(fourth erson; 00 ) 1.1 1. (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) 1. 1..1 Mawell s equatons B D H ρ J t B + = 0 1.1 t ρ H = J 1. t D = ρ 1.3 B = 0 1.4 (materal equaton) 1-1
(fourth erson; 00 ) (statc) (sotropc) ( ) D = 1.5 B = µh 1.6 J = σ 1.7 1.5-1.7 = µ + µσ 1.8 t t ( ) 1 1.8 = µ 1.9 t 1.9 1 = 1.10 µ w= r, t = ( ) ( r ) r Helmholtz + k = 0 r e + wt 1.11 k = µ w = π λ, 0 1.1 ( 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 1.13 1.14 S 1 OSLO σ 1-
(fourth erson; 00 ) S = H S = 0 1.15 (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 = 0 1.19 z (, ) 1-3
(fourth erson; 00 ) wt k r 1.17 1.18 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 1.0 1-4
(fourth erson; 00 ) a = ± 1. a (lnearl polarzed) 0 π a =a =a 1.0 + = a 1.3 (crcularl polarzed) 1 natural partall polarzed degree of polarzaton 1 1..3 Fresnel Fresnel Snell S 1. 1-5
(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 1.4 1.7n 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 = 1 1.9 1.9 s p 1-6
(fourth erson; 00 ) R = R n n' = n + n' s, normal p, normal 1.30 n=1.0,n'=1.5 1.30 4 OSLO s p Fresnel s p s p 1..4 Jones Calculus R. Clark Jones Jones z, Jones = ( t) () t 1.31 1.17 1.18 1.31 a e a e δ = δ 1.3 = - 1.3 a a e = δ 1.33 Jones lnear, 0 a e = δ 1.34 Jones 1 crcular, rght = a Jones 1.35 1-7
(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 = 1.39 0 0 0 0 J pzr = 1.40 0 1 sn φ cosφ snφ Jφ pzr = 1.41 cosφcsnφ cos φ /4 J 1 0 λ = 1.41 1 0 4 /4 J 1 0 λ = 1.43 1 0 4 / 1-8
(fourth erson; 00 ) cos φ sn φ J λ = φ sn φ cos 1.44 1 φ φ ep( δ ) snφ cosφ[ 1 ep( δ )] [ 1 ep( δ )] sn φ ep( δ ) + cos sn φ + cos J φ δ = 1.45 1 snφ cosφ φ 1 1 J larpzr = J 1 rghtcrcu 1.46 1 1 = 1 leftcrcul arpzr 1.47 1.3 Malus's law Malus ( θ ) I( 0) cos θ I = 1.48 I( ) =0 Jones 1 Jones 0 = 1.49 1 1.41 1.41 1.48 1.37 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
(fourth erson; 00 ) ( φ = 0 ) 1.1 1.1 1. 1-10
(fourth erson; 00 ) 1. Jones 30 o 1.3 Jones Malus cos (30 o )=0.75 30 o 1.4 Malus 60 o cos (60 o )=0.5 1-11
(fourth erson; 00 ) 1.5 60 o =90 o 1.6 90 o 1.4 Fresnel (Fresnel rhomb) Fresnel 1.4 1.7 s p =0 s p Fresnel Fresnel s p s p δ tan = cosθ n' sn θ n sn θ 1.5 1-1
(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 =.414 1 1.55 1.56 n Fresnel 51 n' =1. 45.95 o =45 o 90 o n 51 n' = 1. 1.5 =45 o =48.64 o =54.63 o Fresnel OSLO total nternal refecton onl surface TIR Fresnel TIR Fresnel prescrpton 1.7 1-13
(fourth erson; 00 ) 1-14
(fourth erson; 00 ) 1.7 Fresnel 1.3 Fresnel 45 o 1-15
(fourth erson; 00 ) 1.8 full-feld 3 4 54.63 o 1.8 3 0.414 4 1 5 4 Fresnel 1-16
(fourth erson; 00 ) 1.9 Fresnel 1.5 Vector Dffracton 0.55 0.60 z pont spread functon ntegral et pupl,,z OSLO PSF 1 NA NA=0.966 perfect lens 0.966 75 o NA 100mm 0 0.966=sn(75 o ) 0.5 m 1.10 1-17
(fourth erson; 00 ) 1.10 ( 1.4) 1-18
(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 1.1 1.5 ( ) 1.5 PSF 1-19
(fourth erson; 00 ) PSF PSF spot sze NA 1.13 ( ) 1.6 1.7 1.14 1.6 (-as polarzer ) 1-0
(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
(fourth erson; 00 ) [1] OSLO Optcal Reference erson 5.0 (Snclar Optcs, 1996) [] OSLO Optcal Reference erson 6.1 (Lambda Research Corp., 001) 1-
(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, 1167-1169 (001) S. G. Lpson, H. Lpson, and D. S. Tannhauser, Optcal Phscs, 3 rd. ed. Cambrdge Un. 1995, p.58) 1-3