高分子專業(yè)畢業(yè)論文外文翻譯

1、<p>　　高Q 值二維光子晶體微腔</p><p>　　光子腔具有約束光線的特性，這個(gè)特性可以應(yīng)用到物理和工程的許多領(lǐng)域中，包括相關(guān)電-光互相作用[1]，超小濾光片[2,3]，低閾值激光器[4]，光子芯片[5]，非線性光學(xué)[6]和處理量子信息[7]。這些應(yīng)用的關(guān)鍵是實(shí)現(xiàn)腔的品質(zhì)因數(shù)Q，更小的模式體積。比例 Q/V決定了各種腔的互相作用強(qiáng)度，和一個(gè)超小型腔使能夠大范圍互相作用和更寬波長范圍的單模運(yùn)算。可

2、是一個(gè)高Q光波長的腔范圍是很難制作，因?yàn)檩椛鋼p失與腔的體積成反比。除了一些最近的理論研究，在制造高Ｑ值微腔方面沒有權(quán)威的理論和實(shí)驗(yàn)[8-10]。在這里我們使用基于硅的二維光子晶體平板微腔，Q=45,000和V= ；Q/V值是以前研究的10-100倍。這項(xiàng)研究使我們意識(shí)到光線可以被更強(qiáng)烈的約束[4,11-14]。集成與其他光子器件是非常簡單的，已經(jīng)可以證明１００ｎｍ的光譜范圍了。</p><p>　　腔的Ｑ值決

3、定于相對(duì)于原能量的每個(gè)周期的能量損耗。由于腔的材料對(duì)光沒有吸收，Q值決定于腔內(nèi)外界面之間的能量損失。全部內(nèi)部反射（TIR）和/或 布拉格散射常用于對(duì)光的約束。對(duì)于一個(gè)體積大于光波長的腔，已經(jīng)可以得到一個(gè)很高的Ｑ值了[14,15。在這種情況下，被約束在腔中的光線符合光學(xué)理論，每一束在交界面處被反射的光都符合全內(nèi)反射或布拉格散射。腔越小光線對(duì)光學(xué)理論的偏移越嚴(yán)重，因此Q值會(huì)變小。被約束在微腔中的光線是由非常多的平面波組成的，由于光的局部化這

4、些平面波是由很多波矢k組成。設(shè)計(jì)出符合全內(nèi)反射或者布拉格散射的平面波非常困難，高Ｑ值光子晶體諧振腔的產(chǎn)生很好的解決這個(gè)問題。</p><p>　　解決這個(gè)問題的一個(gè)很好的辦法就是在所有方向上運(yùn)用布拉格散射效應(yīng)。二維或者三維的折射率周期性變化的結(jié)構(gòu)可以產(chǎn)生這樣的效應(yīng)，變化基于光波波長的數(shù)量級(jí)。這些被稱為光子晶體，類似于固體晶體[5,16]。對(duì)于一個(gè)三維光子晶體，布拉格散射可以約束所有方向特定頻率范圍的光線，稱為光子

5、帶隙。一個(gè)小擾動(dòng)或缺陷引入三維光子晶體就會(huì)形成光子晶體微諧振腔，并具有極高的Q/Ｖ值?？墒?，三維光子晶體。還不能對(duì)光進(jìn)行很好的約束。</p><p>　　將二維光子晶體環(huán)繞在腔的四周是一個(gè)可行的辦法。一個(gè)二維晶體平板，如圖一所示，其厚度比擬與光波波長，在水平和垂直方向?qū)舛加蟹浅?qiáng)的約束，這種結(jié)構(gòu)式非常有希望的。光子帶隙的作用是把光的方向限制在平面內(nèi)，垂直方向通過平板與空氣的全反射來對(duì)光進(jìn)行約束。顯然，在垂直方向

6、滿足全內(nèi)反射是制造高Ｑ/V腔的關(guān)鍵。</p><p>　　為了進(jìn)一步研究對(duì)二維光子晶體平板垂直方向的光線約束，我們首先考慮一簡單模式（圖2），腔有厚度為Ｔ，長度為Ｌ的介質(zhì)材料構(gòu)成，腔的兩側(cè)是全反射鏡，約束ｘ軸方向上的光。簡單起見，假設(shè)結(jié)構(gòu)在y方向是均勻的。在ｚ軸方向，光線被約束于空氣層的全反射，如上所討論的一樣。圖2b表示的是腔內(nèi)波長為2.5λ的電場的場分布，λ是光在腔的諧振波長。</p><

7、p>　　在垂直方向（z方向）是由全內(nèi)反射對(duì)光進(jìn)約束的。將腔內(nèi)的電場通過傅里葉變換分解為一系列具有不同波矢ｋ的平面波，這樣就可以評(píng)估其約束強(qiáng)度，如參考文獻(xiàn)10中所述。（其中 是在空氣的光波長）當(dāng)每個(gè)平面波波矢ｋ的正切分量在０到變化時(shí)，光波可以從腔中溢出到空氣層中，這是因?yàn)槭睾愣蓪?duì)于| |（或Snell’s定律的廣義）在腔和空氣界面之間產(chǎn)生作用，。這就減弱了垂直方向上的約束強(qiáng)度。注意到| |在空氣層中x-z傳播方向可以取從0到 的

8、值。而| |在腔取不同的值由光的位置決定，如前面所敘述的一樣。當(dāng)| |在腔大于 ，該| |在界面出沒有守恒定律，光在腔內(nèi)被強(qiáng)烈限制，這導(dǎo)致垂直方向的強(qiáng)烈限制。圖2c表示圖2b電場的FT光譜，其中的插圖為漏區(qū)域（| |小于 ）多數(shù)的分量里面存在漏區(qū)域，這表明大腔內(nèi)存在很大的輻射損耗。</p><p>　　我們現(xiàn)在考慮損失機(jī)理的更多細(xì)節(jié)。腔內(nèi)的電場空間分布可以表示為一個(gè)波長為λ的正弦波，和一個(gè)基于腔結(jié)構(gòu)包絡(luò)函數(shù)F（x

9、）的乘積?；ńo出的一個(gè)三角形FT，其峰值為k= ，而包絡(luò)函數(shù)則形成了光譜。如圖2b，包絡(luò)函數(shù)是F（x）=1 （x=-L/2到L/2），和F（x）=0（x為其他），和相應(yīng)的FT光譜是一個(gè)正弦函數(shù)，其寬度約為2 （圖2c）。雖然從基波引起的頻譜峰值是在漏區(qū)域外，但是在包絡(luò)函數(shù)邊緣（x=-L/2,L/2）劇烈的變化形成了泄露區(qū)域的主要部分，并導(dǎo)致了大量的輻射損失。略小的腔，邊緣效應(yīng)越嚴(yán)重，其Ｑ值越低。</p><p>

10、;　　這就給出了一個(gè)抑制輻射損耗的重要的提示：在腔的邊緣的包絡(luò)函數(shù)的空間變化應(yīng)該不是劇烈而是平緩，這樣的話傅里葉頻譜就不會(huì)進(jìn)入泄露區(qū)域?；谶@種思想，我們使用高斯函數(shù)F（x），如圖2d所示；計(jì)算所得的FT頻譜如圖2e所示。這里的情況發(fā)生了很大變化：，相比圖2c泄露區(qū)域的部分很小。這說明可以在不改變模式體積的情況下調(diào)整包絡(luò)函數(shù)可以大幅增加Ｑ值。</p><p>　　因此就設(shè)計(jì)出了利用二維光子晶體平板的高Ｑ值微腔（圖

11、1b，c）。它的基本結(jié)構(gòu)是由三角形空氣柱硅晶體，其晶格常數(shù)為ａ（０.４２ｕｍ）。平板厚度和空氣柱半徑分別為０.６ａ（０.２５ｕｍ），０.２９ａ（０.１２ｕｍ）。我們首先去除腔中三個(gè)在同一排的空氣孔（圖1b）。這種結(jié)構(gòu)，光就由于布拉格散射而被約束在平面內(nèi)。對(duì)于z方向，光是被空氣層限制。</p><p>　　圖３中所示為腔中的平板中心的電場 。我們使用3D有限差分時(shí)域?yàn)橛?jì)算方法。和圖２中所討論的模型不一樣，在垂直方向

12、的約束只需考察ｘ和ｙ方向的傅里葉變換，這是因?yàn)楣馐潜幌拗圃谇坏亩S周期介質(zhì)中的。一樣的原因，TIR狀態(tài)（或| |守恒定律）需要分解為二維情況來討論?？紤]2D面內(nèi)的傳播，TIR狀態(tài)被打破因?yàn)槠矫娌ǖ乃衸 |在一個(gè)直徑為 的圓內(nèi)。</p><p>　　圖1：基于二維光子晶體平板的光子微腔a）腔的基本結(jié)構(gòu)原理圖，柱的三角晶格，晶格常數(shù)為a=0.42 ，平板的厚度和空氣棒的半徑分別為0.6a(0.25 )和0.29a(

13、0.12 )　　 b) 腔為去除在同一排的三個(gè)空氣孔所形成。c)通過移動(dòng)邊上的兩個(gè)空氣柱來獲得超高的Q/V值。</p><p>　　圖2：對(duì)腔的損耗減少的分析a）厚度為Ｔ長度為Ｌ腔的簡化模型。為了對(duì)光進(jìn)行約束，腔的兩側(cè)是ｘ方向的全反射鏡，ｚ軸方向則是同過空氣的全內(nèi)反射來對(duì)光進(jìn)行約束的。b，c）腔內(nèi)很短（2.5λ）長度的電場分布，與空間傅里葉變換。漏區(qū)域顯示于藍(lán)色區(qū)。d，e）電場分布平緩的包絡(luò)函數(shù)（高斯函數(shù)）與其空

14、間傅里葉頻譜。</p><p>　　圖3b表示圖3a相應(yīng)的FT光譜，泄露區(qū)域在灰色圓圈內(nèi)，傅里葉頻譜有很大一部分在泄露區(qū)域中。像之前已經(jīng)討論過的一樣，我們認(rèn)為這是由于腔邊緣的突變。在這我們試圖對(duì)光進(jìn)行更好的約束。方法就是在腔邊緣改變布拉格散射。這樣散射是由腔邊緣的空氣柱的散射的疊加所形成的。當(dāng)我們移動(dòng)的一些棒靠近腔邊緣，布拉格散射將要改變。因?yàn)楸灰苿?dòng)過的空氣柱散射的光的相位發(fā)生了變化，結(jié)果產(chǎn)生相位不匹配而減弱了磁

15、場的布拉格散射。為了補(bǔ)償反射的減小，光更多進(jìn)入鏡面中并被完全反射。這意味著腔邊緣上的電場分布被減弱，對(duì)于空氣柱適當(dāng)?shù)囊苿?dòng)會(huì)使得場分布接近由高斯函數(shù)所表示的理想的約束。根據(jù)這種分析，我們移動(dòng)腔邊緣的兩個(gè)空氣柱（圖1c）。圖3c和d分別表示二維傅里葉變換的電場分布，空氣柱與原來相比移動(dòng)了０.１５ａ。與圖３ｂ相比，圖３ｄ中在泄露區(qū)域中的傅里葉變化更少。因此，可以通過這種辦法使得Ｑ/V的值大幅增加。</p><p>　　

16、通過上面的分析，我們設(shè)計(jì)出不同位移的例子。諧振頻譜的測量使用可調(diào)諧連續(xù)激光作為光源。腔是由線性缺陷波導(dǎo)所激勵(lì)的，波導(dǎo)是腔旁邊的去除一排空氣孔所形成的（圖4b），可以觀察到從腔中所泄露出來的光的強(qiáng)度。結(jié)構(gòu)和實(shí)驗(yàn)方法的細(xì)節(jié)在別的地方說明[17]。腔的本征Q因素取決于去除腔和波導(dǎo)之間的相互作用后的輻射頻譜。有效地模式體積取決于電場空間分布[4]。從這結(jié)果發(fā)現(xiàn)V值小,在（6-7）x .</p><p>　　圖4a，b

17、分別表示移動(dòng)了不同距離空氣孔的腔的諧振頻譜以及相應(yīng)的電子顯微鏡掃描圖。諧振峰值的帶寬隨著空氣孔的移動(dòng)發(fā)生劇烈的變化。當(dāng)空氣孔的移動(dòng)為0.15a時(shí)頻譜帶寬出現(xiàn)最小值0.045nm，Ｑ值４５,０００（考慮到與波導(dǎo)的相互作用。圖４ｃ為以空氣孔移動(dòng)為自變量的Ｑ/V的函數(shù)。在空氣孔移動(dòng)距離到0.15a之前，Ｑ/V以10的速度增加。這樣就得到了6.4x 或者120,000/ 的Q/V。這比之前報(bào)道的腔Ｑ值高了一到兩個(gè)數(shù)量級(jí)，如環(huán)形微諧振腔、微磁

18、盤和光子晶體諧振腔[4,11-14]。通過對(duì)腔邊緣空氣孔恰當(dāng)?shù)恼{(diào)整可以獲得更高的Q/V。插圖4a表示寬的波長范圍的光譜測量，這表明在1,500到1，600nm的范圍不存在其他共振峰值。這結(jié)果表明單模適用于很寬范圍的波長，這對(duì)于不同的應(yīng)用很有幫助。</p><p>　　圖3：高Q/V腔的結(jié)構(gòu)。a） 圖1b顯示腔的基本模式的電場（Ey）分布</p><p>　　的基本模式。b）a的FT光譜。灰

19、色圓內(nèi)部是相應(yīng)的泄露區(qū)域c，d）分別是對(duì)應(yīng)圖1c腔的電場空間分布和2D FT光譜。相對(duì)于圖1b中的原始位置，邊緣上的空氣孔移動(dòng)了0.15a。</p><p>　　圖4：實(shí)驗(yàn)結(jié)果。a,b )不同位移的腔的頻譜及其顯微鏡掃面圖。插圖a為腔的諧振頻譜（0.15a位移）。c）以位移為自變量的所估算的Ｑ／Ｖ函數(shù)。已經(jīng)的得到了最大值是6.4x 或120,000/ 的Ｑ／Ｖ。</p><p>　　我

20、們描述了很重要的設(shè)計(jì)規(guī)則因這種設(shè)計(jì)可以對(duì)光進(jìn)行很好的約束來獲得高Q值并且保持很小的模式體積。通過在2D平板光子晶體引入腔的空氣棒兩個(gè)邊緣的位移得到非常大的Ｑ／Ｖ。我們認(rèn)為這概念能夠應(yīng)用到各種類型的光子微腔；這樣高Q微腔能夠應(yīng)用到科學(xué)和工程的不同場交叉；包括納米激光，非線性光學(xué)，納米生物材料，原子物理學(xué)，與量子計(jì)算。目前的結(jié)果是同樣重要因?yàn)楣庾泳w的制造以集成電路為基礎(chǔ)，例如已經(jīng)使用三維光子晶體實(shí)現(xiàn)了極小體積的微腔，其在垂直方向的泄露得到

21、充分的抑制。</p><p><b>　　參考文獻(xiàn)看原文。</b></p><p>　　附件2：外文原文（復(fù)印件）</p><p>　　High-Q photonic nanocavity in a two-dimensional photonic crystal </p><p>　　Yoshihiro Akahane

22、[1,2], Takashi Asano[1], Bong-Shik Song[1] & Susumu Noda</p><p>　　Photonic cavities that strongly con?ne light are finding applications in many areas of physics and engineering, including coherent electr

23、on–photon interactions[1], ultra-small filters[2,3],low-threshold lasers[4], photonic chips[5], nonlinear optics[6] and quantum information processing[7]. Critical for these applicationsis the realization of a cavity wit

24、h both high quality factor, Q, and small modal volume, V. The ratio Q/V determines the strength of the various cavity interactions, and an ultr</p><p>　　The Q of a cavity is determined by the energy loss per

25、 cycle versus the energy stored. With no absorption by the cavity material, Q is determined by the reflection loss at the interface between the interior and exterior of the cavity. Total internal re?ection (TIR) and/or B

26、ragg reflection are generally used for light confinement. For a cavity with a size much larger than the wavelength of light, a very high Q has already been achieved[14,15]. In that case, the behaviour of light confined i

27、n a la</p><p>　　One of the best approaches to resolving the problem is the extension of the Bragg reflection effect in multiple directions. Structures having a two- or three-dimensional (2D or 3D) periodic c

28、hange of refractive index on the scale of the light wavelength are required for such extension. These are known as photonic crystals,from an analogy to solid crystals [5,16]. For a 3D photonic crystal,Bragg reflection co

29、nditions can be fulfilled for all the propagation directions of light in a certain freque</p><p>　　A cavity surrounded by a 2D photonic crystal is considered a feasible solution. A 2D photonic-crystal slab,

30、as shown in Fig. 1a, with a thickness of the order of the light wavelength is very promising, owing to strong optical cofinement for both in-plane and vertical directions[2,3]. The photonic-bandgap effect is used for lig

31、ht cofinement in the in-plane direction, and TIR, at the interface between the slab and the air clad, in the vertical direction. Apparently, fulfilment of the TIR condition</p><p>　　To investigate vertical c

32、onfinement in 2D photonic-crystal slabs,we first consider a simplfied model (Fig. 2a), where the cavity consists of a dielectric material with thickness T and length L. Both sides of the cavity are closed by perfect mirr

33、ors, cofining light in the x direction. The structure is assumed to be uniform in the y direction for simplicity. Light is confined by TIR in the z direction by the air clad, as discussed above. Figure 2b shows an exampl

34、e of the electric field pro?le insi</p><p>　　The strength of the vertical (z-direction) cofinement by TIR can be investigated by decomposing the electric field inside a cavity into a set of plane wave compon

35、ents with various k-vectors by spatial Fourier transformation (FT), which is a similar approach to that reported in ref. 10.When the tangential component of the k-vector (| |,| |) of each plane wave lies within the range

36、 0 to (where is the wavelength of light in air), the wave can escape from the cavity to the air clad, because the </p><p>　　This gives an important hint for suppressing radiation loss: the spatial variat

37、ion of the envelope function at the cavity edges should not be abrupt but gentle, so that the FT spectrum does not have components inside the leaky region. On the basis of this idea, we have used a gaussian function for

38、F(x), as shown schematically in Fig. 2d; the calculated FT spectrumis shown in Fig. 2e. The situation has drastically changed: there are very small components inside the leaky region, when compared wit</p><p&g

39、t;　　A physical design of a high-Q photonic nanocavity has thus been carried out using a 2D photonic-crystal slab (Fig. 1b and c). The base structure is composed of Si with a triangular lattice of air ‘rods’ with lattice

40、constant a=0.42 . The thickness of the slab and the radii of the air rods are 0.6a (0.25 ) and 0.29a (0.12 ), respectively. We made the initia structure of the cavity with three missing air rods in a line17 (Fig. 1b).Wit

41、h this structure, light can be confined by Bragg reflection for </p><p>　　The electric field profile （ ）of the fundamental mode of the cavity at the centre plane of the slab is shown in Fig. 3a.We used 3D fi

42、nite-difference time-domain methods for the calculation. Unlike the model discussed in Fig. 2, x- and y-directional (2D) FT spectra are necessary for the investigation of the vertical confinement, as light is confined tw

43、o-dimensionally in the cavity. For the same reason, the TIR condition (or | |conservation law) should be expanded two-dimensionally. Considering in</p><p>　　Figure 1: Photonic nanocavities using a 2D photoni

44、c-crystal slab. a, Schematic of the base cavity structure having a triangular lattice of air rods with lattice constant a=0.42 . The thickness T of the slab and the radius R of the air rods are 0.6a(0.25 ) and 0.29a (0.

45、12 ), respectively. b, Starting cavity structure with three missing air rods I a line. c, Designed cavity structure created by displacing the air rods aboth edges to obtain an ultrahigh Q/V value.</p><p>　　F

46、igure 2: Analysis and reduction of cavity loss. a, Simplified model of a cavity consisting of a dielectric material with thickness T and length L. For confinement of light, both sides of the cavity are closed by perfect

47、mirrors for the x direction, and by the air clad based on TIR for the z direction. b, c, The electric field profile inside a cavity with a very short （2.5λ）length, and the spatial FT spectra. The leaky region is indicate

48、d as a blue area. d, e, The electric field pro?le with a ge</p><p>　　Figure 3b: Shows the FT spectra corresponding to Fig. 3a, where the leaky region is inside the grey circle. The FT spectrum contains large

49、 components inside the leaky region. As discussed, we considerthat this is due to the abrupt change at the cavity edges. Here we try to make confinement gentler. The strategy to obtain gentler confinement is to change th

50、e condition for Bragg reflection at the cavity edge. Such reflection is determined by a summation of partial reflections at a series of rods n</p><p>　　Encouraged by the above analysis, we fabricated samples

51、 with various displacements. The resonant spectra were measured using a tunable c.w. laser as a light source. The cavities were excited through a line defect waveguide constructed by filling a row of air holes near the c

52、avity (Fig. 4b), and the intensity of the light emitted from the cavities to free space was observed. Details of construction and experimental methods are given elsewhere[17] . The intrinsic Q factor of the cavity was de

53、termi</p><p>　　Figures 4a and b show resonant spectra of cavities with various air-rod shifts and the corresponding scanning electron microscope (SEM) pictures, respectively. The width of the resonant peak c

54、hanges drastically with shift of air rods. The spectral width becomes a minimum (0.045 nm) for the sample with shift ~ 0.15a, from which a Q factor of 45,000 is derived considering the coupling effect with the waveguide.

55、 In Fig. 4c, the Q/V values are plotted as a function of shift of air rods. Q/V increase</p><p>　　Figure 3: Physical design of high-Q/V cavity. a, The electric field profile （Ey）of the fundamental mode of t

56、he cavity shown in Fig. 1b as the starting structure. b, The FT spectra of a. The region inside the grey circle corresponds to the leaky region. c, d, The electric field profile and 2D FT spectrum, respectively, for the

57、designed cavity shown in Fig. 1c. The displacement of the air rods at the edges is set at 0.15a from the starting structure shown in Fig. 1b.</p><p>　　Figure 4: Experimental results. a, b, Resonant spectra

58、of cavities with various shifts of air rods and their SEM pictures, respectively. PC, photonic crystal. The inset in a shows the resonant spectrum of the cavity (with 0.15a displacement) measured over a wide wavelength r

59、ange. c, The estimated Q/V values as a function of shift of air rods. A maximum value of Q/V =6.4x cm23 , or 120,000/ , has been realized.</p><p>　　We have described the important design rule that light sh

60、ould be confined gently to obtain high Q factors while maintaining a very small modal volume V. An extremely large Q/V value has been achieved by introducing displacement of air rods at both edges of a cavity in a 2D pho

61、tonic-crystal slab. We believe that this concept could be applied to the design of various types of photonic nanocavity; such high-Q nanocavities could be applied across various fields of science and engineering, includi

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