薄膜光学-基础讲义

R&Ddept./AndyYuFundamentalsOfOpticalCoating&Application1Newton(1666年)-光的微粒說(Corpusculartheory)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(wavetheory)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(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?2SS1S2M

r1r2DPxO=r2-r1(波程差)dsin=(2k-1)/2d

(相差)=2/=2kk=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3光的干涉Constructiveinterference,RincreasedDestructiveinterference,Rdecreased兩列頻率,振幅及振動方向相同,但傳播方向相反的波,疊加形成駐波(StandingWave)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4RFVideoFrequencyMicroWaveInfraRedVisibleUVX-Ray-Ray/Hz/m10410810121016102031043100310-4310-8310-12400~760nm1014~1015Hz760nm~6104nm1012~1014Hz電磁波譜5薄膜光學(ThinFilmOptics)光學薄膜是一種用於改變光波傳遞特性的光學元件光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6aaratr’t’Atr’3t’Atr’5t’Atr’7t’atr’Atr’3Atr’5Atr’7atAtr’2Atr’4Atr’6datt’Att’r’2Att’r’4Att’r’6123451‘2‘3‘4‘薄膜干涉透射光振幅反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7OpticalAdmittanceY(光導納)=H/E(電磁波的磁場與電場之比)Y=NYo=(n-ik)YoYo(自由空間之導納)單層光學薄膜的特徵矩陣:cosisin/YiYsincosI=-1(相厚度phasethickness)=2ndcos/D=膜層的幾何厚度EaHa=EbHb薄膜的特徵矩陣8cosisin/NiNsincosBC=1NsQuarterwave(1/4)

o

=/2M=0i/NiN0Halfwave(1/2)

o=1001M=AbsenteelayerY(光導納)=H/E(電磁波的磁場與電場之比)=C/B1NsNE=C/B=N2/Ns1Ns9Equivalentadmittance(等效導納)YE=C/BB和C分別正比於電場(E)及磁場(B)反射光振幅(amplitudeofreflectioncoefficient)=Er/Ei=(Y0-Y1)

/(Y0+Y1)

=

(N0-N1)

/(N0+N1)反射率R=

=(Y0-Y1/Y0+Y1)2R=((N0-N1)

/(N0+N1))2(Er/Ei;反射強度與入射強度之比)FordielectricNs=nse.gBK7ns=1.52R=((n0-n1)

/(n0+n1))2=4.26%FormetalNs=ns-iksNs=0.82-i5.99@550nmR=((n0-n1)

2+k

2

/(n0+n1)2+k

2

)=91.6%10穿透光振幅(amplitudeoftransmissioncoefficient)穿透率T=4

0

s/

(

0B+C)(

0B+C)

=Et/Ei=2Y0/(Y0+Y1)

=2

N0/(N0+N1)=20/

0B+CT=4n0ns/(n0+ns)21=T+R+L(S+A)11n1n2n3n1-n2n1+n2n2-n3n2+n3=SingleLayerARC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)1/2n1=1,n3=1.5n2=1.22512y0y1y21/ysubysub

WithoutARCR=((y0-ys)

/(y0+ys))2BK7=1.52=((1-1.52)/1+1.52))2=4.26%WithoutARC13SingleLayerARCR=((y0-y12/ysub)/(y0+y12/ysub))2IdeaARC,R=0,y0-y12/ysub=0,y1=(y0ysub)1/2y0=1.0Air,ysub=1.52y1=1.23R=((y0-y2f/ys)/(y0+y2f/ys))2R=((1.00-1.382/1.52)/(1.00+1.382/1.52))R=1.23%14yH=y5yH=y3yH=y1yL=y4yL=y2y2Hy2Hy2Hy2Ly2LysubyoysubY1=y2H/ysubY2=y2L/Y1=y2Lys/y2HY3=y2H/Y2=y4H/y2Lysy21y23y25y22y24ysOddlayery0yEy0yE=等效導納(遞推法)15nairnLnHnS123Nair<nL<nH光疏介質進入光密介質;相位變化為

123合向量2-LayerARCnH>ns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162.3521.452121.52N=1.38n=2.20.501.522+2.2221.521+1.38221圓心2.352=圓心1.452=通過(1.52,0)通過(1,0)導納軌跡圖17ARCwithTwoLayer

R=((y0-y12ysub/y22)/(y0+y12ysub/y22)IdeaARCR=0,y0-y12ysub/y22=0;y12/y22=y0/ysubY2=y1(ys/y0)1/2=(1.381.23)1/2y2=1.7R=((y0-y12ysub/y22)/(y0+y12ysub/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%18HighReflectedMirror19HighReflectionMirrorys/HLHLHLHLH….H/y0=ys/(HL)PH/y0yE=yH2(p+1)/=yL2pysR=(y0-yE/y0+

yE)2ys=1.52,yH=2.3,yL=1.46,yo=1,p=8R=?99.92%g=4/Sin-1(yH-yL/yH+yL)G=

0/=g/g=170nm20HighReflectionMirror21HighReflectionMirror22S分量P分量稜鏡偏振鏡:1.65/(HL)5H/1.650=500nm,=45º2324W=R+G+BM=R+BY=R+GC=G+BC=W-RY=W-BM=W-GColor(加法三原色)25Color(減法三原色)C*Y*M=BLR=Y*MG=Y*CB=M*C26DichroicMirror27COLOR：REDWavelength50%：632nmYELLOWWavelength50%：530nmColorFilter28COLOR：GREENWavelength50%：494/554nmBLUEWavelength50%：515nm29COLOLIGHTBLUEWavelength50%：546nmPURPLEWavelength50%：469/644nm30COLPINKWavelength50%452/621nmCOLOR：LIGHTPINKWavelength50%：487/578nm31IncidentRayReflectedRayRefractedorTransmittedRaySSSPPPSurfaceNs=

cos

Np=

/cos

Obliqueincidence

1

0

0IsgivenbySnell’slawP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)-電場垂直於入射平面的偏振光32RsTp=45n0nHnLnHnLn0n0n0MacNeillePBS

H

H

LPBS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33利用Brewsterangle

B,RP=0,

P偏振光之反射為0

H=nH/cos

H=L=nL/cos

LSin2

H=nL2/(nH+nL),tan

H=nL/

nHnHsin

H=nLsinL依Snell’slaw當PrismAOI=45°,sin

H=ngsin45°

/

nHng2=2nH2