基于matlab的光學(xué)薄膜特性分析

1技術(shù)指標(biāo) 12基本原理 12.1單層光學(xué)薄膜 12.2多層光學(xué)薄膜及矩陣?yán)碚?23基于matlab的光學(xué)薄膜特性分析 44結(jié)論 95參考文獻(xiàn) 96附錄：基于matlab的光學(xué)薄膜特性分析源程序代碼 1技術(shù)指標(biāo)對(duì)光學(xué)薄膜的理論進(jìn)行分析，從電磁理論出發(fā)分析單層膜和性；并分析各參數(shù)對(duì)其光學(xué)性能的影響；運(yùn)用Matlab對(duì)單層介質(zhì)薄膜和多層介質(zhì)薄膜的光學(xué)特性進(jìn)行仿真；編寫可用于一般多層膜的圖形用戶界面，并利用該程序?qū)追N典型的2基本原理光射到任何一個(gè)光學(xué)零件的表面上都要發(fā)生反射和折射，不同的光學(xué)系統(tǒng)對(duì)反射率和薄膜光學(xué)發(fā)展至今，已經(jīng)形成一套比較完整的實(shí)用理論。本文將利用多光束的干涉理論和矩陣?yán)碚?，并運(yùn)用matlab對(duì)薄膜光學(xué)系統(tǒng)的光學(xué)性質(zhì)做簡(jiǎn)要分析。加將會(huì)發(fā)生多光束干涉。利用已有的結(jié)果，可得反射光疊加后的合震動(dòng)的復(fù)振幅式中，r,是薄膜表面上的反射振幅比，r,是下表面的反射振幅比，δ是兩相鄰光束之間的相位差武漢理工大學(xué)《能力拓展訓(xùn)練》報(bào)告書2而反射率2.2多層光學(xué)薄膜及矩陣?yán)碚撛诮缑?E?=E+E=E+E?H?=Hcosθ?-Hcosθ=Hcosθ?-H?cosO?取μ=Lo則9在界面2E?=E?+E,?=E3E?=Eexp(iδ)E?=E?exp(iδ平面波通過薄膜一次A,B兩點(diǎn)的位相變當(dāng)膜系包含N層膜時(shí)，則有整個(gè)膜系的特征矩陣M=M?M?…Mx。令M的矩陣元為A,B,C,D即4膜系反射系數(shù)膜系透射系數(shù)薄膜結(jié)構(gòu)。利用傳輸矩陣計(jì)算光在介質(zhì)薄膜。本文中所選取的色散材料，如[11,12],LiF(模型中的A層)的折射率在1.25～2.35μm范圍內(nèi)的關(guān)系為：n=1.38761+0.001796L-0.00041L2-0.0023045d2-0.00000557a?Si(模型中的B層)的折射率在同一波段為：n=3.41696+0.138497L+0.013924L2-0.0000209λ2+0.000000148λ?其中L=1/λ2-0.028。3基于matlab的光學(xué)薄膜特性分析matlab是一種以矩陣運(yùn)算為基礎(chǔ)的交互式程序語言，廣泛應(yīng)用于自動(dòng)控制、數(shù)學(xué)運(yùn)算、信號(hào)分析、航天工業(yè)和繪圖等各行各業(yè).本文使用Matlab計(jì)算膜系特征矩陣，進(jìn)行數(shù)值的武漢理工大學(xué)《能力拓展訓(xùn)練》報(bào)告書5運(yùn)算仿真研究與驗(yàn)證。仿真模擬的光學(xué)特性matlab程序見附錄。圖(c)光學(xué)特性分析的GUI交互界面圖(d)單膜反射率和透射率與入射波長的關(guān)系(正入射)6圖(e)單膜反射率和透射率與入射波長的關(guān)系(斜入射)圖(f)多膜反射率和透射率與入射波長的關(guān)系(正入射)武漢理工大學(xué)《能力拓展訓(xùn)練》報(bào)告書7圖(g)單膜反射率和透射率與入射波長的關(guān)系(斜入射)圖中，縱坐標(biāo)表示反射率和透射率，其中，紅實(shí)線表示反射率，藍(lán)虛線表示透射率，二者之和等于1。橫坐標(biāo)則表示入射光的波長(um)。從圖中分別對(duì)比分析知，對(duì)于一個(gè)介質(zhì)折射率和厚度固定等參數(shù)固定的薄膜系統(tǒng)，其反射率或透射率達(dá)到最大值的時(shí)候所對(duì)應(yīng)的這一固定波長稱為中心波長，當(dāng)入射光偏離中心波長的時(shí)候，其反射率必定會(huì)相應(yīng)的下降，因此，每一種具體的膜系，只對(duì)一定波長范圍的光波才能有反射率。以上各圖反射率最大值(接近于1)時(shí)所對(duì)應(yīng)的波長范圍稱為反射帶的寬度。8圖(h)8層膜(偶數(shù))系反射率和透射率與波長的關(guān)系圖(i)9層膜(奇數(shù))系反射率和透射率與波長的關(guān)系從上面兩個(gè)圖對(duì)比可知，在同一波長情況下，奇數(shù)層膜的反射率要比偶數(shù)層反射率略高。這是因?yàn)?，膜系第一層的折射率高于第二層折射率，如果膜系為奇?shù)層，那9么最后一層的折射率也是高反射率層。層數(shù)為2m+1時(shí)，4結(jié)論由上述的計(jì)算公式可知，光學(xué)薄膜的特性計(jì)算在引入矩陣?yán)碚摵蟪蔀橐粋€(gè)相對(duì)簡(jiǎn)單的問題，只要給定每一層膜系的參數(shù)，多層膜就可以利用矩陣的連乘方便地求出在每一特定入射角和波長下的透射率、反射率等參數(shù).許多計(jì)算機(jī)軟件的出現(xiàn)，能方便進(jìn)行自動(dòng)數(shù)值計(jì)算，如matlab軟件的應(yīng)用，不僅能計(jì)算并保存數(shù)據(jù)，而且更好地調(diào)用資源，作圖、仿真模擬使得研究清晰明了，易于操作理解，為光學(xué)薄膜的研究提供了有利的計(jì)算工具.因此，計(jì)算機(jī)軟件的應(yīng)用促進(jìn)了光學(xué)薄膜的發(fā)展，它與傳統(tǒng)的理論研究相輔相成，是理論應(yīng)用與實(shí)踐的有力保障，使光學(xué)薄膜的發(fā)展邁上了新的臺(tái)階.光學(xué)薄膜已經(jīng)在光學(xué)技術(shù)發(fā)展的歷史中創(chuàng)造了光輝的成績，如今廣泛地滲透到各個(gè)新型的科技領(lǐng)域.各種新型微結(jié)構(gòu)的功能薄膜正在不斷開發(fā)出來，并造福于人類.[1]廖延彪.光學(xué)原理與應(yīng)用.電子工業(yè)出版社.2006.10武漢理工大學(xué)《能力拓展訓(xùn)練》報(bào)告書6附錄：基于matlab的光學(xué)薄膜特性分析源程序代碼functionvarargout=untitled(varargin)%UNTITLEDM-fileforuntitled.f%UNTITLED,byitself,createsanewUNTITLEDorraisestheexisting%%H=UNTITLEDreturnsthehandletoanewUNTITLEDorthehandleto%theexistingsingleton*.%%UNTITLED(CALLBACK',hObject,eventData,handles,…)callsthelocal%functionnamedCALLBACKinUNTITLED.Mwiththegiveninputarguments.%%UNTITLED('Property',Value',…)createsanewUNTITLEDorraisesthe%appliedtotheGUIbeforeuntitled_OpeningFunctiongetscalled.An%unrecognizedpropertynameorinvalidvaluemakespropertyapplication%stop.Allinputsarepassedtountitled_OpeningFcnviavarargin.%%instancetorun(singleton)".%%Seealso:GUIDE,GUIDATA,GUIHANDLES%Copyright2002-2003TheMathWorks,Inc.%Edittheabovetexttomodifytheresponsetohelpuntitled%LastModifiedbyGUIDEv2.525-Aug-201112:50:11gui_Singleton=1;gui_State=struct('gui_Name',mfilename,.'gui_Singleton',gui_Singl'gui_OpeningFcn',@untitled_OpeningFcn,…gui_OutputFcn',@untitled_OutputFcn,…ifnargin&&ischar(varargin{1})gui_State.gui_Callback=str2func(varargin{1});ifnargout[varargout{1:nargout}]=gui_mainfcn(gui_State,varargin{:});武漢理工大學(xué)《能力拓展訓(xùn)練》報(bào)告書gui_mainfcn(gui_State,varargin{:});%---Executesjustbeforeuntitledismadevisible.functionuntitled_OpeningFcn(hObject,eventdata,handles,varargin)reserved-tobedefinedinafutureversionofMAstructurewithhandlesanduserdata(seeGUIDATA)commandlineargumentstountitled(seeVARARGIN)%Choosedefaultcommahandles.output=hObject;guidata(hObject,handles);%UIWAITmakesuntitledwaitforuserresponse(seeUIRESUME)%uiwait(handles.figurel);functionvarargout=untitled_OutputFcn(hObject,eventdata,handles)%hObjecthandletofigure%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstruvarargout{1}=handles.output;functionedit1_Callback(hObject,eventdata,handles)reserved-tobedefinedinafutureversionofMAstructurewithhandlesanduserdata(seeGUIDATA)%Hints:get(hObject,'String)returnscontentsofeditlastext%str2double(get(hObject,'String))returnscontentsofedit1asadouble=str2num(get(hObject,String));if(isempty(input))guidata(hObject,handles);武漢理工大學(xué)《能力拓展訓(xùn)練》報(bào)告書%---Executesduringobjectcreation,aftersettingallproperties.functionedit1_CreateFcn(hObject,eventdata,handles)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesempty-handlesnotcreateduntilafterallCreateFcnscalled%Hint:editcontrolsusuallyhaveawhitebackgroundonWindows.%SeeISPCandCOMPUTERifispcset(hObject,'BackgroundColor','white');set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));functionedit2_Callback(hObject,eventdata,handles)%hObjecthandletoedit2(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)%Hints:get(hObject,'String)returnscontentsofedit2astext%inputstr2double(get(hObject,String))returnscontentsofedit2asadouble=str2num(get(hObject,'String'));if(isempty(input))set(hObject,'String','0')guidata(hObject,handles);%---Executesduringobjectcreation,aftersettingallproperties.functionedit2_CreateFcn(hObject,eventdata,handles)%hObject%eventdata%handleshandletoedit2(seeGCBO)reserved-tobedefinedinafutureversionofMATLABempty-handlesnotcreateduntilafterallCreateFcnscalled%Hint:editcontrolsusuallyhaveawhitebackgroundonWindows.%SeeISPCandCOMPUTER.ifispcset(hObject,'BackgroundColor',white');set(hObject,BackgroundColor',get(0,defaultUicontrolBackgroundColor'));functionedit3_Callback(hObject,eventdata,handles)%hObjecthandletoedit3(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)%Hints:get(hObject,'String)returnscontentsofedit3astext武漢理工大學(xué)《能力拓展訓(xùn)練》報(bào)告書%str2double(get(hObject,String))returnscontentsofediinput=str2num(get(hObject,'String'));if(isempty(input))set(hObject,'String','guidata(hObject,handles);%---Executesduringobjectcreation,aftersettingafunctionedit3_CreateFcn(hObject,eventdata,handles)reserved-tobedefinedinafutureversionofMATL%Hint:editcontrolsusuallyhaveawhitebackgroundonWindows.ifispcset(hObject,'BackgroundColor','white');set(hObject,'BackgroundColor',get(0,defaultUicontrolBackgroundColor'));functionedit4_Callback(hObject,eventdata,handles)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDA%Hints:get(hObject,'String)returnscontentsofedit4astext%str2double(get(hObject,'String'))returnscontentsofedit4asadoubleinput=str2num(get(hObject,'String));if(isempty(input))guidata(hObject,handles);%---Executesduringobjectcreation,aftersettingafunctionedit4_CreateFcn(hObject,eventdata,handles)%hObjecthandletoedit4(seeG%eventdatareserved-tobedefinedinafutureversionofMAT%Hint:editcontrolsusuallyhaveawhitebackgroundonWindows.ifispcset(hObject,BackgroundColor','white');武漢理工大學(xué)《能力拓展訓(xùn)練》報(bào)告書set(hObject,BackgroundColor',get(0,defaultUicontrolBackgroundColor'));functionedit5_Callback(hObject,eventdata,handles)%hObjecthandletoedit5(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)%Hints:get(hObject,'String)returnscontentsofedit5astext%inputstr2double(get(hObject,'String))returnscontentsofedit5asadouble=str2num(get(hObject,'String'));if(isempty(input))set(hObject,'String,'O')guidata(hObject,handles);%---Executesduringobjectcreation,aftersettingallproperties.functionedit5_CreateFcn(hObject,eventdata,handles)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesempty-handlesnotcreateduntilafterallCreateFcnscalled%Hint:editcontrolsusuallyhaveawhitebackgroundonWindows.ifispcset(hObject,'BackgroundColor',white');set(hObject,BackgroundColor',get(0,defaultUicontrolBackgroundColor'));functionedit6_Callback(hObject,eventdata,handles)%hObjecthandletoedit6(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)%Hints:get(hObject,String)returnscontentsofedit6astext%inputstr2double(get(hObject,'String))returnscontentsofedit6asadouble=str2num(get(hObject,'String'));if(isempty(input))set(hObject,'String','O')guidata(hObject,handles);%---Executesduringobjectcreation,aftersettingallproperties.functionedit6CreateFcn(hObject,eventdata,handles)武漢理工大學(xué)《能力拓展訓(xùn)練》報(bào)告書%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesempty-handlesnotcreateduntilafterallCreateFcnscalled%Hint:editcontrolsusuallyhaveawhitebackgroundonWindows.%SeeISPCandCOMPUTER.ifispcset(hObject,'BackgroundColor',get(0,defaultUicontrolBackgroundColor'));%---Executesonbuttonpressinpushbutton1.functionpushbutton1_Callback(hObject,eventdata,handles)%hObjecthandletopushbutton1(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)%以下為計(jì)算模擬輸出的主程序nO=1;n1=get(handles.edit1,'String);n1=str2num(n1);n2=get(handles.edit2,'String);n2=str2num(n2);n=get(handles.edit6,'String);n=str2num(n);thetal=get(handles.edit5,'String');thetal=str2num(thetal);d1=get(handles.edit4,'String');d1=str2num(d1);d1=d1*1e-6;d2=get(handles.edit3,'String');d2=str2num(d2);forlambda=1250:2350;theta2=asin(n0*sin(thetal)/n1);theta3=asin(n0*sin(theta2)/n2);delta1=2*pi*n1*d1/cosdelta2=2*pi*n2*d2/cos(m=sqrt(144*pi^2*100);eta0=n0*cos(thetal)/m;eta