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1、1,R& D dept. /Andy Yu,Fundamentals Of Optical Coating & Application,2,Newton(1666年) -光的微粒說(Corpuscular theory),光是由發光物體發射出來的,以非常微小的粒子做高速運動 用微粒說解釋光在均勻介質中的直線傳播,光在界面上的反射,折射;確無法解釋光的繞射,干涉,偏振現象,Huygens(1679年)-波動說(wave theory),光是在整個空間介質ether中傳播的某種彈性波,用波動說解釋光的傳播速度;用波動說推出反射定律與折射定律,並解釋方解石的雙折射現象,發現了光的偏振現象,Young
2、(1801年)-楊氏雙狹縫干涉實驗,出現明暗相間的條紋(微粒說無法解釋) (波動說確可圓滿解釋),光是甚麼?,3,S,S1,S2,M,r1,r2,D,P,x,O,=r2-r1 (波程差) d sin=(2k-1)/2,d,(相差 ) =2/=2k k=0,1,2,3,兩束光在P點振幅最大,形成明亮條紋,(相差 ) =2/=(2k-1) k=0,1,2,3,兩束光在P點振幅最小,形成暗紋,楊氏雙狹縫干涉,4,光的干涉,Constructive interference, R increased,Destructive interference, R decreased,兩列頻率,振幅及振動方向相
3、同,但傳播方向相反的波,疊加形成駐波(Standing Wave),對光波來說,滿足一定條件的兩束光疊加時,在疊加區域,光的強度或明暗有一穩定分佈,5,RF,Video Frequency,Micro Wave,Infra Red,Visible,UV,X-Ray,-Ray,/Hz,/m,104,108,1012,1016,1020,3104,3100,310-4,310-8,310-12,400760nm 1014 1015 Hz,760nm6 104nm 1012 1014 Hz,電磁波譜,6,薄膜光學 (Thin Film Optics),光學薄膜是一種用於改變光波傳遞特性的光學元件,光
4、學薄膜是由特定光學常數和厚度的分層介質所組成,薄膜光學的理論基礎是干涉光學(Interference),光束將在每一個界面 上多次反射,因此涉及到大量光束疊加問題;有效的計算方法: (1)矩陣法 (2)等效導納遞推法-將所有膜層等效成一個界面,用總的反射反射係數和位相來表示 理想的光學薄膜:,(1) 光學薄膜層與層之間相互平行 (2) 介面光滑且界線分明,7,a,ar,atrt,Atr3t,Atr5t,Atr7t,atr,Atr3,Atr5,Atr7,at,Atr2,Atr4,Atr6,d,att,Attr2,Attr4,Attr6,1,2,3,4,5,1,2,3,4,薄膜干涉,透射光振幅,反
5、射光振幅,炫麗的彩色膜,因薄膜的兩個表面反射光互相干涉而產生的,8,Optical Admittance Y(光導納)=H/E(電磁波的磁場與電場之比) Y=N Yo=(n-ik) Yo Yo (自由空間之導納),單層光學薄膜的特徵矩陣:,cos i sin /Y iY sin cos ,I=,-1,(相厚度 phase thickness)=2 nd cos/ D=膜層的幾何厚度,Ea Ha,=,Eb Hb,薄膜的特徵矩陣,9,cos i sin /N iN sin cos ,B C,=,1 Ns,Quarter wave (1/4)o = /2,M=,0 i/N iN 0,Half wav
6、e (1/2)o = ,1 0 0 1,M=,Absentee layer,Y(光導納)=H/E(電磁波的磁場與電場之比)=C/B,1 Ns,NE=C/B= N2/Ns,1 Ns,10,Equivalent admittance(等效導納)YE=C/B B和C分別正比於電場(E)及磁場(B),反射光振幅 (amplitude of reflection coefficient) =Er/Ei =(Y0-Y1 ) /(Y0+Y1 ) = (N0-N1 ) / (N0+N1 ),反射率 R= = (Y0-Y1/Y0+Y1 )2 R=(N0-N1 ) / (N0+N1 ) 2,(Er/Ei ;反射強
7、度與入射強度之比),For dielectric Ns=ns e.g BK7 ns=1.52 R=(n0-n1 ) / (n0+n1 ) 2=4.26%,For metal Ns=ns-iks Ns=0.82-i5.99 550nm R=(n0-n1 ) 2+k 2 / (n0+n1 ) 2+k 2 ) =91.6%,11,穿透光振幅 (amplitude of transmission coefficient),穿透率T=4 0 s / ( 0 B + C) ( 0 B + C),=Et/Ei =2Y0 /(Y0+Y1 ) =2 N0/ (N0+N1 ) =20 / 0 B + C,T=4
8、n0 n s /(n0 +n s )2,1 = T + R +L(S+A),12,n1,n2,n3,n1-n2,n1+n2,n2-n3,n2+n3,=,Single Layer ARC,若薄膜的兩個表面光振幅相等,相位相反,則兩反射光相互抵消,透射光就增強了,n2 = (n1n3)1/2,n1 =1, n3 =1.5,n2=1.225,13,y0,y1,y21/ysub,ysub,Without ARC R=(y0-ys ) / (y0+ys ) 2 BK7=1.52 =(1-1.52)/1+1.52) 2 =4.26%,Without ARC,14,Single Layer ARC R=(y
9、0-y12/ysub)/ (y0+y12/ysub)2 Idea ARC ,R=0, y0-y12/ysub=0, y1=(y0ysub)1/2 y0 =1.0 Air, ysub =1.52 y1 =1.23,R=(y0-y2f/ys)/ (y0+y2f/ys)2 R=(1.00-1.382/1.52)/ (1.00+1.382/1.52) R=1.23%,15,yH=y5,yH=y3,yH=y1,yL=y4,yL=y2,y2Hy2Hy2H y2Ly2Lysub,yo,ysub,Y1=y2H/ y sub,Y2=y2L/ Y1 = y2L ys/y2H,Y3=y2H/ Y2 = y4H/ y
10、2Lys,y21y23y25 y22y24ys,Odd layer,y0yE y0yE,=,等效導納(遞推法),16,nair,nL,nH,nS,1,2,3,Nair,nL nH,光疏介質進入光密介質;相位變化為,1,2,3,合向量,2-Layer ARC,nHns 光密介質進入光疏介質; 相位沒有變化,HL雙層減反射膜,反射率可降至0.05%以下,17,2.352,1.452,1,2,1.52,N=1.38,n=2.2,0.5,0,1.522+2.22,21.52,1+1.382,2 1,圓心2.352=,圓心1.452=,通過(1.52,0),通過(1,0),導納軌跡圖,18,ARC wi
11、th Two Layer R=(y0-y12ysub/y22)/ (y0+y12 ysub/y22) Idea ARC R=0, y0- y12ysub/y22 =0; y12/y22=y0/ ysub Y2=y1 (ys/y0) 1/2=(1.38 1.23) 1/2 y2=1.7,R=(y0-y12ysub/y22)/ (y0+y12 ysub/y22) R=(1.00-1.382 1.52/1.72)/ (1.00+ 1.382 1.52/1.72) =(1-1.00162) /(1+1.00162) =0.81%,19,High Reflected Mirror,20,High Ref
12、lection Mirror,ys/HLHLHLHLH.H/ y0= ys/ (HL)PH/ y0,yE =yH 2(p+1) /= yL 2p ys,R= (y0 -yE / y0+ yE ) 2,ys =1.52, yH =2.3,yL=1.46,yo=1 ,p=8 R=?,99.92%,g=4/Sin-1(yH - yL/yH + yL) G=0/ = g/g=170nm,21,High Reflection Mirror,22,High Reflection Mirror,23,S 分量,P分量,稜鏡偏振鏡:1.65/(HL)5 H/1.65 0=500nm,=45,24,25,W=R
13、+G+B M=R+B Y=R+G C=G+B,C=W-R Y=W-B M=W-G,Color(加法三原色),26,Color(減法三原色 ),C*Y*M=BL R=Y*M G=Y*C B=M*C,27,Dichroic Mirror,28,COLOR：,RED Wavelength 50%：632nm,YELLOW Wavelength 50%：530nm,Color Filter,29,COLOR：GREEN Wavelength 50%：494/554nm,BLUE Wavelength 50%：515nm,30,COLOLIGHT BLUE Wavelength 50%：546nm,PU
14、RPLE Wavelength 50%：469/644nm,31,COLPINK Wavelength 50% 452/621nm,COLOR：LIGHT PINK Wavelength 50%：487/578nm,32,Incident Ray,Reflected Ray,Refracted or Transmitted Ray,S,S,S,P,P,P,Surface,Ns = cos Np= /cos ,Oblique incidence,1,0,0, Is given by Snells law,P偏振光(TE偏振光)-電場平行於入射平面的偏振光,S偏振光(TM偏振光)-電場垂直於入射平
15、面的偏振光,33,Rs,Tp,=45,n0,nH,nL,nH,nL,n0,n0,n0,MacNeille PBS,H,H,L,PBS偏振分光鏡,隨入射角增加,P偏振光高低折射率比nH/ nL愈來愈小,S偏振光高低折射率比愈來愈大,造成/4膜堆P偏振光和S偏振光之高反射區,使P偏振光愈來愈窄S偏振光愈來愈寬;出現S偏振光R很大P偏振光R很小的波域,34,利用 Brewster angle B ,RP=0 , P偏振光之反射為0,H =nH/cos H= L =nL/cos L,Sin2 H=nL2/(nH+nL), tan H = nL/ nH,nHsin H=nLsin L,依 Snells law,當Prism AOI=45, sin H=ngsin 45 / nH,ng2=2nH2nL2/ (nH2 +
