第十二章偏振$polarization$

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1 (fourth erson; 00 ) (polarzaton) 1..1 Mawell s equatons 1.. (Polarzaton ellpse) 1..3 Fresnel 1..4 Jones Calculus 1.3 Malus's (Malus s law) 1.4 Fresnel (Fresnel rhomb) 1.5 Vector Dffracton 1.1 (polarzaton) Mawell s equatons B D H ρ J t B + = t ρ H = J 1. t D = ρ 1.3 B = (materal equaton) 1-1

$3 Malus's (Malus s law) 1.4 Fresnel (Fresnel rhomb) 1.5 Vector Dffracton 1.$

2 (fourth erson; 00 ) (statc) (sotropc) ( ) D = 1.5 B = µh 1.6 J = σ = µ + µσ 1.8 t t ( ) = µ 1.9 t = 1.10 µ w= r, t = ( ) ( r ) r Helmholtz + k = 0 r e + wt 1.11 k = µ w = π λ, ( r t) = ep( ± λ( k r wt δ ) k k s ) = ŝ ( 1.1 ) t s r = lonst 1.1 = µ S H 1.13 H = S 1.14 µ S 1 OSLO σ 1-

10 µ w= r, t = ( ) ( r ) r Helmholtz + k = 0 r e + wt 1.11 k = µ w = π λ, 0 1.

3 (fourth erson; 00 ) S = H S = (1.15 (transerse), H S ŝ Pontng ( S = H ) S, H S S 1890 Wener ( ) Lorentz 1.. (Polarzaton ellpse) ( ) z 1.1 { } ( ) { ( wt k r + δ wt k r + δ = R aeˆ )} a cos 1.16 R L z = a cos wt k r + δ 1.17 = a ( ) ( wt k r + δ ) sn 1.18 = z (, ) 1-3

4 (fourth erson; 00 ) wt k r a + a cosδ = sn a a δ 1.0 δ = δ δ (, ) aa tan θ = cosδ 1.1 a a (polarzaton ellpse) 1.1 θ 1.1 π =0( ), sn 0 (left handed) sn 0 left-handed 1 3 OSLO polarzaton operatng condtons

5 (fourth erson; 00 ) a = ± 1. a (lnearl polarzed) 0 π a =a =a = a 1.3 (crcularl polarzed) 1 natural partall polarzed degree of polarzaton Fresnel Fresnel Snell S

6 (fourth erson; 00 ) s, p, θ p, s, t p, s, 1. p TM transerse magnetc s T transerse electrc s senkrecht t r t Fresnel r n cosθ n' cosθ t s = 1.4 n cosθ + n'cosθ t r t t n'cosθ ncosθ t ρ = 1.5 n'cosθ + n cosθ t n cosθ s = 1.6 n cosθ + n'cosθ t n cosθ ρ = 1.7 n'cosθ + n cosθ t n n' permeablt = '= 0 R R = r r R = r r 1.8 s * * s s, p p p s + s p p r t = 1, r + t = s p 1-6

4 n cosθ + n'cosθ t r t t n'cosθ ncosθ t ρ = 1.5 n'cosθ + n cosθ t n cosθ s = 1.

7 (fourth erson; 00 ) R = R n n' = n + n' s, normal p, normal 1.30 n=1.0,n'= OSLO s p Fresnel s p s p 1..4 Jones Calculus R. Clark Jones Jones z, Jones = ( t) () t a e a e δ = δ 1.3 = a a e = δ 1.33 Jones lnear, 0 a e = δ 1.34 Jones 1 crcular, rght = a Jones

Clark Jones Jones z, Jones = ( t) () t 1.31 1.17 1.18 1.31 a e a e δ = δ 1.

8 (fourth erson; 00 ) crcular, left 1 = a 1.36 Jones Jones t Jones J = J 1.37 t t t J = J A C J J B D 1.38 Jones J A,J B,J C J D Jones Jones OSLO Jones OSLO Jones J J A =J P =1;J B =J C =0 Jones 1 0 J pzr = J pzr = sn φ cosφ snφ Jφ pzr = 1.41 cosφcsnφ cos φ /4 J 1 0 λ = /4 J 1 0 λ = / 1-8

9 (fourth erson; 00 ) cos φ sn φ J λ = φ sn φ cos φ φ ep( δ ) snφ cosφ[ 1 ep( δ )] [ 1 ep( δ )] sn φ ep( δ ) + cos sn φ + cos J φ δ = snφ cosφ φ 1 1 J larpzr = J 1 rghtcrcu = 1 leftcrcul arpzr Malus's law Malus ( θ ) I( 0) cos θ I = 1.48 I( ) =0 Jones 1 Jones 0 = Jones = J t sn φ = cosφ snφ cosφ snφ 0 cosφ snφ = cos φ 1 cos φ 1.50 t I ( φ ) = cos = cos = t + t 4 = cos φ sn φ + cos φ φ φ ( sn φ + cos φ ) 1.51 I(0)=1 Malus OSLO 1-9

45 1 snφ cosφ φ 1 1 J larpzr = J 1 rghtcrcu 1.46 1 1 = 1 leftcrcul arpzr 1.47 1.

10 (fourth erson; 00 ) ( φ = 0 )

11 (fourth erson; 00 ) 1. Jones 30 o 1.3 Jones Malus cos (30 o )= o 1.4 Malus 60 o cos (60 o )=

12 (fourth erson; 00 ) o =90 o o 1.4 Fresnel (Fresnel rhomb) Fresnel s p =0 s p Fresnel Fresnel s p s p δ tan = cosθ n' sn θ n sn θ

4 Fresnel (Fresnel rhomb) Fresnel 1.4 1.

13 (fourth erson; 00 ) m n' n' 1 snθ n n δ m tan n' 1 n = n' n 1.53 Fresnel 45 o s p =90 o =90 o 1.53 δ m 0 = 45 δ m tan = 1 n' 1 n 1 < 1.54 n' n n > n' n' < n 1 1 = n Fresnel 51 n' = o =45 o 90 o n 51 n' = =45 o =48.64 o =54.63 o Fresnel OSLO total nternal refecton onl surface TIR Fresnel TIR Fresnel prescrpton

54 n' n n > n' n' < n 1 1 =.414 1 1.55 1.56 n Fresnel 51 n' =1. 45.

14 (fourth erson; 00 ) 1-14

15 (fourth erson; 00 ) 1.7 Fresnel 1.3 Fresnel 45 o 1-15

16 (fourth erson; 00 ) 1.8 full-feld o Fresnel 1-16

17 (fourth erson; 00 ) 1.9 Fresnel 1.5 Vector Dffracton z pont spread functon ntegral et pupl,,z OSLO PSF 1 NA NA=0.966 perfect lens o NA 100mm =sn(75 o ) 0.5 m

60 z pont spread functon ntegral et pupl,,z OSLO

18 (fourth erson; 00 ) 1.10 ( 1.4) 1-18

19 (fourth erson; 00 ) 1.4 spot dagram equal mage space ra ncrements 1.11 ON 1.11 use equal mage space ra ncrements ON PSF ( ) 1.5 PSF 1-19

20 (fourth erson; 00 ) PSF PSF spot sze NA 1.13 ( ) (-as polarzer ) 1-0

21 (fourth erson; 00 ) 1.7 (-as polarzer) PSF Hopkns 1.8 ABCD O HB A, B, C D A, B, C, D A C z B D z A C D B B cos D cos ABCD cos θ D, A C B 1.8 Hopkns s H. H. Hopkns, Resolng power of the mcroscope usng polarzed lght, Nature 155, 75 (1945). 1-1

22 (fourth erson; 00 ) [1] OSLO Optcal Reference erson 5.0 (Snclar Optcs, 1996) [] OSLO Optcal Reference erson 6.1 (Lambda Research Corp., 001) 1-

23 (fourth erson; 00 ) 1. Catalog lens trplet lens NA(numercal aperture). ball lens 3. Perro prsms (Perro prsm bnocular telescope Born and Wolf Prncple of Optcs, chapter 6) (You wll fnd a good achromatc polarzaton-preserng beam dsplacer.) 4. polarzer geometrcal phase (Berr phase/pancharatnam phase) optcal mplementaton (e.g., N. Baba, N. Murakam, T. Ishgak, Optcs Letters 6, (001) S. G. Lpson, H. Lpson, and D. S. Tannhauser, Optcal Phscs, 3 rd. ed. Cambrdge Un. 1995, p.58) 1-3

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第十二章 偏振\(polarization\)

第十二章偏振\(polarization\)