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Manipulation optique de l’organisation de chromophores
non-linéaires et luminescents
Sébastien Bidault
To cite this version:
Sébastien Bidault. Manipulation optique de l’organisation de chromophores non-linéaires et luminescents. Physique Atomique [physics.atom-ph]. École normale supérieure de Cachan - ENS Cachan,
2004. Français. �tel-00008635�
HAL Id: tel-00008635
https://tel.archives-ouvertes.fr/tel-00008635
Submitted on 2 Mar 2005
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publics ou privés.
École Doctorale des Sciences Pratiques de l’ENS Cachan
Département de formation doctorale en sciences physiques
Option : Physique
Manipulation optique de l’organisation
de chromophores non-linéaires et
luminescents
THÈSE
présentée et soutenue publiquement le 19 juillet 2004
pour l’obtention du grade de
Docteur de l’École Normale Supérieure de Cachan
(spécialité Sciences Physiques)
par
Sébastien Bidault
Composition du jury
Président :
M. Martial Ducloy
(Institut Galilée, Université Paris XIII)
Rapporteurs :
M. Eric Freysz
M. François Hache
(CPMOH, Université Bordeaux I)
(LOB, École Polytechnique)
Examinateurs :
Mlle Sophie Brasselet
M. Fabrice Charra
M. Olivier Maury
M. Joseph Zyss
(LPQM, ENS Cachan)
(DRECAM, CEA Saclay)
(Institut de Chimie, Université Rennes I)
(LPQM, ENS Cachan)
Laboratoire de Photonique Quantique et Moléculaire — UMR 8537
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pinduit
(r, t) = µ0 i (r) + αij Ej p (r, t) + βijk Ej p Ek q (r, t) + γijkl Ej p Ek q Elωr (r, t) + . . . ,
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k
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pinduit (r, t) = p0 (r, t) + pω (r, t) + p2ω (r, t) + p3ω (r, t) + . . . + c.c.
> ö b;@
:m40BAŽ
pnω (r, t) = P nω eni(k·r−ωt)
P nω = σ (n) E ω . . . E ω
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0
p
f luo
(r, t) =
Z
pωF (r, t)dωF + c.c.
pωF (r, t) = P ωF (t)enik·r e−iωF t
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,
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n
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0FGI:P, 34/r60/,2Ž
i
ρ̇nm = −iωnm ρnm − [V̂ , ρ̂]nm − γnm (ρnm − ρeq
nm ),
~
iX
ρ̇nm = −iωnm ρnm −
(Vnν ρνm − Vνm ρnν ) − γnm (ρnm − ρeq
nm ),
~ ν
> ö [email protected]
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nm = −iωnm ρnm − γnm (ρnm − ρnm )
iX
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(j)
(j−1)
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=
−iω
ρ
−
− µνm ρnν
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(µnν ρνm
nm nm
nm
nm
~ ν
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> ö b ö @
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1
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X
> ö b ö @
Pjkl [µi0n µjn0 µk0m µlm0 ]
−
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n,m
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γijkl (−ω, −ω, ω, ω) = 3
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> ö b öO÷ @
Pjkl [µj0n µinm µkmν µlν0 ]
+
[(ωn0 −ω)−iγn0 ][(ωm0 −2ω)−iγm0 ][(ων0 −ω)−iγν0 ]
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¤/[email protected]#=ƒ60h!/k4m:ihˆ1 e^,qD<[email protected]/G,AW:6¦[0C0/B#[email protected],.Y0/G,# 1
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γ(−3ω, ω, ω, ω)
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[email protected], FG01
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6I:/1
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β(−2ω, ω, ω)
µ01 µ21ν µν0
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n
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Ienω (R) =
(nω)4
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nω ∗
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Ω2 , r2
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nω
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B8]01J, =K6dFGE :^34/5B,.34/#6526 1J,.5,.34/rD<05,}121DI:}/p6ih#3/B, 34/1f650D<0/L
6I:/,.1`1D<0B,[email protected]/G,65 ,f6 Ž
b
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r f (Ω, r) = f (Ω)g(r)
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b|vo ,.:6l,[email protected]<30&/G, 1\[email protected],C,.051`108]hiDC @A 63/B
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= kn |R − r| ≈ kn · (R − r)
n0 c
U: 0B 34/510FG/G,mS§V8ZFGI:P,.34/_> ö b öOü @}D<5,21CA1C @AD {I0j/‡1C0DI::/G,d01 /G,0g4:P,.34/1j1C
S , Ž
Ω r
t
Icoh nω
e (R)
Z hZ
i
(nω)4
−i(kn−nk)·r
e
g(r)dr
= 2 4 4
R c kn (16π 2 )2 N A
i
ihZ
hZ
iΨ(t)
(kn ∧kn ∧P nω (Ω))·ef (Ω)dΩ dkn
e
dt
2
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t
t = 0 δt
C0/G,^101 6DQI:1:g41d,[email protected]<34 1j601 [email protected],C,.051 /^13/G,dD:1 B34C0 10boj:/1 7Bm:6C
6/3P,.f0D501C0/,:P, 34/[email protected] {I0PSGV8Z/G,0/1C,.`65}g0/.:P, 34/KB34Q0/,.}6 eme QI:@A3PL
n
/FG~z:k,/G,0J40/5/^,[email protected]~0/
FGI1C0: /g4 g4HDI:TW:}1k,.Pbvw:j{Ig
2
sinc (nωδt/2)
bovo^@K:ahi @[email protected] 6&[email protected] 34/„B03Q0C0/G,
ö b ö lD501C0/,.A 1 a: :P,.34/51j6^ :-34/B, 34/
sinc2
01J,`/GVSiB8]01J,f=E6 C}FGI:/6l‰8]hiB,:a,. 3/-1C,\/34/L€134/5/I:/G,b
1C,\634/B}341C4 FGI:/56
δt
51d34/ƒ108Z:DDC3BMQK65AW:l134/I:P/B0PS§D 1 [email protected],,0C121C34/G,2/‡@K3Ou40//5K34/g,[email protected]
6I:P/1}‰8],.:P,}MhiB0k,.E,}D [email protected]/YB03Q0C0/G,701J,jz:P 2:PpDC3{,}6E‰8][email protected] 1C134/Y /B3PL
Q/G,.Pb
Ò©ÓÑÔ³Õ ö b ö Ö “T4345,.34/r65#B0:C 6 W:E34/B,. 3/r1/1`B0:6/I:Vb
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r
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n
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g:[email protected]/G,0b
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j
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g(r)
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N
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g(r)
b|’H,,.dB34/65,.34/l01J,}:D5D<0 B034/56, 34/l6&8Z:BB034C6#6 DQI:P1b
kn − nk = 0
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6:/1 :^60B,.34/Y6#4B,0
/3,. L
kn − nk
z
,[email protected] 6&8Z:BB034C6#6 DQI:P1dDC0/6Y/ [email protected] 1C @AD 7Ž
n
2
N S
2
Z
L
e−i(kn−nk)z dz
0
2
= N 2 S 2 L2 sinc2
(k −nk)L n
2
> ö bú ÷ @
3­ 01C,W:^1CCz:B20BW:P [email protected]:P,0 :r,
S|d/[email protected] [email protected] 1`D11
S
N SL = N
0/ˆ[email protected],.l6I:P/1^lD53B011510bNx :/6%W:pB34/6k,. 3/>6&8Z:BB034C6ˆ6rDQ:1r1C,A1D<B,.S
‰8] /,.0/51,f6jg0/.:P, 34/-6 eme QI:[email protected]/5 FGB3e,HFGI:65.:P, [email protected]/,\:m40Bj :234/g4
n
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01C,§6¦[0C0/,
6XD534DI:Pg:P,.34/ bO}XDI:o‰8]4345,.34/ 6_W:H34/B,. 3/
L
sinc
kn
6
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nk
6 C0B,. 3/ƒ6&[email protected] 11C 34/ƒ65KDQ3P,.34/1dB031D<34/560/‡[email protected]:PDD3mhi @K:P,.3/ƒ=
b§j:P/1
nk
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Icoh nω
e (R)
(nω)4
=N
(16π 2 )2 R2 c4
2
Z
[P nω (Ω)·e]f (Ω)dΩ
2
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˜ /‚,.354-6:/12B0,,.K0FGI:P, 34/‡W:r6D<0/6:/B0q/ 2 6501ED53B011C17B034Q50/G,17FG
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Œ_/£D:P,.FGr ~01J,-6g eAB0 l65YB034/1C0J40-V8;:PB0B346ˆ6YDQ:1#:£B34C1K65YW:„D34D:g:aL
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g(r)
6^[email protected]<0/1C0dD:C, [email protected]/G, 601:B0B346‡6^DQI:1CA6I:/51d :l60B,.34/65ADC34DI:g4:P,.34/
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2/(kn − nk)
b
2
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D53Oi0/,6>601C346Cl1DI:P,W:PN>z6k¦91C 3/
nω
0 :1C, FG&@_,~601NýIB,.I:P, 34/51N,[email protected]<30 1">z6k¦91C 34/K/0 :1C, FG&@61~6D<‹4 1N341CB0 :/,.1
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a ø4øc bvo1,[email protected]:P101^0/,.Cr 16k¦9/G,[email protected],,.16 1CDI:: 1C10/,^D<345‰8][email protected] 1cL
1C 34/#/B034Q50/G,EB0:01f /,.0/51,[email protected] 1C01D:01f6k¦90/,.1}@A340B05 01`13/G,j:656, 34/L
/01b_j:/1 [email protected],[email protected]‰8]0FGI:P, 34ñ
/ > ö b ömü @2N01C,^63/BlD<3411C [email protected]:PB00
DI: nω bj:/51§ B0:1§698Z/[email protected]:a,.0CW:[email protected]/5Î>ì34/B,. 3/ 6_6 1J,.5, 3/
pnω (Ω, r, t)
P (Ω)
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/ > ö b ömü @U1Cf1C @AD {I\:m40B`DI:6{I/5,.34/ R
Ž
r
Ω
Iincoh nω
e (R) =N
(nω)4
16π 2 R2 c4 kn2
g(r)dr = N
ZZ
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2
(kn ∧kn ∧P nω (Ω)) · e f (Ω)dΩdkn ,
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H
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1C,`FGI:P1kLÉ[email protected]/ 65B, 3// k,\63V
, o,.C /rg4/0:9B034 B,0}D[3Û
o,[email protected]®§34iL
,341T 1C0D<34/1C01_0/^D<34W:C 1:P,.k34/[email protected] 34/1U6\DQ3,34/1/\13/G,[email protected];:m40B
V8Z5, k1.:P,3/ 6&8] @AD<34C,.:/G,01o34540J,.C01«/[email protected] FG1V> @=a ø c ba}:/1«_B034/,.Mh,.N6XB0,,.
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bTv8ZFGI:P,.34î
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n
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° 345124k{I34/125 0/‡FG- :rý341B0/B0q1C,EDI:Jz:,[email protected]/G, /B34Q0/,.PbUŒ/‚/g4 g4m:P/G,
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0D501C0/,.f \D536k,T,.0/[email protected]<341:/G,01_Bm:PC,.10//501X6AD536k,_698Z/^,0/1C0
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(n) b§Œ/‚B03//I:11.:P/G,2W:[email protected],.C A6
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634/B D<@A,, 6&8]a: 50`B0C,:P /1`[email protected]<341.:P/G,.1 J b
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S
J ≤ n+1
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σ
,. 3/16`P:P 6m,~6f : [email protected], \6± /@K:P/134/,N1CDD<[email protected] 01bj:P/1XB0fB0:10S 1
[email protected]<341:/G,0121DQ50FG01E601211CB0D5,. 5 ,[email protected] B05W:k1 D[3201CF50 01 , 13/G,
J
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0
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ν
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6 :76 1CDI:C,.3/l65
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6I:/1`W:760B,.34/ Ž
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e Im(αem (ωF ))•(e ⊗ e)
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134 h5:/G,L€65kh:p,.56 qW:[email protected],.C q6lDC3B001C11A/534/iLÉ /m:C01E698Z34C6Y}aZÿiS_ÿ ühc , ÷
a ù 5S ù5rö c 0/Y5, k1.:/,\B,C,. 0B0C, 60B34D0 6 V8Z/G,0/1C,.}.:Ou43//0PS|1C @Ak,.:/,~634/B
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n
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134CD5,.34/-6 DQ3P,.34/510b’H,,jg40/abs
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B0 : C01d1C34/G,[email protected]:/12 AC0D<[email protected]:B0C341B34D FGA0/‚5,. 1:/G, [email protected]/,.126KW:
@-:a,.B065Xªç g4/w634/,«01wD3D,.1§6&8]34J,.Q34g34/I:k,.T634//50/,UD<345§‰8]F:P,.34T
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W:AD3I: k,[email protected]/# /,.0g0215}W:^,.3,.: k,d65„1CD<0B,.762ý341B0/B0^:m40B
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6I:/17V8ZFGI:P, 34M
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SI/#/5dD50/:/G,f0/[email protected], FG 601`,[email protected]`6&8Z36CdD: b
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∗
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> ö b ÷4ü @
X X µi µl ei E ω γν0 µjν0 µk0ν Ejω∗ ek γν0
0ν ν0
l
|P · e| =
2
2
2
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ω
2
∗
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f (Ω) = R
P
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ωi
P
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ωi
(1 − i Φi P0→1 (Ω)dΩ)
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3­-01NB3reAB00/,.1
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nω
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X
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X
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m,m0 ,J≤n+1
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J
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01N /,./1k,[email protected]:[email protected]:P10bv8Z:/I:ku16} :[email protected],.C 6501H1 g/I:ihA6 5–}¨^SG®`–j¨û,~®`_‘
:D5R01340/,:P, 34/Y1C,j¦[0B,07DI:P3P,:P,.34/Y6?BMQI:[email protected] ω /0:@A0/,fD<34W:C 1Cd6I:P/1
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@b
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,34Dr‰8]346C DQ3P,.3PLÉ /65™
, > ω
2 @b
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’ [email protected]@Af/3451H‰8Z:O434/51HMhiD FGj:-DI::g4:DQjib ÷ b ÷ S6:/1HBm:P1H3­qV8ZMhiB0k,:P, 34/^z:k,
H
/G,.C4/ §‰8] /,.0J0C0/BH/G,H61:5134CD5,.34/1U=/7,T650ihEDQ3P,.34/1SPW:`3/B, 34/26H61JL
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fs (Ω) = (f (Ω) + f (Ω + π))/2
f (Ω)
[email protected],F5A 1cLc=aL‰ 1 6&8Z5/K3P,:P,.34/6 @j,
W:rD:C,
π
fa (Ω) = (f (Ω) − f (Ω + π))/2
/3/iL€B0/,[email protected],.FGb
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,
18ZMh5D5 @A0/,
fs (Ω) fa (Ω)
1C @AD @A0/G,~0/r34/B, 34/l6 ‰8Z:/g4j6&8ZŒ 6&8Z:DCR01fV8]0FGI:P, 34/Yibúÿ^:m40B^Ž
ϕ
1
2
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1
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p
p
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fa (ϕ) =
16π 2 1 − p31 − p53
fs (ϕ) =
>÷ bö @
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H
°f341 : 34/516I:/1j/„[email protected] ,[email protected]/3451 /G,011C0 :[email protected]<31.:/,[email protected]:P167W:
34/5B,.34/65^6 1J,.5,.34/pFG/34/G, /G,.C4/ FG^W:[email protected]<341:/G,^ /,.C0C0/,. E6
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D<3jW:PF50 f (Ω)
01 D<3461 W:P,1j6012:1C34D5, 34/51d=r/‡,d60h‡DQ53,.3/T
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601§BQI:@AD10bv8] /,.0/51,,3,:P 65H5–}¨!1C,«34i,.0/GX0/2:66k,. 3//I:/,o‰8] /,./1k,.:/I:kui1C0
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X
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I SHG(φ) = N 2 p22 kβk2
+
1
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Λ
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2J + 1
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2 " X J 2
kb k
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(e(2) • FX (φ))J
2J
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1
J=1,3
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2
2
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v 8ZzeKB0:B0k,.}6lD53B011C1`6&8]34C 0/,:a,. 3/K/34/iLÉB00/,[email protected],.C FG /&8] /,.C /G,H634/B}DI:1
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/ > ÷ b; @[email protected]/,.C FG D<34\/ B034/5{g4.:a,. 3/r6534//d61
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b
b
ρ = kβ k/kβ k
FG1 (2) J D///G,K61^[email protected]¦[0C0/,.01^15P:P/G,^ 01D<34 :1.:P,3/1761ABQI:@AD1
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B034/i{Ig4:P,.34/1j6D<34 :1.:P,3/1}134/, 63//01d6:/1 ‰8]©}//5hiK’³@Mbo¤/5^@A01CzeKB0:B0
6 /0B01C1,.#/£B034D5W:gYzeKB0:B?0/,.Y 1A60h£[email protected]<341.:P/G,.1K65 ,Kr,0/1C0
ρ
β
6&8ZB0C,Pb5’HB34D :g4f:d,.61B5,.:KB03451N65W:j,.QR16}¥ b34
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iD<0C -6q’~:BQI:/ @[email protected]/G,KFGq :YB034/i{Ig4:P,.34/‡3 ­‚ 012BQI:@AD126&8ZB0C,.5
134/,2D<D</6 B : C01 1C,2 :lD1 zeKB0:B0AD<34 @A01Cd :[email protected],.C ^@A340BW:PCpa;ÿ h÷ c b
vw:d{Ig ÷ b S4,. C0f65W: 0/B0{aZÿ h÷ c SGD1/G,.}‰8]reAB0:B0k,.f6BB034D5W:g4`0/K34/B,.34/
6 W:[email protected],.C @K340BW:PCjD<34\6¦[0C0/G,01`B034/i{Ig4:P,.34/1\6&8]0B,Pb
Ò©ÓÑÔ³Õ ÷ b pÖ ŒìeABm:B,q6>B34D :g4 >
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@d0/,.qK,0/1C0BQI:[email protected]6&8]0Bk,.Cq,7‰8]QGuL
<D 0D<3W:C 1.:Pkk,EFGI:65.:P, [email protected]:k2/3/B, 34/p6V8;:/5 13P,[email protected] 0BW:PC
ρ
D<34D5 1C 051B34/5{g4.:a,. 3/6\D<34W:P1.:P,34/51U6&8ZMhiB0k,:P, 34/6&8Z:DCR01W:},QR01C`6`¥db4 C34/
a;ÿ ÷ c b
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f (Ω)
’ [email protected]@AMh5D5 FG}6:/1H BQI:D5,.C Si6:/1H B0:1~65jBQI:[email protected],.5 ,
H
B034/,.:aL
ω 2ω
B BW:P C01 7,.0/5105 (2) /AD<341C1R6-FG&8]/[email protected]<31.:/,.A3B,.D<3W: (2) 3 bw¬€/A1
e
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B34D 63/B F98;=W:[email protected]<341:/G, 3B,D<34 : C}6 W:[email protected] 0B ,`/ D<0i,fDI:P1`±3D<@A,C,.
:[email protected] bo®§345,341 W:lDI:J,. B :k,698Z/5A,0 B03/5{Ig4:P,.34/ƒ1C,2W:lD<341C1 k,.
ρ
6&8] /56 Cj/ /FG [email protected]<31.:/,. 1DQ50FGd6 ‰8]QGuD<0CD<34W:P 1:kk,.}FGI:P6.:P, FG @-:L
B341CB034DFG (2) 3 :m40B^Ž
χ
±3
3
χ(2) 3
p2 N kβk
=−
7
1
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Λ
2
kb3 k2 e(2)33
> ÷ b÷ @
’ \DQ50/[email protected]/5\01C,_5/^Bm:P1DI:C, B U65q{Ik,.:g4X6&8]/\/F5\[email protected]<341:/G,~1DQF5
H
67,./11 /34/iLÉ /m:P1jFG:l,.g40/.: 1C:BQI:Dk,.CAib&E8]/ƒD<34/G, 67^D1
:D5D F5S|5/ (2) [email protected]/,}3B,.5D[3W: /5E1CEB34D2FG&8Z=KW:[email protected]<341.:P/G,.d3B,D<34W:P χ
6?BQI:@AD#62 B, (2) ,}DC01C0/,.75/2D[3/1i–j¨ã[email protected] k0Y/6D<0/6I:P/G,.E=AW:
Fe
D<34 :1.:a,.3/l6YBQI:@ADY6 0B,ba; 8c b
j:P/1 B0:1 6^BQI:[email protected] 698ZB0k,.C ,
B3PL€B BW:P10S[ E,./1 (2) 01J,dD1j3JL
ω
2ω
e
,[email protected]/G,A65 D<34 :Cr:m40B (2) 3
>ì434 ©//hip’³@bX’[email protected]@[email protected]/,.lW:
(2) 1
ke k/ke k = 1/2
{Ig ÷ b SB0,,dB34/5{Ig.:P, 3/r1CdB34D 01C10/,.0 [email protected]/,f:m40B W:[email protected]<341.:/,. 6D<34W:k
6Y,.0/5105}@K340BW:PC b|©} /51w1 :[email protected]/,.PS|‰8Z:/13,.C34Dk 67i–j¨ã1C0.:KFGI:P1 @A/G,
β
ρ
/BMQ:/g4 ,`/ .:DI:1\ /,.C40/5 ~W:[email protected]<341.:/,. 3B,.D<34 : C}6 6 @-:P/ Rj1C g4/5kL
β
{IB0:P,.k4b§¬€X/01J,[email protected]@KAD<3452601EBQI:@AD12 /m:[email protected]/G,dD<34 :11d,EDI:.:P R01d3 ­
p
,23 ­‡ ^B03reAB /G,E6KB34D5W:g4
6B03Pe ,d3C,[email protected]/G,2:O4B
3
1
ke(2) k/ke(2) k = 2/3
C(ρ)
b|U:`B34/,. D<34`6501fBQI:@AD1 ,
D<34W:P101\ /0:@A0/,\D<0CD[/6B0 : C01\0/,.
ρ
ω
2ω
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@Si }B03D :g4}0/,. , (2) 01J,`DC01CF5 B034/1J,:/,`FG FG 1C34,
1
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β e
V8;:/5 13P,.3DH6`W:[email protected] B0b4’H,,fB34/5{Ig.:P, 34/D1/G,.f\@K [email protected]@K1T/G,
zeKB0:B,.7, /60D</6I:/5B0A=-W:[email protected],[email protected]:k265B34D :g42,./134C [email protected] 0B ML
BQI:@AD&b|© /1Cw/E:[email protected]/G,.:P,.34/r6?B0:.:B,.R23B,D<34 : C 6dW:^@A34 B05 D[3d
: o,.C
@A01CdDI:`:/I:Pu1 /#D<3W:C 1:P,.3/l6 V8;:/5 13P,.3Dj65dV8Z/G,0/1C,.j625–}¨^b
vw:[email protected] A6lj’\y :?,.q34C /G,.-0/5,. 1:/G,265017BQI:@AD1E /5m:[email protected]/,2D<34W:P101
DI:P.: R01§,TD<0CD<0/65 B05W:01bvo1TD<34/110/7D<34W:P 1:P,.k34/265~V8Z/G,./1k,.X6\5–j¨çD<34
B01j60hpB034/5{g4.:a,. 3/1}1C34/G,j63//01 15j :A{Ig4C ÷ b;-:O40B75/:nC1C,[email protected]/,j,Q03 FG
5, 1.:/,\V8ZFGI:P,.34ä
/ > ÷ b; @bI’H,:anC51C,[email protected]/G,`5,. 1jV8ZMhiD1134/Y601\,./11BQI:[email protected]\6
0B, (2)
0/34/5B,.34/!6p‰8Z:/g
6p3P,:P, 34/£6pW:‡D<34 :C 1:P,.3/!65çBMQ:@AD
FX,Y (φ)
φ
34/56I:@A0/,:}FG 134/,Y6„1 @AD01qD<34kui/5‹[email protected]
,
63/G,r [email protected]<3PL
cos(φ)
sin(φ)
1:/G,01A1DQ50FG01K1C34/G,A634/5/01K6I:/51A‰8]©}/5/hi?’}b_vw1A634/5/01KhiD<0C @A0/,:01^D<JL
@A,C,.0/,f6&8]a: fV8;:P/ 1C3,.C34D :m40Bd61f10/51 5 k,.1~,.CR01`6¦[0C0/G,01dŽW:B34/5{Ig.:P, 34/
DI:P.: R7634//
:P 34C1 F5KV8;:P/I:kui1C^65‡Bm:P1dD<0CD<0/6B0 :634//5
ρDCM = 0, 5 ± 0, 5
b
ρDCM = 0, 93 ± 0, 05
ÿ
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Ò©ÓÑÔ³Õ ÷ Zb Ö ¥`0D<34/1C / D<34W:P 1:P,.k34/ 6 V8Z/G,0/1C,. 6 5–}¨ 6&8]0BQI:/,. 3/1 6
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,`D<0cL
5%
I = 0, 4J/cm2
D<0/6B05W:01\:O40B ω
@b
2 > I = 0, 6J/cm
v 8Z~040j6j :[email protected]&8Z:/13P,.34D5 6I:P/1~ }B0:1~6jBQI:@AD1~D:.:R001NB34C34<34C
W:pz: l1/1 ,l6YB0,C,.#B34/5{Ig.:P, 34/ˆD<3K:/I:Pu1A/#[email protected],[email protected]:kPb
Œ_/q¦[,\D<3H601~BQI:@AD1HDI:.:P R010SV8Z3 /G,.:P,.k34/K/34/L€B0/G,[email protected],[email protected] 1
DQ3,34 [email protected]:P01_345/k,H5/j/G,0/1C,.f6 5–j¨ 34J,[email protected]/G,H6g40fDI:P.: [email protected]/G,H:Pih
BMQ:@KD51EMh5B,.:P,.1bUŒ_/D501C0/Bl6&8]/C,dz:A13,34D<A6I:/12W:[email protected]/G,./iL
1,i–j¨SH :‚@A015p6 DC01/G,/p /B0J,.,6?04b\vw:‚{Ig ÷ b ü L€:‚@K3/G,
ρ
1 :/13,34D016Ai–j¨ 6&8ZBQI:/G, 34/134C /G,.1jD<34
, ö b&’H01 6ih„B03<01
ρ = 0, 5
345,0/5q:m40BK01d634/5/01
,.Q34FG01d,[email protected] :01 hiD FG0/,EV8Z/B0C,,.56^6
0, 5
hiD<0C @A0/,:01_6fW:j{Ig ÷ b;aL€:5bj:/51N`Bm:P1N65fBMQI:[email protected]_ /m:C01D<D<0/56 BW:10SW:
[email protected],.C 26p1g4/I:w65–j¨)[email protected],[email protected]/G,}D<34601j:/13,[email protected] B0 :C01
6¦[0C0/,.01bI©}/19/Y5k,`13,34D< :g,~D<0Y15`‰8] /5B00J,.k,.6}6 :[email protected] [email protected]@K}34/
D<05,2 ^B03/1C,.:P,.2152W:q{Ig45 ÷ b ü L€ƒ3 ­‡01J,ED<341C1 5 ^6Az:P W:l6¦[0C0/BK0/,.CKW:
p
[email protected],.C
,
,j=^34J,. 3o:m40B
b<°31}:C34/1V8Z3BBm:P1 3/
ρ = 2/3 = 0, 816 ρ = 1
ρ = 0, 5
6f40k{I0NB}D<3 /G,N:-B341N6-BMQ:D, 3 ­K/341N/3451H /,.1134/51\[email protected] 1
@7,D[3 :PC01~D1`[email protected] hi10b
¤/ P:0\6&8Z:/13,34Dj6
D[3`  ’\yâ/6F5 FG&8] &108Z:g4k,`6&8]/ @K3PL
0, 93 ± 0, 05
B0„DC3BMQ56&8Z5/ 1Cu1C,[email protected]ƒ/6 @A/134//‰bNŒ_/ ¦9,mS~ ?,./1Y6„11B0Di,. 5 k,.
F:6.:a,.F526&8Z5/[email protected] /5 [email protected]/134// k /52D[311R67FG&8]/[email protected]<341.:/,.dBm:J,.L
1 //
bivof,:5 0:l’}b;d6}V8Z©//hi ’!/6F5FG} [email protected]<341:/,.01N1DQF501~6
βzzz
13/G,:341 1 , 3 :m40BAŽ
β
β0
ù
β01 =
r
β0
3
βzzz ,
5
β03 =
r
2
βzzz ,
5
3
1
ρ = kβ k/kβ k =
r
2
= 0, 816
3
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f (Ω)
Ò©ÓÑÔ³Õ ÷ b üÎÖ ©/ 1C3,.3D H65–}¨ /AD<34W:P1.:P,34/51TDI:P.: R01.>z:@UD<3
>D[3 /,. [email protected]
ρ = 0, 5
,
> ,.:k,XD /[@,H/qD<34 :1.:a,.3/1_D<0CD<0/6B0 :01">[email protected]<34
>zD<34/G, [email protected]
ρ=1
ρ = 0, 5
z> D<3 /G,1nH
@ ,
ì> ,..:P,\D0/@ b
ρ = 0, 816
ρ=1
13/G,01C10/,.0 [email protected]/,
wv :[email protected] 62 ’\y 63/G,01fDC34DC ,.01f/3/iL€ /5m:C01`=
532nm
g43540C/01TDI:«_,..:P/1CC,U6NBMQI:Pg4N0/,.CH Xg4C34D<@K/G,U63//05T:@A /_,UNg34D<ML
@A0/,:P,C,..:PB,.U6Bu:P/3jD<05,T634/BH0/[email protected]:[email protected]:a,.3R
/ o,.C~B34/1C [email protected]@A
/[email protected] B05 jI—P,34//,mb
Œ/-5,. 1:/G,_‰8Z:/13,34D5`@A01C}D<345N f ’\y 6I:/1NV8ZMhiD1134/-601NDI::@KR,.C01X @L
DI:P 196_ :H3/B, 34/j66 1J,.5,.34/9S1C,§D<311 T698ZP: 50o‰8Z:/13,34D5 J=3
kf
k/kf J=1 k
6 W:761C, 55,.34/-{I/I:P bj:/1` B0:1`6 BMQ:@KD51`/B060/,.1\DI:P.: R01S5B0 :DD<34J,f:,.
1C,[email protected] = J=3
,= J=3
D<3f6501fBMQI:[email protected]<0CD<0/iL
kf
k/kf J=1 k = 0, 735
kf
k/kf J=1 k = 1, 8
6B0 :10b9’H,C,.6k¦90/5B07B034/5{@A7 EBm:P.:B,.R0CD1j3B,.D<3W:26p,./1 BQI:[email protected]
6&8]0Bk,.C D<34`61fBQI:@AD1`D<34 :11\ /m:P [email protected]/G,\D<D</6 BW:P C010b
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Œ_/^/g4 g40:/G,U 01U,[email protected]\D3DI:g:a,. 3/&SPV8ZMhiD1134/^6\V8Z/G,0/1C,.H65\®`–j¨ 108]0B,
>ì434 ~0FGI:P, 34x
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h
2
N
(3)
I T HG(φ) = 2 kγk2 c00 FX (φ)00
Λ
i 2
X 1+DΛ
(3)
(3)
−
p1 (aabs • c)J(e(1)•FX (φ))J+p3 (cabs • c)J(e(3)•FX (φ))J
+
2J
+1
J=0,2,4
h
> ÷ b;ÿ@
i 2
X 1+DΛ
(3)
(3)
(3)
p1 (aabs • c)J(e(1)•FY (φ))J+p3 (cabs • c)J(e(3)•FY (φ))J
c00 FY (φ)00 −
2J +1
J=0,2,4
#
›€œ 9ž‰VœMš™ý¬Ÿ ~œžšŸ[¨5VžC¢Ÿ„¼¢¬¡XW¼¢zUVž £¡šN줥¡PŸ[š}›p¢8 k8¡iš. ¡P›KžŸ[š.¡0š.Ÿ[€š
3 ­‡,.0/5105 /G,.C4/I:/,E6:/1d ^DC3B01151765K0B,.CA6A‰8]34C6^DQ53,.3 /65, B34JL
c
01CD<34/6?:l,.0/5105/[email protected]: k1j6 W:711CB00Di,. 5 k,.jB FG 6 g40/50.:a,. 3/Y65 ,341 [email protected]
QI:@A34/5 FG
bIv8ZFGI:P,.34/º>Vib ÷ @H65 /G,fFGI:/G,=0 7Ž
γ(−3ω, ω, ω, ω)
"
X 1 + DΛ I T P F(φ) = (aem ⊗ cabs )00 F 2ph(φ)00 −
p1 (aabs •(aem ⊗cabs ))J(e(1) •F 2ph(φ))J
2J
+
1
J=0,2,4
#
N
> ÷ bù @
+p3 (cabs •(aem ⊗cabs ))J(e(3) •F 2ph(φ))J
kIm(γabs )kkIm(αem )k,
Λ
3­ 2ph
1C,\,0/1C0~BMQ:@KDq65j B,}6ýI34C01CB00/5B0d=E6ih
F (φ) = FX2ph(φ) + FY2ph(φ)
DQ3,34/1d1.:/12:/I:ku1050b§j:/12^Bm:1d6AW:r®`_‘HSw ,0/1C02g43454/I:P/G,2 ^D3B01C11
FGTB034C1D<34/6‡=qV8;:5134CD5,.34/[email protected],.:/E66ih
6 B,701C,
Im(αem )⊗Im(γabs )
DQ3,34/1 1k 6 ‰8][email protected] 1C134/l698Z/YDQ3,34/Y6 ýI5341B0/B0b
ω
’H01j0FGI:a,. 3/1}/E171C @AD {I/G,DI:1}[email protected]@A26:/1} 2Bm:[email protected]/Y6^i–j¨)Bm: 1
B03zeKB /G,.1 , /G,.C ///G,~:O40B}61~D<3461N6k¦9/G,.1N6I:/1H :[email protected],.C [email protected]
p1 p3
1 3/1X6f®`–j¨t,N®`_‘Hbi’H01NhiD1134/1X34/G,X /,.C40/5 ,.3 1,[email protected]Ž \,[email protected] 1C3,.C34D<
>
@_D534/I:/,~6} :d6 1J,.5, 34/K:mP:/,H340/G,.:P,.34/A,~ 1X,[email protected]&8;:P134CD5,.34/q=2/
J =0
,f60ihYD5Q3,.3/
1 >
@b|}dD1` B03zeKB /G,6 /[email protected]:1:P,.k34/
1C,0g4: @K/G,
J = 0, 2, 4
Λ
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,K13/£hiD1134/!D<0iT
, o,.CYP:P #=ƒD:C,[email protected]<341:/G,01
34/B,. 3/ˆ6
p1
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1DQF501A61^,0/[email protected]:PC017,A6501,.0/51051ABQI:@AD1^698ZB0k,.Cr63//01A0/
©}//5hi-’}boj:/51 7B0:1 65^BQI:@AD1 /B060/,.1j /5m:[email protected]/G,jD<34 :110S9B^B3reAB00/,d6
/[email protected]:1:P,.k34/‡108]hiDC @[email protected]@A
bxj:/6 ω , 2ω 13/G,
Λ = 16π 2 [1 − p1 /3 − p3 /5]
E
E
√
√
√ b
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2
Λ = 16π [1 − ( 2p1 )/3 − ( 8p3 )/(5 3)]
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030/G,.:P,.34/?/6k,.01j=q5/, 650ih„D5Q3,.3/10b&°31j43/1 FG&8Z5/ƒ1C @AD E:nC1J,[email protected]/G,
,.Q34FGN61U634/5/01T65N®`–j¨34E®`_‘#D<34§/NB03/5{Ig4:P,.34/d6ND<34W:C 1:P,.k34/1o6&8ZB0CkL
,.C2/&8]01J,jDI:P11 eK1:/G,0b[®§345,3410S|o01J,}D<3411d62C0DC01/G,0}W:34/B,.34/
/L
fs (Ω)
6k,.-6I:/17-D :/6qV8ZBMQI:P/G, k34/‡B034C1D<34/6I:P/G,A:Pih6534//01hiD<0C @A0/,:01E1.:/51
DI:11C0 DI:Pj :[email protected]:.:[email protected],.1b>
@b9«345jB00 :q/5341j5,. 1C03/1}/[email protected]
p1 , p 3
D<341k,. 3/ƒ1C @AD 6
1201dD<34ku/‹[email protected]/6K6
3 ­
01C,EV8;:P/g4
fs (Ω)
cos(ϕ)
ϕ
6&8;Œ0`65{I/5w6I:/51f DW:/l6dV8ZBQI:/G, 3/&b
Eû½iÄmïw¿½„ò§ï¿Èë«ëð|¿OÃ-òw½iÄ^½on>À4ÈIÀÁìÃOÆÄ^ò_ók½wÀÁìÃOÈ5ÐÁð<Â_F‡ï§Â½ÃKò§½ï*!ë ê ðIÃOð<§Ä
 :P/1 -B0:176qBMQI:[email protected] CB0 :1p>B03PL 34>B34/,..:L«@d017D53B011C1A698;:5134CD5,.34/>=
j
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@N>z‰8Z:ahij6 DC3PL
X, Y
DI:g:a,. 3/
6KW:[email protected]^1C,E/:ahiK6K 5LÉ3P,:a,.k34/ƒ651Ju1C,[email protected]@bUU:dB03/1F50/G,
Z
4
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f (Ω)
01`[email protected] 11C 34/51`6 ýI31B0/B0E,652®`–}¨Ù43/G,Îo,d 1C3,.C34D<01`6I:/51 DW:P/&b|U:`B03/G,.C
D<345H61~D<3W:C 1:P,.3/1X698ZMh5B,.:P,.34/-D:.: R01N= Si :d6 1J,.5, 3/K/6k,.f01J,~ 13P,.3D<
X
6I:P/1X `D :
/ >
@[email protected]:101J,~:P/ 1C3,.3D<`6I:/1X`DW:/^6f‰8]0BQI:/,. 3/&b°f341N: 3/1T434
Y, Z
DI:PjW:K1k,.7FG0 1j /[email protected]:a,.k34/51}1C :-6 1J,.5, 3/#{I/I:7D<540/q
, o,6506k,.1 601
@D<34N01
C0D<34/1C01H0/-D<34W:C 1:P,.k34/1_61H/G,./1k,.1N6®`–j¨ ,H®`_‘‡6I:/1N `DW:/ >
X, Y
6k¦9/G,.1fB34/5{Ig.:P, 3/1\6&8ZB0C,.5b
päãnö()
ùAãZ!)Þ*%qiâr # øtsTãzâ[àvu # áhà4áhøÑâBZ!) øÑà
wv :Y{Ig ÷ b ö #D1/G,.q012D<34/1C0170/D<3W:C 1:P,.3/ƒ601E /,./1k,.1E6K®`–j¨ ,7®`_‘
@A01C01D<3`601fBMQ:/G, 34/51\6d ’\y
PN’ DQ3,3PL€3 /G,01`:O4Bd601fBQI:@AD1` L
(5%)
/0: C01DI:: R010bTvo1A65¦[0/G,01^B0345<01^B034C1D<34/6/G,-=„61AB34/6k,. 3/176&8Z/g4
P:P001b°f341_,34534/1X /A6I:/51XW:j{g4 ÷ b ö FGf01X:/5 13P,.3D 16f®`–}¨t,X®`_‘
1C34/G,ND<D</6 BW:P 1X:ih^D<34W:C 1:P,.k34/1T601XBMQI:[email protected]: [email protected],.C `6f ~3,.:P,.34/A:L
,34N65 6W:d65 1C,5,.34/A/6k,.:m40B}6501HBMQ:@AD1HD:.:R001X= D<@A,H6&8]P:P X
X
^5W:/B[email protected]/G, DQ3,34 /56k, 61[email protected] /‡ /,.g4.:/, 1g4/I:T65^ýI301CB0/B0
{I/:Î
>D34D<3C,.34//_:ƒ/[email protected]{I/:[email protected] B05 [email protected],20/‡ ^[email protected]:.:P/G,2:P‡1g4/I:T6
ýI5341B0/B02 /5,. :PVb
Ò©ÓÑÔ³Õ ÷ b ö Ö ¥`0D<3/11H/KD<34W:C 1:P,.k34/601X /,.0/51,01_6f®`–j¨t,N®`_‘ƒD<34_601XBMQI:[email protected]
DI:P.: R01:O40B 2ω
V> :[email protected] S_:O0B 2ω
I = 0, 3mJ/cm2 , I ω = 0.5J/cm2
I = 0, 3mJ/cm2 , I ω =
>
z
@
H
,
O
:
0B
>
&
B
@
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b
w
v
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341\B03<1/5d1C34/G,fDI:P1
1J/cm2
I 2ω = 1, 5mJ/cm2 , I ω = 1J/cm2
=jW:}@d0o @A~BQ0 ~,/\@K,,0/G,DI:P10/^60/B`‰8Z:[email protected]/G,:a,.3/76^DQ53,.3W:/[email protected]/G,
:m40Bd01\ /,.0/51,01\ /B 6/G,.10b
[email protected]@AlBm:B0\D<5,uo,Y¦9B,.5?=ƒD:C, 6£1C g/I:~6Y®`–j¨ /!D50/:/G,Kg4:6Y=
:6D<0/6I:P/B0?6YB0Y1 g/I:\/ 2 >1
01C,K r/[email protected]#@A340B05 [email protected]}#D1A01
N
N
:i,.1l @K/G,1q6ç@K3/G,:Pg4?,:/,l151B0D5,. p6&8][email protected],C,.p65ç,[email protected]#QI:[email protected]/ FG
>11J,..:a,mSND<[email protected] @SX01K1g4/I:ihˆ6?®`–j¨ @K1C01q1C34/,l=‚B34C g4-=‡‰8Z:6Y6&8]/
ü
›€œ 9ž‰VœMš™ý¬Ÿ ~œžšŸ[¨5VžC¢Ÿ„¼¢¬¡XW¼¢zUVž £¡šN줥¡PŸ[š}›p¢8 k8¡iš. ¡P›KžŸ[š.¡0š.Ÿ[€š
0BQI:/,. 3/ 6D<34JiE6Nj’\y ,«DC0DI:PX6I:/1§[email protected]@K1wB034/65,.34/1o6XB0/,.kg:P, 34/9b
vo^1C g4/I:[email protected]:m40B^V8ZBMQI:P/G,. k34/p60/B0A:ih„B03/6, 3/1j6&8] /,.0/51,6134/56
> ω
@j63//^/‡1C g4/:T6^®`–j¨ /0g gm:7D: :DD<34J,2:Pih0BQI:/,. 3/1
I = 0, 3J/cm2
634D<1q0/ç ’\y :Oa:/G,-340/,:P, 3/&b_©DR1q34C /G,:a,. 3/!:m40B?601- /,.0/51,01K /B 6/G,01
Sw
[email protected]@K^6I:P/12 AB0:126KW:l{Ig45 ÷ b ö aLÉBA3 ­‡ ADQ53,.3W:/[email protected]/G, P:5,
99%
,.3 [email protected]:@A34/5 FG g40/dDI:` 1`[email protected]/G,1f65#@K3/G,:Pg4 :P,,0 /,
6#1g4/I:9{I/:
2%
,f1C e^,}=^/5ýI/B0f :1C34/6d6501fDI:P.:@AR,01\DI:1\6 :734/5B,.34/r6 61C, 55,.34/&b
vo01l1C g4/I:Pih65pýI5341B0/B06&8Z5/Ô0BQI:/,. 34/!6„ ’\y >
@-:Oa:/G,l,r:DR1
0, 4%/P C
340/,:P, 34/‡13/G,6534//1157W:Y{Ig45 ÷ b ö4ö :m40Bq6017BQI:@AD17DI:P.: R012D<345701FG 1
, ω
b&vw1d:/13,34D01j65^®`_‘Ô13/G,d:anC51C,.01 DI: /5
I 2ω = 300µJ/cm2
I = 0, 6J/cm2
34/B,. 3/E/
,T :fDQ3,3601J,.CB, 34/E01C,UP:P ~=
b
A0 +A2 cos(2φ)+A4 cos(4φ)
61%±4%
v8Z/B0C,.k,.65 15`W:EDQ3,3601J,.B,.34/Y650B34 01C1/G,.0 @K/G,\601` /5B0C,.k,.61\1\ 1
@K1Cd6501f/G,./1k,.1`6 ®`_‘ˆ/k,. :P01~,`{I/I:01`,f/34/Y6 V8;:nC1J,[email protected]/,\,.Q34C FGb
Ò©ÓÑÔ³Õ ÷ b ö4öÎÖ ¥`0D<3/11f0/rD<34 :1.:a,.3/q6 ‰8] /,./1k,.}6 ®`_‘ˆ:mP:/,R> 341:/[email protected],f:D5R01
>zB0B [email protected]_30/G,.:P,.34/6&8]/-BMQI:P/G, 34/^ ’\y
PN’!D<345 2ω
,
(0, 4%)
I = 300µJ/cm2 I ω =
2 :m40B2:nC1J,[email protected]/G,.1\,.Q5034C FG01R> ,.:k,.1~B034/,./[email protected]
0, 6J/cm
’ ,C,.P:I:P, 34/6ÔD5Q3,.3W:/5BMQ5 @A0/G,-D<[email protected],r6&8]P: 50lpB03zeKB /G,r6„/[email protected]: L
H
1.:P, 34/
/%34/B,.34/%65 b_voq,[email protected] 1C3,.C34D<l65rW:?3/B, 34/>6r65 1C,5,.34/‚{I/:
Λ
D
108][email protected] 0/Y /G,0g4:/,`‰8]hiDC01C1 3/#6
634//dDI:\‰8]0FGI:a,. 3x
/ >‰bú ø @}Ž
f (Ω)
0
f00
1
Λ
=
−D 1−
16π 2
16π 2
> ÷ b @
§© 4Bdj :/BQ @A0/,~6&8]/ :B, 34/
6 B[email protected] },[email protected] 13P,.3D[j65 W:E3/BL
F
,. 3/K6}61C, 55,.34/^{I/I:P f01C,~B0|0g4:[:K,[email protected] 1C3,.C34D<f6} : 34/B, 34/K66 1J,.C 5, 3/
ü
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/, :k
1/(16π 2 )
@7k,.DkjDI:P
(1−F)
f (Ω)
,f6534/B^Ž
> ÷ [email protected]
D(16π 2 − Λ) = F
v 8Z:/I:ku1 601f634//5001MhiD<[email protected]/G,.: 1`6d®`–}¨Ù,®`_‘ˆ/50B011k,.2 :B034/5/I:11.:P/B0d601
[email protected]<31.:/,.11CDQ0C FG1}6111CB0D5,. 5 ,.1`B05 FG162®\–j¨ã,6&8Z:13D5, 34/#=A650ih
DQ53,.34/51f:P /1C9FG B0 01~6 W:E151B0D5,. ,}6&[email protected] 34/q6&8Z5/YDQ53,.34/9bIŒ/Y1CDD<341:/G,`W:
@A34 B05 ~6f ’~y 5/ [email protected]/134//50PS [email protected]<341.:P/G,.1_Bm:J,.01C //01X61X1C1B0D5, ,01
/0:1l,#BFG01#1C‡ @A ,0/G,r=%W:>[email protected]<341:/G,ƒ1C034/ V8;:h5@A340BW:k ,#01
z
[email protected]<31.:/,.1K1DQ50FG01-13/G,K634//01-D:A‰8]0FGI:P, 34ó
/ >Vib ö ÿ @b_Œ/!B0YF5fB034/5B00C/?
,0/1C0
g43540C/I:/,[email protected]/q65 ýI5341B0/B02=6ihrDQ3P,.34/1S [email protected]<341:/G,01
a⊗c
1CDQ0C FG113/G,f 1`1Ca:/G,01dŽ
1
(a ⊗ c)00 = √ ,
7
(a ⊗ c)20 = 2
r
5
,
42
(a ⊗ c)40 = 2
r
6
,
77
(a ⊗ c)60 = 8
r
2
1913
> ÷ bü @
ov 01`,.0/51051}FG§g43540C/0/,}W:^®`_‘HS
,
SI3/G,f /G,0J40/
γ(−ω, −ω, ω, ω) α(−ωF , ωF )
[email protected]@Ar,.:P,.1A 0B,.C34/ FG1KFG
b_v_8]QGuD<3,QR01C?6&8Z5/#@K3 B0r5/ 65kL
β(−2ω, ω, ω)
@A0/1C 34/5/0 jD<345`  ’\y‡S|66k,. 6dV8;:P/I:u1C 601f1C g4/I:Pihr65E5–}¨ÙD<5,6534/B™o,.C
5, 1 D<34f‰8Z:/I:Pu1 62 :ýI301CB0/B0=A650ih#DQ3P,.34/510b<®§34i,.3 10SI [email protected]<341.:P/G,.1
65 ‰8]0FGI:P, 34ä
/ > ÷ b ü @N134/,f345,./501f0/Y15DD<341.:P/G,FG 1`6D<‹4 1\698;:5134CD5,.34/
(a ⊗ c)Jm
,`6&8][email protected] 1C134/l65Y ’\y 13/G,`B34 /0:01H: 34C1HF5 :E0 :ah5:P,.34/-/34/iLÉ.:6 :P,. 4}6 V8Z,:P,
Mh5B,#401-‰8],.:P,[email protected] /501B0/,-108Z:[email protected]:g4/#,34anC3451K6&8Z5/Ô:P/g4 Y/34/L€/5/G,?B01
6ihY65 D<‹401™a ö4ö c b
j:P/1B0:1„6>W:!1C1B0D5, ,‚B05 FG>6>g4/0:P,.34/û65>,[email protected]‡QI:@A34/FGS
S<‰8]QGuD<3,QR01C76&8]/ 65 @A0/1C 34/5/I: ,.d1C g4/k{IdF57 1},.:P,.1} 0B,.C34/ FG1
γ(−3ω, ω, ω, ω)
C013//I:/,.1f=
/j34/,\ /G,0J40/~FG 61\,..:P/1k,.34/1HB03 /5m:1~= bj:/51` jB0:1\6
3ω
z
 ’\yƒST 12,.:/1k,.34/12 B,.C34/F5017C013//I:/,.1A=
B034C01CD<34/6/G,A=?61
3ω = 355nm
6DW:[email protected]/G,\6&8]0 B,34/1\/G, 1~g43D<[email protected]/,.1\6534//\,`:B0B0D5,0`FG&1C34/,`¦[0B,. L
[email protected]/G,~65 g401_1034/ >z 1X,..:P/1k,.34/1X B,.C34/F501H /,./1~:ihK/3Ou:ih-</”0/F501
z
1C34/G,fFGI:P/G,=^ 1\134/5/I:/G,01`40C1
@b
250nm
w B
â !%Ix8ö&ã.Z¬ãy%qŒùA÷zu[áhâö&ãäãzâ{u[á&%qiùzø *ö ià
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/G,./1k,.1f62®`_‘£34#62®`–}¨):DR1340/,:P, 3/YD:f/2Mh5B,.:P,.34/#:O4BE6501BMQI:[email protected]
DI:P.: R01Sw_/98Z1C,7DI:P1ED<311 A698ZP:[email protected]/G,E601dP:0C12hiD<0C @A0/,:01d6
,
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p1
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hiD FGY6:/1A‰8]©}//5hi?2bXvw:ƒC3,:a,. 3/%61KD<34kui/5‹[email protected]^6#vo0g0/6C#6I:P/1A rC0D<R
>
@f01C, P:0=-DI:C, 6501 MhiD1134/1 g40/50.:P 1j634//5001 6I:P/1j ED:.:g.:DQ5
X, Y, Z
:m40B
b
[email protected]
ö b;ib ÷ 1C34,
J
(π/2, 0, 0)
RΩ (P (cosϕ))Jm = P J (cosϕ)D0m
−J ≤ m0 ≤ J gs (ϕ)
634/B 6I:P/1f D<R0d65# :<34:P,.3}0/Y3/B, 34/l601fB3reAB00/,.1 J :m40BAŽ
P J (cos(ϕ))
gm
J
J
gm
= D0m
π
2
, 0, 0 g J
> ÷ b ö @
ov 01dB3reAB 0/,.1 J
134/,dP:P 1d6:/1 ‰8]©}//5hiK :/1TFG^ 01 /,.0/51,01
D0m (π/2, 0, 0)
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,.Q34FGf601N634/5/01HhiD<0C @A0/,:01X65W:j{Ig4C ÷ b ö d:O4B 1 J [email protected]@K`D:.:@AR,1
g
,[email protected]: 1 1k,:P,.1 34i,.0/G1dDI: ®`–}¨þ,d®`X‘Nb§vo012:nC1C,[email protected]/,.1 ,.Q5034C FG1
134/,KC0DC01C0/G,01-1CA :p{Ig ÷ b ö ÿ:P /1C\FGY013/B, 34/1
:Ou:P/G,A1C 1AD<34
gs (ϕ)
1\:nC1J,[email protected]/,.™
1 > T HG , T P F 1D<0B,[email protected]/,`D<34HW:2®`–j¨Ñ,~W:2®`_‘[email protected]}:/1
g
(ϕ) g
(ϕ)
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/0CdDI:P` @K34/,:gd>ì434 ~D 1\QI:il, @b
Œ_/%D.:P, FGl/5r /B0J,.,6q/34/iLÉ/0g4 gm:kq1C,A34510J40YD<34V8ZP:I:P,.34/61^B03PL
reAB00/,.1 > 0 2 4 @b§Œ/‚¦[,2D<34d/‡,[email protected] 13P,.3D< 0 {5hiS§/[email protected]/G5,.3/ƒ65 2
g ,g ,g
g
g
:11C3B00K=l/A:[email protected]/,:P, 34/„65 4 3/k, 6501 34/5B,.34/1 6^6 1J,.C 5, 3/
[email protected] L
g
gs (ϕ)
W:10b|’}8]01J,}D[3FG3w6I:/1fW:7{Ig45 ÷ b ö ÿiS/341:m434/1fD0d634/5/0f/dD1/G,:L
,. 3/g4:[email protected]//61 34/B,. 3/1
D5,.‹P, FGA65A6534//d01 DI:.:[email protected],.1
gs (ϕ)
6 ‰8Z:anC51C,[email protected]/G,f:m40Bd6501f1`0 4010b
vo01234/B, 34/51 T P F
, T HG P:0171D<0B,[email protected]/G,=?DI:PC,.d601E1g4/I:ih‡65
gs (ϕ)
g
(ϕ)
ýI34C01B0/5B07,6d®`–j¨ãg.—sB2:ihYhiDC01C1 34/1f,.Q34FG01652‰8]©}/5/hiE /5213/G,DI:1
6/G, FG01H1.:5§D<3~ :2{g4 ÷ b ö ÿL€BPb5«3~ 1HBm:1NL€:E,NL€q3 ­l01H0/50g 01~698ZMh5B,.:P,.34/
134/,dD1 z:P 010S[ 01j34/B,.34/1 T HG P:P 012=lDI:PC,.j601 634//01d6^®`–}¨þ1C34/G,
gs
ü4ù
(ϕ)
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f (Ω)
Ò©ÓÑÔ³Õ ÷ b ö ÿ Ö ©nC1C,[email protected]/G,1~,.Q34FG01™>,.:,1HB34/G, /[email protected]`:/13,34D01NhiD<0C @A0/,:01
6N®`–j¨ç,T®`_‘?63//01U{Ig ÷ b ö ,«34/5B,.34/1
:Ou:/,T1C0Ji01UD<34«V8;:nC1J,[email protected]/,
gs (ϕ)
61f1g4/I:Pihl6d®\–j¨ >D<34 /,[email protected],f6d®\X‘ >,.:k,.1~B034/,./[email protected]
D1213,34D<12FG-B0 01d345,0/G017:O4B- 121C g4/I:Pihƒ6K®`X‘NbT’HB0N1C,7D534I:P @K/G,
6²ƒ:„,.:/1J0C, C013//I:/,d6&8]hiB0k,:P, 34/„67,cuD<A‘€1C,0 34ƒ‘U¥Œ® FG:DDI:P.:Pe, 6I:P/1
EBm:1j6&8]0BQI:P/G,. 34/1B03/B0/G,.C01 /„[email protected]}, FGU /iýI0/[email protected] 3/?6EýI53PL
C01B0/Bb&’[email protected]@K /5341V8ZMhiD F503/1f6I:P/1dBQI:D5,.C ø SI d‘T¥fŒ®t,0/6p=A1C1C, @A0
6I:/51\ 1~1g4/I:hq6j®`X‘Nb|’H,,. 6/R0C @K:FGj1g4/k{I}F5
V8;:/5 13P,.3D6
fs (Ω)
:^g4/0:P,.34/YB034Q/G,.26 ,.3 [email protected] QI:[email protected]/ FG 1C,/d,0BQ/F5ED1f1C²[email protected]
1Cj6&8]346C01~340/,:P, 3//01N1C9‰8]34/-D/6rg4:6j=EBm: C0N01H1g4/I:h-6j®`–tg40/501
DI:P01f [email protected]/,[email protected]/,:g4 ,} 151C,.:P,}6010BQI:P/G,. 34/1b|[email protected] B001` :/BQ 1
D<540/,Hg: @A0/G,g40/50X6^,341 [email protected]~QI:[email protected]/ FG\C01C 6‰bvw:j{Ig4C ÷ b ö ÿL€B\@A34/,.
,345,.34 1~F5dB0,,. ®`–j¨ 01J,/g4 g4m:Pb
Œ/p‰8Z:1C0/B76EB0: .:P,3/&SI 01f34/B,.34/1 T HG P:P 01 =KDI:J,. f6501j6534//01jhGL
g
(ϕ)
D< @A0/,:01\C5,.11.:0/,B,C,.d3 1\D 51fs13,34D<1fFGdW:61C,.C 5, 3/rC0 Pb©} /51
D<345}6501}0BQI:/,. 3/1fD<„B34/B0/,.d
1 >[email protected]@AdD<34W:^{Ig ÷ b ö ÿL€B2:DCR01}DQ53,.345W:/L
BQ @A/Gl, @MSGV8Z,.6f6W: ýI301CB0/B0jD<[email protected],H618;:P¦[.:P/BMQ5 X6V8Z,.6f6&8Z5/qBMQ:/G, 34/
6 C0C0/B2,f601` /B0C,,601\hiD<0C @A0/,:01\F5dB0W: @ADFGPb
j:P/1H fB0:1H65}BQI:@AD1N6&8]hiB0k,:P, 34/K /0:1XD:.: R01SG :dB34//I:P 11:/B}6
6I:/1
gs (ϕ)
-D5W:/‚6-‰8]0BQI:/,. 3/‡1 eA,7D<34EC0DC01/G,0
g4.—Bq=?W:Y A3P,:P, 34/‡6-W:
fs (Ω)
61C, 55,.34/A34C 0/,:P, 3// k:P5,.3N6}V8;:[email protected]@7/K6}D<3W:C 1:P,.k34/&bG«3H01H:P5,.1
B34/5{Ig45.:P, 34/510S< §1C0:,}D<341C1 5 26&8Z,.65 0}V8;:P/ 1C3,.C34Dd657®`–}¨ 34p6E®`_‘6I:P/1j01
D :/{
1 >
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@f/?,.345/I:/,}‰8]0BQI:/,. 3/#65
b9’[email protected]@[email protected] 3/#62®`X‘
X, Z
Y, Z
π/2
1C,[email protected]/ 65 C0B,.34/5/0PS\1.:k,K0g4: @K/G,A0/i1.:Pg4m:5 Y6#B34 0B,.0^[email protected],.:/@A0/G,
ü
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,. 3/&b
åبÜÛØ å
Ö Û}Õ|ÍiÎJÖ_Û ß}Ï!ß}ÎcÚÍÌÎ4õjÞ`Í5ÎcÖ_Û ÍiÖTÍiË_àJÏ H
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«345q1I: 1C0- :‡34/5B,.34/6p6 1J,.5, 34/ˆ,.3,.: PSNfz:5,qD<[email protected]:C0- 1
[email protected]<341:/G,01 D: C01j, @ADI:C01}65
bo’[email protected]@KE/6F576I:P/1 V8ZF:P,.34/->‰b öO÷ @S[01
f (Ω)
B03zeKB /G,.1 /5_134/,§DI:P1w /650D<0/56I:/G,1§B0:wV8ZMhiB0,.:P,.34/j/34/iLÉB0/G,[email protected], FG_D530/,
pi
6 ‰8] /,.0J0C0/B 61:1C34D5, 34/51f=/Y,f6ihYD5Q3,.3/10b
¼q½ôzÈ5ÃOÁzð<ˆ½Â[ÃO¿½pô½Ä½nÀ4ÈIÀÁìÃOÆÄAò_ó ÈJI«Ä0ð|¿aëwÐÁð<Â*¿Æð|¿aÁ½iÂ<ÃOÈ5ÐÁð<Â
°f341`.:DD< 34/51`V8ZF:P,.34/x>Vib öm÷ @HD<34\/ hiB0k,:P, 34/r=^5/#,f60hYDQ3P,.34/1 Ž
p2 2 = p 1 p3
"
#
kIm(β)k2
Φ2 2
cos2 (∆kZ + ∆Ψ)
Φ1 Φ3 kIm(α)kkIm(γ)k
> ÷ b öO÷ @
ov 01q0/[email protected]/,.1
34/,l/G,0C4/- ?B34D :g4?/3/iL€:6 :P,.kj0/,.C„01-,.:P,.1q 0B,.C3PL
Φi
/ FG1qhiB0k,.01q,q 01-,:P,1qDQ3,34 [email protected]~’HpB34D :g4?,:/,r=‚DC 34Cf /650D<0/56I:/G,
6#DQ0/[email protected]/26&8]hiB,:a,.34º
/ >z/#,.35,B0:1f6I:/1f/#1Cu1C,[email protected]/534/iL€B0/,[email protected],.C [email protected]|34/
D<05,f0/[email protected] :DDC3Ohi @K:P,34/l1CDD<341C0fFG 2
bIvo .:DD<3C,`@K3 B0 :C
Φ2 /Φ1 Φ3 = 1
01C, 6D 1 :B0B01C1 5 hiD<0C @A0/,:[email protected]/,mbo’}bo‘U34/³
ãzà
kIm(β)k2 /kIm(α)kkIm(γ)k
!%[email protected]/G,lB„.:D5D[3C,l6:/1l :‚0C0/BŒa; ü c /Ô5,. 1:/G,-5/Ô@A36R0p=60hç/kL
4m:hçD<3-W:‡@A34 B0#65
,lMhiD F50/,lFG
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DR1
p2
i1JL€=aLÉ1N6q.:PDD<34C,
B34C01CD<34/6I:P/G,`=
b’HD[/6I:P/G,mS5B0}DQ0/53PL
p1 /p3 ∝ I 2ω /(I ω )2
p1 = p 3
@KR/^:D5DI:.:ae ,j/[email protected]/, 108] «up:l1.:a,.:P,.34/„65^V8ZMhiB0,.:P,.34/p:O40B
p1 + p 2 + p 3 = C
3 ­
01J,-/YB03/1C,.:/G,bX©113B ?=ƒV8ZFGI:P,.34ó
/ > ÷ b öO÷ @STB0,,.YB034/65,.34/%634//5#V8Z43PL
C
5, 34/6 >
@ 0/‡34/B, 34/ƒ6
0D501C0/,.0q1CE :r{g4 ÷ b öOù >z:O4B
,
p1 , p 2 , p 3
p1
C =1
@Mb
(kIm(β)k2 /kIm(α)kkIm(γ)k) cos2 (∆kZ + ∆Ψ) = 0, 5
vw:l{Ig4C ÷ b öOù 40C{I^0/ƒFGA‰8]34D5, @[email protected] 6
1C,235,./‡D<345
bwvw:[email protected]
p2
p1 = p 3
6ˆ@K:ahi @[email protected]â6&8] /,./1k,.Y5–j¨ = :?{I/ˆ6rV8Z34C /G,.:P,.3/>:D<@A 176l40C{I^Mh5D< L
@K/G,.: @K/G,XV8ZMhi 1C,0/B6&8Z5/[email protected]:[email protected]@Ù6 6:/1N :dC/B0{aZ ü c bG®§345,.34 1SGFG0
p2
01C,dW:q1 g/{IB0:P, 34/p6AB,C,.AB34/6k,. 3/65A1.:a,.:P,.34
/ K«3 601d/0Cg401d698ZMh5B,.:P,.34/
6 2ω
, ω
>6cn=„:P11”r [email protected]/[email protected],.34/17DI:
I = 1mJ/cm2
I = 1J/cm2
@AD13/^:A/k4m:A6`‰8]0BQI:/,. 3/01J,N6`‰8]3465\6
=
,X6
2, 5 1015 photons/cm2 2ω
= b[vo01}1B,.34/1}reAB0:B01 6&8Z:1C34D5, 3/„=K/?,j6ih?DQ3,34/1}6
5 1018 photons/cm2 ω
@K3 0B 1fD<34u4/ FG1}634//50cLc:BB00Di,.05 1C34/G,}6E‰8]34C6d6
−16
2
ü
σ1ph ≈ 10
cm /photon
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Ò©ÓÑÔ³Õ ÷ b öOù
Ö
¢X:CW:P, 3/1 65
>
p1 , p 2 , p 3
(kβk2 /kαkkγk) cos2 (∆kZ + ∆Ψ) = 0, 5
a c ,
σ2ph ≈ 40 10−50 cm4 s/photon
b
@
0/
34/5B,.34/
6
p1
D<345
f (Ω)
,
C = 1
a øöc bj:/1^lB0:1^6rV8ZMhiB0,.:P,.34/>=„/ˆDQ53,.34/9S
bG°f3,34/1
D</6I:/,NBQI:FGf @AD13/&S : D<34D5W:P, 34/76fV8],:a,_hiB0k,.f:P,,0/G,_6534/B
25%
N
j/[email protected] @K3 0B 1~6I:P/1` :7”03/ MhiB0,0PbI©§4Bd/rW:P10~D<341C106:/G,f61` @AD134/51
6
,j5/?,:ih#6EC0D<,, 34/#6
S<‰8]hiB,:a,. 3/?=K6ihpD5Q3,.3/1}0/,..:aeW/2/
22ps
10Hz
:5134CD5,.34/A6&8]0/G34/
D5Q3,.3/1H= BQI:FG @AD134¦
/ a ööOh÷ c bG}34/Bf‰8Z:13D5, 34/A=d650ih
5N
DQ53,.34/51^D<D lV8Z,:P,MhiB0,Y=„Q:5,.6
D[/6I:P/G,A :p6C0r6l‰8] @AD513ñ
/ >‰
25%
DQ53,.34/51XDI:_DC3iB01C11H698;:5134CD5,.34/ @b4©§4BB01N /,.0/51,01SG`@A k0^1C,N634/BfD53BQf6
:q1.:P,.:a,. 3y
/ u[ãzâBZoiâ[à-%} øts„uB),%tözø¨áhâIb&U:P B034/,.0/ƒDC0/I:P/G,d/ƒ[email protected],W:q65A65
6^V8Z,:a, Mh5B,G
>z0/ C34/ƒ5/^/I:/310B34/[email protected] /,C,[email protected]/,dD1 B0345C,.^FG^ 760 :T/G,
6ih„ @AD1C 3/10S< :-1.:P,.:a,. 3/[email protected]//567W:K,.:/1C,.34/?01J, /g4 g4m:Pp>
2, 5 10−9 N
@A34 B05 01f6:/1}‰8],.:P,hiB0k,.ED:[email protected] /?698ZMh5B,.:P,.34/ @\B0EFG«B34C34<[email protected]:P [email protected]
D<C,.5I:P,[5, k1~D<34_650B0C C`‰8] /,.0:B, 3/@A34 B0LÉBMQ:@AD10b4°f341X:C34/1_V8Z3BBm:1C 34/
:YB34C1f6#BQI:Dk,.C2ÿ6&8]341C0C4‰8Z:DD:k,.3/l6d :1.:P,.:a,. 3/r0/#DQ53,.3/[email protected]
/?:[email protected]/G,.:/G,\ 01\ /,.0/51,01\6&8ZMhiB0,.:P,.34/&b
«345XD<34i434 634//50X/5f0D501C0/,:P, 34/KB0:.:PB,.1C,.FG`6fW:j3/B, 34/^6f65 1C,5,.34/
34C /G,:a,. 3// kH,.3,.: PS4/3451X /,.365 1C34/1/KD<3461_C0W:a,.</G,f 1_346501X3 /G,.:P,.34/iL
/ 17D: C1E,@KDI:P1b«°317634//3/16I:P/17W:#{g4 ÷ b 8ö :#3/B, 34/65l65 1C,5,.34/
,3,:\D<3_ 1_634/5/01NhiD<0C @A0/,:01_D501C0/,.01H15XW:}{Ig4C ÷ b ö aLc:j,X0/A1DD<341:/,
DI:P [email protected] FG J=1
bw’[email protected]@A7 1 BQI:@AD1 1C34/G, D:.:R001S[ 1 [email protected]^L
kf
k/kf J=0 k = 0, 2
D<341:/G,01 @ADI:C01j65^W:-3/B, 34/„6^61C, 55,.34/p1D<0B,./G, J=3
b
kf
k/kf J=1 k = 0, 735
vo01`[email protected]<341.:/,.1`DI:1\345,./1f0/[email protected]:/,
15` 1\D<34u/‹[email protected]~6dvo0g0/6C
fs (Ω)
6I:P/1`W:7{g4 ÷ b ö ÿOL€r1C34/G,dŽ J=2
, J=4
b
J=0
J=0
kf
k/kf
ëwÐÁz¾ÁzÄ0ÈiÐÁð<£ò§½pôJókÁzÂ[ÃO½Â§ÄmÁìÃOÆYò§½ 6 LŠJ
k = 0, 65
kf
k/kf
k = 0, 03
½Â!ë«È¿ÈIôzô Oô½#ò§½pôJó ÈI§ÁVÄð|Ãm¿að|ë«Á½#ò§½ %2ÅR#
’ [email protected]@A2/5341}‰8Z:O434/51}hiD FGPS[W:A/B0pa; ühc [email protected]/G,EFG7V8Z/G,0/1C,265–}¨
H
DQ53,.34/6k,.dDC01/G,/p34D5, @[email protected] D<3}/p.:PDD<34C,}63//E601j/G,0/1C,.1j= , b
ω
2ω
ü4ü
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@2,7,.3P,:
fs (Ω)
>
@H6&8]/Y0BQI:/,. 3/rj’\y}>‰ÿ’‘[email protected]’}b[vo01`BQI:@AD1`698ZMh5B,.:P,.34/r13/G,fD:.: R01\:m40B
f (Ω)
ob vo7z:PB,. J=1
:q,.BQ341UD<34
kf
k/kf J=0 k = 0, 2
@ ,,.C 0/Y 6/B0d :/3/iL€B0/G,[email protected],. 6 :61C,.C i,. 3/q,3,:b
K
I 2ω = 0, 3mJ/cm2 , I ω = 0.5J/cm2
 :/1^W:?{Ig ÷ b ö iST/3451A6534//3/1^0g:[email protected]/,^V8Z4345,.34/>65rW:p/[email protected] (2) DQ3PL
j
χ
,.34/6k,^@K: 1:11Cf65Y‰8Z:/ 1C3,.C34Dq6YW:„D<34/1C#6Y®`_‘ /ˆ34/B, 34/%6£.:D5D<34C,
b9j:/1jB01 hiD<0C 0/5B010So‰8]0BQI:/,. 3/?01J, 65ƒ ’\y
X’Ñ, 01
I 2ω /(I ω )2 ∝ p3 /p1
(0, 4%)
BMQ:@KD51}6&8ZMhiB0,.:P,.34/?13/G,jDI:: R01= b9v8ZzeKB0:B,.E65–j¨)1C, P:0E0/p61.:/,
X
‰8] /,.0/51,\@-:[email protected]:P\65j5–}¨[email protected]:PX‰8] /,./1k,.\6KBMQI:[email protected]^34/6I:[email protected]/G,:P|:KB0:Cb
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∗
e
IeT P F
= kIm(γabs )kkIm(αem )k
ZZ
|z(θ, ϕ) · Eω |4 |z(θ, ϕ) · e|2 f (ϕ)sin(θ)dθdϕ
>ø bö @
3 ­> :?/3P,:P, 34/
B031D<34/6ˆ=?/[email protected]//5q,[email protected]<34 A17 :#FG0/Br34D5, FG
(...)
6#‰8][email protected] 1C1 3/ˆFGf1.:‡[email protected] 1CYDI:PK :ƒ1C,bH’[email protected]@AYMhiD F5?:!B34C1-61-BQI:Dk,.C01
DB060/,.10So :KýI5341B0/B0A=q650ihpDQ3,34/1j/&8]01J, DI:1j1C0/1C :ih?,[email protected] @ADI:C16
W:K34/B,.34/„656 1J,.C 5, 3/&b[U:jB034/510FG/G,
D<0iq
, o,[email protected] :B0EDI:
6I:/51
f (ϕ)
fs (ϕ)
‰8]0FGI:P, 34/ > ø b ö @[email protected]&8Z:/ 1C3,.C34DN65HýI5341B0/B0\134/,T¦[0B,.01DI:«3,.:P,.34/
6 W:7D<34W:C 1:P,.k34/q6#BQI:[email protected] ω 6I:/1` DW:ä
/ >
@[email protected]~6&8]/#:/g4 :O4BAŽ
E
X, Y
∗
∗
IeT P F (φ) = (e⊗e⊗Eω ⊗Eω ⊗Eω ⊗Eω )(φ)
∗
ö 4
∗
φ
ZZ
•
(Im(α)⊗Im(γ))(θ, ϕ)fs (ϕ)sin(θ)dθdϕ
= (e ⊗ e ⊗ Eω ⊗ Eω ⊗ Eω ⊗ Eω )(φ) • U,
> ø bú[email protected]
H¬ŸgžŸ32€Ÿhš9¡šŸ[šR 9
¡ @T™^N¡y¡Pœl¤ k.›Kž¡¡Cž
¢OŸš™š*¡¬¢Oœš¡M0š.Ÿ[0š
RR
3 ­
01J,qY,0/1C0-6#.:P/g‚1Ckhˆ6{I/
U = (Im(α) ⊗ Im(γ))(θ, ϕ)fs (ϕ)sin(θ)dθdϕ
[email protected]@A ,0/[email protected]:B0C341B34DF5d6d®`X‘Nb[vodDC36,`B034/,..:PB,.dB0 L€65011C1D<05,Îo,d6L
4 34D5D[d=‰8Z:[email protected]<341.:P/G,.1`Bm:J,.01C //01f1 3/ƒŽ
X
IeT P F (φ) =
i,j,k,l=X,Y
vo01`hiDC01C1 34/1f61
Ei Ej Ek El (φ)
> ø b÷ @
Ueeijkl Ei Ej Ek El (φ)
1C34/G,f63//016:/1`‰8]©}//5hi2Œ!,dŽ
ZZ
ze ze zi zj zk zl (θ, ϕ) fs (ϕ)sin(θ)dθdϕ
ZZ
ze ze zi zj zk zl (θ, ϕ) P J (cos(ϕ))sin(θ)dθdϕ
Ueeijkl = kIm(γabs )kkIm(αem )k
> ø bø @
,
13/G,01UD3anC0B,.34/1U66D<‹4 N6H,.:/1C, 34/2,6BQI:[email protected]&8ZMhiB0k,:P, 34/71CT‰8Z:ahi
Ej
D<345P:P/G,Îo,.C S 34 b|v8;:P/I:u1Cd/#D<34W:P1.:P,34/l65
108]¦[0B,.2DI:`C3,:a,. 3/
j
X Y
Z
fs (ϕ)
6\ ◦ = ÷4ù ◦ 6~‰8Z:/g4 :11C3B00\=jW:@A015~6~‰8][email protected] 1C1 3/E6~®`_‘„1C034/01T65 B, 34/51
φ
6&8Z:/I:Pu1
, b««342D<34i434 d6k¦9/B00dW:YB34/G,5,.34/ƒ601E65¦[0/G,1E36C01
X
Y
J
67W:A34/B,. 3/p665 1C,5,.34/9S<61 B03zeKB /G,.1 1C34/G, B0: B 1jD<345jBMQ:FG^36C76
U
:[email protected]<31, 34/ƒ6
1E012D<34ku/‹[email protected]/65;> P J J
@d:O0B
fs (ϕ)
J f P (cos(ϕ))
P J
J ,dŽ
zj
Ueeijkl =
J
Ueeijkl
J
Ueeijkl f
= kIm(γabs )kkIm(αem )k
> ø búÿ[email protected]
ov 01dB3reAB 0/,.1d/[email protected]:1C01 J
13/G,d634//126:/1dV8Z©//Mh5
Ueeijkl /kIm(γabs )kkIm(αem )k
ŒÑ,B34/1J,.,0/,5/qI:P1q6-B03zeKB /G,.1715701FG 1EW:#C0D<34/1Cl/>D<34 :1.:P,3/‡6
[email protected] 34/q6 ýI34C01CB00/5B0ED<5
, o,[email protected]<310d1C034/ƒŽ
IeT P F (φ) =
X
i,j,k,l=X,Y
[
X
J
> ø bù @
J
f J ]Ei Ej Ek El (φ)
Ueeijkl
’ [email protected]@A`:m40Bf010FGI:P, 34/1>VEb ø @T5, k1.:/,/^[email protected]:[email protected]~1CDQ FGPSG 1_DI:P.:@AR,01 J
H
f
Mh5D<@K/G,:PihAD<054/G,Ûo,.f /i01X6V8Z,.6f/-D<34 :1.:P,3/^6 T P F 0/KB034//: 1cL
Ie (φ)
1:/G,f01\B03zeAB0 /G,1 J
>z :7B034/B346:/Bd601`[email protected]:[email protected]~1C,`40C{Id6I:P/1
UAABCDE
V8Z©//hi-Œ©@Mb«vo01EB3reA
B 0/,.1 J D<345a:/G
, o,AP:C 1E=#D:C, 6012B034/65,.34/1 hiD<0CkL
f
@A0/,:01X6&8Z3 /G,.:P,.34/&S/31~: 34/51XD<34543 XP:P HV8Z/5ýI/B06l‘T¥fŒ®ç15 T P F
Ie (φ)
/Y34/5B,.34/r65dV8;:P/ 1C3,.C34Dj65#@A k09b
úØ«×2بÜ
+ÛÎcÚiÖTÍÌÖØjÎcÏûßÏóò}Þ}ÖÌÏoÚÕ[ÏoÛ}Õ9Ï ÏoÛ
ØÌÓoÚÏoÛ}Õ[Ï ß}Ï
?Ÿ_Ý]D
Œ /?DC01C0/B76d,.:/1CC,01C34//I:P/G,}6&8]hiB0k,:P, 34/&SIV8;:/5 13P,.3D 65dýI34C01CB00/5B076L
_
<D /6l6}W:[email protected],.C 6}W:2D5Q3,.3MhiB0k,:P, 34/K,~6}W:d6D<0/6I:P/B0 :/gW:Cf6qB0345DW:g
öü
›€œ 9ž‰VœMšdH¬Ÿ–^˜—wšOV ¡[email protected]™™^"¡y¡œ.§{š0X¡œš šO=z¤ k0.œž‰v¡œMššÎz¤ ¢œzœš© œ ¢¼¢žŸZ ¡ž‰
0/,. 1 B[email protected] " Z¬áhâ[â/ã() ùAö " , " ,enãzu à4ã() ùAö " b9v_8]zeKB0:B0k,.6„,..:P/1CC, 6&8]hiB0 L
,:P, 34/‚650D<0/56ˆ6z:PB,.7C0 :P,.k\6&8]34C /G,:a,. 3/ 2 0/,.q-6 D<‹ " Z¬áhâ[â/ã()¬ù " 340/,.
κ
1034/
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>ì434 f©//MhiŒ[email protected]
z1 (θ1 , ϕ1 )
z2 (θ2 , ϕ2 , ρ, ξ, θ1 , ϕ1 )
(ρ, ξ)
6{/,H‰8]34C 0/,:P,3/K6-0B,0
FG[ f [email protected] 0B01X6I:/1HD<R0Cb>
@
u12
θ1 , φ 1
,
‰8]34C 0/,:P,3/%6ˆ[email protected] " ,enãzu à¼ã()¬ù " 6I:/51A rC0D<R0C
bX’[email protected]@K
(θ2 , φ2 )
(ρ, ξ)
hiD FG#6I:P/1KW:/B0}a ø c SX/5341K1D5D[3134/51qFG|>
@S
,
1C34/,
θ1 , φ1 (θ2 , φ2 )
(ρ, ξ)
601 P:PW:P 1j /650D<0/56I:/,.01b§vw:lB34/G, 55,.34/„65‡‘T¥fŒ®Ù=lV8Z/G,./1k,.E6ý341B0/B0
:/I:ku10Y1 34/ 1C,-63/B#Mh5D5 @A#/! /,.g4.:/,A1A101A,.C34 1^B34D01A6YP:PW:P 1
e
340/,:P, 34/5/01~1034x
/ aö ÷ S ø c Ž
IeT P F/F RET
ZZZZZZ
= kIm(γabs )kkIm(αem )k
|z(θ1, ϕ1 )·Eω |4 |z(θ2, ϕ2, ρ, ξ, θ1, ϕ1 )·e|2
×κ2 (ρ, θ2 , ϕ2 )f (ϕ1 )f (ϕ2 )sin(θ1 )sin(θ2 )dθ1 dϕ1 dρdξdθ2 dϕ2
> ø b @
’ [email protected]@K^[email protected]@K/G,mSw1 A :rDI:J,.^B0/G,[email protected], FGA6AW:l3/B, 34/ƒ65K61C, 5iL
H
,. 3/ç/G,.C /G,0bH¬€j01J,YD<311 p6&8]5, 1C0-/[email protected]#,./134C #B034/,..:PB,.D<34qhGL
[email protected];:P/ 1C3,.C34D?6pýI34C01CB0/B0‡/Ôz:1.:/,l /,.0J40/5 q ?,./1Y6&8]@K1134/ç6
[email protected] " ,enãzu à¼ã()¬ù " ,~f,./1~6&8Z:1C34D5, 34/q=26ihqD5Q3,.3/1H6qB[email protected]
" Z¬áhâ[â/ã() ù " 1 3/ƒŽ
ZZZZZZ h
∗
∗
IeT P F/F RET (φ) = (e⊗e⊗Eω ⊗Eω ⊗Eω ⊗Eω )(φ)•
(α2 ⊗γ1 )(θ2, ϕ2, ρ, ξ, θ1, ϕ1 )
i
2
×κ (ρ, θ2 , ϕ2 )fs (ϕ1 )fs (ϕ2 )sin(θ1 )sin(θ2 )dθ1 dϕ1 dρdξdθ2 dϕ2
∗
∗
= (e ⊗ e ⊗ Eω ⊗ Eω ⊗ Eω ⊗ Eω )(φ) • U F RET ,
> ø [email protected]
3­ F RET B034C01CD<34/6Ô:£,.0/[email protected]:B31B03D FG#6&8Z36C ù 65?ý341B0/B0=‡60h
U
DQ3,34/1`0/YD1/B026d‘T¥fŒ® b<[email protected]<341:/G,01`Bm:J,.01C //11C34/G,fMh5D5 @A01`DI: Ž
ZZZZZZ
F RET
Ueeijkl
=kIm(γabs )kkIm(αem )k
z2,e z2,e (θ2, ϕ2, ρ, ξ, θ1, ϕ1 ) z1,i z1,j z1,k z1,l (θ1, ϕ1 )
×κ2 (ρ, θ2 , ϕ2 )fs (ϕ1 )fs (ϕ2 )sin(θ1 )sin(θ2 )dθ1 dϕ1 dρdξdθ2 dϕ2
> ø bü @
’ [email protected]@Kq0/ˆV8;:P1/B0r6Y‘U¥Œ® STB0l,0/[email protected]:B341CB034DFGlD<05,do,[email protected]<341r0/
H
D3anC,.:/G,2W:r3/B, 34/‡6K6 1J,.5, 3/‡1CE012D<3u/‹[email protected]/65q:O4B F RET
Ueeijkl =
P
F RET,(J,K) J K ,dŽ
J,K
Ueeijkl
f f
ZZZZZZ h
F RET,(J,K)
Ueeijkl
= kIm(γabs )kkIm(αem )k
ö4ö z2,e z2,e (θ2, ϕ2, ρ, ξ, θ1, ϕ1 )
×z1,i z1,j z1,k z1,l (θ1, ϕ1 )κ2 (ρ, θ2 , ϕ2 )P J (cos(ϕ1 ))P K (cos(ϕ2 ))
i
>ø
×sin(θ1 )sin(θ2 )dθ1 dϕ1 dρdξdθ2 dϕ2
b ö @
H¬ŸgžŸ32€Ÿhš9¡šŸ[šR 9
¡ @T™^N¡y¡Pœl¤ k.›Kž¡¡Cž
¢OŸš™š*¡¬¢Oœš¡M0š.Ÿ[0š
ov 01_B3izeAB00/G,1X/[email protected]:P k101 F RET,(J,K)
1C34/G,_634//1X6I:P/1_‰8]©}/iL
Ueeijkl
/kIm(γabs )kkIm(αem )k
/MhiEŒ£,fV8Z/G,./1k,.j6 ýI5341B0/[email protected] 1C :DR1`,.:/1J0J,f108]hiDC @A [email protected]@AŽ
IeT P F/F RET (φ) =
X
[
X
i,j,k,l=X,Y J,K
F RET,(J,K)
Ueeijkl
f J f K ]Ei Ej Ek El (φ)
> ø b ö4ö @
v 8] /[email protected]:a,.k34/A1HW: 34/B,. 3/-6}6 1J,.5, 3/-:DD<34J,.jD:HB,,jhiD501C1 34/qz:P,N /,.JL
4/ \/[email protected]:/5g4 6501fDI:P.:@AR,01\6&8]3465 6I:/1` D365, J K b
f f
úØ«×2Ø å
ÐÛHÍiÏoÛÚiÎÉÍiÓûßÏóò}Þ}ÖÌÏoÚÕ9ÏoÛÕ9Ï ÍiÖTÍiËXàcÏ
«34~D<345434HP:P \ :2.:B,.34/q6j‰8] /,.0/51,}6}ýI34C01CB00/[email protected]:~61`BQC3PL
@A34DQ301 " ,enãzu à4ã() ùAö " S|/31j: 34/51fhiDC @A0V8Z/G,0/1C,. 62ýI34C01CB00/5B0^=K60ih?DQ53PL
,34/1 ,.3,.: 70/ƒ,0/I:P/G,[email protected],^601dD<3DW:a,. 3/1 @A340BW:k1 @K,,.:/G, 0/‡DC01C0/B-,
/?:510/5B02652‘U¥Œ® Ž
IeT P F/total (φ) = IeT P F (φ) + T IeT P F/F RET (φ),
> ø b ö [email protected]
3­
01J,^/>DI:.:[email protected],.-698;:nC1C,[email protected]/,^D<@A,,.:/G,76&8]P:P V8ZzeABm:B,.-6,..:P/1CC,mb
T
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B 6/G,}, :P/I:u1C001}1C034/
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e = X, Y
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V8ZzeKB0:B,.f6f,..:P/1CC, 108Z:[email protected]:g/6&8Z5/[email protected]:/5g4fD534g4C01C1o6501H1g4/I:Pih-:/:u11
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X
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T = 1,2
@A0 :/g4d0FGkP: /G,j61jD<34W:C 1:P,.k34/1f6&8][email protected] 11C 34/^nC51FG&8Z=l6D<34W:P 1:P,.3/#67‰8][email protected]/
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1:/1:P/I:u1C0R
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DI:.:P [email protected]/,`=
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kf J=2 k/kf J=0 k = 0, 3
,
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34/G,:13<201fDQ3P,.34/51 /5B0 650/G,1>zD:.:@A,.01fDI:
6I:/51 D :/Y62V8ZBMQ:/G, k34/@
ϕ1
,f/#DI:PC,. 1`B[email protected] " ,enãzu à4ã() ùAö " >zD:.:@A,1`DI:P @b
ϕ2
°3451 : 34/51}D1/G,.dB0«W:-650D<0/56I:/BK:/gW:CE6501 [email protected]<341:/G,01 67W:-DC34I:5kL
/‡D10/5B0-6K‘U¥Œ® b§vw:[email protected], ^6A :lDQ3,3hiB0k,:P, 34/61
k,.698;:5134CD5,.34/
Pabs
[email protected] " ,enãzu à4ã() ùAö " B34C01D<3/6q:KD365,X65 : DQ3P,.3Mh5B,.:P,.34/A61NB[email protected]
DQ34C01 " Z¬áhâ[â/ã()¬ùAö " DI: W:-34/B,.34/6,.:/1CC, 2 bwj:/51d B0:1 6^‰8]hiB0k,:P, 34/„=r/
κ
DQ3,34/„6I:/1 7D5W:/p6V8ZBMQ:/G, k34|
/ >zBP8Z1C,d=q6 C7D<345
@MS90 E18ZMh5D5 @A
θ1 = θ2 = π/2
[email protected]@AŽ
1ph/F RET
Pabs
(ϕ2 )
=
ZZ
π
1ph
Pabs
(ϕ1 )κ2 (ρ, , ϕ2 )f (ϕ1 )dϕ1 dρ
2
> ø b öm÷ @
’ ,C,.NMh5D501C1 3/765N :\DQ3,3hiB0k,:P, 34/ @K3/G,_FG&8]0 P:C X:m40BN :`[email protected],.X65N :\3/BL
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bU}:/1EB0-B0:1E 12,[email protected]<341.:P/G,.1E6- :
f (ϕ1 ) = 1/(16π 2 )
DQ3,3hiB0k,:P, 34/l0/YD1/B026 ,.:/1J0C,`D[54/G,}[email protected]`[email protected]@AŽ
ZZ
π
1ph
Pabs
(ϕ1 )κ2 (ρ, , ϕ2 )dϕ1 dρ
2
ZZ
π
2ph/F RET
2ph
Pabs
(ϕ2 ) =
Pabs
(ϕ1 )κ2 (ρ, , ϕ2 )dϕ1 dρ
2
ZZ
π
1,2ph/F RET
1,2ph
Pabs
(ϕ2 ) =
Pabs
(ϕ1 )κ2 (ρ, , ϕ2 )dϕ1 dρ
2
1ph/F RET
Pabs
(ϕ2 )
=
> ø b ö0ø @
i34k, tot
W:qD3I: k,76&8Z:1C34Di,. 3/,3,:P 70/ƒDC01/B0
F RET
Pabs (ϕ) = Pabs (ϕ) + T 0 Pabs
(ϕ)
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cos(∆kZ + ∆Ψ) = 1 50%
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D<34}‰8]hiB,.:P,.34/?=
T = 0, 02
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b|}3/B
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Pabs
(ϕ) = 0
50%
[email protected]/G5,.3/l6&8]/rz:B,0`650ihr6dV8]hiB0k,:P, 34/q/34/iLÉB0/G,[email protected], FGPb
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kf
kp
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f (Ω)
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Pabs (ϕ)
:/B[email protected]/G, Ž
1ph/tot
f (ϕ)∝1 − p1 Pabs
1,2ph/tot
(ϕ) − p2 Pabs
2ph/tot
(ϕ) − p3 Pabs
(ϕ)
> ø b ö ÿ[email protected]
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@}61 34/B,.34/1j66 1J,.C 5, 3/1}DQ3,34 /L
X, Y
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50%
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b
X, Y
p1 = p3 = 0, 3
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[email protected]
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P:P ^01 DI:.:[email protected],.1 6&8]34C6^DI:1 ,d @ADI:C1j6^W:-34/B, 34/„6^6 1J,.5,.34/pDQ3,3PL
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DI:.:[email protected],.C01\6&8]3465 @KD:C1~,f65 ‰8Z:/13,34D5}@K3 0BW:PC}/&8Z1C,fDI:1\@K1j0/YB0:1Cb
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SU :?0D501C0/,:P, 34/%65lW:#3/B, 34/6l65 1C,5,.34/=pDI:J,.
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B0345<01E,[email protected]<34C0 [email protected]>43 d{Ig1^ÿib ö =„ÿib ö4ö @S§X/&8]01C,DI:P17D<341C1 K6&8Z35,.ML
/ ~/#:nC1J,[email protected]/G,`B034C0B,f61f63//01fhiD<0C @A0/,:01\D<34\/r/ FG B034D5 d> 0 S @MS
R d
B8]01J,}=76 C D<3\/ / FGj,:P }6501`Bm:m,.1\6 C}3,.:P,.34/q601`@A340B 1~6I:/51`W:
@-:a,.B0 :@A34DQ5b|’HdDQ/[email protected]/d6B0345 6d :61C,.C i,. 3/l601`,.: 1\6 D<341f6I:/1
~D<[email protected]\43FG0f6I:/51_W:}/B0Ra ÿ c bvw1_01C1.:[email protected],.D1T6&8Z:nC1C,[email protected]/,X61_634/iL
/01 hiD<0C @A0/,:01}34/G,[email protected]/,.2W:K/0B01C1,^6576¦[0C0/B j6501 D<301j3 ­pW:K6k¦91C 34/
[email protected] 0B0101C, D1}[email protected]/1}:1b9Œ_/„D:P,.FGE/341 :m434/1j,7B034/56,1 =- /,.3aL
6 ø B0345D 1w> 0 S @`B031D<34/56I:/,.1 =K601}D<341}62,:P 01`60B3411.:P/G,.1j,}634/BE=
R di
601B03reAB /G,.1 6i0B3411:/G,10bGv8]0FGI:P, 34/6\6¦[1C 34/701J,XC013 \D<3BQI:FG`B34D
di
,\ 01H3/B, 34/1H6 61C, 55,.34/K{I/I:P 01~1C34/G,`:anC35,.01`:m40B 601\D<3461~ 650/,. FG1q>
@b
25%
vo01jP: 1j601 B03reAB 0/,.1 /13/G, DI:P1 / FG1 @K: 1B034C01CD<34/6/G,2=lV8Z35,./G,.34/
di
6&8;:nC1J,[email protected]/G,.1Y1:P,.1Cz:1.:/,.1l6501Y1g4/I:hÔ@A01C1#:O40Bƒ/ D:P,.FG%Ž
S
d1 /d4 = 8000
,
b
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«345\/ B0:Ok,. 6 g4.:P/6j,:P PSiW:E6¦[134/l3 /G,.:P,.34// k}61`@K3 0B 1~DQ53,.3MhL
B,.01 1C,dFGI:160/,. FG^=lB0 [email protected] 1 :PƒD<3410bwvo12:nC1J,[email protected]/,.1 6,345,.1
01^634/5/01K34/G,A,.Y¦[0B,.1q:m40B 0
b_vw:ƒ65 @A/5,34/>[email protected]/134/161
R1 /d1 = 3, 5
S
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B0:O,01-1C#,.:6k,KDI:K/!.:D5D[3C, 0 B0C34 1C1.:/,q:O4BŽ 0
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bf’[email protected]@AphiD FG„6I:/51rW:‚/B0_a ÿ c S~ :D1/B0ƒ6B0:O,01l3 ­ÔW:
R40 /d4 = 20
6k¦951 3/‚&3 æ`/0//- 13P,.3D<-1C,0/,.-Mh5D5 FG-V8Z34i,.0/,.34/‡6&8Z5/>346C-DQ3,34 /56,
1J,:P, 34//: CE:PDR1j340/G,.:P,.34/9b<U:}B034/,.E‰8Z:@ADk,6265„B03zeAB0 /G,
>,j6I:/51j/
d1
@A34 /[email protected] @P:r/67/^6 @A/5,3/„/3,.:6^V8;:/5 13P,.3DE6^W:q6 1J,.CkL
d2
i,. 3/r601fB[email protected]
vo#5,- Bf/&8]01J,lD:1-698ZP:0KDB0 [email protected]/,q61qB34/1J,:/,.01-DQGu1C FG01q6#W:ƒ@K:P,.C B
D<[email protected]@K:[email protected],,.C-:‚D<34 /,E5/@K365R0 A65u/I:[email protected]/Ga: :/G,d15E F50N/31
: 3/1TD<34543 ,6 _‰8]43 5, 3/601XDI:P.:@AR,1 S , 0/^34/B,. 3/^6 ω , 2ω b
p1 p2 p3
I
I
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R di
1:/1XDB0 1C0X 1X/B0C,,.5601bvo1H:nC1C,[email protected]/,.1X34/G,X,.f¦[0B,.1~:O4B5/B34/1J,:/,.if6
6k¦951 3/[email protected] B001~DQ3,3hiB0k,.01f6I:/51f01`D5 1\D<,.k,.1`Bm:mik,.1f65 0
b
R4 = 10−3 s−1
v8Z:anC51C,[email protected]/G,U601U634/5/01ThiD<0C @A0/,:01«61T/G,./1k,.1U65\5–j¨,U6H®`_‘[email protected]:P01
:[email protected] `,.Q34FGj:[email protected]/G,FGjW:P/BMQ5 @A0/,HD5Q3,.3 /65,H:2/}65u/I:@A FG}D1
0/G,`FG`W:j340/,:P, 34/&bŒ/KD5.:P, FG\ \DI:P.:@AR, FG|: D<[email protected]`C0/[email protected],.
D
b
61d1 g/I:ih„@K1C01dD<34 6¦[0C0/,.1d /G,0/1C,01 6AD<[email protected]<^B34C01D<3/6= 0
R4 /D = 10
y#17=?DI:PC,71C7012{Ig1^ÿibúSTÿib ÷ ,Aÿb ö ÿiS«B017DI::@AR,.C01E1C34/G,7B03/1C41^B034/51C,:P/G,.1
,345,f:Y34/g6 B0dBQI:PD,b
°f341jDC01/G,34/1 1j :K{g4ÿib ö Lc:KW:K65u/I:@AF576&8]43 5, 34/?601j /,.0/51,01}6^5–}¨
, ®`_‘ÔFGI:P/6ƒV8ZBMQ:/G, k34/?01C, hiB,A:m40BQ> ω
@j:/1
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FG2‰8Z:/13,34Dk {/I: u>{Ig45Eÿib ö L€&@~6011g4/I:PihY62®`_‘!:nC1C,01}=A‰8Z: 65 [email protected]
6B0C, B0kLÉ601C11b§’H,d:anC1J,[email protected]/G, /3451 D<@A, 615‰8]43 5, 34/?6^ :qC0D<34/1C^0/
D<34 :1.:a,.3/-6 V8Z/G,./1k,.6 ®`_‘%:lB341\65 ‰8]340/,:P,3/[email protected]@K}/5341\[email protected]/G,34/51
1C\01N{Ig4C01fÿib ö LÉ&SGL€B},HLÉä
6 >zD<345~61\.:134/1HD:P,.FG01~1 jW:2D<34/1 /rD<34 :1.:L
, 34/q{I/I: 01C,[email protected]@b
°f341X:O43/1X1CD<0CD<341/A{Igÿib; 01634//5001XhiD< @A0/,:P 01DB060/,.01N,XV8Z434 L
, 34/2,Q03 FG~:a,,./6~6501T1g4/I:hE6\5–}¨Ô,®`_‘?1.:/1TD5Q3,.3aL€ :/BQ @^0/,mbaj:/51TB0
B0:1T‰8]34C6NDQ3,34 /56,U:P,,0/G,U//k4m:71C,.:P,.34//I:X,T‰8] /,.0/51,N6`i–j¨ç{I/: H1:/1
DQ53,.361C,B,. 3/q1C,~1CD<0C j:hK634//5001HhiD<0C @A0/,:010bvw:2D<34/1Cj/qD<34 :1.:L
, 34/?67‰8] /,.0/51,26®`_‘[email protected]:P07=q :KýI5341B0/B0^ /5,. :P 40C{I7 :-B34/1CP:a,. 3/
6Y/[email protected] 6 [email protected]`B034/5B00C/01D:`V8Z3 /G,.:P,.k34/&b
°f341:O434/51D1/G,.E/#{Ig45Eÿib ÷ ‰8Z:nC1C,[email protected]/,f60163//01}Mh5D<@K/G,:P 1f0/#5,. L
1.:P/G,f/[email protected]/,j5/EQuiD<3P,.QR176E5W:/B[email protected]/G,:/13,34D<d1.:P/1}340/,:P, 34/YDQ53PL
ö
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1.:/g01A
@ ,j®`_‘ >zB0CB0 [email protected],jB03<1},.Q34FG01j:nC1J,.01b>,.:k,.1fB34/G, /[email protected]`D<34{> ω
I =
@ bN¥fD<34/1Cp/D<34W:P1.:P,34/ˆ61-1 g/I:ihˆ6?®`_‘ã:D5R01
2 2ω
2M
0, 6J/cm ; I = 0, 3mJ/cm
> @ S
340/,:P, 34/}z> B0CB0 1n
@ [email protected]::hpB34<1j,.Q34FG01j34i,.0/G01 =
t = 0s
t = 20s
z> B&[email protected] S
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@ ,
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¯
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t = 400s
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t = 4000s
d1 = 0, 4s
−1 ¯
R20 = 0, 2s
−1 ¯
p1 = 0, 3 p2 = 0, 26
¯
¯
¯
¯
¯
b9y# 1=KDI:J,}01B3reAB00/,.1
d3 = 10−3 s−1 R40 = 10−3 s−1 d4 = 5 10−5 s−1 D = 10−4 s−1
S 01`:5,01`DI:P.:@AR,01\6&8Z:anC51C,[email protected]/G,1f134/,fB034/510J401B03/1C,.:/G,1fDI:\W:71k,.b
p3 = 0, 55 R10 = 1, 4s
−1 ¯
d2 = 0, 05s−1 R30 = 10−2 s−1
pi
,.34/6k,. >
@bUvo017B0345<017,Q03 FG17D10/,./G,^/>[email protected]<34J,[email protected]/G,76iui/:@KFG
R=0
/65 1C, /B, 61 63//01 hiD<0C @A0/,:010b&Œ/DI:C, B } :qB3411:/B0.:PD 657601 1 L
g4/I:hKMh5D< @A/G,:PihK6ji–j¨û:K6055,~65‰8]340/,:P,34/^/&8]01J,~DI:1_40C{Ibivw:[email protected] L
1.:P, 34/YDI:Pf/?5W:/B[email protected]/G,`/34/iLÉB0/G,[email protected], FGPS<FG§1C,}/1/1 d=A :^6 1J,.C 5, 3/
601d,: k01 6KD<34C0126‚D<[email protected]/,.q:‚B34/,..:P ^/A,:/5g40/,.K/G K=
t = 0s
1 W:-B0345<^6&8]43 5, 34/„65^V8Z/G,./1k,.E6A5–}¨þ:m40B^7,[email protected]’H,,,:/5g40/,./
01C,H6j=dW:d1C0/1C k,.`6‰8] /,.0/51,f65 5–}¨Ñ:PqB0:C6} :d151B0D5,. ,fFGI:65.:P, FG
@-:PB031B03D FG (2)
FG01C,_/ \:mP:/,_340/,:P, 3/&bΠ~/&8]01J,XDI:1Ti1
χ (−2ω, ω, ω)(t)
1` 1`1 g/I:ihlhiD<0C @A0/,:hY625–}¨ã=^B0:1d61fBm:mik,.1f6 g4.:P/601\,: k01~6I:/1`
D<[email protected]/G,.:Pe /0/,U5/~:[email protected]/,:P, 34/d:D6X6N‰8] /,./1k,._6N1C0B03/6Q:@A34/FG
=^V8ZBMQ j,[email protected]<34 j6 ‰8]hiD< /B0Pb
vw:r{Ig45-ÿib ÷ @A34/G,^0/ƒF5K ^[email protected]<3C,[email protected]/G,d6iui/:@KFGA6121g4/I:hƒ6-5–}¨þ,
ö OŸtçŸ3iŸIj¡Mš
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6 ®`_‘ˆ/dD<5,Îo,dMhiD FGdD:`/#@A36R 6 W:/5BMQ5 @A0/G,`:/13,34D< @K: 1~/0B01cL
1C,./}340/,:P, 34/K6501~B[email protected]/1 }:q6134C6j1J,.5B,.5096} :[email protected]:P,.C B
:@A34CDQb ˜ /740C{IH,345,341UFG&8]/^34C6H/34/iLÉB0/G,[email protected], FG~D<5s
, o,.C~ /65,U6I:P/1
/[email protected] k0d/34/L€DQ3P,[email protected]:5_DI:§W:P/BQ @A0/,«:/13,.C34D<X1V8ZMhiB0,.:P,.34/d1C,T:X o,.
:mP:/,f61DI:C, 3/q,.3P,: 6501fB[email protected]
Ò©ÓÑÔ³Õ iÿ b; Ö :@‡Ž f
 ui/:@KFG>6&8]43 5, 34/ 611g4/I:Pih hiD< @A0/,:hû6ˆi–j¨ > 3PL
1:/[email protected],q®`_‘ >zB 0B [email protected],qB34C<01-,.Q5034C FG01-1.:P/1q5W:/[email protected]/G, >ì,.:,1KB34/G, /[email protected]
D<345> ω
@[email protected]Ž;¥`0D<34/512/#D<34W:P1.:P,3/r6501f1 g/I:ihl6
I = 0, 6J/cm2 ; I 2ω = 0, 3mJ/cm2
®`_‘ :DCR01E34C 0/,:a,. 3/$> B0B001A2
@ [email protected]:q=# :Yý341B0/B0l/, :k>D<34 /,[email protected] ,=
:7ýI5341B0/B0d{I/I: 0/Y‰8Z:1/Bd6 W:P/BQ @A0/,q> ,.:,\B34/,. /[email protected] bIvo1fDI::@AR,.C01\6
@A36R0 6iui/:@KFG 1C34/G,f60/,.F501f=^ :7{g42ÿib ö =^DI:PC,
D = 0s−1
Ò©ÓÑÔ³Õ5ÿb ÷"Ö :@~Žu/I:[email protected]&8]4345,.34/A61N1g4/I:h^hiD<0C @A0/G,.:ihA65}5–j¨?>z341.:P/[email protected]
,}®`_‘ > [email protected]`,}B34<1,.Q34FG011.:/1340/G,.:P,.34/YD5Q3,.3 /65,.u>ì,..:P,.1`B03/G,. L
/[email protected] D<3©> ω
[email protected] [email protected] ŽZ¥fD<34/1X/2D<34 :1.:P,34/j601§1g4/I:Pih
I = 0, 6J/cm2 ; I 2ω = 0, 3mJ/cm2
6E®`_‘ç:DCR01j34C /G,:a,. 3/}z> B0B 1n
@ [email protected]:7=-W:AýI5341B0/B0^/, :kT>zD<34/G, k01A`
@ ,
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DI:P.:@AR,01\6&8Z:anC51C,[email protected]/G,f13/G,dŽ
¯
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p1 = 0, 18 p2 = 0, 3 p3 = 0, 2
,
D = 2 10−3
b
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3­ 2ω 01J,/5w,f634/B
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p1 = p 2 = 0
601 @K3 0B 1}01C, 63/B6^=q‰8]¦[,jª‡0g40J, =l650ih„DQ3,34/[email protected]/I:[email protected]
01C,N5, k1\D<34X:anC51C,.N=d : 341_V8Z434 i,. 3/,[email protected]<34 \,N : 0D<3/10/KD<34 :1.:a,.3/{5L
/I:f65V8Z/G,./1k,.\6f®`X‘Nbivo1N634/5/01HhiD< @A0/,:01_,N 1XB03<1N,Q034C FG1N13/G,
0D501C0/,.01-15A017{Ig4501Kÿib ø S_ÿib;ÿ„,-ÿib ù D<3^016¦[0C0/,.01^ /,./1k,.016ˆBQI:@AD
34/6I:[email protected]/G,:P‰bvo01ND:.:@AR,1 P: 501N6D<0/650/G,~6fW: a: X61HB34/1J,:/,.01N66kWL
p3
134/KBQ34 1C 10bi’}8]01C,HD[3FG3</341H: 3/1_/[email protected]: k10W: P:[email protected]:ahi @K:P\6
>zD<345
p3
:ihr01\ /B0C,,601\hiD<0C @A0/,:01\DR10b
ω
2 @~=
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1
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,.Q34FG01;>,.:k,-B34/G, /[email protected]<34 ω
>
,q 01-DI:P.:@AR,01-65uL
I = 0, 28J/cm2 p3 = 0, 25
/I:@A FG1K134/,- /BQI:/[email protected] bXr
@ ŽZ¥fD<34/11q0/!D<34W:C 1:P,.k34/ˆMhiD<[email protected]/G,.: º>[email protected]^,
,.Q34FGu>,.:k,\B034/,./H
@ 61f1g4/I:hr65d®`_‘ˆ:DCR01`340/G,.:P,.34/&b
wv : FGI:P k,.~61N:nC1C,[email protected]/,.1_01J,X1.:P, 1Jz: 1:/G,~1.:596:/1_\Bm:P1_6`W:jC0D<34/1Cf/AD<34W:C 1:aL
bP’H,C,.N0C0«B34C01D<3/67DC34I:[email protected]/,
,. 3/265N‰8] /G,0/1C,_6N®`_‘#D<34 ω
I = 1, 2J/cm2
=}/[email protected]/G,1DI:P,W:/G,~ 1U”034/165H3Bm: 1:P,.k34/261BQI:@AD1U6&8ZB0CkL
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B34DI:P/G,X \BQI:@ADAQI:[email protected]/F5q>434T{Ig
F1
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vw:‡{Ig45„ÿib D501C0/,.„V8Z4345,.34/£65
0/!34/B,. 3/!6 ω 2 =‚D:C, A601-DI:.:L
p3 (I ω )
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@KR,.1\01J,. @[email protected]@K/G,0b<’H,,. {g4 @A34/,.jFG V8;:[email protected]/,:P,.k34/q6 V8Z/G,./1k,.
6 BQI:@AD /5B0 650/G,l34/56I:@A0/,:j108Z:[email protected]:g/ƒ6&8]/ƒ1:P,.:P,.34/Ô6
,Y634/5Bƒ6
p3
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,Q034C FG1 > ,.:, B03/G,./[@ D<34 ω
I = 0, 6J/cm2 p3 = 0, 55
1:P,.34/lhiD<0C @A0/,:b>zB0B 01A~
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,Q034C FG1d>,.:,}B034/,./@fD<34 ω
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@[email protected]ŽZ¥`0D<34/1C01 0/D<3W:C 1:aL
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‰ 8]hiB0k,:P, 34/ˆ61Cu1C,[email protected]~Œ/ç:1/B0p6?1.:P,.:P, 3/&SX#DI::@AR,.C
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p3
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800mJ/cm2
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σ2ph ≈ 100 10−50 cm4 s/photon
6
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6„6 :@AR,.C26E3B0: 1.:P,3|
/ >01J,. @AE=-‰8Z: 6d6&8]/„@KB0C341B34D<ED<34 :1y @b<v§:Ka: }6
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34/6I:[email protected]/G,:P PSo:[email protected]/G,0 V8Z/G,./1k,.76‡BQI:@ADƒQI:@A34/FG/&8]0/G,.:Pe /^DI:1 /K:5gPL
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bPU:UB03/1ML
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0/ :[email protected]/G,:P/G,lV8Z/G,0/1C,.?65ÔBMQI:[email protected]çQI:[email protected]/ FGPb ˜ /Ô@K:FG„65„D 1qFGD<3
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300µJ/cm2
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/ :O4B ω b5v§:E1.:P,.:P, 3/q0/lDQ3,34/1~60/G,\¦[0B,.k4 ,\V8ZQuiD<3P,.QR1 FG 01C,~{5hi
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>Bm:C1^g4C [email protected]
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>B00CB001D /[email protected]?, ω
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>‰ÿib ö4ö @
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1:P,.Cb&¬€U1C, 634/5BB03Q0C0/G, FGW:-B34<7,Q03 FG76 :K{Ig45Aÿb ömø 1341cL€1C,[email protected]:
P:P `65 b
p2
vw:[email protected]:: 1C34/#601}{g41 ÷ b ö K, ÿb ömø @A34/,[email protected][email protected]@ hiD<0C @A0/,:§6&8Z/iL
,0/1C,.i–j¨ /fB34C01CD<34/6KDI:1X:AD:.:@AR, @-:[email protected]:zb’HB0|01J,N6K= V8Z/5ýI/B0\6
p2
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D10/,.3/115T :f{Ig\ÿib ö ÿiSW:f65u/I:@A FGH698Z434 i,. 3/E601U1 g/I:ih26\5–}¨Ô:anC1J,.~0/
1DD<31.:/,j W:P/BMQ5 @A0/,f/wD<34
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@b<v8;:P/I:u1C26
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ρ = kβ J=3 k/kβ J=1 k
[email protected] B001K=‚ /65 C#/?/34/iLÉ /m:Pk,YFGI:6:P,[email protected]:B341CB034D5 FG?DI:
340/,:P, 34/-,.34i,CL€3D5,.F5b
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I = 14µJ/cm2
©}DCR01X30/G,.:P,.34/&SP011g4/I:h6`®`–j¨ /` 0/5/0/,NDI:P1X= 0UP:0 /5,.:k\= Bm:51
6 ‰8Z:/13,[email protected]:/50/,. ,f65#5W:/B[email protected]/G,\DQ53,.34/6k,mb
vo01H1C g4/:ihA6j5–}¨ D<[email protected],C,./G,[email protected]:PN01X/34/iLÉ /0:k,01_FGI:6:P,.FG01N /65,01
6I:/1^5/%{I @ 6rD<34kuBm:C<34/I:P,r6534D<rDI:[email protected]/ >z¬C«¬ @r>Vj†H©}[©[email protected] 2+ [email protected]:
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6`‰8]340/,:P,3/^65`{[email protected]j¥ ö >
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g4/0C01fDI:\ j{ @þ652j¥ ö 1C34/G,f6k 1C01`DI:P ù b
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= 14µJ/cm2
b5vo1~1g4/I:Pih
=#/63DI:g4KDI:2 Kj¥ ö bUŒ/DC0/I:/,70/[email protected],.K 1E6k¦9/[email protected]:[email protected]:k1
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[email protected] Mh523B,.D<3W: B03/160Cb9U:P}B34/1C0FG0/G, :[email protected] B0d657j¥ ö 108Z30/G,2/,C,.L
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>ì434 \ @A34/,:g4 65dW:7{g4 ÷ b;@b|’[email protected]@K MhL
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1, 064µm
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=ƒ :[email protected],.r6YW:„@K3 [email protected]:P 17P:ƒ:£B34/G,.:r/5341K:DD<3C,.A61K/[email protected]:P,3/1
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ρ
B034C1D<34/6?=601fBQI:@AD1` /0:1~D<0D</6B0 : C010b
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I = 100µJ/cm2
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[email protected]
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63D<012s9/L> ¬C¬«@>Vj†N©j<© [email protected]> ˜ ©\B&@ > @{>V:@,2s9/L>z¬C¬«@>zj†H©j<© @ 2+ > @w>@j:PDR1 34C /iL
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bivo01H:anC51C,[email protected]/G,1N,.Q5034C FG1H134/,H345,0/51H0/qi,. 1.:P/G,XV8ZF:P,.34/ ÷ b;
I 2ω = 100µJ/cm2
6YBQI:Dk,.C ÷ b
2
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[email protected] Mh510SOV8ZMh5D<0/BXD1/G,0N1wW:H{Ig4C b ø :`,._¦[0B,.H:O4BX601wBMQI:[email protected]
D<D<0/56 BW:10bv8Z:/13,.C34D6 ,.0/5105«BQI:@AD2698ZB0C,.5X1C,«6I:P/1§B0XB0:1
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DC01C0/G,/57/G,0/1C,.E5–j¨)6I:/51j :A6 C0B, 34/#6ED<34 :1.:a,.3/#6pBQI:@AD#34/6I:aL
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ρ=1
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D<#D1`6 ÷ 34 1~1D< d=^B0 6&8]/Y{ @þ6534D< DI:fs9L/ >z¬C«¬ @>zj†H©j<© [email protected]> ˜ 3©\&B @ b
2
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ρ=2
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