硅基光子晶體異質(zhì)結(jié)的單向傳輸特性?

劉丹1) 胡森1)2) 肖明1)

1)(湖北第二師范學(xué)院物理與機(jī)電工程學(xué)院,武漢 430205)

2)(華中師范大學(xué)物理科學(xué)與技術(shù)學(xué)院,武漢 430079)

硅基光子晶體異質(zhì)結(jié)的單向傳輸特性?

劉丹1)?胡森1)2) 肖明1)

1)(湖北第二師范學(xué)院物理與機(jī)電工程學(xué)院,武漢 430205)

2)(華中師范大學(xué)物理科學(xué)與技術(shù)學(xué)院,武漢 430079)

(2016年7月24日收到;2016年12月2日收到修改稿)

基于光子晶體異質(zhì)結(jié)結(jié)構(gòu)實(shí)現(xiàn)高效的單向傳輸特性的光二極管是光電集成及全光通信領(lǐng)域的研究熱點(diǎn).根據(jù)光子晶體方向帶隙差異構(gòu)建了正交和非正交光子晶體異質(zhì)結(jié)結(jié)構(gòu),利用時(shí)域有限差分法計(jì)算透過(guò)譜及場(chǎng)分布圖.對(duì)比研究發(fā)現(xiàn),非正交光子晶體異質(zhì)結(jié)結(jié)構(gòu)能夠?qū)崿F(xiàn)光的單向傳輸.通過(guò)界面結(jié)構(gòu)的調(diào)整,優(yōu)化了單向傳輸性能,構(gòu)造了一種能實(shí)現(xiàn)寬頻帶、高效率單向傳輸?shù)漠愘|(zhì)結(jié)結(jié)構(gòu).優(yōu)化后的光子晶體異質(zhì)結(jié)的單向傳輸效率高達(dá)54%,且結(jié)構(gòu)簡(jiǎn)單、尺寸小,實(shí)用性強(qiáng).

光子晶體異質(zhì)結(jié),單向傳輸,時(shí)域有限差分法

1 引 言

硅是一種性能優(yōu)越的半導(dǎo)體材料,在集成電路的發(fā)展過(guò)程中起到了重要作用.硅材料還是一種被廣泛運(yùn)用的光子材料,使得硅基集成光電子學(xué)研究備受青睞.但是硅基光電集成器件的尺寸要求達(dá)到微納米級(jí)別,因此無(wú)法用經(jīng)典的幾何光學(xué)理論來(lái)研究,需要研究操縱和利用光的新機(jī)理[1,2].光子晶體是一種有效的方法,其獨(dú)特的光子禁帶和光子局域特性被廣泛研究,應(yīng)用的領(lǐng)域也不斷擴(kuò)大[1,3?7].電子二極管是集成電路的基本結(jié)構(gòu)單元,與此類似,如何實(shí)現(xiàn)光信號(hào)的單向傳輸,即光二極管,是光電集成及全光通信領(lǐng)域中需要解決的基本問(wèn)題[8].

光的單向傳輸通常要求滿足時(shí)間反演對(duì)稱破缺或空間反轉(zhuǎn)對(duì)稱破缺.采用時(shí)間反演對(duì)稱破缺的方案來(lái)實(shí)現(xiàn)光二極管的報(bào)道較多,其中材料電光[9]、磁光[10,11]、非線性[12]效應(yīng)通常作為實(shí)現(xiàn)光二極管的有效途徑[2].這種方案均需外界條件(電場(chǎng)、磁場(chǎng)或光場(chǎng))才能實(shí)現(xiàn),其應(yīng)用受到限制.采用空間反轉(zhuǎn)對(duì)稱破缺的方案可以彌補(bǔ)這個(gè)缺點(diǎn),因此備受關(guān)注[13?24].其中,基于光子晶體結(jié)構(gòu)的光二極管由于其獨(dú)特的性能成為研究熱點(diǎn).Li等[13]首先報(bào)道了基于空間反轉(zhuǎn)對(duì)稱破缺的聲子二極管,為設(shè)計(jì)光子晶體光二極管提供了參考.Kurt等[14]設(shè)計(jì)了空氣中非對(duì)稱分布的硅柱型光子晶體波導(dǎo),破壞了結(jié)構(gòu)的對(duì)稱性,通過(guò)數(shù)值計(jì)算和實(shí)驗(yàn)驗(yàn)證了光波的單向傳輸.Zhang等[15]以光柵和正方排列的硅柱型光子晶體為單元設(shè)計(jì)了硅基光柵-光子晶體結(jié)構(gòu),實(shí)現(xiàn)了光波在寬頻帶內(nèi)高對(duì)比度的單向傳輸.這些研究成果為硅基光子晶體光二極管的實(shí)現(xiàn)提供了重要的途徑.光子晶體異質(zhì)結(jié)結(jié)構(gòu)如同電子電路系統(tǒng)中的PN結(jié),能極大地改進(jìn)光子晶體器件的性能,高效單向傳輸?shù)漠愘|(zhì)結(jié)結(jié)構(gòu)連接合適參數(shù)的輸入、輸出波導(dǎo)將構(gòu)造出高性能的光二極管[2,25].Wang等[2]首次利用硅基平板光子晶體異質(zhì)結(jié)結(jié)構(gòu)實(shí)現(xiàn)了近紅外波段的光子晶體全光二極管.馮帥課題組也先后設(shè)計(jì)了多種二維硅基光子晶體正交異質(zhì)結(jié)結(jié)構(gòu),成功地獲得了光的單向傳輸特性[16?18].他們?cè)O(shè)計(jì)了二維硅基正方排列的空氣孔型光子晶體異質(zhì)結(jié)結(jié)構(gòu)(含界面耦合區(qū)),基于優(yōu)化的界面耦合區(qū)結(jié)構(gòu)實(shí)現(xiàn)了光的單向傳輸[18].這些光二極管的設(shè)計(jì)一般采用正交或非正交光子晶體異質(zhì)結(jié)結(jié)構(gòu),針對(duì)這兩類光子晶體異質(zhì)結(jié)結(jié)構(gòu)的對(duì)比分析還沒(méi)有系統(tǒng)的研究.因此,本文構(gòu)建了二維硅基光子晶體異質(zhì)結(jié)結(jié)構(gòu),對(duì)比分析了正交及非正交異質(zhì)結(jié)界面情況下的傳輸特性,發(fā)現(xiàn)正交異質(zhì)結(jié)結(jié)構(gòu)無(wú)法實(shí)現(xiàn)光的單向傳輸,而非正交異質(zhì)結(jié)結(jié)構(gòu)能在較寬頻率范圍內(nèi)實(shí)現(xiàn)單向傳輸.與文獻(xiàn)[18]的結(jié)果相比,該結(jié)構(gòu)更簡(jiǎn)單、尺寸更小、實(shí)用性更強(qiáng).此外,本文還探討了非正交異質(zhì)結(jié)結(jié)構(gòu)中界面耦合區(qū)的結(jié)構(gòu)對(duì)單向傳輸特性的影響,通過(guò)優(yōu)化異質(zhì)結(jié)界面,實(shí)現(xiàn)了寬頻帶、高效率的單向傳輸特性.

2 光子晶體模型及能帶結(jié)構(gòu)分析

光子晶體異質(zhì)結(jié)結(jié)構(gòu)由兩個(gè)晶格常數(shù)相同、空氣孔半徑不同的二維正方晶格光子晶體(PC1和PC2)拼接而成.光子晶體的結(jié)構(gòu)如圖1所示,PC1和PC2長(zhǎng)度均為21列空氣孔,寬度均為21行空氣孔,且基底為硅材料(折射率為3.45).設(shè)兩光子晶體晶格常數(shù)為a,空氣孔半徑分別為r1=0.15a和r2=0.4a(選用文獻(xiàn)[18]中提到的結(jié)構(gòu)參數(shù)).完整的正方晶格光子晶體有兩個(gè)基本的對(duì)稱方向:沿x軸的Γ-X方向和與x軸成45?夾角的Γ-M方向(Γ,X,M分別表示正方晶格對(duì)應(yīng)的第一布里淵區(qū)的高對(duì)稱點(diǎn)).

圖1 光子晶體的結(jié)構(gòu)示意圖 (a)PC1;(b)PC2Fig.1. Schematic of photonic crystal structure:(a)PC1;(b)PC2.

采用平面波展開(kāi)法分別計(jì)算PC1及PC2光子晶體的橫電(TE)模式的能帶結(jié)構(gòu),結(jié)果如圖2所示.

由圖2(a)可知,PC2光子晶體在0.18—0.29a·λ?1頻率范圍內(nèi)沿著Γ-X方向是禁帶,處于該頻率范圍內(nèi)的入射光將被禁止沿Γ-X方向穿過(guò)PC2區(qū)域;同時(shí),PC2光子晶體在0.18—0.26a·λ?1頻率范圍內(nèi)沿著Γ-M方向是通帶,處于該頻率范圍內(nèi)的入射光可沿Γ-M方向穿過(guò)PC2區(qū)域.由圖2(b)可知,入射光頻率為0.18—0.26a·λ?1時(shí),既可沿Γ-X方向穿過(guò)PC1區(qū)域,也可沿Γ-M方向穿過(guò)PC1區(qū)域.以上分析說(shuō)明,在一定的頻率范圍內(nèi),PC1光子晶體為全方向?qū)?而PC2光子晶體存在方向帶隙,這正是異質(zhì)結(jié)結(jié)構(gòu)能實(shí)現(xiàn)單向傳輸?shù)谋匾獥l件[2,18].因此,以PC1和PC2光子晶體來(lái)構(gòu)建異質(zhì)結(jié)結(jié)構(gòu),有望實(shí)現(xiàn)光的單向傳輸.

圖2 光子晶體TE模的能帶結(jié)構(gòu) (a)PC2;(b)PC1Fig.2. TE band structure of photonic crystal:(a)PC2;(b)PC1.

3 異質(zhì)結(jié)結(jié)構(gòu)的構(gòu)建與透過(guò)譜分析

基于PC1和PC2光子晶體構(gòu)建了兩種光子晶體異質(zhì)結(jié)結(jié)構(gòu),一種具有正交異質(zhì)結(jié)界面,另一種具有非正交異質(zhì)結(jié)界面,結(jié)構(gòu)如圖3所示.正交光子晶體異質(zhì)結(jié)結(jié)構(gòu)指的是交界面與入射光方向(沿x軸方向)正交,而非正交則是指交界面與入射光方向非正交.由于交界面與入射光方向夾角為45?時(shí),結(jié)構(gòu)的單向傳輸性能最佳且更容易制備[2,25],因此本文提到的非正交異質(zhì)結(jié)結(jié)構(gòu)特指交界面與入射光方向成45?角.

圖3 光子晶體異質(zhì)結(jié)結(jié)構(gòu)示意圖 (a)二維正交異質(zhì)結(jié);(b)二維非正交異質(zhì)結(jié)Fig.3.Schematic of photonic crystal heterojunction structures:(a)2D orthogonal heterojunction;(b)2D non-orthogonal heterojunction.

利用時(shí)域有限差分法計(jì)算異質(zhì)結(jié)結(jié)構(gòu)的透過(guò)譜.將每個(gè)晶格常數(shù)a分為40個(gè)網(wǎng)格,并將整個(gè)結(jié)構(gòu)包裹在理想匹配層吸收邊界條件下以保證計(jì)算的準(zhǔn)確性.所使用的光源為類TE模式高斯波形電磁波(包含Ex,Ey,Hz分量),脈沖的頻譜寬度為0.10—0.36a·λ?1,覆蓋了所需要的頻率范圍.在異質(zhì)結(jié)結(jié)構(gòu)的輸入端設(shè)置光源,并在輸出端設(shè)置接收屏,記錄能流強(qiáng)度隨時(shí)間演化的數(shù)據(jù),再通過(guò)傅里葉變換得到頻率強(qiáng)度譜,將光源的頻率強(qiáng)度譜歸一化即可得到異質(zhì)結(jié)結(jié)構(gòu)在不同頻率上的透過(guò)率[2].定義由PC1射向PC2的光,即從左至右的入射光為正向光,由PC2射向PC1的光,即從右至左的入射光為反向光.兩種異質(zhì)結(jié)結(jié)構(gòu)的透過(guò)譜如圖4所示.

由圖4(a)可知,二維正交光子晶體異質(zhì)結(jié)結(jié)構(gòu)的正向和反向透過(guò)率在頻率為0.16—0.30a·λ?1的區(qū)域內(nèi)幾乎重合,在頻率為0.18—0.28a·λ?1的區(qū)域內(nèi),正、反向透過(guò)率幾乎為0,說(shuō)明不管入射光從左入射還是從右入射都無(wú)法穿透此異質(zhì)結(jié)結(jié)構(gòu),此結(jié)構(gòu)不具有單向傳輸特性,因此直接利用圖3(a)所示正交光子晶體異質(zhì)結(jié)結(jié)構(gòu)(不包含界面耦合區(qū))無(wú)法實(shí)現(xiàn)光二極管的功能[18].

圖4(b)是二維非正交光子晶體異質(zhì)結(jié)結(jié)構(gòu)的正、反向透過(guò)譜.該圖顯示了完全不同于圖4(a)的特性,正向和反向透過(guò)率有很大的差異.當(dāng)頻率為0.18—0.28a·λ?1時(shí),反向透過(guò)率為0,說(shuō)明入射光無(wú)法從右至左穿透異質(zhì)結(jié)結(jié)構(gòu);當(dāng)頻率在0.18—0.23a·λ?1區(qū)域時(shí),正向透過(guò)率在10%—45%之間變化,且當(dāng)頻率為0.22a·λ?1時(shí),正向透過(guò)率約為45%.由此可見(jiàn),圖3(b)所示非正交異質(zhì)結(jié)結(jié)構(gòu)能實(shí)現(xiàn)單向傳輸,基于此結(jié)構(gòu)可以構(gòu)造光子晶體光二極管,與文獻(xiàn)[18]中的正交光子晶體異質(zhì)結(jié)結(jié)構(gòu)(含界面耦合區(qū))相比,該結(jié)構(gòu)更簡(jiǎn)單,尺寸更小,實(shí)用性更強(qiáng).

圖4 (網(wǎng)刊彩色)光子晶體異質(zhì)結(jié)結(jié)構(gòu)的透過(guò)譜 (a)二維正交異質(zhì)結(jié);(b)二維非正交異質(zhì)結(jié)Fig.4.(color online)Transmission spectra of photonic crystal heterojunction structures:(a)2D orthogonal heterojunction;(b)2D non-orthogonal heterojunction.

為了更直觀地觀察和比較異質(zhì)結(jié)結(jié)構(gòu)的傳輸特性,利用時(shí)域有限差分法模擬了類TE模式電磁波Ey分量在頻率為0.22a·λ?1時(shí)的場(chǎng)分布情況,結(jié)果如圖5所示.

由圖5(a)可知,當(dāng)光正向入射時(shí),能直接穿透PC1區(qū)域到達(dá)界面,但無(wú)法繼續(xù)穿透PC2區(qū)域,在結(jié)構(gòu)的右側(cè)觀測(cè)不到出射場(chǎng).因?yàn)樵擃l率雖然位于PC1光子晶體Γ-X方向?qū)^(qū)域,但卻位于PC2光子晶體Γ-X方向帶隙區(qū)域,所以光無(wú)法穿透此異質(zhì)結(jié)結(jié)構(gòu).由圖5(b)可知,光反向入射時(shí),由于無(wú)法沿Γ-X方向穿過(guò)PC2區(qū)域,因此在結(jié)構(gòu)的左側(cè)無(wú)出射場(chǎng)存在.即正交光子晶體異質(zhì)結(jié)結(jié)構(gòu)在頻率為0.22a·λ?1時(shí),正、反向透過(guò)率均為0.由圖5(c)和圖5(d)可知,當(dāng)光正向入射時(shí),可直接透過(guò)PC1區(qū)域到達(dá)交界面,同時(shí)由于此頻率位于PC2光子晶體Γ-M方向?qū)^(qū)域,因此部分光沿著異質(zhì)結(jié)交界面衍射進(jìn)入PC2區(qū)域,在結(jié)構(gòu)的右側(cè)明顯地觀測(cè)到出射場(chǎng);當(dāng)光反向入射時(shí),不能沿Γ-X方向穿過(guò)PC2區(qū)域,因此在PC1的左側(cè)幾乎觀測(cè)不到出射場(chǎng).即非正交光子晶體異質(zhì)結(jié)結(jié)構(gòu)在頻率為0.22a·λ?1時(shí),顯現(xiàn)出良好的單向傳輸特性.以上由場(chǎng)分布圖觀察的現(xiàn)象與透過(guò)譜的計(jì)算結(jié)果保持一致.

圖5 (網(wǎng)刊彩色)頻率為0.22a·λ?1時(shí)電場(chǎng)分量Ey的場(chǎng)分布圖 (a),(b)正交異質(zhì)結(jié)結(jié)構(gòu)正、反向場(chǎng)分布;(c),(d)非正交異質(zhì)結(jié)結(jié)構(gòu)正、反向場(chǎng)分布Fig.5.(color online)Eyfield distribution at 0.22a·λ?1:(a),(b)The forward and backward field distributions of orthogonal heterojunction structure;(c),(d)the forward and backward field distributions of non-orthogonal heterojunction structure.

分析結(jié)果表明,能帶結(jié)構(gòu)顯示基于PC1與PC2光子晶體的異質(zhì)結(jié)結(jié)構(gòu)具有實(shí)現(xiàn)光單向傳輸?shù)谋匾獥l件,但透過(guò)譜和場(chǎng)分布圖的對(duì)比分析說(shuō)明能否實(shí)現(xiàn)光的單向傳輸還與異質(zhì)結(jié)界面的方位有關(guān).

4 光子晶體異質(zhì)結(jié)結(jié)構(gòu)的優(yōu)化設(shè)計(jì)

第3節(jié)的分析表明,非正交異質(zhì)結(jié)結(jié)構(gòu)能實(shí)現(xiàn)光的單向傳輸,且單向傳輸效率達(dá)到45%.為了進(jìn)一步提高單向傳輸效率,構(gòu)造高性能的光二極管,對(duì)非正交異質(zhì)結(jié)結(jié)構(gòu)實(shí)行了界面優(yōu)化設(shè)計(jì).

將PC2結(jié)構(gòu)中靠近交界面的一組空氣孔的半徑減小至0.15a,形成第一種優(yōu)化結(jié)構(gòu),如圖6(a)所示.采用時(shí)域有限差分法計(jì)算該異質(zhì)結(jié)結(jié)構(gòu)的正、反向透過(guò)譜和場(chǎng)分布,結(jié)果如圖6(b)—(d)所示.由圖6(b)可知,當(dāng)入射光頻率為0.22a·λ?1時(shí),該結(jié)構(gòu)顯示出單向傳輸特性.由圖6(c)和圖6(d)可知,優(yōu)化后的結(jié)構(gòu)對(duì)應(yīng)的反向透過(guò)譜與未優(yōu)化結(jié)構(gòu)的反向透過(guò)譜差異很小,都處在0.18—0.28a·λ?1頻率區(qū)域內(nèi),反向透過(guò)率為0;優(yōu)化后與未優(yōu)化結(jié)構(gòu)的正向透過(guò)譜的變化趨勢(shì)幾乎相同,當(dāng)頻率為0.18—0.26a·λ?1時(shí)仍表現(xiàn)出單向傳輸特性,但最大正向透過(guò)率有所提高,達(dá)到了50%.

在圖6(a)結(jié)構(gòu)的基礎(chǔ)之上,直接將PC2結(jié)構(gòu)中靠近交界面的一組空氣孔去掉,形成第二種優(yōu)化結(jié)構(gòu),如圖7(a)所示.采用時(shí)域有限差分法來(lái)計(jì)算該異質(zhì)結(jié)結(jié)構(gòu)的正、反向透過(guò)譜和場(chǎng)分布,結(jié)果如圖7(b)—圖7(d)所示.場(chǎng)分布圖顯示,當(dāng)入射光頻率為0.22a·λ?1時(shí),該結(jié)構(gòu)能實(shí)現(xiàn)單向傳輸.透過(guò)譜計(jì)算結(jié)果說(shuō)明,與未優(yōu)化結(jié)構(gòu)相比,反向透過(guò)譜基本保持不變,而正向透過(guò)譜峰值明顯增大,最大透過(guò)率超過(guò)54%,透過(guò)率提高了10%,此結(jié)構(gòu)能在0.18—0.26a·λ?1的頻率區(qū)域內(nèi)實(shí)現(xiàn)高效的單向傳輸.

圖6 (網(wǎng)刊彩色)(a)二維非正交光子晶體異質(zhì)結(jié)結(jié)構(gòu)的優(yōu)化設(shè)計(jì);(b)透過(guò)譜;(c),(d)頻率為0.22a·λ?1時(shí)電場(chǎng)分量Ey的正、反向場(chǎng)分布Fig.6.(color online)(a)Optimized 2D non-orthogonal photonic crystal heterojunction structure;(b)transmission spectra;(c),(d)the forward and backward field distributions of Eyat 0.22a·λ?1.

圖7 (網(wǎng)刊彩色)(a)二維非正交光子晶體異質(zhì)結(jié)結(jié)構(gòu)的優(yōu)化設(shè)計(jì)圖;(b)透過(guò)譜;(c),(d)頻率為0.22a·λ?1時(shí)電場(chǎng)分量Ey的正、反向場(chǎng)分布圖Fig.7.(color online)(a)Optimized 2D non-orthogonal photonic crystal heterojunction structure;(b)transmission spectra;(c),(d)the forward and backward field distributions of Eyat 0.22a·λ?1.

綜上可知,通過(guò)優(yōu)化異質(zhì)結(jié)界面,光子晶體異質(zhì)結(jié)結(jié)構(gòu)的單向傳輸效率有了明顯的提高.

5 結(jié) 論

本文基于光子晶體方向帶隙差異構(gòu)建了二維硅基光子晶體異質(zhì)結(jié)結(jié)構(gòu),對(duì)比分析了正交和非正交異質(zhì)結(jié)界面情況下的傳輸特性,發(fā)現(xiàn)正交異質(zhì)結(jié)結(jié)構(gòu)無(wú)法實(shí)現(xiàn)光的單向傳輸,而非正交異質(zhì)結(jié)結(jié)構(gòu)能在較寬頻率范圍內(nèi)實(shí)現(xiàn)光的單向傳輸.由此得出,能否實(shí)現(xiàn)光的單向傳輸與異質(zhì)結(jié)界面的方位緊密相關(guān).此外,針對(duì)非正交光子晶體異質(zhì)結(jié)結(jié)構(gòu)提出了兩種改變界面耦合區(qū)結(jié)構(gòu)的設(shè)計(jì)方案,使得單向傳輸效率提高了10%左右.基于該光子晶體異質(zhì)結(jié)結(jié)構(gòu),連接合適參數(shù)的輸入、輸出波導(dǎo)將構(gòu)造出高性能的光二極管,從而為光二極管的設(shè)計(jì)提供重要的參考.

[1]Hou J 2011Ph.D.Dissertation(Wuhan:Huazhong University of Science and Technology)(in Chinese)[侯金2011博士學(xué)位論文(武漢:華中科技大學(xué))]

[2]Wang C,Zhou C Z,Li Z Y 2011Opt.Express19 26948

[3]Yablonovitch E 1987Phys.Rev.Lett.58 2059

[4]Joannopoulos D J,Mead D R,Winn N J 2008Photonic Crystals:Molding the Flow of LightSecond Edition(Princeton:Princeton University Press)pp190–206

[5]Wu H,Jiang L Y,Jia W,et al.2012Chin.Phys.Lett.29 034203

[6]Zhu Q Y,Fu Y Q,Hu D Q,et al.2012Chin.Phys.B21 064220

[7]Zhou Y,Yin L Q 2012Chin.Phys.Lett.29 064213

[8]Zhang X Z,Feng M,Zhang X Z 2013Acta Phys.Sin.62 024201(in Chinese)[張學(xué)智,馮鳴,張心正 2013物理學(xué)報(bào)62 024201]

[9]Ibrahim S K,Bhandare S,Sandel D,et al.2004Electron.Lett.40 1293

[10]Zaman T R,Guo X,Ram R 2007Appl.Phys.Lett.90 023514

[11]Bi L,Hu J,Jiang P,et al.2011Nat.Photonics5 758

[12]Fan L,Wang J,Varghese L T 2012Science335 447

[13]Li X F,Ni X,Feng L,et al.2011Phys.Rev.Lett.106 084301

[14]Kurt H,Yilmaz D,Akosman A E,et al.2012Opt.Express20 20635

[15]Zhang Y Y,Kan Q,Wang G P 2014Opt.Lett.39 4934

[16]Feng S,Wang Y Q 2013Opt.Express21 220

[17]Feng S,Wang Y Q 2013Opt.Mater.36 546

[18]Cheng L F,Ren C,Wang P,Feng S 2014Acta Phys.Sin.63 154213(in Chinese)[程立鋒,任承,王萍,馮帥2014物理學(xué)報(bào)63 154213]

[19]Lu C C,Hu X Y,Zhang Y B,et al.2011Appl.Phys.Lett.99 051107

[20]Cicek A,Yucel M B,Kaya O A,et al.2012Opt.Lett.37 2937

[21]Feng L,Ayache M,Huang J,et al.2011Science333 729

[22]Colak E,Serebryannikov A E,Cakmak A O,et al.2013Appl.Phys.Lett.102 151105

[23]Wang L H,Yang X L,Meng X F,et al.2014Chin.Phys.B23 034215

[24]Cao Z,Qi X Y,Zhang G Q,et al.2013Opt.Lett.38 3212

[25]Li L 2015M.S.Dissertation(Taiyuan:Taiyuan University of Technology)(in Chinese)[李琳 2015碩士學(xué)位論文(太原:太原理工大學(xué))]

PACS:42.70.Qs,42.25.Bs DOI:10.7498/aps.66.054209

Study on unidirectional transmission in silicon photonic crystal heterojunctions?

Liu Dan1)?Hu Sen1)2)Xiao Ming1)

1)(School of Physics and Mechanical and Electrical Engineering,Hubei University of Education,Wuhan 430205,China)
2)(College of Physical Science and Technology,Central China Normal University,Wuhan 430079,China)

24 July 2016;revised manuscript

2 December 2016)

Electronic diode plays an important role in electronic circuits owing to its capability of unidirectional movement of the current flux.An optical diode offers unidirectional propagation of light beams,which plays key roles in the all-optical integrated circuits.Unidirectional wave propagation requires either time-reversal or spatial inversion symmetry breaking.The former can be achieved with the help of nonlinear materials,magnetic-optical materials and so on.The realization of these schemes all needs the external conditions(electric field,magnetic field or light field),and thus their applications are limited.In contrast,spatial inversion symmetry breaking can make up for this shortcoming and has been widely studied.

Through breaking the structure’s spatial inversion symmetry,much research demonstrated that the unidirectional light propagation could be achieved in a photonic crystal structure.Specially,the optical diode based on the photonic crystal heterojunction has been drawing much attention.Though relevant studies have been reported,how to find a more simple structure to realize high-efficiency optical diodes is always pursued by people.The previous design of optical diode is generally based on the orthogonal or non-orthogonal photonic crystal heterojunctions.However,the comparative analysis of the two types of heterojunctions has not been systematically carried out.The transmission characteristics of two-dimensional orthogonal and non-orthogonal silicon photonic crystal heterojunctions are obtained and compared.Firstly,the directional band gap mismatch of two-dimensional square-lattice silicon photonic crystals with the same lattice constant but different air hole radii is calculated by the plane wave expansion method.The band structure indicates that in a certain frequency range,one photonic crystal is the omni-directional pass band,while the other has directional band gap.This is just the necessary condition for the unidirectional light transmission through the photonic crystal heterojunctions.Therefore,the heterojunction constructed by the two photonic crystals is expected to achieve optical diode.Based on this,the orthogonal and the non-orthogonal heterojunctions are proposed.Their transmission spectra and field distributions are calculated by the finite-difference time-domain method.The results show that the unidirectional light transmission can be realized by the non-orthogonal heterojunction structure(unidirectional transmission efficiency reaches 45%)but not the orthogonal heterojunction structure.That is to say,the realization of unidirectional transmission is closely related to the orientation of the hetero-interface.Moreover,the non-orthogonal photonic crystal hetero-interface is optimized.It is found that the unidirectional transmission efficiency increases to 54%and the overall increases by 10%.More importantly,it greatly improves the performance of optical diode for its simple structure and small size,and provides another more effective design method.

photonic crystal heterojunction,unidirectional transmission,finite-difference time-domain method

PACS:42.70.Qs,42.25.Bs

10.7498/aps.66.054209

?國(guó)家自然科學(xué)基金(批準(zhǔn)號(hào):11504100)和湖北省教育廳中青年人才項(xiàng)目(批準(zhǔn)號(hào):Q20153004)資助的課題.

?通信作者.E-mail:liudanhu725@126.com

*Project supported by the National Natural Science Foundation of China(Grant No.11504100)and the Fund for Excellent Youths of the Hubei Provincial Department of Education,China(Grant No.Q20153004).

?Corresponding author.E-mail:liudanhu725@126.com