q π =0 Ez,t =ε σ {e ikz ωt e ikz ωt } i/ = ε σ sinkz ωt 5.6 x σ σ *105 q π =1 Ez,t = 1 ε σ + ε π {e ikz ωt e ikz ωt } i/ = 1 ε σ + ε π sinkz ωt 5.7 σ

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1 H k r,t= η 5 Stokes X k, k, ε, ε σ π X Stokes Maxwell H = A A *10 A = 1 c A t 5.1 A kη r,t=ε η e ik r ωt 5. k ω ε η k η = σ, π ε σ, ε π σ π A k r,t= q η A kη r,t+qηa kηr,t 5.3 η q η E = 1 c A t, H = A E k r,t= η {q η A kη r,t q ηa kηr,t}, 5.4 ˆk {q η A kη r,t q ηa kηr,t} 5.5 * k z k xy ε σ = 1, 0, 0, ε π = 0, 1, 0 *104 E H E H E q σ =1 q π *10 Appendix A *103 Appendix *104 ε σ ε π = ˆk 45

2 q π =0 Ez,t =ε σ {e ikz ωt e ikz ωt } i/ = ε σ sinkz ωt 5.6 x σ σ *105 q π =1 Ez,t = 1 ε σ + ε π {e ikz ωt e ikz ωt } i/ = 1 ε σ + ε π sinkz ωt 5.7 σ π 45 q π = 1 45 q π = e iπ/ = i Ez,t ={ε σ + iε π e ikz ωt ε σ iε π e ikz ωt } i/ = ε σ sinkz ωt+ε π coskz ωt = ε σ sinkz ωt+ε π sinkz ωt + π 5.8 z=0 k z σ π Right-handed Circular Polarization * q π = e iπ/ = i Ez,t ={ε σ iε π e ikz ωt ε σ + iε π e ikz ωt } i/ = ε σ sinkz ωt ε π coskz ωt = ε σ sinkz ωt+ε π sinkz ωt π 5.9 q π = i 5. q π =e iπ/ =i Ez,t ={ε σ +iε π e ikz ωt ε σ iε π e ikz ωt } i/ = ε σ sinkz ωt+ε π coskz ωt 5.10 σ π q σ q π ε = q σ q π 5.11 *105 i/ *106 z 46

3 ε x ε y ε x ε y z z ε x ε y ε y ε x t t x x y z y z 5.1: z z z z 5.: z z z z 1 0 σ π i i E RCP z,t =ε σ coskz ωt+ε π coskz ωt + π = ε σ coskz ωt ε π sinkz ωt = {ε σ + iε π e ikz ωt +ε σ iε π e ikz ωt }/, ,i 47

4 5. Stokes 3 P 1, P, P 3 [3] P =P 1,P,P P 1, P, P σ π 1 1 P 1 =1 +45 P 1 = 1 45 P =1 P = 1 P 3 =1 σ P 3 = 1 π σ : P = 0, 0, 1, π : P = 0, 0, 1 45 : P = 1, 0, 0, 45 : P = 1, 0, 0 : P = 0, 1, 0, : P = 0, 1, 0 P 0 = P 1 + P + P 3 =1 P 1 = P = P 3 =0 P 1, P, P 3 Stokes ˆµ photon ˆµ ˆµ = 1 Î + P ˆσ 5.14 = 1 1+P 3 P 1 ip P 1 + ip 1 P Î ˆσ Pauli i ˆσ x =, ˆσ y =, ˆσ z = 1 0 i ˆµ ε = ε ˆµε = 1 1+P 3 P 1 ip = 1 P 1 + ip 1 P P P 3 / ε = 1 0 σ P 3 =1 1 P 3 =0 1/ P 3 = 1 0 P ε ε ˆµε *107 1 σ or π: ε = ε 0 ˆµε = P 0 3, ε = ε 1 ˆµε = 1 1 P or 45 : ε = 1 1 ε 1 ˆµε = P 1, ε = 1 1 ε 1 ˆµε = 1 1 P 1. right or left: ε = 1 1 ε i ˆµε = P, ε = 1 1 ε i ˆµε = 1 1 P. *107 Stokes 1,i P =1 1, i P = 1 1,i ε σ ε π = ˆk Ar,t=ε σ + iε πe ik r ωt +ε σ iε πe ik r ωt ε π ε σ = ˆk 1,i P =1 48

5 5.3 k r ωt ωt k r k r ωt ωt k r σ π cosωt k r = cosk r ωt *108 σ π 5.8 σ π π +π/ kz ωt ωt kz E RCPz,t =ε σ sinωt kz+ε π sinωt kz + π = {ε σ + iε π e iωt kz ε σ iε π e iωt kz } i/ 5.17 π π σ Stokes 5.17 e iωt kz ε σ + iε π 1 1,i Stokes P =1 1 1, i P = E RCPz,t = {ε σ iε π e ikz ωt ε σ + iε π e ikz ωt } i/ 5.18 A RCPz,t ={ε σ iε π e ikz ωt +ε σ + iε π e ikz ωt }/ e ikz ωt ε σ iε π 1 1, i Stokes P = 1 Appendix k π c A k r,t= ε η a kη e ik r ωt + ε V ω ηa e ik r ωt kη 5.0 η k k r ωt ωt k r e ik r ωt e ik r ωt X X k ω e ik r ωt , i Stokes P = 1 *108 sin sinωt k r = sink r ωt 49

6 5.4 Ĝ 4 Ĝ X Stokes P 1,P,P 3 [3] Ĝ Ĝ σ-σ, σ-π, π-σ, π-π 4 G σσ, G σπ, G πσ, G ππ G σσ G πσ Ĝ = G σπ G ππ Î ˆσ 5.1 Ĝ = βî + α ˆσ β + α 3 α 1 iα = α 1 + iα β α 3 5. Ĝ β, α β =G σσ + G ππ / α 1 =G πσ + G σπ / α = ig πσ G σπ / α 3 =G σσ G ππ / photon Stokes P ˆµ = 1 Î + P ˆσ Tr{ˆµĜ} Tr trace *109 ˆµĜ = 1 Î + P ˆσβÎ + α ˆσ = 1 {βî + α ˆσ + βp ˆσ +P ˆσα ˆσ} = 1 {β + P αî +α + βp + ip α ˆσ} 5.4 β + P α 0 = 0 β + P α α 3 + βp 3 + ip 1 α P α 1 C C 1 α 3 βp 3 ip 1 α P α 1 Tr{ˆµĜ} = β + P α = β + P 1 α 1 + P α + P 3 α Stokes P *110 *109 C 1 = α 1 + βp 1 + ip α 3 P 3 α iα + βp +P 3 α 1 P 1 α 3, C 1 = α 1 + βp 1 + ip α 3 P 3 α +iα + βp P 3 α 1 P 1 α 3 *110 Stokes ˆµ 50

7 5.4. photon Stokes P Ĝ Ĝ Ĝ ˆµ = 1 Î + P ˆσ dσ =Tr{ˆµĜ Ĝ} 5.7 σ-σ, σ-π, π-σ, π-π 4 G σσ, G σπ, G πσ, G ππ X 5. *111 Ĝ Ĝ =β Î + α ˆσ βî + α ˆσ = β βî + β α ˆσ + α β ˆσ +α ˆσα ˆσ 5.8 = {β β +α α}î + {β α + α β+iα α} ˆσ 5.9 ˆµĜ Ĝ = 1 {β β + α α + β P α+p α β + ip α α}î + 1 {β βp + iα α+β α + α β+ip β α + α β} ˆσ 5.30 Tr{ˆµĜ Ĝ} Î dσ =Tr{ˆµĜ Ĝ} = β β + α α + β P α+p α β + ip α α dσ = 1 Ĝ = g σσ + ig σσ g σπ + ig σπ g πσ + ig πσ g ππ + ig ππ { g σσ + g σσ +g πσ + g πσ +g σπ + g σπ +g ππ + g ππ } + P 1 g σσ g πσ + g σσ g πσ + g ππ g σπ + g ππ g σπ + P g σσ g πσ g σσ g πσ + g ππ g σπ g 1{ + P 3 g σσ + g σσ g πσ + g πσ +g ππ g σπ σπ + g σπ g ππ + g 5.3 ππ } 5.33 P 1,P,P 3 C 0,C 1,C,C 3 dσ = C 0 + C 1 P 1 + C P + C 3 P *111 i ˆσ = ˆσ ii α, β P, ˆσ 51

8 5.4.3 Stokes P dσ P =Tr{ˆµĜ ˆσĜ} 5.35 dσ P = β α + α β iα α+β βp iβ P α+ip α β + α P α α P α Ĝ X P X ω P κ = k k ψ φ A Ĝ X *11 X X 4.3 Stokes P φ A Ĝ Ĝ P φ A 5.5 Thomson Thomson Ĝ P Ĝ Thomson Ĝ =ε εf c 1 0 = F c 0 cos θ 5.37 F c * β = F c 1 + cos θ =F c cos θ α 1 =0 α =0 α 3 = F c 1 cos θ =F c sin θ 5.38 *11 X *113 c Charge c. 5

9 5.5. Thomson 5.31 dσ = F c cos 4 θ + sin 4 θ +P 3 sin θ cos θ = F c {1 1 } 1 P 3 sin θ Stokes Stokes 5.36 dσ P = F c { sin θ cos θ + P 3 sin 4 θ0, 0, 1 + cos 4 θp 1,P,P 3 sin 4 θp 1,P, 0 }. dσ dσ dσ P 1 = F c P 1 cos θ, P = F c P cos θ, P 3 = 1 F c {sin θ + P cos θ} = F c {P } 1 P 3 sin θ P dσ P dσ 5.39, 5.40 Thomson Stokes P 1 = P = P 1 cos θ P 3 sin θ P cos θ P 3 sin θ,, P P 3 = 1 P 3 sin θ P 3 sin θ 5.3 P = 1, 0, 0 Thomson Stokes θ 5.40 θ = 90 P 1 = P =0 P 3 1 P 3 =1 53

10 5.5.4 θ A Thomson 5.39 P 3 P 3A *114 P 3A = P 1 sin φ A + P 3 cos φ A. 5.4 K dσ I = K {1 1 } 1 P 3A sin θ A 5.43 dσ 5.31 Thomson Stokes 5.40 P 3A 5.4 P 1 cos θ sin φ A + {P P 3A = 1 P 3 sin θ} cos φ A P 3 sin θ 5.39 Thomson K I = K F c {1 1 1 P 3 sin θ }{1 1 } 1 P 3A sin θ A : P = 1, 0, 0 Thomson Stokes θ P = 0. *114 ε σ ε π = ˆk 4.3 φ A > 0 P 1 < 0 ε π ε σ = ˆk 54

11 5.6 X X π σ *115 SPring-8, BL Phase Retarder ε σ-π *116 X η 4.3 *117 η =0 σ η = 90 π XY Z ε σ = 1, 0, 0 ε π = 0, sin θ, cos θ 5.46 ε = ε σ cos η ε π sin η = cos η, sin η sin θ, sin η cos θ 5.47 Stokes P =P 1,P,P 3 = sin η, 0, cos η 5.48 Stokes Stokes P 0 0 P 0 1 *118 χ PR η P 0 σ 45 π 45 P 1 = P 0 sin η, P 3 = P 0 cos η 5.49 *119 Direct Beam Direct Beam 5.45 θ =0 polscanbrw,x tth=0 5.4 Bragg Thomson Igor-Pro Fitting 5.5 η-scan etascanbrw,x POL-scan φ A -scan polscanbrw,x Function etascanbrw,x Wave w Variable x Variable tth, ttha, p1in, p3in, int,p1out,p3out,p3a //w[0]: POL, w[1]: tth deg, w[]: ttha deg, w[3]: PL, w[4]: Intensity, w[5]: offset *115 *116 6 X *117 η ε σ ε π P 1 Thomson φ A η φ A *118 *119 [39] η = 90 P 0 σ η =0 P 0 55

12 tth=w[1]*pi/180; ttha=w[]*pi/180 p1in=-w[3]*sin*x*pi/180 p3in=w[3]*cos*x*pi/180 int=1-1-p3in/*sintth^ p1out=p1in*costth/int p3out=p3in+1-p3in/*sintth^/int p3a=-p1out*sin*w[0]+w[5]*pi/180+p3out*cos*w[0]+w[5]*pi/180 return w[4]*int*1-1-p3a/*sinttha^ End Function polscanbrw,x Wave w Variable x Variable tth, ttha, p1in, p3in, int,p1out,p3out,p3a //w[0]: eta, w[1]: tth deg, w[]: ttha deg, w[3]: PL, w[4]: Intensity, w[5]: offset tth=w[1]*pi/180; ttha=w[]*pi/180 p1in=-w[3]*sin*w[0]*pi/180 p3in=w[3]*cos*w[0]*pi/180 int=1-1-p3in/*sintth^; p1out=p1in*costth/int p3out=p3in+1-p3in/*sintth^/int p3a=-p1out*sin*x+w[5]*pi/180+p3out*cos*x+w[5]*pi/180 return w[4]*int*1-1-p3a/*sinttha^ End 5.4: σ Direct Beam POL = φ A 5.5: φ A =0, 30, 60, 90 η θ = 53.95,θ A =

N cos s s cos ψ e e e e 3 3 e e 3 e 3 e

3 3 5 5 5 3 3 7 5 33 5 33 9 5 8 > e > f U f U u u > u ue u e u ue u ue u e u e u u e u u e u N cos s s cos ψ e e e e 3 3 e e 3 e 3 e 3 > A A > A E A f A A f A [ ] f A A e > > A e[ ] > f A E A < < f ; >