基于matlab的光学薄膜特性分析

1技术指标 12基本原理 12.1单层光学薄膜 12.2多层光学薄膜及矩阵理论 23基于matlab的光学薄膜特性分析 44结论 95参考文献 96附录：基于matlab的光学薄膜特性分析源程序代码 1技术指标对光学薄膜的理论进行分析，从电磁理论出发分析单层膜和性；并分析各参数对其光学性能的影响；运用Matlab对单层介质薄膜和多层介质薄膜的光学特性进行仿真；编写可用于一般多层膜的图形用户界面，并利用该程序对几种典型的2基本原理光射到任何一个光学零件的表面上都要发生反射和折射，不同的光学系统对反射率和薄膜光学发展至今，已经形成一套比较完整的实用理论。本文将利用多光束的干涉理论和矩阵理论，并运用matlab对薄膜光学系统的光学性质做简要分析。加将会发生多光束干涉。利用已有的结果，可得反射光叠加后的合震动的复振幅式中，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是两相邻光束之间的相位差武汉理工大学《能力拓展训练》报告书2而反射率2.2多层光学薄膜及矩阵理论在界面1E₁=E+E=E+E₂H₁=Hcosθ₁-Hcosθ=Hcosθ₂-H₂cosO₂取μ=Lo则9在界面2E₂=E₂+E,₂=E3E₂=Eexp(iδ)E₂=E₂exp(iδ平面波通过薄膜一次A,B两点的位相变当膜系包含N层膜时，则有整个膜系的特征矩阵M=M₁M₂…Mx。令M的矩阵元为A,B,C,D即4膜系反射系数膜系透射系数薄膜结构。利用传输矩阵计算光在介质薄膜。本文中所选取的色散材料，如[11,12],LiF(模型中的A层)的折射率在1.25～2.35μm范围内的关系为：n=1.38761+0.001796L-0.00041L²-0.0023045d²-0.00000557a⁴Si(模型中的B层)的折射率在同一波段为：n=3.41696+0.138497L+0.013924L²-0.0000209λ²+0.000000148λ⁴其中L=1/λ²-0.028。3基于matlab的光学薄膜特性分析matlab是一种以矩阵运算为基础的交互式程序语言，广泛应用于自动控制、数学运算、信号分析、航天工业和绘图等各行各业.本文使用Matlab计算膜系特征矩阵，进行数值的武汉理工大学《能力拓展训练》报告书5运算仿真研究与验证。仿真模拟的光学特性matlab程序见附录。图(c)光学特性分析的GUI交互界面图(d)单膜反射率和透射率与入射波长的关系(正入射)6图(e)单膜反射率和透射率与入射波长的关系(斜入射)图(f)多膜反射率和透射率与入射波长的关系(正入射)武汉理工大学《能力拓展训练》报告书7图(g)单膜反射率和透射率与入射波长的关系(斜入射)图中，纵坐标表示反射率和透射率，其中，红实线表示反射率，蓝虚线表示透射率，二者之和等于1。横坐标则表示入射光的波长(um)。从图中分别对比分析知，对于一个介质折射率和厚度固定等参数固定的薄膜系统，其反射率或透射率达到最大值的时候所对应的这一固定波长称为中心波长，当入射光偏离中心波长的时候，其反射率必定会相应的下降，因此，每一种具体的膜系，只对一定波长范围的光波才能有反射率。以上各图反射率最大值(接近于1)时所对应的波长范围称为反射带的宽度。8图(h)8层膜(偶数)系反射率和透射率与波长的关系图(i)9层膜(奇数)系反射率和透射率与波长的关系从上面两个图对比可知，在同一波长情况下，奇数层膜的反射率要比偶数层反射率略高。这是因为，膜系第一层的折射率高于第二层折射率，如果膜系为奇数层，那9么最后一层的折射率也是高反射率层。层数为2m+1时，4结论由上述的计算公式可知，光学薄膜的特性计算在引入矩阵理论后成为一个相对简单的问题，只要给定每一层膜系的参数，多层膜就可以利用矩阵的连乘方便地求出在每一特定入射角和波长下的透射率、反射率等参数.许多计算机软件的出现，能方便进行自动数值计算，如matlab软件的应用，不仅能计算并保存数据，而且更好地调用资源，作图、仿真模拟使得研究清晰明了，易于操作理解，为光学薄膜的研究提供了有利的计算工具.因此，计算机软件的应用促进了光学薄膜的发展，它与传统的理论研究相辅相成，是理论应用与实践的有力保障，使光学薄膜的发展迈上了新的台阶.光学薄膜已经在光学技术发展的历史中创造了光辉的成绩，如今广泛地渗透到各个新型的科技领域.各种新型微结构的功能薄膜正在不断开发出来，并造福于人类.[1]廖延彪.光学原理与应用.电子工业出版社.2006.10武汉理工大学《能力拓展训练》报告书6附录：基于matlab的光学薄膜特性分析源程序代码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{:});武汉理工大学《能力拓展训练》报告书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);武汉理工大学《能力拓展训练》报告书%---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武汉理工大学《能力拓展训练》报告书%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');武汉理工大学《能力拓展训练》报告书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)武汉理工大学《能力拓展训练》报告书%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)%以下为计算模拟输出的主程序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