可用于拓寬光波單向傳輸帶寬的光子晶體異質(zhì)結(jié)構(gòu)界面?

費(fèi)宏明 徐婷 劉欣 林瀚陳智輝 楊毅彪張明達(dá) 曹斌照 梁九卿

1)(太原理工大學(xué)物理與光電工程學(xué)院,太原 030024)

2)(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)

3)(斯威本科技大學(xué)微光子中心,墨爾本 3122,澳大利亞)

4)(山西大學(xué)理論物理研究所,太原 030006)

可用于拓寬光波單向傳輸帶寬的光子晶體異質(zhì)結(jié)構(gòu)界面?

費(fèi)宏明1)2)?徐婷1)2)劉欣1)2)林瀚3)陳智輝1)2)楊毅彪1)2)張明達(dá)1)2)曹斌照1)2)梁九卿4)

1)(太原理工大學(xué)物理與光電工程學(xué)院,太原 030024)

2)(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)

3)(斯威本科技大學(xué)微光子中心,墨爾本 3122,澳大利亞)

4)(山西大學(xué)理論物理研究所,太原 030006)

光波單向傳輸,全反射界面,光子晶體異質(zhì)結(jié)構(gòu)

基于光波單向傳輸?shù)娜舛O管在集成光通信、全光網(wǎng)絡(luò)和光信息處理中有重要應(yīng)用.基于方向帶隙失配設(shè)計(jì)的光子晶體異質(zhì)結(jié)構(gòu)可實(shí)現(xiàn)光波單向傳輸,但正向透射率較低,帶寬較窄.基于對(duì)光子晶體異質(zhì)界面傾斜角度的研究,根據(jù)界面全反射條件,利用可集成材料硅和二氧化硅設(shè)計(jì)了一種空氣孔型二維光子晶體異質(zhì)結(jié)構(gòu).異質(zhì)結(jié)構(gòu)界面兩側(cè)的光子晶體對(duì)1550 nm波長(zhǎng)附近的TE模光波在Γ-X方向均呈導(dǎo)帶,避免了方向帶隙失配.研究發(fā)現(xiàn)當(dāng)異質(zhì)界面滿足全反射條件時(shí),由于光子晶體的自準(zhǔn)直效應(yīng),較寬波段的正向光波得以高效傳播,而反向光波在界面由于全反射而被禁止傳播.光子晶體異質(zhì)結(jié)構(gòu)界面的全反射效應(yīng)打破了方向帶隙對(duì)光波單向傳輸?shù)南拗?使得反向光波在光子晶體中為導(dǎo)帶時(shí)同樣可實(shí)現(xiàn)近零透射率,從而拓寬了光波單向傳輸?shù)牟ㄩL(zhǎng)范圍.基于全反射界面的光子晶體異質(zhì)結(jié)構(gòu)經(jīng)過(guò)優(yōu)化后,其正向透射率達(dá)0.64,透射對(duì)比度為0.97,單向傳輸帶寬可達(dá)553 nm.

1 引 言

隨著電子信息技術(shù)的發(fā)展,集成電路芯片成為信息傳輸?shù)闹饕ぞ?而電子由于庫(kù)侖力產(chǎn)生熱效應(yīng),使得集成電路存在能量消耗大、信息傳輸慢等問(wèn)題.光子作為信息傳輸?shù)妮d體,傳輸速度快,光子間相互作用弱,可極大地降低能量消耗,提高傳輸效率[1],利用光子替代電子已成為科技發(fā)展與社會(huì)進(jìn)步的要求.光子晶體是以光子為信息載體的新型材料[2,3],通過(guò)實(shí)現(xiàn)集成光路推動(dòng)全光通信的發(fā)展,成為提高信息傳輸效率的一大助力.

在光通信系統(tǒng)中,為了保證有源器件的正常運(yùn)行,抑制反射光波,近年來(lái)不少研究小組專注于光子晶體單向傳輸器的研究.早期,實(shí)現(xiàn)光波單向傳輸?shù)墓庾泳w主要是在其內(nèi)部加入磁性材料[4,5]或非線性材料[6,7].Inoue和Fujii[8]將磁光介質(zhì)摻鈰釔鐵石榴石薄膜和SiO2薄膜排列形成一維周期磁光子晶體,利用磁場(chǎng)產(chǎn)生的法拉第旋光效應(yīng)實(shí)現(xiàn)了光波單向傳輸,為光波單向傳輸?shù)募苫峁┝诵滤悸?Xue等[9]將一維光子晶體(SiO2/TiO2)m和Ag薄膜相結(jié)合,利用金屬的非線性吸收,實(shí)現(xiàn)了光強(qiáng)為0.93 GW/cm2時(shí)557.2 nm附近的光波單向傳輸,正向透射率為0.42,透射對(duì)比度為0.984.這兩種方法均可實(shí)現(xiàn)光波單向傳輸,但磁性材料需要外加磁場(chǎng),非線性材料則要求較高的光強(qiáng),在實(shí)際應(yīng)用中存在非常大的局限性.于是人們又通過(guò)改變光子晶體的空間結(jié)構(gòu),破壞其空間反演對(duì)稱性,以實(shí)現(xiàn)光波單向傳輸,主要方法有界面耦合[10?13]或方向能帶失配[14?16].Kurt等[17]在二維光子晶體波導(dǎo)結(jié)構(gòu)中,通過(guò)改變縱向相鄰介質(zhì)柱的間距形成非對(duì)稱結(jié)構(gòu),實(shí)現(xiàn)光波的單向傳輸,透射對(duì)比度最高可達(dá)0.75.Feng和Wang[18]利用不同能帶特性的光子晶體組合,不僅實(shí)現(xiàn)了光波單向傳輸,還有分束效果,最大光波單向傳輸范圍為0.1(c/a),其中c為真空中的光速,a為晶格常數(shù),單位為nm.

通過(guò)方向能帶失配實(shí)現(xiàn)的光波單向傳輸要求其中一個(gè)方向?qū)鬏敼獠ㄊ墙麕?增加了寬頻帶光波單向傳輸?shù)碾y度,本文通過(guò)對(duì)不同光子晶體組成的異質(zhì)結(jié)構(gòu)中異質(zhì)界面傾斜角度的研究,發(fā)現(xiàn)該界面滿足全反射條件時(shí)可以擺脫能帶限制,實(shí)現(xiàn)光通信波段的光波單向傳輸,并優(yōu)化了界面結(jié)構(gòu),實(shí)現(xiàn)了1550 nm附近553 nm帶寬的TE模式光波單向傳輸,透射對(duì)比度達(dá)到了0.97,并對(duì)厚度為1500 nm的平板光子晶體異質(zhì)結(jié)構(gòu)進(jìn)行了分析.

2 結(jié)構(gòu)與分析

光子晶體中異質(zhì)結(jié)界面有兩種情況:一種是異質(zhì)界面與入射光垂直,一種是異質(zhì)界面與入射光存在不為90°的夾角.當(dāng)異質(zhì)界面與入射光夾角不為90°時(shí),因?yàn)榻缑鎯蓚?cè)背景材料不同,如果入射角滿足界面處的全反射定律則可實(shí)現(xiàn)光波的全反射,改變了原有光波的傳播方向.設(shè)計(jì)光子晶體異質(zhì)結(jié)構(gòu),異質(zhì)界面左右兩側(cè)背景材料分別選用二氧化硅和硅,其折射率在1550 nm附近分別為1.495和3.48,當(dāng)光波反向傳播時(shí),即從硅(光密介質(zhì))進(jìn)入二氧化硅(光疏介質(zhì))向左傳播時(shí),根據(jù)全反射定理可知,異質(zhì)界面傾斜角度θ小于63.55°時(shí),可發(fā)生光波全反射,從而起到阻止反向入射光傳播的作用.因此本文將對(duì)異質(zhì)界面傾斜角度分為三種情況進(jìn)行討論:1)異質(zhì)界面與入射光垂直,θ=90°(圖1(a));2)異質(zhì)界面存在傾斜角度但不滿足界面全反射條件,63.55°＜θ＜90°(圖1(b));3)異質(zhì)界面存在傾斜角度且滿足界面全反射條件,0°＜θ＜63.55°(圖1(c)).圖1中黑色線為正向入射光,紅色線為反向入射光,入射方向沿Γ-X方向.

圖1 (網(wǎng)刊彩色)異質(zhì)界面不同傾斜角度θ和光子晶體異質(zhì)結(jié)構(gòu)示意圖 (a)θ=90°;(b)63.55°＜θ＜ 90°;(c)0°＜θ＜63.55°;(d)空氣孔型二維光子晶體異質(zhì)結(jié)構(gòu)示意圖Fig.1.(color online)Schematic of different tilt angles θ at heterostructure interface and 2D photonic crystal heterostructure with air holes:(a)θ =90°;(b)63.55°＜θ＜ 90°;(c)0°＜θ＜ 63.55°;(d)sketch of 2D photonic crystal heterostructure with air holes.

基于以上三種異質(zhì)界面基本結(jié)構(gòu),光子晶體異質(zhì)結(jié)構(gòu)包括左右兩個(gè)二維四方晶格光子晶體PC1和PC2,如圖1(d)所示.PC1是在二氧化硅背景中打空氣孔,PC2是在硅背景中打空氣孔,兩者具有相同的晶格常數(shù)(a=490 nm)和空氣孔半徑(r=140 nm),當(dāng)光波從PC1向右傳播時(shí)為正向入射光,當(dāng)光波從PC2向左傳播時(shí)為反向入射光.選取異質(zhì)界面與水平方向夾角θ分別為90°,80°,70°,55°,45°和35°, 選用Tf和Tb分別代表正、反向透射率,透射對(duì)比度定義為C=(Tf?Tb)/(Tf+Tb)[19].該結(jié)構(gòu)在不同異質(zhì)界面傾斜角度下的透射譜如圖2所示,取高于90%最大正向透射率的波段區(qū)間為單向傳輸?shù)耐干浞宸秶?透射對(duì)比度大于0.8的波段區(qū)間為單向傳輸范圍.

圖2 (網(wǎng)刊彩色)不同傾斜角度異質(zhì)界面的透射譜 (a)θ=90°;(b)θ=80°;(c)θ=70°;(d)θ=55°;(e)θ=45°;(f)θ=35°Fig.2.(color online)Transmittance spectra of heterostructure interfaces with different tilt angles:(a)θ=90°;(b)θ =80°;(c)θ =70°;(d)θ =55°;(e)θ =45°;(f)θ =35°.

當(dāng)異質(zhì)界面與入射光垂直(圖2(a)),即界面角度θ=90°時(shí),正、反向透射率基本相同,在1550 nm處正向透射率只有0.019,反向透射率接近于0.009,沒(méi)有形成光波單向傳輸.當(dāng)異質(zhì)界面存在傾斜角度且不滿足界面全反射條件,即界面角度θ=80°,70°時(shí)(圖2(b)和圖2(c)),正、反向透射率存在差異:θ=80°時(shí),在1550 nm處正向透射率低于0.24,反向透射率為0.059,透射對(duì)比度均在0.8以下,且反向透射率很高,單向傳輸性能較差;θ=70°時(shí),在1550 nm附近正向透射率約為0.317,反向透射率為0.032,與θ=80°時(shí)相比正向透射率增加、反向透射率降低,在1533—1684 nm的單向傳輸范圍內(nèi)透射對(duì)比度均大于0.8.當(dāng)異質(zhì)界面存在傾斜角度且滿足界面全反射條件,即界面角度θ=55°,45°,35°時(shí)(圖2(d)—圖2(f)),在1550 nm附近反向透射率在較大的范圍內(nèi)幾乎接近于0,只是正向透射率有所不同,均可實(shí)現(xiàn)光波單向傳輸.θ=55°時(shí),正向透射率在0.4附近大范圍波動(dòng),反向透射率低于0.015,單向傳輸范圍為1400—1694 nm,此范圍內(nèi)透射對(duì)比度大于0.8;θ=45°時(shí),在1550 nm處正向透射率為0.546,反向透射率低于0.006,透射峰范圍為1521.63—1611.86 nm,單向傳輸范圍為1400—1974 nm,單向傳輸效果較好;θ=35°時(shí),在1550 nm處正向透射率為0.33,最高正向透射率可達(dá)0.55,整個(gè)正向透射峰波動(dòng)挺大,且反向透射率在0.04左右,單向傳輸范圍為1525—2000 nm,但在1550 nm處正向透射率太低.

表1 不同傾斜角度異質(zhì)界面的單向傳輸性能Table 1.The unidirectional transmission performance of heterostructure interfaces with different tilt angles.

對(duì)比以上6種不同傾斜角度界面的透射率和單向傳輸帶寬,如表1所示,通過(guò)分析可知,界面的傾斜不僅能改變光波的傳輸方向,還可以引起正反向透射率的不同.當(dāng)界面傾斜角度為90°和80°時(shí),都沒(méi)有實(shí)現(xiàn)透射對(duì)比度大于0.8的光波單向傳輸;當(dāng)界面傾斜角度為70°時(shí),單向傳輸帶寬約為150 nm,但1550 nm處正向透射率較低;當(dāng)界面傾斜角度滿足界面處的全反射條件,即θ=55°,45°,35°時(shí),該界面使得反向入射光波發(fā)生全反射,確保反向透射率幾乎為零,而界面的傾斜使得光波正向透射率有所增加,反向透射率也大范圍降低,實(shí)現(xiàn)了光波單向傳輸.尤其是θ=45°時(shí) (圖2(e)),透射峰范圍為1522—1612 nm,且1550 nm處正向透射率可達(dá)0.55,單向傳輸帶寬約為570 nm,實(shí)現(xiàn)了寬波段下1550 nm附近的TE模式光波單向傳播.

為了更好地分析結(jié)構(gòu)的單向傳輸特性,計(jì)算了θ=45°時(shí)PC1和PC2的TE模式能帶結(jié)構(gòu),如圖3(a)和圖3(b)所示,其中紅色線區(qū)域?yàn)橥干浞宸秶?兩者的等頻率面(EFC)如圖3(c)和圖3(d)所示,其中黑色箭頭代表光波正入射傳播方向,紅色箭頭代表光波反入射傳播方向.

圖3 (網(wǎng)刊彩色)TE模式單向傳輸特性 (a)PC1能帶圖;(b)PC2能帶圖;(c)PC1第二能帶等頻圖;(d)PC2第三能帶等頻圖Fig.3.(color online)Unidirectional transmission performance for TE mode:(a)Band of PC1;(b)band of PC2;(c)EFCs of PC1in the second band;(d)EFCs of PC2in the third band.

θ=45°時(shí)透射峰位于1521.63—1611.86 nm,對(duì) 應(yīng) 頻 率 為0.304a/λ—0.322a/λ, 在 圖3(a)中PC1在Γ-X方向?yàn)閷?dǎo)帶,在圖3(b)中PC2在 頻 率 為0.313a/λ—0.334a/λ, 即 波 長(zhǎng) 為1467.06—1566.5 nm時(shí)在Γ-X(0°入射光)方向?yàn)閷?dǎo)帶,在頻率為0.296a/λ—0.313a/λ,即波長(zhǎng)為1566.5—1655.96 nm時(shí)為禁帶.光波正向入射到PC1時(shí),在透射峰頻段0.304a/λ—0.322a/λ內(nèi),可沿著Γ-X方向水平向右傳播,如圖3(c)中黑色箭頭所示傳播方向,經(jīng)過(guò)異質(zhì)界面處耦合進(jìn)入PC2時(shí)將沿非Γ-X方向傳播,由于PC2具有Γ-X方向上的自準(zhǔn)直效應(yīng),因此光波被準(zhǔn)直到Γ-X方向輸出,如圖3(d)中黑色箭頭所示.光波反向入射到PC2時(shí),透射峰頻段0.304a/λ—0.313a/λ內(nèi)的光波因禁帶作用,其傳播被阻止,0.313a/λ—0.322a/λ頻段內(nèi)的光波則會(huì)在PC2內(nèi)沿著Γ-X方向傳播,并逐漸偏轉(zhuǎn)到M-X方向即豎直向上傳播,無(wú)法到達(dá)異質(zhì)界面,如圖3(d)中紅色箭頭所示.因此,光子晶體異質(zhì)結(jié)構(gòu)可以實(shí)現(xiàn)正向透射、反向阻止的光波單向傳輸.

為了能更直觀地觀察光波的傳輸情況,選取PC4導(dǎo)帶中的0.316a/λ(1550 nm)和禁帶中的0.306a/λ(1600 nm)這兩個(gè)頻率的光波,分析其正反向入射場(chǎng)強(qiáng)圖,如圖4所示.

這兩個(gè)頻率的光波傳輸結(jié)果與上述分析一致:光波正向入射時(shí),由于0.306a/λ和0.316a/λ位于PC1和PC2的Γ-X方向?qū)?在圖4(a)和圖4(c)中,該頻率的光波均可沿Γ-X方向水平向右傳播,經(jīng)過(guò)異質(zhì)界面后被準(zhǔn)直到Γ-X方向輸出;光波反向入射時(shí),0.306a/λ的光波由于是禁帶而被阻止傳播,0.316a/λ的光波則可沿Γ-X方向水平向左進(jìn)入PC2,并逐漸被準(zhǔn)直到M-X方向即豎直向上方向傳播,也無(wú)法到達(dá)異質(zhì)界面.

經(jīng)過(guò)以上分析可知,當(dāng)θ=45°時(shí),由于光子晶體的自準(zhǔn)直效應(yīng),滿足全反射條件的光子晶體異質(zhì)結(jié)構(gòu)的正向透射率提高,反向透射率降低,實(shí)現(xiàn)了寬波段下0.316a/λ即波長(zhǎng)為1550 nm附近的光波單向傳輸.

圖4 (網(wǎng)刊彩色)(a)0.306a/λ光波的正向入射場(chǎng)強(qiáng);(b)0.306a/λ光波的反向入射場(chǎng)強(qiáng);(c)0.316a/λ光波的正向入射場(chǎng)強(qiáng);(d)0.316a/λ光波的反向入射場(chǎng)強(qiáng)Fig.4.(color online)(a)Field intensity distribution of forward transmission at the frequency of 0.306a/λ;(b) fi eld intensity distribution of backward transmission at the frequency of 0.306a/λ;(c) fi eld intensity distribution of forward transmission at the frequency of 0.316a/λ;(d) fi eld intensity distribution of backward transmission at the frequency of 0.316a/λ.

3 優(yōu) 化

在影響光子晶體異質(zhì)結(jié)構(gòu)正向傳輸率和透射對(duì)比度的因素中,除界面傾斜角度外,界面兩端光子晶體結(jié)構(gòu)與界面間的距離也有重要作用,距離的不同會(huì)改變光波在光子晶體PC1和PC2之間的耦合效率,從而改變結(jié)構(gòu)的透射率和單向傳輸帶寬.因此,在不改變結(jié)構(gòu)平均折射率的條件下,進(jìn)一步對(duì)界面傾斜角度為45°的異質(zhì)結(jié)構(gòu)進(jìn)行優(yōu)化.定義異質(zhì)界面與左側(cè)PC1相鄰空氣孔水平距離為d1,與右側(cè)PC2相鄰空氣孔水平距離為d2.

d1=d2=a時(shí),在圖5(a)中,透射峰位于1553.25 nm,正向透射率為0.613,反向透射率為0.007,透射對(duì)比度為0.976,透射峰范圍為1537.38—1594.67 nm,正向透射率都在0.55以上,寬度約為57.3 nm,在1550 nm處透射率為0.608,單向傳輸范圍為1400—1904.5 nm,帶寬約為505 nm.

圖5 (網(wǎng)刊彩色)TE模式下異質(zhì)界面與兩側(cè)相鄰空氣孔不同水平間距條件下的透射譜 (a)d1=d2=a;(b)d1=d2=1.5a;(c)d1=a,d2=1.5a;(d)d1=1.5a,d2=aFig.5.(color online)Transmission spectra for the TE mode with different level distances between heterostructure interface and adjacent air holes:(a)d1=d2=a;(b)d1=d2=1.5a;(c)d1=a,d2=1.5a;(d)d1=1.5a,d2=a.

d1=d2=1.5a時(shí),在圖5(b)中,透射峰位于1573.68 nm,正向透射率為0.547,反向透射率為0.009,透射對(duì)比度為0.966,透射峰范圍為1561.36—1590.43 nm,寬度約為29 nm,在1550 nm處正向透射率為0.447,單向傳輸范圍為1400—1947.9 nm,帶寬約為548 nm.

d1=a,d2=1.5a時(shí),在圖5(c)中,透射峰位于1480.2 nm,正向透射率為0.537,反向透射率為0.007,透射對(duì)比度為0.973,透射峰范圍為1476.54—1483.87 nm,寬度僅為7.3 nm,透射峰較窄,在1400—1950 nm波段內(nèi)實(shí)現(xiàn)了單向傳輸,單向傳輸范圍為1400—1904.5 nm,帶寬約為505 nm,但透射率波動(dòng)較大,沒(méi)有形成平坦的單向傳輸.

d1=1.5a,d2=a時(shí),在圖5(d)中,透射峰位于1573.68 nm,正向透射率為0.643,反向透射率為0.011,透射對(duì)比度為0.97,透射峰范圍為1533.33—1603.22 nm,正向透射率在0.55以上,寬度約為70 nm,光波單向傳輸范圍為1400—1933.3 nm,寬度約為533 nm,而在1550 nm處正向透射率為0.624,反向透射率為0.009,透射對(duì)比度為0.970.

比較以上四種優(yōu)化結(jié)構(gòu),為了能實(shí)現(xiàn)近紅外波段1550 nm附近的高透射率光波單向傳輸,不僅需要較高的正向透射率和透射對(duì)比度,還需要較寬的透射峰和單向傳輸帶寬.綜合表2的各項(xiàng)參數(shù),發(fā)現(xiàn)當(dāng)d1=1.5a,d2=0.5a時(shí),1550 nm位于透射峰范圍內(nèi),且最高正向透射率可達(dá)0.643,透射對(duì)比度為0.970,透射峰寬度也較大,單向傳輸帶寬可達(dá)553 nm,可以很好地實(shí)現(xiàn)TE模式下寬波段內(nèi)近紅外1550 nm波段的光波單向傳輸.

表2 異質(zhì)界面與兩側(cè)相鄰空氣孔不同水平間距條件下的單向傳輸性能Table 2.The unidirectional transmission performance with different level distances between heterostructure interface and adjacent air holes.

考慮到實(shí)際器件的制備,分析了厚度為1500 nm[20]的平板光子晶體異質(zhì)結(jié)的單向傳輸性能. 當(dāng)a=490 nm,r=140 nm,θ=45°,d1=1.5a,d2=a時(shí),其正反向透射率及透射對(duì)比度如圖6所示,透射峰位于1510.1 nm處,正向透射率最高可達(dá)0.564,透射對(duì)比度為0.967,透射峰范圍為1476.54—1607.53 nm,寬度約為130 nm,當(dāng)透射對(duì)比度大于0.8時(shí),單向傳輸波段為1350—2000 nm,帶寬約為650 nm.與二維光子晶體異質(zhì)結(jié)構(gòu)相比,在此厚度下的平板光子晶體異質(zhì)結(jié)構(gòu)的正向透射率降低了12.3%,透射對(duì)比度基本保持不變,透射峰范圍增大了60 nm,單向傳輸帶寬也增加了100 nm.由此可見(jiàn),我們?cè)O(shè)計(jì)的二維光子晶體異質(zhì)結(jié)構(gòu)可應(yīng)用于實(shí)際中,為制備性能良好的光子晶體單向傳輸器件提供支持.

圖6 (網(wǎng)刊彩色)TE模式下厚度為1500 nm的平板光子晶體異質(zhì)結(jié)構(gòu)的透射譜Fig.6.(color online)Transmittance spectra of photonic crystal heterostructure slab with a thickness of 1500 nm for the TE mode.

4 結(jié) 論

本文設(shè)計(jì)了一種空氣孔型二維光子晶體異質(zhì)結(jié)構(gòu),研究異質(zhì)界面的傾斜角度發(fā)現(xiàn),界面滿足全反射條件時(shí),基于光子晶體的自準(zhǔn)直可以實(shí)現(xiàn)TE模式下1550 nm附近的光波單向傳輸.分析了界面與相鄰兩側(cè)空氣孔水平間距對(duì)透射率的影響,發(fā)現(xiàn)與左側(cè)空氣孔距離為1.5a、與右側(cè)空氣孔距離為a時(shí),可以實(shí)現(xiàn)正向透射率為0.643、單向傳輸帶寬為553 nm、透射對(duì)比度為0.97的寬波段光波單向傳輸.對(duì)厚度為1500 nm的平板光子晶體異質(zhì)結(jié)構(gòu)單向傳輸性能進(jìn)行分析發(fā)現(xiàn),雖然其正向透射率降低了12.3%,但透射對(duì)比度還保持在0.97左右,單向傳輸帶寬也有所增加,該光子晶體異質(zhì)結(jié)構(gòu)有望應(yīng)用于光子晶體單向傳輸器件中.

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Interface of photonic crystal heterostructure for broadening bandwidth of unidirectional light transmission?

Fei Hong-Ming1)2)?Xu Ting1)2)Liu Xin1)2)Lin Han3)Chen Zhi-Hui1)2)Yang Yi-Biao1)2)Zhang Ming-Da1)2)Cao Bin-Zhao1)2)Liang Jiu-Qing4)

1)(School of Physics and Optoelectronics,Taiyuan University of Technology,Taiyuan 030024,China)
2)(Key Laboratory of Advanced Transducers and Intelligent Control System,Ministry of Education,Taiyuan University of Technology,Taiyuan 030024,China)
3)(Micro-Photon Center,Swinburne University of Technology,Melburne 3122,Australia)
4)(Institute of Theoretical Physics,Shanxi University,Taiyuan 030006,China)

24 April 2017;revised manuscript

23 May 2017)

An all-optical diode(AOD)is a spatially nonreciprocal device that in the ideal case and for a speci fi c wavelength allows light to totally transmit along the forward direction but totally inhibits light to propagate along the backward direction,yielding a unitary contrast.AODs are widely considered to be the key components for the next-generation all-optical signal processing,and completely analogous to electronic diodes which are widely used in computers for processing electric signals.Most of AOD designs su ff er some serious drawbacks which make them not suitable for commercial and large-scale applications.Relatively large physical sizes are often needed,the balance between fi gure of merit and optical intensity is usually inadequate,and in some cases cumbersome structural designs are necessary to provide structural asymmetry.Among different approaches,the AOD based on two-dimensional(2D)photonic crystal(PC)heterostructure has shown signi fi cant advantages due to the capability of on-chip integration with other photonic devices.However,current PC heterostructure AOD(PCH-AOD)is based on the mismatch of directional bandgaps,which shows poor performance as a result of the relatively low forward transmittance(＜0.40)and contrast ratio(＜0.75)with a narrow bandwidth(about 10 nm).In order to improve the performance,here we propose a new PCH-AOD design based on the total re fl ection principle,which is able to achieve high forward transmittance and contrast ratio within a broad wavelength range.Our design is composed of two rectangle lattice 2D PC structures,in which periodically distributed air holes are embedded in silica(PC1)and silicon(PC2)materials,respectively.The two PCs are combined with an inclined interface along theΓ-Mdirection of both PCs.In this way,the total re fl ection condition is satis fi ed when light propagates from silicon to silica material.The forward and backward propagating optical waves are incident along theΓ-Xdirection of both PCs,in which direction there are transmission bands for TE mode centered at 1550 nm wavelength.A commercial software(R-soft)based on the fi nite-di ff erence time-domain(FDTD)method is used to study the unidirectional transmission performance of the PCH-AOD.The results show that the forward propagating optical waves(from PC1to PC2)can transmit efficiently through the device.In addition,we further improve the forward transmittance by exploiting the self-collimation e ff ect of PCs and optimizing the coupling from PC1to PC2.In the meantime,the light propagating along the backward direction(from PC2to PC1)is blocked at the total re fl ection interface with near-zero transmittance.In this way,the unidirectional transmission is achieved without the reliance on the directional bandgap mismatch,and thus broad bandwidth is achieved.The AOD has a forward transmittance of 0.64 and a transmission contrast of 0.97 with a bandwidth of 553 nm at 1550 nm.The equal frequency contours(EFCs)of the PCs is plotted to demonstrate the working principle of the PCH-AOD.Finally,considering the experimental fabrication of the AOD device,we analyze the unidirectional transmission performance of a planar PCH-AOD with a fi nite thickness of 1500 nm.Despite a small reduction(12.3%)in the forward transmittance,the transmission contrast is maintained at about 0.97,and the unidirectional transmission bandwidth is increased to 600 nm.Therefore,our design can be implemented in practice and our work provides a theoretical framework for designing high performance PCH-AOD.In addition,our design allows an unprecedented high forward transmittance,contrast ratio and broad working bandwidth of the device at extremely low operational optical intensity,due to the total re fl ection condition,and the optimized forward propagation and coupling condition.The proposed device has a small footprint that is promising for next-generation on-chip applications.

unidirectional transmission of light waves,interface of total re fl ection,photonic crystal heterostructure

(2017年4月24日收到;2017年5月23日收到修改稿)

10.7498/aps.66.204103

?國(guó)家自然科學(xué)基金(批準(zhǔn)號(hào):61575138)、國(guó)家自然科學(xué)基金青年科學(xué)基金(批準(zhǔn)號(hào):61505135)、山西省自然科學(xué)基金(批準(zhǔn)號(hào):2016011048)和國(guó)家留學(xué)基金委(批準(zhǔn)號(hào):201508140067)資助的課題.

?通信作者.E-mail:feihm187491@126.com

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

http://wulixb.iphy.ac.cn

PACS:41.20.Jb,85.60.Dw,42.70.QsDOI:10.7498/aps.66.204103

*Project supported by the National Natural Science Foundation of China(Grant No.61575138),the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.61505135),the Natural Science Foundation of Shanxi Province,China(Grant No.2016011048),and the Chinese Government Scholarship(Grant No.201508140067).

?Corresponding author.E-mail:feihm187491@126.com