?張明江1)2)王云才1)2)

1)(太原理工大學(xué),新型傳感器與智能控制教育部重點(diǎn)實(shí)驗(yàn)室,太原 030024)

2)(太原理工大學(xué)物理與光電工程學(xué)院,光電工程研究所,太原 030024)

混沌,半導(dǎo)體激光器,光反饋,弛豫振蕩頻率

1 引 言

光通信在人們的生活中顯示了越來(lái)越重要的作用.混沌作為光通信的一個(gè)領(lǐng)域,由于其物理熵源具有寬帶、不可預(yù)測(cè)、類(lèi)隨機(jī)等特征,近年來(lái)在保密通信[1?3]、隨機(jī)數(shù)生成[4,5]、混沌雷達(dá)[6,7]、混沌光時(shí)域反射儀等[8,9]方面具有重要的應(yīng)用.

光反饋半導(dǎo)體激光器系統(tǒng)是混沌激光生成的最重要的方式之一,該系統(tǒng)有兩種不同類(lèi)型的振蕩,即弛豫振蕩和外腔反饋振蕩[10].一定條件下,腔長(zhǎng)固定時(shí),增大弛豫振蕩頻率可以實(shí)現(xiàn)由短腔機(jī)制到長(zhǎng)腔機(jī)制的轉(zhuǎn)換[11],但是它們僅僅改變了注入電流,弛豫振蕩頻率的改變有限,其集成腔為13.5 mm,反饋延遲高達(dá)0.25 ns,換算成真空距離為37.5 mm,這個(gè)距離遠(yuǎn)遠(yuǎn)大于蝶形封裝的尺寸.

基于分立器件的混沌半導(dǎo)體激光器存在結(jié)構(gòu)不穩(wěn)定、體積大、應(yīng)用受限、成本高等問(wèn)題,只適用于實(shí)驗(yàn)室.因此混沌半導(dǎo)體激光器的集成成為混沌激光技術(shù)實(shí)用化的關(guān)鍵.與離散器件組成的裝置相比,光子集成電路具有其獨(dú)特的優(yōu)點(diǎn),如尺寸較小、成本較低、穩(wěn)定性較好和適用于大批量生產(chǎn)等[12?14].作為光子集成電路中的一種,單片集成半導(dǎo)體激光器因其獨(dú)特性引起了廣泛關(guān)注[15?34].因此,陸續(xù)報(bào)道了單片集成半導(dǎo)體激光器的動(dòng)態(tài)特性及其應(yīng)用,例如光微波生成[24,25]、高速物理隨機(jī)數(shù)的產(chǎn)生[26?28]、混沌同步和通信[18,29?31]以及時(shí)鐘恢復(fù)[32,33]等.Ushakov等[16]研究了一種超短集成分布式光反饋單片集成半導(dǎo)體激光器的動(dòng)態(tài)特性,并且觀(guān)測(cè)到了兩種與不同頻率規(guī)則自脈沖有關(guān)的霍普夫分岔.Youse fi等[17]報(bào)道了單片集成半導(dǎo)體激光器中倍周期進(jìn)入混沌的現(xiàn)象,并且證明了,與離散器件組成的裝置相比,單片集成半導(dǎo)體激光器在整個(gè)壽命周期中都具有更加穩(wěn)定的動(dòng)態(tài)特性.Argyris等[18,26,31]設(shè)計(jì)并研制了一種新奇的四段式單片集成半導(dǎo)體激光器,這種集成結(jié)構(gòu)被視為一種結(jié)構(gòu)緊湊并具有潛力的發(fā)射器.2011年,Harayama等[27]聯(lián)合研制了一種環(huán)形的單片集成半導(dǎo)體激光器芯片,此芯片包含一個(gè)分布式反饋激光器(DFB)激光器、兩個(gè)獨(dú)立的光放大區(qū)(SOA)、環(huán)形無(wú)源光波導(dǎo)以及一個(gè)快速光電探測(cè)器(PD).同年,Harayama等又聯(lián)合研制了另外一種單片集成半導(dǎo)體激光器芯片,此芯片包含一個(gè)DFB激光器、兩個(gè)SOA、一條無(wú)源光波導(dǎo)作為直腔反饋裝置以及一個(gè)快速光電探測(cè)器[20],然后將兩片此種混沌半導(dǎo)體激光器芯片封裝在一個(gè)模塊中,并行輸出兩路不相關(guān)的混沌電信號(hào)[21,28].Tronciu等[19]研制了帶有空氣隙的多反饋光子集成半導(dǎo)體激光器芯片,并在理論和實(shí)驗(yàn)上討論了這種新型結(jié)構(gòu)的動(dòng)態(tài)特性.Wu等[22]設(shè)計(jì)并研制了一種尺寸為780μm的單片集成放大反饋半導(dǎo)體激光器芯片,并研究了這種單片集成芯片的動(dòng)態(tài)特性.Liu等[23]也設(shè)計(jì)了一種新型的單片集成混沌半導(dǎo)體激光器芯片,理論上分析了這種結(jié)構(gòu)的動(dòng)態(tài)特性和優(yōu)點(diǎn).以上的集成結(jié)構(gòu)里面包含了放大區(qū)、相位區(qū)或者高反射層中的一種及以上,這些區(qū)域集成的成本較大,且集成的工藝復(fù)雜度及難度較大,更致命的是其生成混沌的參數(shù)空間較小,混沌態(tài)對(duì)參數(shù)的變化很靈敏.

外腔半導(dǎo)體激光器的外腔機(jī)制包括長(zhǎng)腔機(jī)制和短腔機(jī)制,弛豫振蕩頻率小于或接近于外腔振蕩頻率時(shí),外腔半導(dǎo)體激光器輸出態(tài)是短腔機(jī)制;弛豫振蕩頻率大于外腔振蕩頻率時(shí),外腔半導(dǎo)體激光器輸出態(tài)是長(zhǎng)腔機(jī)制.外腔機(jī)制轉(zhuǎn)換方法有兩種情形:一是固定弛豫振蕩頻率,調(diào)節(jié)外腔振蕩頻率;二是固定外腔振蕩頻率,調(diào)節(jié)弛豫振蕩頻率.弛豫振蕩頻率的影響因素有載流子壽命、注入電流比、光子壽命、增益系數(shù)和閾值載流子密度等,外腔振蕩頻率與外腔長(zhǎng)度有關(guān).總之,改變外腔長(zhǎng)度、載流子壽命、注入電流比、光子壽命、增益系數(shù)和閾值載流子密度等都可能實(shí)現(xiàn)短腔機(jī)制向長(zhǎng)腔機(jī)制的轉(zhuǎn)換.本文研究了蝶形封裝尺寸下集成混沌半導(dǎo)體激光器的特性,發(fā)現(xiàn)毫米級(jí)別的外腔半導(dǎo)體激光器對(duì)激光器內(nèi)部參數(shù)和外部參數(shù)的變化都極其敏感.這一特性勢(shì)必會(huì)給混沌集成外腔半導(dǎo)體激光器的制作帶來(lái)一定的難度,故而我們?cè)诩沙叽缦聦⒍糖粰C(jī)制轉(zhuǎn)換到長(zhǎng)腔機(jī)制,進(jìn)而保障集成外腔半導(dǎo)體激光器混沌態(tài)的穩(wěn)定性.本文同時(shí)調(diào)節(jié)注入電流和載流子壽命來(lái)大幅度地增加弛豫振蕩頻率,從而實(shí)現(xiàn)由短腔機(jī)制到長(zhǎng)腔機(jī)制的轉(zhuǎn)換,進(jìn)而分析長(zhǎng)腔機(jī)制下毫米級(jí)外腔半導(dǎo)體激光器輸出混沌態(tài)的穩(wěn)定性,為混沌外腔半導(dǎo)體激光器的集成化提供理論支撐.制作集成混沌激光器時(shí),需要首先確定外腔腔長(zhǎng)和外腔反饋率,本文重點(diǎn)分析了外腔反饋率和外腔腔長(zhǎng)對(duì)頻譜帶寬和混沌區(qū)域的影響.

2 理論模擬

2.1 原理圖

本文提出的光子集成混沌激光器的設(shè)計(jì)原理,用半透半反鏡取代高反射層,根據(jù)預(yù)先測(cè)試的激光器芯片的內(nèi)部參數(shù)和仿真結(jié)果,構(gòu)建高帶寬混沌產(chǎn)生所需的條件和結(jié)構(gòu),即外腔腔長(zhǎng)和外腔反饋功率比等.將所需的激光器芯片、半透半反鏡、準(zhǔn)直透鏡和耦合透鏡蝶形封裝在圖1所示的結(jié)構(gòu)中.封裝之后,穩(wěn)定蝶形封裝模塊的內(nèi)部參數(shù),精確控制外部注入電流,有效保證整個(gè)模塊的穩(wěn)定性.如圖1所示,DFB激光芯片的一部分輸出光經(jīng)過(guò)紅色虛線(xiàn)所示的路徑進(jìn)行傳播,并在半透半反鏡處將光反饋回到DFB激光芯片,形成光反饋.最后經(jīng)耦合透鏡將混沌光輸出.

圖1 面向蝶形封裝的混沌外腔半導(dǎo)體激光器的原理圖Fig.1. Schematic diagram of a chaotic integrate external-cavity semiconductor lasers face to butter fly packaging.

2.2 理論模型與速率方程

針對(duì)如圖1所示的裝置圖,采用典型的單反饋半導(dǎo)體激光器的速率方程(1)—(3)模擬半導(dǎo)體激光器的電場(chǎng)振幅A、相位Φ和腔內(nèi)載流子密度N.

方程(1)—(6)中各個(gè)參數(shù)的具體含義及其單位如表1所列.方程(5)是弱反饋時(shí)激光器固有的弛豫振蕩頻率的方程[35].由方程(5)可知,弛豫振蕩頻率的大小與注入電流和載流子壽命有關(guān).由于弛豫振蕩頻率的大小與注入電流比和載流子壽命有關(guān),因此本文通過(guò)調(diào)節(jié)注入電流比和載流子壽命來(lái)實(shí)現(xiàn)弛豫振蕩頻率的大幅度增加,進(jìn)而實(shí)現(xiàn)毫米級(jí)外腔半導(dǎo)體激光器的腔長(zhǎng)機(jī)制的轉(zhuǎn)換.載流子壽命是指載流子間的復(fù)合使載流子逐漸消失時(shí),其平均存在的時(shí)間.一般來(lái)說(shuō),載流子壽命取決于復(fù)合概率和材料中的載流子濃度,實(shí)際操作中可以利用縮減激光器基底區(qū)厚度的方法將載流子壽命縮減到ps量級(jí).挪威科技工業(yè)研究院的Bjerkan等[36]以及Wen[37]測(cè)了三組半導(dǎo)體激光器的載流子壽命的范圍為0.2—0.4 ns.根據(jù)以上小組的測(cè)試范圍及我們課題組使用激光器載流子壽命的范圍,選擇載流子壽命在0.1—2 ns的范圍進(jìn)行了理論仿真.對(duì)方程(6)求微分可得

由方程(7)可知,腔長(zhǎng)變化量相同時(shí),外腔振蕩頻率增量與腔長(zhǎng)的平方成反比,腔長(zhǎng)越小時(shí),外腔振蕩頻率增量越大;反之,外腔振蕩頻率增量越小.腔長(zhǎng)長(zhǎng)度較小時(shí),外腔振蕩頻率會(huì)嚴(yán)重影響頻譜的帶寬,生成的混沌的參數(shù)空間區(qū)域較小,這也是集成混沌激光器方面國(guó)內(nèi)外各個(gè)小組所面臨的難題之一.另外腔長(zhǎng)的長(zhǎng)短機(jī)制是相對(duì)的,它是由外腔振蕩頻率和弛豫振蕩頻率這兩個(gè)參數(shù)的相對(duì)比來(lái)決定的,外腔長(zhǎng)度只是參考量,并不是其本質(zhì)因素.這也是后面模擬結(jié)果中短腔長(zhǎng)變化時(shí),外腔半導(dǎo)體激光器的動(dòng)態(tài)在混沌與非混沌之間波動(dòng)的兩個(gè)主要原因.

表1 基于光反饋混沌激光系統(tǒng)的不同參數(shù)Table 1.Different parameters of chaotic system based on optical feedback semiconductor laser.

2.3 帶寬計(jì)算

頻譜的帶寬是指該信號(hào)所包含的各種不同頻率成分所占據(jù)的頻率范圍,本次計(jì)算的是80%能量所占的頻率范圍.

3 模擬結(jié)果

3.1 5.6 GHz的弛豫振蕩頻率

圖2 當(dāng)弛豫振蕩頻率為5.6 GHz時(shí),不同反饋腔長(zhǎng)下混沌外腔半導(dǎo)體激光器的頻譜帶寬Fig.2.Spectral bandwidth value of the output from the chaotic external-cavity semiconductor lasers under different external-cavity length when relaxation oscillation frequency is 5.6 GHz.

為了分析外腔腔長(zhǎng)對(duì)頻譜帶寬的影響,圖2給出了不同反饋腔長(zhǎng)下、弛豫振蕩頻率為5.6 GHz時(shí)混沌外腔半導(dǎo)體激光器的頻譜帶寬的變化曲線(xiàn).由圖可知,增大腔長(zhǎng),頻譜帶寬會(huì)出現(xiàn)波浪式下降和上升;另一方面,與腔長(zhǎng)為40—100 mm的區(qū)間相比,頻譜帶寬對(duì)1—20 mm外腔半導(dǎo)體激光器的腔長(zhǎng)變化極其敏感.腔長(zhǎng)為1—20 mm時(shí),隨著腔長(zhǎng)變化,頻譜帶寬會(huì)在0和高帶寬之間波動(dòng),而造成波動(dòng)范圍較大的原因是隨著腔長(zhǎng)變化,外腔半導(dǎo)體激光器的動(dòng)態(tài)在混沌與非混沌之間波動(dòng);腔長(zhǎng)為40—100 mm時(shí),隨著腔長(zhǎng)變化,頻譜帶寬只在很小的區(qū)域波動(dòng),造成波動(dòng)范圍較小的原因是隨著腔長(zhǎng)變化,外腔半導(dǎo)體激光器的動(dòng)態(tài)在混沌態(tài)內(nèi)波動(dòng).為了探究波動(dòng)峰與谷的區(qū)別,放大7—14 mm這個(gè)區(qū)間,頻譜帶寬在7.6 mm處出現(xiàn)極大值,頻譜帶寬在11.5 mm處出現(xiàn)極小值.總之,頻譜帶寬并沒(méi)有隨腔長(zhǎng)的增加而減小,而是波浪式下降和上升.短腔機(jī)制下,頻譜帶寬對(duì)腔長(zhǎng)變化極其敏感,外腔半導(dǎo)體激光器的動(dòng)態(tài)會(huì)在混沌與非混沌之間波動(dòng);長(zhǎng)腔機(jī)制下,頻譜帶寬對(duì)腔長(zhǎng)變化不太敏感,頻譜帶寬值會(huì)小范圍變化,但外腔半導(dǎo)體激光器的動(dòng)態(tài)一直都是混沌態(tài).

為了得出外腔反饋率和外腔長(zhǎng)對(duì)外腔半導(dǎo)體激光器頻譜帶寬的影響規(guī)律,圖3給出了當(dāng)弛豫振蕩頻率為5.6 GHz時(shí),外腔半導(dǎo)體激光器的頻譜帶寬在外腔反饋率和外腔長(zhǎng)的參數(shù)空間中的分布,其中圖3(b)為圖3(a)的放大圖,黑色區(qū)域頻譜帶寬小于1 GHz,則被確定為非混沌區(qū)域;其他顏色區(qū)域?yàn)榛煦鐟B(tài),不同顏色代表不同值.腔長(zhǎng)為1—20 mm時(shí),隨著腔長(zhǎng)變化頻譜帶寬會(huì)在0和高帶寬之間波動(dòng),造成波動(dòng)范圍較大的原因是隨著腔長(zhǎng)變化,外腔半導(dǎo)體激光器的動(dòng)態(tài)在混沌與非混沌之間波動(dòng);腔長(zhǎng)為30—60 mm時(shí),隨著腔長(zhǎng)變化,頻譜帶寬只在很小的區(qū)域波動(dòng),而造成波動(dòng)范圍較小的原因是隨著腔長(zhǎng)變化,外腔半導(dǎo)體激光器的動(dòng)態(tài)在混沌態(tài)內(nèi)波動(dòng).弛豫振蕩頻率為5.6 GHz,對(duì)應(yīng)的弛豫時(shí)間是0.179 ns,相應(yīng)的長(zhǎng)度為26.7 mm.可見(jiàn)穩(wěn)定混沌區(qū)域與非穩(wěn)定混沌區(qū)域的分界處在短腔與長(zhǎng)腔的分界處附近.總之,短腔機(jī)制下,頻譜帶寬對(duì)腔長(zhǎng)變化極其敏感,頻譜帶寬不連續(xù)變化,外腔半導(dǎo)體激光器的動(dòng)態(tài)會(huì)在混沌與非混沌之間波動(dòng);長(zhǎng)腔機(jī)制下,頻譜帶寬對(duì)腔長(zhǎng)變化不太敏感,頻譜帶寬值會(huì)小范圍變化,但外腔半導(dǎo)體激光器的動(dòng)態(tài)一直都是混沌態(tài).

圖3 (網(wǎng)刊彩色)當(dāng)弛豫振蕩頻率為5.6 GHz時(shí),外腔半導(dǎo)體激光器頻譜帶寬在外腔反饋率和外腔長(zhǎng)參數(shù)空間中的分布,(b)為(a)的放大圖Fig.3.(color online)Mapping of the spectral bandwidth value of the external-cavity semiconductor lasers in the parameter space of power re flectivity and length of the external cavity when relaxation oscillation frequency is 5.6 GHz,(b)is the enlarging figure of(a).

3.2 增加弛豫振蕩頻率來(lái)實(shí)現(xiàn)腔長(zhǎng)機(jī)制的轉(zhuǎn)換

為了大幅度地增加弛豫振蕩頻率,在增大注入電流的同時(shí)減小載流子壽命.圖4給出了不同載流子壽命下,固定腔長(zhǎng)為5.4 mm(外腔振蕩頻率為27.8 GHz),面向蝶形封裝的集成外腔半導(dǎo)體激光器輸出的頻譜和自相關(guān).第一行載流子壽命為2 ns時(shí),弛豫振蕩頻率為21.6 GHz,小于外腔頻率,屬于短腔機(jī)制,自相關(guān)曲線(xiàn)在0.05和0.09 ns處有峰值;第二行載流子壽命為0.2 ns時(shí),弛豫振蕩頻率為44.1 GHz,大于外腔頻率,屬于長(zhǎng)腔機(jī)制,自相關(guān)曲線(xiàn)在0.02,0.05,0.07和0.09 ns處有峰值.結(jié)果表明:增大注入電流的同時(shí)減小載流子壽命可以將弛豫振蕩頻率提高到40 GHz以上.如果弛豫振蕩頻率是40 GHz,對(duì)應(yīng)的弛豫振蕩是0.025 ns,換算成長(zhǎng)度為3.75 mm,即腔長(zhǎng)大于3.75 mm為長(zhǎng)腔機(jī)制,這個(gè)尺寸完全符合蝶形封裝尺寸的標(biāo)準(zhǔn).

圖4 不同載流子壽命下,面向蝶形封裝的集成外腔半導(dǎo)體激光器輸出的(a)頻譜,(b)自相關(guān)Fig.4.(a)Power spectra and(b)autocorrelation of output from the integrate external-cavity semiconductor lasers face to butter fly packaging under different carrier lifetime.

3.3 40 GHz的弛豫振蕩頻率

為了大幅度增加弛豫振蕩頻率,以期在集成尺寸內(nèi)達(dá)到外腔半導(dǎo)體激光器進(jìn)入長(zhǎng)腔機(jī)制所需的條件,在40 GHz的弛豫振蕩頻率下分析了外腔長(zhǎng)度對(duì)頻譜帶寬的影響.圖5給出了不同反饋腔長(zhǎng)下混沌外腔半導(dǎo)體激光器的頻譜帶寬的變化曲線(xiàn).與腔長(zhǎng)為6—12 mm的區(qū)間相比,頻譜帶寬對(duì)1—6 mm外腔半導(dǎo)體激光器的腔長(zhǎng)變化極其敏感.腔長(zhǎng)為1—6 mm時(shí),隨著腔長(zhǎng)變化頻譜帶寬會(huì)在0和高帶寬之間波動(dòng),造成波動(dòng)范圍較大的原因是隨著腔長(zhǎng)變化,外腔半導(dǎo)體激光器的動(dòng)態(tài)在混沌與非混沌之間波動(dòng);腔長(zhǎng)為6—12 mm時(shí),隨著腔長(zhǎng)變化,頻譜帶寬只在很小的區(qū)域波動(dòng),造成波動(dòng)范圍較小的原因是隨著腔長(zhǎng)變化,外腔半導(dǎo)體激光器的動(dòng)態(tài)在混沌態(tài)內(nèi)波動(dòng).總之,短腔機(jī)制下,頻譜帶寬對(duì)腔長(zhǎng)變化極其敏感,外腔半導(dǎo)體激光器的動(dòng)態(tài)會(huì)在混沌與非混沌之間波動(dòng);長(zhǎng)腔機(jī)制下,頻譜帶寬對(duì)腔長(zhǎng)變化不太敏感,頻譜帶寬值在小范圍變化,但外腔半導(dǎo)體激光器的動(dòng)態(tài)一直都是混沌態(tài).腔長(zhǎng)為6—12 mm時(shí),可以實(shí)現(xiàn)比較穩(wěn)定的混沌態(tài),考慮到實(shí)際中集成材料的折射率,相同延遲時(shí)間下,可以將實(shí)際中的腔長(zhǎng)縮短到模擬腔長(zhǎng)的1/3左右,這樣就可以實(shí)現(xiàn)毫米級(jí)的集成混沌外腔半導(dǎo)體激光器的穩(wěn)定性.

圖5 當(dāng)弛豫振蕩頻率為40 GHz時(shí),不同反饋腔長(zhǎng)下的混沌外腔半導(dǎo)體激光器頻譜帶寬Fig.5.Spectral bandwidth value of the output from the chaotic external-cavity semiconductor lasers under different external-cavity length when the relaxation oscillation frequency is 40 GHz.

為了與圖3(b)形成對(duì)比,選擇腔長(zhǎng)在2—20 mm范圍內(nèi)進(jìn)行理論模擬.為了得出外腔反饋率和外腔長(zhǎng)對(duì)外腔半導(dǎo)體激光器頻譜帶寬的影響規(guī)律,圖6給出了當(dāng)載流子壽命為0.1 ns和弛豫振蕩頻率為40 GHz時(shí)外腔半導(dǎo)體激光器的頻譜帶寬在外腔反饋率和外腔長(zhǎng)的參數(shù)空間中的分布,其中圖6(b)為圖6(a)的放大圖,黑色區(qū)域頻譜帶寬小于1 GHz,則被確定為非混沌區(qū)域;其他顏色區(qū)域?yàn)榛煦鐟B(tài),不同顏色代表不同值.外腔反饋率從2%增加到11%,外腔長(zhǎng)度從2 mm增加到20 mm時(shí),得到了外腔半導(dǎo)體激光器頻譜帶寬的分布圖.腔長(zhǎng)為2—4 mm時(shí),隨著腔長(zhǎng)變化頻譜帶寬會(huì)在0和高帶寬之間波動(dòng),波動(dòng)范圍較大,而造成這種波動(dòng)的原因是隨著腔長(zhǎng)變化外腔半導(dǎo)體激光器的動(dòng)態(tài)在混沌與非混沌之間波動(dòng);腔長(zhǎng)為4—20 mm時(shí),隨著腔長(zhǎng)變化頻譜帶寬只在很小的區(qū)域波動(dòng),造成波動(dòng)范圍較小的原因是隨著腔長(zhǎng)變化,外腔半導(dǎo)體激光器的動(dòng)態(tài)在混沌態(tài)內(nèi)波動(dòng).腔長(zhǎng)為4—20 mm時(shí),可以實(shí)現(xiàn)比較穩(wěn)定的混沌態(tài),考慮到集成材料的折射率,相同延遲時(shí)間下,可以將實(shí)際中的腔長(zhǎng)縮短到模擬腔長(zhǎng)的1/3左右,可以實(shí)現(xiàn)毫米級(jí)集成混沌外腔半導(dǎo)體激光器混沌態(tài)的穩(wěn)定性.

圖6 (網(wǎng)刊彩色)弛豫振蕩頻率為40 GHz時(shí),外腔半導(dǎo)體激光器頻譜帶寬在外腔反饋率和外腔長(zhǎng)參數(shù)空間中的分布圖,(b)為(a)的放大圖Fig.6.(color online)Mapping of the spectral bandwidth value of the external-cavity semiconductor lasers in the parameter space of power re flectivity and length of the external cavity when the relaxation oscillation frequency is 40 GHz,(b)is the enlarging figure of(a).

4 結(jié) 論

分析結(jié)果表明:短腔機(jī)制下,輸出混沌態(tài)不穩(wěn)定,0.1 mm的偏差就會(huì)導(dǎo)致混沌態(tài)與非混沌態(tài)之間的轉(zhuǎn)化;長(zhǎng)腔機(jī)制下,輸出混沌態(tài)穩(wěn)定,輸出混沌區(qū)域較大,證明長(zhǎng)腔機(jī)制下更有益于獲得寬帶連續(xù)的混沌區(qū)域.在弛豫振蕩頻率為40 GHz、外腔長(zhǎng)度為mm級(jí)時(shí),實(shí)現(xiàn)了外腔半導(dǎo)體激光器的長(zhǎng)腔機(jī)制,從而增大了高帶寬混沌的參數(shù)空間.考慮到集成材料的折射率,集成長(zhǎng)腔機(jī)制下的腔長(zhǎng)最小可以達(dá)到1—2 mm.這種腔長(zhǎng)完全符合蝶形封裝尺寸的要求.

外腔機(jī)制轉(zhuǎn)換方法有兩種情形:一是固定弛豫振蕩頻率,調(diào)節(jié)外腔振蕩頻率;二是固定外腔振蕩頻率,調(diào)節(jié)弛豫振蕩頻率.弛豫振蕩頻率的影響因素有載流子壽命、注入電流比、光子壽命、增益系數(shù)和閾值載流子密度等,外腔振蕩頻率與外腔長(zhǎng)度有關(guān).總之,改變外腔長(zhǎng)度、載流子壽命、注入電流比、光子壽命、增益系數(shù)和閾值載流子密度等都可能實(shí)現(xiàn)短腔機(jī)制向長(zhǎng)腔機(jī)制的轉(zhuǎn)換.這些轉(zhuǎn)換方法的綜合應(yīng)用和效果疊加也許會(huì)幫助實(shí)現(xiàn)超短尺寸外腔半導(dǎo)體激光器的外腔機(jī)制的轉(zhuǎn)換,生成具有數(shù)十GHz外腔振蕩頻率和數(shù)百GHz弛豫振蕩頻率的超高帶寬且特性穩(wěn)定的混沌激光.

[1]Sciamanna M,Shore K A 2015Nature Photon.9 151

[2]Argyris A,Syvridis D,Larger L,Annovazzi-Lodi V,Colet P,Fischer I,García-Ojalvo J,Mirasso C R,Pesquera L,Shore K A 2005Nature438 343

[3]Soriano M C,García-Ojalvo J,Mirasso C R,Fischer I 2013Rev.Mod.Phys.85 421

[4]Uchida A,Amano K,Inoue M,Hirano K,Naito S,Someya H,Oowada I,Kurashige T,Shiki M,Yoshimori S,Yoshimura K,Davis P 2008Nature Photon.2 728

[5]Reidler I,Aviad Y,Rosenbluh M,Kanter I 2009Phys.Rev.Lett.103 024102

[6]Lin F Y,Liu J M 2004IEEE J.Quantum Electron.40 815

[7]Lin F Y,Liu J M 2004IEEE J.Sel.Topics QuantumElectron.10 991

[8]Wang A B,Wang N,Yang Y B,Wang B J,Zhang M J,Wang Y C 2012J.Lightw.Technol.30 3420

[9]Wang Y C,Wang B J,Wang A B 2008IEEE Photon.Technol.Lett.20 1636

[10]Erzgr?ber H,Krauskopf B,Lenstra D,Fischer A,Vemuri G 2006Phys.Rev.E73 055201

[11]Toomey J P,Kane D M,McMahon C,Argyris A,Syvridis D 2015Opt.Express23 18754

[12]Koch T L,Koren U 1991IEEE J.Quantum Electron.27 641

[13]Charbonneau S,Koteles E S,Poole P J,He J J,Aers G C,Haysom J,Buchanan M,Feng Y,Delage A,Yang F,Davies M,Goldberg R D,Piva P G,Mitchell I V 1998IEEE J.Sel.Topics Quantum Electron.4 772

[14]Hofstetter D,Maisenh?lder B,Zappe H P 1998IEEE J.Sel.Topics Quantum Electron.4 794

[15]Bauer S,Brox O,Kreissl J,Sartorius B 2004Phys.Rev.E69 016206

[16]Ushakov O,Bauer S,Brox O,Wünsche H J,Henneberger F 2004Phys.Rev.Lett.92 043902

[17]Youse fiM,Barbarin Y,Beri S,Bente E A,Smit M K,N?tzel R,Lenstra D 2007Phys.Rev.Lett.98 044101

[18]Argyris A,Hamacher M,Chlouverakis K E,Bogris A,Syvridis D 2008Phys.Rev.Lett.100 194101

[19]Tronciu V Z,Ermakov Y,Colet P,Mirasso C R 2008Opt.Commun.281 4747

[20]Harayama T,Sunada S,Yoshimura K,Davis P,Tsuzuki K,Uchida A 2011Phys.Rev.A83 031803

[21]Sunada S,Harayama T,Arai K,Yoshimura K,Davis P,Tsuzuki K,Uchida A 2011Opt.Express19 5713

[22]Wu J G,Zhao L J,Wu Z M,Lu D,Tang X,Zhong Z Q,Xia G Q 2013Opt.Express21 23358

[23]Liu D,Sun C,Xiong B,Luo Y 2014Opt.Express22 5614

[24]Yu L Q,Lu D,Pan B W,Zhao L J,Wu J G,Xia G Q,Wu Z M,Wang W 2014J.Lightw.Technol.32 3595

[25]Yee D S,Leem Y A,Kim S B,Kim D C,Park K H,Kim S T,Kim B G 2004Opt.Lett.29 2243

[26]Argyris A,Deligiannidis S,Pikasis E,Bogris A,Syvridis D 2010Opt.Express18 18763

[27]Harayama T,Sunada S,Yoshimura K,Davis P,Tsuzuki K,Uchida A 2011Phys.Rev.A83 031803

[28]Takahashi R,Akizawa Y,Uchida A,Harayama T,Tsuzuki K,Sunada S,Arai K,Yoshimura K,Davis P 2014Opt.Express22 11727

[29]Wünsche H,Bauer S,Kreissl J,Ushakov O,Korneyev N,Henneberger F,Wille E,Erzgr?ber H,Peil M,Els??er W,Fischer I 2005Phys.Rev.Lett.94 163901

[30]Pérez T,Radziunas M,Wünsche H J,Mirasso C R,Henneberger F 2006IEEE Photon.Technol.Lett.18 2135[31]Argyris A,Grivas E,Hamacher M,Bogris A,Syvridis D 2010Opt.Express18 5188

[32]Monfils I,Cartledge J C 2009J.Lightw.Technol.27 619

[33]Sun Y,Pan J Q,Zhao L J,Chen W X,Wang W,Wang L,Zhao X F,Lou C Y 2010J.Lightw.Technol.28 2521[34]Sunada S,Shinohara S,Fukushima T,Harayama T 2016Phys.Rev.Lett.116 203903

[35]Uchida A 2012Applications of Nonlinear Dynamics and Synchronization

[36]Bjerkan L,Royset A,Hafsker L,Myhre D 1996J.Lightw.Technol.14 839

[37]Wen Y F 2012Ph.D.Dissertation(McMaster University)

Conversion of external cavity mechanism of millimeter-level external cavity semiconductor laser by significantly increasing relaxation oscillation frequency?

Wang Yong-Sheng1)2)Zhao Tong1)2)Wang An-Bang1)2)?Zhang Ming-Jiang1)2)Wang Yun-Cai1)2)

1)(Key Laboratory of Advanced Transducers and Intelligent Control System of Ministry of Education,Taiyuan University of Technology,Taiyuan 030024,China)
2)(Institute of Optoelectronic Engineering,College of Physics and Optoelectronics,Taiyuan University of Technology,Taiyuan 030024,China)

16 April 2017;revised manuscript

25 June 2017)

Optical chaos has conducted in-depth investigation and attracted widespread attention in recent years,owing to its important applications in chaos-based secure communication,fast physical random bit generation,chaotic laser radar,lidar,chaotic optical time domain reflectometer,distance measurement,and optical fiber sensor.The key to these applications is a compact and broadband chaotic light source,because the integrated circuits have an advantage over those setups composed of discrete components in some unique virtues such as smaller size,lower cost,better stability,and better reproducibility via mass production.In order to combine the advantages of the chaotic application and integrated circuits,the integrated chaotic external-cavity semiconductor laser has aroused great interest.Note that,the integrated chaotic external-cavity semiconductor laser can work in both short-and long-cavity mechanisms,which depends on the laser relaxation oscillation frequency.The output of chaotic external cavity semiconductor laser has obvious relaxation oscillation characteristic.When the relaxation oscillation frequency is less than the external-cavity oscillation frequency,the external-cavity semiconductor laser works in short-cavity mechanism.Otherwise,it works in long-cavity mechanism.In this paper,we comparatively analyze the effects of fine-tuning cavity length on the effective bandwidth of the integrated external-cavity semiconductor laser under both short-and long-cavity mechanisms.

First,we comparatively analyze the effects of fine-tuning cavity length and external-cavity feedback rate on the effective bandwidth of the integrated external-cavity semiconductor laser when relaxation oscillation frequency is 5.6 GHz.At the same time,the injection current and carrier lifetime are adjusted to observably increase the relaxation oscillation frequency.Finally,we comparatively analyze the effects of fine-tuning cavity length and external-cavity feedback rate on the effective bandwidth of the integrated external-cavity semiconductor laser when relaxation oscillation frequency is 40 GHz.Results show that for short-cavity mechanism,the chaotic output is not stable:0.1-mm deviation will lead to the conversion from chaotic state into non-chaotic state.By contrast,for the long-cavity mechanism,the chaotic output is more stable and has a larger chaotic area.It proves that the long-cavity mechanism is more feasible and conducive to the continuous achievement of a broadband chaotic laser and broadband continuous chaotic region.According to this feature,we realize the transition from short to long cavity regime by adjusting the injection current and carrier lifetime to substantially increase the relaxation oscillation frequency at the same time.We realize the transition from short to long cavity regime in a cavity length range from 2 mm to 10 mm,and then analyze the in fluences of the external cavity rate and external cavity length on the spectrum bandwidth of the external cavity semiconductor laser.The results show that under the long cavity mechanism,it is more conducive to the achievement of a broadband continuous chaotic region in a cavity lengt range from 4 mm to 20 mm.Considering the refractive index of integrated material,the external-cavity length for long-cavity mechanism can be shortened to a range from 1 mm to 2 mm.This length fully conforms to the butter fly packaging size.

chaos,integrated semiconductor lasers,optical feedback,relaxation oscillation frequency

PACS:42.55.Px,05.45.Gg,05.40.–aDOI:10.7498/aps.66.234204

*Project supported by the International Science and Technology Cooperation Program of China(Grant No.2014DFA50870)and the National natural science foundation of National Major Scientific Instruments Development Project(Grant No.61527819).

?Corresponding author.E-mail:wanganbang@tyut.edu.cn

(2017年4月16日收到;2017年6月25日收到修改稿)

混沌外腔半導(dǎo)體激光器輸出明顯存在弛豫振蕩特征,弛豫振蕩頻率小于外腔振蕩頻率時(shí),外腔半導(dǎo)體激光器輸出態(tài)是短腔機(jī)制;反之,外腔半導(dǎo)體激光器輸出態(tài)是長(zhǎng)腔機(jī)制.首先對(duì)比分析了弛豫振蕩頻率為5.6 GHz,腔長(zhǎng)對(duì)頻譜有效帶寬的影響.然后同時(shí)調(diào)節(jié)注入電流和載流子壽命來(lái)大幅度地增加弛豫振蕩頻率.最后在弛豫振蕩頻率為40 GHz、腔長(zhǎng)為毫米級(jí)(4—20 mm)時(shí),實(shí)現(xiàn)由短腔機(jī)制到長(zhǎng)腔機(jī)制的轉(zhuǎn)換,進(jìn)而分析了外腔反饋率和外腔長(zhǎng)對(duì)外腔半導(dǎo)體激光器頻譜帶寬的影響.分析結(jié)果表明:短腔機(jī)制下,輸出混沌態(tài)不穩(wěn)定,0.1 mm的偏差就會(huì)導(dǎo)致混沌態(tài)與非混沌態(tài)之間的轉(zhuǎn)化;長(zhǎng)腔機(jī)制下,輸出混沌態(tài)穩(wěn)定,輸出混沌區(qū)域較大,證明長(zhǎng)腔機(jī)制下更有益于獲得寬帶連續(xù)的混沌區(qū)域.在弛豫振蕩頻率為40 GHz、外腔長(zhǎng)度為毫米級(jí)時(shí),實(shí)現(xiàn)了外腔半導(dǎo)體激光器的長(zhǎng)腔機(jī)制,從而增大了高帶寬混沌的參數(shù)空間.

10.7498/aps.66.234204

?國(guó)家國(guó)際科技合作專(zhuān)項(xiàng)(批準(zhǔn)號(hào):2014DFA50870)和國(guó)家自然科學(xué)基金國(guó)家重大科研儀器研制項(xiàng)目(批準(zhǔn)號(hào):61527819)資助的課題.

?通信作者.E-mail:wanganbang@tyut.edu.cn