1、基于光子晶體的表面環諧振器任洪亮 ，張靜紅 ，秦亞麗 ，劉凱 ，吳哲福 ，胡偉勝，江春， 金耀輝，浙江工業大學信息工程學院 杭州 310023 中國高級光通信系統和網絡國家重點實驗室，上海交通大學，上海 200240 中國_文章索引文章歷史：2010，8，30收到2011，3，30收到修訂稿2011，4，1接受2011，4，21網上可用關鍵字：圓形光子晶體（CPC）表面波導模式（SMW）表面環形波導模式（SMRW）環形諧振器概要：我們設計一個基于光子晶體（PCs）的緊密環型諧振器。這個結構是通過將環形波導一個的表面模式夾在一個二維光子晶體波導的兩個平行的表面模式中形成。這種波導的表面模式SMR

2、W是在一個具有高傳輸效率的環型光子晶體結構的表面上制作的。在某一固定的頻率下，在輸入波導的表面模式中SMRW作為一個基本的模式被引進，這種SMRW模式由于諧振而加強，光波耦合到輸出SMW波導表面模式。這個結果已經通過一個諧振器的模擬結果證明。由于基于光子晶體的表面模式有良好的導波性，所以該表面模式的環型諧振器有非常少量的輻射損失并且可以利用在未來的波分復用（WDM）的光通信系統中。1、介紹光波導環型諧振器可以被用在光濾波器中。光濾波器在光波分復用通信系統，光綜合回路和光學計算是非常重要的組成部分1-7。為了利用珍惜的帶寬資源，可以通過直接減小圓環半徑來有規律地顯著地增加自由光譜帶范圍（FSR）

3、。但是在剝離SOI的環型諧振器上，隨著圓環半徑的減小輻射損失指數增大，所以在這種情況下圓環最小半徑大約是3m4-7。為了減少圓環半徑并且獲得更大的自由光譜帶（FSR）范圍，光子晶體圓環諧振器通過Qiang.等人的方法來設計8。通過在正方格子組成的光子晶體的內部設計線缺陷而得到環形諧振器，但是由于這個在環型諧振器的拐角處有很大的傳播損失，所以基于六角格子的光子晶體設計這個儀器是很困難的8-12。最近，光子晶體表面光波導被認識到具有高效率的光波透射13-14。光子晶體表面波導制作在一個圓形光子晶體（CPC）結構的表面，通過消除來自CPC的一個同軸層而形成14。這個曲線型的波導被認為有高的能量透射因

4、為該波導帶有更光滑的彎曲具有中心對稱性和更小不連續性。與在傳統的具有六角晶格的光子晶體線缺陷波導相比，曲線形波導更容易利用去建立一個光子晶體環形諧振器。本文是設計基于六角晶格光子晶體表面模式的環型諧振器。對稱諧振濾波器是通過將一個SMRW夾進兩個平行的SMWs中而形成的。通過增加在六角晶格光子晶體介質和空氣間的桿排之間的半徑來獲得表面波導模式SMWs。環形波導表面模式SMRW是在圓形光子晶體CPC結構的表面上制作的，通過增加圓形光子晶體同軸圓最外層周長的那排半徑而得到。這個儀器通過對于完全吸收匹配層的所有邊界條件用有限時域差分法計算得到（FDTD）。和環型諧振器的其他表面模式相比3，這種基于六

5、角晶格光子晶體環型諧振結構有非常低的能量損失，輸入波導中的大部分光由于諧振轉移到輸出波導。該儀器結構簡單，提供了通道濾波器的可能性，并能用于未來波分復用光通信系統或其他領域。2、環型諧振器的設計我們認為在空氣背景中一個半無限六角晶格組成的靜電常數=11.6964和一個直徑為Db=0.392a圓柱狀的光子晶體，這里的a是晶格常數。正如圖1（a）所示，在相應的表面狀態下（增加最外層表面棒直徑至D=0.5a，并且兩個最近鄰表面桿滿足d=0.5a），對表面幾何形態進行研究。對光子晶體表面電磁光波的有效局限，必須滿足兩個條件：表面模式必須在光子帶隙中和在光線帶下的僅是表面模式的一部分作為考慮13。六角晶

6、格的光子晶體頻率在0.28481（c/a）與0.4557（c/a）范圍內TM偏振下有基本的禁帶，并且在圖1（a）所示的條件下，低于光線下存在兩種表面模式，其中是指光在真空中的波長。對于圖1（B）所示的結構，每個柱在其強度范圍內都有一個最大值并延伸到空氣中，當進入到有寬度為a的晶體中迅速衰減。對于圖1（b）所示增大柱表面的結構條件下，兩個表面模式主要分布在柱表面和其在空氣中的范圍內整個能量分布變化很小14。圖1（a）直徑為Db=0.392a和介電常數=11.6964桿形成六角晶格的光子晶體沿著投影表面模式的TM模能帶結構。表面柱直徑D = 0.5a，兩個最近鄰表面柱之間的距離是d= 0.5a。（

7、b）歸一化強度Ez部分表面模式的色散曲線。對于傳統的線缺陷曲線波導的光子晶體13，就像布拉格反射曲線鏡，光波被波導兩邊的光子禁帶所控制。然而，環型表面模式僅只有一側的波導周期結構。在SMRW中傳播的光波不得不改變他們的大小和方向向量。SMRW大的同心圓距離和小的曲率半徑導致波矢量在大小和方向上的突然改變。因此，光波可以更容易的輻射到周圍的空氣背景中。一個減少輻射損失的的方法是減低表面同心距離dc，然后波導具有了較高的表面有效折射率和高的限制因子。圖2（a）顯示一半SMRW，SMRW是通過增加表面棒的半徑到0.25a由最外層的同心層（即N=8）組成的，在最外層的最近鄰表面棒間的距離dc為0.48

8、87a。圖2（b）所示，一半SMRW的高功率傳輸，在dc=0.4887a和dc=0.6109a的透射率分別由粗細的實線來表示。前者比后者在工作頻率的改變下有更高的傳輸效率。這表明由于大的表面棒半徑和最近鄰表面棒之間的的小距離dc，在有高的表面有效折射率下有高的傳輸效率。圖2。（a） SMRW的一半，環型光子晶體晶胞結構原理圖。 （b） 一半SMRW在dc=0.4887a（薄黑線）和dc=0.6109a（厚黑線）處的透射譜。因此，在對稱諧振系統利用兩個平行波導設計SWMs如圖3（a）。這種結構通過在兩個平行的SMW之間夾一個SMW。SMRW是在環型光子晶體表面結構上制造的。圖3（a）所示二維圓柱

9、桿是直徑為0.392a和介電常數為11.6964的環型光子晶體結構，這些柱子有與上述提到的六角結構的光子晶體完全一樣的參數。這些環型光子晶體有鏡像對稱性，并且同心層之間的距離不變都是a。這種結構有六重對稱性，每層柱子的數目通過公式6（N-1）得到，這里的N表示層數，N2。通過消除環型光子晶體的一個同心層而形成SMRW。如圖3（a）所示在這里，最外層的同心層形成環型波導（即N=8）通過增加表面柱的半徑到0.25a，最外層最近鄰棒間的距離dc為0.4887a。正如圖3（a）所示的對稱諧振濾波器是基于光子晶體設計的。共振結構是通過夾在兩塊平行的SMWs中的SMW形成的。環共振器是通過一塊SMRW和兩

10、塊SMRW被獨立的用做輸入和輸出波導而實現的。為了認識到表面波導模式和環型表面波導模式之間的模式匹配，一般可以考慮兩種方法。一個是六角晶格光子晶體和環型光子晶體之間的參數是相似的，包括晶格常數之間的距離等于每個同心層和他們的背景圓柱棒有相同的半徑和折射率，很可能SMWs和SMRW模式匹配實現基于類似的晶體結構。另一種就要取決于設計SMRW和 SMWs，包括這些表面棒有相同的半徑和最近鄰表面柱之間的距離是一致的。在這種情況下，SMRWs和SMRW之間分別的距離為0.5a和0.4887a。類似的模式設計方便地降低表面波導的不匹配是很容易理解的方式。圖3。（a） 基于R=7a六角晶格組成的二維光子晶

11、體一個SMRW夾在兩個平行SMWs之間形成的環形諧振器的原理圖。（b） 當光從輸入波導端口A入射時能量在端口B、C、D的透射譜。 （c）頻率在0.4165（c/a）<f<0.4185（c/a）之間的能量透射譜。 （d） 當歸一化頻率f = 0.41735（c/a）時，諧振環內的電場分布。（e） 頻率在0.4275 （c/a）<f<0.43125 （c/a）之間的能量透射譜。（f） 當歸一化頻率f = 0.4294 （c/a）時，諧振環內的電場分布。標示在圖2（a）中的參數分別是R = 7 a、D = 0.5 a，D = 0.5 a，dc= 0.4887a ，gu= gb

12、 = 0.734a。在共振結構，傳統的共振微環中波導/環距離是相同的重要參數。諧振濾波器高效沒有實現是因為波導/環波導帶隙的不適當數值。正如圖3（a）所示，SMWs和SMRW之間的帶隙分別記為gu和gb。在這里，gu=gb=0.734a。值得注意的是，表面棒必須小心的安置在SMWs和SMRW之間的耦合區域內。在SMWs和SMRW之間的最近桿中心必須是在y軸，否則不能獲得SMWs模式和SMRW模式之間的良好的耦合。究其原因可能是是兩個表面模式節點與相應的耦合區域相一致，導致他們耦合現象的發生。當一個基本的TE模（電場區域垂直于x-y平面）被引入輸入波導，TE波將會與SMRW相耦合，并且激發基于這

13、些最外層同心圓波長表面棒的表面模式。在一定的頻率下，SMRW內的表面模式將會因為共振而增大，并且能量被轉移到輸出波導中。環的FSR（自由光譜帶）可以從以下公式中獲得： FSR= （1）這里c是光在空氣中的速度，neff是環的有效折射率，R是環的半徑。如圖3（a）所示，端口A作為光源發射端，三個時間檢測器檢測傳輸光波能量分別設置在端口B、C和D。然后，設計的裝置對在所有相應的將邊界有完全吸收條件下進行了有限差分法計算。歸一化能量傳輸光譜通過將端口B、C和D的能量總和作為總輸入的能量。圖3（b）描繪的傳輸譜諧振腔半徑的環R = 7 a，這里的能量傳輸端口B、C和D分別用厚實線，虛線，薄曲線表示。在

14、共振頻率下，絕大部分能量通過環諧振腔從輸入波導轉移到輸出波導。FSR的數值通常通過環諧振器傳輸光譜獲得。即FSR之間應滿足的相鄰兩個共振峰頻率間隔，在這里是0.00602（c/a）。所以根據方程（1）環的有效折射率neff是3.7768。圖3（c）描述的是頻率在0.4165（c/a）<f<0.4185（c/a）之間的能量傳輸譜。D端口的下降譜線不再是洛倫茲線性曲線是顯然的，這可能是因為在SMW和SMRW之間的模式不匹配引起的。諧振器有大約6474的品質因子，這是相對于其他類型的環諧振器最高的品質因子結果，可以通過增大環諧振器的半徑來改善品質因子。圖3（d）闡述了在環諧振腔半徑為環R

15、 = 7a ，頻率為f = 0.41735（c/a）電場分布。通過光波端口A在f = 0.41735（c/a）下，輸入波導被激活。SMRW條件下共振發生和絕大部分能量轉移到輸出波導。你可以看到，在SMRW的共振頻率下電磁場強烈增強。然而，在共振發生時有少量光輻射到周圍的空氣背景中，這導致波導表面模式的少量輻射損失。這些光波輻射在兩個平行SMWs之間反復地反射。從圖3（d）中得在兩個平行波導間有少量的能量分布在空氣背景中。圖3（e）顯示的是頻率在0.4275（c/a）<f<0.43125（c/a）之間的透視圖。有趣的是， 在端口C頻率f= 0.4294（c/a）前端支配下降了，對于傳

16、統的單微環共振結構后方下降共振的支配很明顯地不同。在某些頻率下，前端下降提高了，到目前為止具體機制還不了解。在這種情況下，在端口A入射波在只會產生順時針傳播的共振模式，并且入射波和其他逆時針傳播的模式沒有直接的耦合關系 15。然而，順時針和逆時針傳播的諧振模式由于相互耦合而相關。逆時針方向共振模式可以通過兩個共振模式之間的耦合關系改進，大部分的光波在端口C前端下降。圖3 （f）闡述了在半徑為環R = 7a，頻率f = 0.4294（c/a）的環諧振腔電場的分布。圖4。（a） 在R = 4a時環諧振器原理示意圖。（b）在R = 4 a時在端口B、C和D的透射譜。（c） 頻率在0.41 （c/a）

17、<f<0.4175 （c/a）之間的能量透射譜。 （d） 當歸一化頻率f = 0.41386 （c/a）時，諧振環內的電場分布。標示在圖3（a）中的參數分別為R =4a、D = 0.5 a，d = 0.5a，dc = 0.5027a和gu= gb = 0.644a。圖4（a）顯示了半徑R = 4 a的對稱諧振器原理圖，在最外層最近鄰表面柱之間的距離調整到dc= 0.5027，并且SMRW /SMW距離的改變到gu= gb = 0.644a。圖4（b）顯示的是在端口B、C和D的透射光譜，它們分別用厚實，點虛線形和薄實曲線表示。很明顯，從圖4（b）中得到FSR是0.01（c/a），對于

18、SMRW的有效折射率neff=3.979的。圖4（c）顯示的是頻率在0.41（c/a）<f<0.4175（c/a）之間的透射特性，諧振腔品質因子有1223左右。3、結論我們呈現了一個基于電介質PC的表面模式環諧振器的設計。如果在頻率f = 0.41386 （c/a）下波長是1550nm，晶格常數是641.5m，所以SMRW半徑為R = 4 a大約是2.5m。與環諧振器其他表面模式相比3，計算結果表明，環形諧振器有較小量的輻射損失的因為表面模式有很好的波導特性。這種結構提供了通道濾波器的可能性，并可用于未來光波分復用通信系統。4、鳴謝這項研究受到中國國家自然科學基金 （Nos.609

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24、ymp. 2009, 281, 119125DOI: 10.1002/masy.200950716119Latex Film Formation in the Environmental ScanningElectron MicroscopeKalin Dragnevski,*1 Athene Donald,1 Phil Taylor,2 Martin Murray,3 Simon Davies,3Elizabeth Bone3Summary: Environmental scanning electron microscopy (ESEM) was used to study the fil

25、m formation mechanisms and extent of coalescence of three acrylic latex com- positions with different glass transition temperatures (Tg), here defined as standard- low Tg, standard-high Tg (both carboxymethyl cellulose- stabilised) and novel (stabilised with a novel polysaccharide derived from agric

26、ultural waste). The ESEM analysis revealed that the microstructure of the standard low-Tg system consisted of individual particles in dispersion and upon evaporation a continuous film formed, whereas in the case of the standard - high Tg latex particle deformation was not observed, but particle aggr

27、egation resulted in the formation of crystal-like structures that have formed via the formation of stacking faults. However, in the case of the novel system the microstructure consisted of individual particles and clusters and during evaporation a discontinuous film formed with voids present within

28、its structure and some of the clusters accumulating on the surface of the specimens.Keywords: ESEM; film formation; polymer latexIntroductionPolymer latices, with their wide range of applications, have been the subject of many theoretical and experimental studies. When used for its traditional appli

29、cations, i.e. as paint or adhesive, the latex is applied in its wet state to a surface and allowed to dry and form film under ambient conditions. Therefore, conventional electron micro- scopy, with its extreme drying and sample preparation requirements, will not be suitable for the examination of la

30、tices in their natural wet state. On the other hand, environmental scanning electron micro-scopy1, which offers the possibility of1 Sector of Biological & Soft Systems, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge, CB30HE, UKE-mail: kd281cam

31、.ac.uk2 ICI Paints, Slough, Berkshire, SL2 5DS, UK3 ICI Wilton Applied Research Group, The WiltonCentre, Redcar, TS10 4RF, UKimaging wet and insulating specimens, has been successfully used in the study of a number of systems and dynamic processes including latices and film formation.26ESEM is based

32、 on the use of a multiple aperture graduated vacuum system, which allows specimens to be imaged under water vapour or other auxiliary gases, such as nitrogen or nitrous oxide.4 In this way, the chamber can be held at pressures usually in the range of 110 Torr7, while the gun and column remain at pre

33、ssures of 7.5 10 7 Torr. Moreover, by using acorrect pumpdown procedure8 and by controlling the temperature of the speci- men, which in the ESEM is usually done by using a Peltier stage, dehydration can be inhibited and hence samples can be imaged in their natural state. Furthermore, bytaking into c

34、onsideration the saturated vapour pressure (SVP) curve for water as a function of temperature8 and by increas- ing the temperature of the specimen or reducing the chamber pressure, it is possi-Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim120Macromol. Symp. 2009, 281, 119125Figure 1.S

35、chematic representation of an idealized film formation process. Adapted from Keddie et al. to include the intermediate Stage II .ble to produce evaporation conditions within the specimen chamber, which allows examination of the process of film forma- tion.As mentioned above, polymer latices are impo

36、rtant industrial products and the subject of many research studies. Latex, which is an example of a wet insulating material, can be defined as a colloidal suspension of spherical polymer particles with varying diameters. When water is allowed to evaporate from the system, the aqueous suspension unde

37、rgoes a series of transformations, which result in the forma- tion of a continuous dry polymer film. This process, known as film formation, contains four main stages that can be described asfollows:917 Stage I dispersed suspensionof polymer particles; Stage II concen- trated suspension of particles

38、in contact with each other, surrounded by solvent- filled interstices; Stage III ordered array of deformed particles; Stage IV a molecularly continuous and homogeneous film formed as a result of polymer interdiffusion.In 1995, Keddie et al. 4 used environ-mental scanning electronmicroscopy (ESEM) an

39、d Multiple-Angle-of-Incidence Ellipsometry (MAIE) in the study of latex film formation. They concluded that an intermediate stage, between II and III, has been omitted in the conventionaldescriptions.917 The stage, defined as II , is characterized by a randomly packed array of deformed particles whi

40、ch still contain water-filled interstices. A schematic representation of the process is shown in Figure 1.More recently, Keddie et al.18,19 inves-tigated the possibility of creating hetero- geneous films, by mixing carbon nanotubes (CNTs) with waterborne polymer particles. It was found that the mech

41、anical properties of the nanocomposite coatings can be greatly improved, while maintaining their optical clarity. However, it is important to note that all of the above studies were carried out using continuous polymer films.In this paper we present the results from an ESEM investigation into the fi

42、lm for- mation mechanisms of novel acrylic latex, which has been stabilised by using a new polysaccharide, derived from agricultural waste, and two standard polymer systems, where the conventional carboxymethyl cellulose (CMC) has been used as a stabiliser. The novel polysaccharide con- sists of a n

43、umber of monosaccharides (including arabinose and xylose) formed from five- and six-membered rings and has a low molecular weight, only a few thousand a.m.u.s rather than the hundreds of thousands found in cellulose for exam- ple. The polysaccharide also contains aCopyright 2009 WILEY-VCH Verlag Gmb

44、H & Co. KGaA, Weinheimwww.ms-journal.deMacromol. Symp. 2009, 281, 119125121significant amount of interfacially active protein 15%. It is suggested that the initial latex particle stabilization comes from the protein component and ultimately the polysaccharide component stabilises the latex parti

45、cles by adsorbing on their surface, rather than by chemically grafting on the growing polymer particles, which is the case for the conventionally used CMC. Initial examinations20 have indicated that the novel latex can form film without theaddition of coalescing solvents, which, as suggested above,

46、on one hand would provide an alternative method for the production of VOC-free architectural coat- ings and, on the other, would comply with the stringent EU and DEFRA regula- tions.21Materials and MethodsThree aqueous latex compositions, sup- plied by ICI Plc, based on copolymers of methyl methacry

47、late (MMA) and 2-ethyl- hexyl acrylate (2-EHA) were studied. In this paper the latices stabilised with carbox- ymethyl cellulose (CMC) will be referred to as standard-low and high Tg; the other stabilised with the new polysaccharide as novel. The three latices were initially about55 wt% polymer. The

48、 glass transition temperatures (Tg) of latices were deter- mined by differential scanning calorimetry (DSC), carried out on dry specimens, using a Perkin Elmer Pyris 1 instrument. The measured temperatures were 274 K for the standard-low Tg, 328 K for the standard- high Tg and 280 K for the novel la

49、tex.The microstructural analysis was carriedout on an FEI XL-30 environmental scanning electron microscope equipped with a Peltier stage. Wet samples from the above formulations were placed onto the cooling stage in the microscope chamber at a temperature of ca. 274 K. Anevaporation-inhibitingpumpdo

50、wn sequence was then performed, with the ambient air progressively replaced by water vapour. Once the purging cycle was com- pleted, water vapour pressures and workingdistances of 3.54.5 Torr and 9.511.5 mm were set, which provided optimal imaging environments, i.e. sufficient resolution and minimal

51、 beam damage. Imaging of the specimens was carried out at an accelerat- ing voltage of 10 kV. Increasing the tem- perature of the specimens by 1 or 2 degrees above the starting temperature of 273 K, as explained above, resulted in further dehydration of the latices, which allowed examination of the

52、process of film formation.Results and DiscussionPrior to considering the results from the ESEM examination, it is important to note that when we refer to latices as being wet, some water has in actual fact been removed from the surface of the specimens in order to obtain better quality images. Keddi

53、e et al.1,4 used a similar approach in the study of latex film formation by means of ESEM. It was found that despite the fact that some of the surface water had been removed, the bulk of the samples remainedwet.Standard Latex low TgFrom the ESEM images of the standard- low Tg latex (Figure 2), it ca

54、n be seen that under wet conditions (Figure 2a) the microstructure of the specimen consists mainly of randomly distributed individual particles with an average size of ca. 300 nm. Due to the fact that some of the water has already been removed, as explained above, some of the polymer particles are i

55、n contact. Despite that, they are still physi- cally distinct, i.e. no significant deformation has occurred, and therefore it can be concluded that the latex is in Stage II/II . By increasing the temperature of the specimen (Figure 2b), water evaporation takes place, which resulted in the formation of a continuous polymer film. However, due to the fact that not all particles have lost their identity and boundaries are still clearly vi