Tán xạ Raman kích thích


Mục lục
 !
"# 
$%&'()*+,-- '
1.1Tổng quan về tán xạ Raman..........................................................................1
' ' '). '
' ' /0123.4567809 '
' ' !:;<3 /
' ' =>8?8@A.8B.;<3 =
' ' CDE@F23.;<3 G
' ' HI. J
' ' GI,363 'K
1.2Đặc tính của tán xạ Raman kích thích........................................................12
' / 'LMNF,363 '/
' / /0O,363 '!
' / !P023EQ38B.;R 'G
' / =P023ST. 'G
1.3Ảnh hưởng của tán xạ Raman kích thích trong thông tin quang.............18
' ! 'P023:,:4U1NV 'W
' ! /P023:,:8BXY /!
1.4Thí nghiệm tán xạ Raman kích thích..........................................................27
' = 'D6B.N@F,363 /G
' = /D6B0O,363 !K
$%&/(ZY[)*+,--\]$]$\^$+
]_>- !/
2.1Sự cần thiết phải khuyếch đại quang..........................................................32
2.2Những khái niệm cơ bản về khuyếch đại quang........................................33
/ / 'LMN@F45`a`bN@F !!
/ / /c8B`bN@F<3 !C
/ / !$deQN@F !G

2.3Bộ khuyếch đại quang Raman.....................................................................38
/ ! '@Vfg`16 !W
/ ! /.N@F45`a23`bN@F,363 =K
/ ! !aD<3,363 ='
/ ! =aN@F ==
/ ! Cc8B`bN@F,363 =G
/ ! H\@F,363S`Y,-hY.8`ie,363-6fji8k =J
/ ! G\@F,363l8m,-hm6ie,363-6fji8k C/
/ ! WnbN@F<3f3o,363pqYr- CC
2.4Ứng dụng bộ khuyếch đại quang Raman trong hệ thống WDM..............55
$%&!($%&,stLu CW
3.1Tính toán tham số.........................................................................................58
! ' '36.vX3fNwBjjxe CW
! ' /.N@F,363 CW

3.2Các lưu đồ thuật toán...................................................................................59
! / 'm0lBDy.f38@A.z CJ
! / /m0lBD.N@F,363 HK
! / !m0D.@F H'
! / =m0lB67{:,: H/
3.3Kết quả mô phỏng và giải thích...................................................................63
! ! '\F<|67{MN@F,363 H!
! ! /\F<|67{|023:,: H=
! ! !}@F7.E HW
\m HJ
~m_-\P• GK
$%&=(L[m[$- L01`FMrB8i8898 G'
L[m[$n $018?67{ G!

THUẬT NGỮ VIẾT TẮT

nq, nq88B8,3i €.f•`
Y$r Y.i8.B$B6i.3r`i8 :;`‚.ƒ
Y,- Y.8`ie,363-6fji8 nbN@F,363S`
Y,: YB`fi,3@fi:3i8 I,3@fiNo
Y:r Y.i8.B:jier`i8 :;e„.ƒ
qYr- q8`6Y8Bier`i8-6fji8 \@F<3.;3q8`6
rX rB8X34iI 8b`.z
Y 8BifB@Y.i8.B .ƒ4lz6
m,- m6ie,363-6fji8 nbN@F,363l8
rY BeirifeY36ii8 09ND8096Bei
r B.ir8i .S6
m:q Bfi38:8Bei8q<3B L018?:8Bei8@F
,… Bw,i8wBw…i8B †,…
:n: :6f3ien8ffB:3i8 In8ffBNDD
:r :fiBeir`i8 :;16Bei
:, :3fwBwB.i,3B €.D8Vc
:L :ifjL3.iBef3B AFTe„3
:,: :6f3ie,363:3i8 I,363NDD
XY X34ifiY4.BffiI oNVS3iB`0U.z
*L $8B..L3.iBef3B AF3oB

Đồ án tốt nghiệp Đại họcMở đầu
MỞ ĐẦU
I,363f5<8?IN75‡I|@83eB.T0123.
4U678094lE8B.;<3 
I,363`3B6I,363T45I,363NDD:,: b
6}I,363S@|0IEF<8?8@AD8B.;<3‡f56
ac8B<306}NI,363ˆz‰
|0DT‡M`lEf5N|aN@FD<3 n4l@‡3@
ŠN6U0;‡I,363†‹8EA.T<3S6‡Vd 

$Vd5@l8iB30U(|6Œ|0VT45d
eQI,363NDD8BN@FD<3 I,363ND
D:,:Df51.Œ8Œ`bN@F<3,363 $`b
N@F<3,363z8EA0Œ6.B4U‰fBN@F<3†
0;.•eQ80Uz458E‚;4UXY30;8ŒN3
3@ $`bN@F<3,3630;Bf5f9|B`5BN@F
<38B8@AeŽ<3ef0;fU‡Tf@e5458Ee5
ld0;6<38234EA450;.T0UeŽ23@B‡
: @cdS‡i6A5vI,363NDDxŒf56A5

be0;8?`5@8B`301(
$01'8?`5@M<34A<8?I.‡I,363‡9
8?`5@‰}Dˆ0|023I,363NDD8B
1NV45XY
$01/8?`5@6b.N61`|4AN@F<3‡VdeQ
23I,363NDD8BN@FD<3‡@Vfg23`b
N@F,363S`‡N@F,363l8
 $01!IS@eT018?67{‡f568•|023I
,363NDD4U<8?8@A.8B.;<3‡f0l
BI„36.fV<3
Mai Nguyên Dũng- D2001VT Học viện Công nghệ Bưu chính Viễn thông
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Đồ án tốt nghiệp Đại họcMở đầu
}e‚†F.dƒ0eBI,363NDDf56b4EANzV
beNz8N{F.z ,E6Bl0;.T€`|B‡zg23
@‡$7B‡`.4VŒ5@0;B51
q6IS5|61@B‡: @cdS†?0U
eŽi6B555@
q6I|61@‡$7B8B`b677<3‡\B34c7
†e@e•‡e?eƒi68B.Ca64Š3<3

*|613?‡09S45``•†b4V‡‹O8B.9
3<3
5b‡5@/K'Ka6/KKC
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Mai Nguyên Dũng
Mai Nguyên Dũng- D2001VT Học viện Công nghệ Bưu chính Viễn thông

CHƯƠNG 1: TÁN XẠ RAMAN
1.1 Tổng quan về tán xạ Raman
1.1.1 Ánh sáng
).zDf0OD.z DE.z23.0;<3.
E@<30;3BB3‡.ƒ ).z`|E.zŠ $
6Bei809Šf5l623018?.z DE23
.0;Œ<3N|aS6I@V‡0;<3‡eQBB 
).`3B6BB63af0;I„`yj8Bzf5y.
Lf3N‘jf5.23.
1.1.2 Tương tác của ánh sáng và môi trường
b‚6.ŠSN745B67809`„|I6b6}a
 LN‹I45B67809f`„.ƒ‡`„67809EQ45`„I6b
4A6D3
iBmB8iI3Š3l‰|F1`|.3S@(
 LS•236E0;B5ŠB45ifi8B qfi8BzNf0;6
4563D@V
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 nV8B4leŽ‡ifi8B@ŒbB5B5TeB $@Œbz0U

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E@0;‡B0N7N„e„@Œ $€N5BN|B.8B6A
B36UNŒF|023B
‰ifi8BzN|ae3Bb0O`d4U.
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8B4‚<3f5ifi8B<3 $‹f5ifi8BfUB5 
$ifi8By68BfU.S‡S@V•‡fV}’14U
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mB8iI45`y(
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8BzNf5y.“23fT5‡I„.e3Bb8V23
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f0OTe3Bb‡`dI.zŠdE m0OTe3BbˆzŒ43
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1.1.3 Sợi quang
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8‹de0? ' / 8Bz6•@V•.f0;`3B<3``
@V••I@i
?' /$E8‹de23:feBIei8BR
:;<3ˆzŒ0;34UAEN3Œ3@M€.
F.E DeQ
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45
C/

OP
0;3V645BŒaF.E23f• Œ|6
F.E23f•‡zŒ.•eQ4lf0f5nB8Bhnk45rfB8ihrk•B5
836b.EN0q8`6ˆ0;.•eQ8B`bN@F<3
1.1.4 Quá trình truyền ánh sáng trong sợi quang
Suy hao
l8@A.8B.;<3{14l8@A.8BS
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.;‡Nz4l8@A.8B.;<30;DiB7dh' Hk
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α
–'p6—f5..@3B23
.;<3‡
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0;DiB7d(
L
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−
=
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h' Kk
ŒDB..@3B‡14„090;.•eQf5
dB
α
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kmdB p

L018?@ŒM14„(
[ ]
m
dB
p'
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'Kf
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

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h' Kk
$7.E<3ˆ090;DiB14„f5en63@BX3 >3
‰3314„5@0;`Œ„8B7dh' Jk
[ ]
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




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=
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WP
dBmP
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fB 'K
h' Kk
Tán sắc
.ƒf50;e†8bI.N8@A8B.;<3 .ƒz
AfB0.ƒ6Bei‡.ƒ6545.ƒ6BeiST
.ƒ6Bei€I|@838B.;<336Bei YB6Beizbf38@A
N3V938@A6Beif5N3‡S@83.ƒ6Bei
.ƒ650;S35.ƒ4lf45.ƒeŽ.z .ƒ
4lfI|@83eB.TQb23F.E45B`0U.z .ƒeŽ.zI|@
83eB.8@A8B.;N7|f5.1.ƒ‡y.f38@A

β
f5
5623`0U.z $5`0U.zN3z4lz6N3
S@83.ƒeŽ.z .ƒ65z|08EfUF7
<3 .ƒ65f56a|023d@F8B.;<3eŽ
FU4ANB|8@AeŽ8B7<3
mB.;<3M`FE8VFU3@f5.;<316BeiV
“hiBN@F„ HC/23wk:rw/W
TM
z..ƒ(
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λ
λλ
S
D
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
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kmnm
ps

h' Kk
8BzYf5..ƒ‡
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`0U.z.ƒN7h…YXk .ƒ23fB.;5@0;`Œec
8V?' !
?' !..ƒ23.;<3:rw/W
TM

Chiều dài hiệu dụng
\6bD8@AeiB.;<3‡7.ED`„|6eeB.@
3B @V‡8BTFzŒ|.•8y7.Ef5y.8V6bAe5

eQ
eff
L
`4?Fd@FAI|@83D323.; „
˜3Ae5eQ23.;<30;Œ8V?' = 
?' =h3k$7.E8@AeiB.;zAe5mh`k7?01d23
Ae5eQ
"?' =h3k7.E`„.@3BN8@AeiBB5`b.;zAe5m‡
?' =h`k7.E0;Bf5N7M8V6bAe5.;(
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K
K
h' Kk
Diện tích hiệu dụng
E|d@F8B.;<3AQb45B09b.
8@AeiB.; @V8BTFoBATB7.E
45B4583.;<3 $7.E83N{.;<3Df5DS23S`
09b.8VeD6}ƒ23.;<3 F
core
A
f5eD6}
ƒ23.;<3‡
meas
P
f57.EB0;8323.;<3 |F09b
S`A8VeD6}ƒ23.; 3z(
core
meas
A
P
I =
h' Kk
@V8B.;<316Bei‡09b.N7S`A8V
B5`beD6}ƒ23.;‡09b..’aeŠfUF‰3f•
454{U8Q23.; dbaQb45BF.E23.; 
YBzŒDB8B809;5@‡36.eDeQ
eff

A
0;D
iB7d(
( )
( )
rdrrE
rdrrE
A
eff
=
K
/
K
/
/
∫
∫
∞
∞








=
π
h' Kk

U
( )
rE
f509b809236Bei1`|NB|8.B4U8Q23
.; 4U.;F.E`leDeQ
eff
A
zŒ0;DiB7d(
( )
λπ
/
wA
eff
=
h' Kk
8Bz
( )
λ
w/
f50‘ND8096Bei23.;`0U.z
λ

1.1.5 Tính chất phi tuyến của sợi quang
8B@V•z•63DS645S63D
e01 YBzN809b45B4lf•45S`„e„
@Œ4A30U0;3 mT809f56B@V•`„ST‡
Ngf5L‡Qb45B809b45`|E234lf450;D
0.3(
k h
k!hk/hk'h

K
+++= EEEEEEP
χχχε
h' Kk
8Bz
K
ε
f5y.678BSN7 
kh j
χ
f5b|6E™
b|6@FD
k'h
χ
z438‘8EfU8BL‡‰|0eBzi6
f0;`Œ<3.F.E‡..@3B
α
b|6E3
k/h
χ
f5
@VSS@83d0.B5S6E3 @V4US•z
E8‹Id0
/
SiO
‡
k/h
χ
0`yKVzŒ`{<3 $b|6
k=h

χ
‡
kCh
χ
8E{.B4U
k!h
χ
?4l@€z
k!h
χ
f5@VS2@FS@83
d@F
$d@FzŒ353fB mBdE.83eB.T01
23.z.4UBB mB5@`3B63d<38f5
I,363NDDh:,:w:6f3ie,363:3i8k45In8ffBNDD
h:n:w:6f3ien8ffB :3i8k mBd36d@F\i88‡
.83eB.TQb23F.E@F45B09b809q $
d@F\i88`3B6(:L‡*L45rX
Fd@F8B.;<3A.83eBF.E@F‡
zf5.TQb2309b.f38@A8B.;45BF.E <3
‰309b.‡F.E457.EL0;`Œ„`y018?(
P
A
n
nInnn
eff

/
K/K









+=+=
h' Kk
8Bz
K
n
f55Qb`0U.z23F.E
n
‡
eff
A
f5eD
eQ23.;<3‡
/
n
0;f5€.F.E@F €.
eff
An p
/
0;
f5.@F 36.5@zŒB0;65N7`FeD
eQ23.;<3
B583NVdd@F8B.;<36b36.‰3
ˆ0;0383f5

γ
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B583}D23d@F8B.;<3‘„|0
23A36.009b23D‡Ae5.;‡NB|‰3NV
h8BXYk 
1.1.6 Tán xạ ánh sáng
\.8@A<3678094lE8B.?fU.8@A
›456b{.’`„I 7809zŒS@83AfBI8Bz
Œ?f5I,3@fi‡In8ffB‡I,363•œb45BfB4l
E‡.‡AN67809•656•fBII|@83N3
I,3@fif5<8?I5‡..I`y.
.U 823S•4lEeBI,3@fiN73@M.3N
.8@A<3 0;f‡In8ffB45I,3663f5<8?
IN75‡@V•`„NDDNz.<345..
I`„e„@Œ.B4U.23.U 

3w>8?I5`w>8?IN75
?' C>8?I.
>8?IN75z.T36323BB 8B<8?5@
BBzŒ.83B}`„EQ d3@M.23.I.B
4U.U`y4U.23BB In8ffBfV<3FBB
S6‘I,363fV<3FBB<3 YBz.I
,363z6de„@Œ.fU1.In8ffB F.I
z.{1.U?.I0;f5.:BNi45<

8?I0;f5I:BNi 0;f‡F.Iz.fU1
.U?.I0;f5.|:BNi45<8?I
0;f5I|:BNi UIN75‡14„Bbe„23
.If5h83ep.kB}f56
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f5e„@Œ.iB83ep.45f54l23.8BSN7iB
6p.k
$dI.’f56U7.E<3fUEzŒ8@A8B
.; 8BXYIf5@VSS@c‰3NV @V
I,363ˆ0;deQ8B`bN@F<3,363‰
`0U.z65`bN@F<3qYr-N7‚; dIn8ffBf5
@Vfg8B`b|6dBb67809‰165`b|6d
N7‚;

.
?' H.23.I
1.1.7 Tán xạ Raman
I,3630;S353fB(I,363Th:B3iB.
,363:3i8k45I,363NDDh:6f3ie,363:3i8k d
I,363T†0;eTB`:6iN3f45Ba6'J/!45Fa6'J/W
0;,363€83`yT6
8B<8?I,363T‡.U014U67809f56
.83BB œb45B`|E2367809BB.83.’z
.fU1B}{1.23.U
|af0;23<8?I,3630;Œ8V? ' G 
qfi8B.’@ŒŠ8Nh81`|kfV8|Bh8
NDDkNEQ6bBBzaf0;`yaf0;‰38
|B458N \@ŒŠ8|B4A8ifi8B.’
I6bBBzaf0;`yaf0;8|B458
F08Nzaf0;E1af0;238‡
.BBI.’{1..U45<8?IB83.
:BNi
?' G|af0;<8?I,363
h3kI:BNih`kI|:BNi
|.•
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Ω
f5.
BB0;.83 \ziB„fl`|BB5@ŒBaf0;?

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0;fF8zaf0;E1?<8?IB83
.|:BNiz.
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458Df5af0;236bBB TF‡I|:BNi
09@F1I:BNi
.23BBI0;I„`y.e3Bb23@V• 
UR‡<3M23.I,3636A5.N
3f5eB@V•8BRe3Bb8B6bNB|.8E8b
dI,363T0;deQŒI„E8‹23S•‡
5EB45fBfVNF8BS•z
\3ae7.E`1645B?7.E23.z:BNiˆae 
0F07.E.z`1640;<6b8„I„?7.E.z
:BNi.’afV8E3iB566ˆ @VSS@830;5@f5<
8?I,363NDD
1.2 Đặc tính của tán xạ Raman kích thích
1.2.1 Phổ khuếch đại Raman
?' WLMN@F,36323.;:f`0U.z`16
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8Bz
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P
 f509b.z`1645
R
 f5.
N@F,363 .NF,363fV<3F6}ƒF.E23
IT,36345zŒBf090;`yT6 "6db1`|
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709
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Qb45B5f•.;<345zŒ3@M8EfU
F3V6E45Bf•.; ?' W`Œec
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'!• A5@I|@83f5eBDŒTV23R.f 8B4l
f47„?0.f.e3BbS•8|8b5Ae|oB
fV345856be|fVQ \F<|f5N›4U018@A
eŽ80US@hzMN@F,363y68B6be|.žk‡MN@F

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Œ65@65.;<3zŒf56406b`bN@Fe|8b
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1.2.2 Ngưỡng Raman
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45B
.0;Œ8V?' W l6DFN7`Fe235623

kh
ω
R
g

34ŽzŒDB0;DSh' /Wk4?8„23zQb2@F45B
4‚ž€NF Šh' /Wk3D830;(
[ ]
LLoIgPLP
seffpsR
eff
Sos
αω
−= k hkhiI kh
h' Kk
8Bz7.EeQ45B•šKf5(
eff
So
P
š
effs
B
ω

h' Kk
U(
/p'
khŸkhŸ
/









′′
=
effpsR
eff
LoIg
B
ω
π
‡
S
R
sR
g
g
ωω
ω
ω
=









∂
∂
=
′′
/
/
kh
h' Kk
eff
B
f5e|eQ23.z`dI:BNil8€N@F4U
s
ωω
=
}e‚
eff
B
Qb45B09b`1645Ae5.;08„€
23M8V?' Wz438‘<388B4„f0;
eff
B

0O,3630;„˜3f57.E`1645B.3BB837
.E`16457.E:BNif5`y3
kiIh khkh LPLPLP
pops
α

−==
h' Kk
8Bz(
eff
AoIP k h
KK
=
h' Kk
LfU7.E`16.’@Œ57.E:BNiF07.E`16
40;<8„0O
K
P
f57.E`1645B45
eff
A
f5eD4‚f•eQ Š01
8?h' /Jk45h' !/k45|.•
ααα
==
ps
‡AN0O85(
OeffeffOR
eff
so
PALPgP =kpiIh
h' Kk
8Bz
eff
so
P

ˆQb45B
o
P
7<33018?h' /Jk45h' !Kk 
Š018?h' !=k3zŒD0;8„0O,363 8„7.E`16
Uh
th
O
P
k‹0;B`(
effeff
th
oR
ALPg p

'H≈
h' Kk
$7d8Vf5AN0O,363l‡AN0O,3630;
z0;`y3@8„'H8B018?h' !Ck`y/K $ˆ|‹
gf5NIS@eT018?h' !Ck3|.•ST23.z`1645.ze‘
`|BB58B<8?f38@A F.TSTN70;`|BB5‡0O
,363.’afV6b.8BNB|'F/ }`‡F0.TST`„
IB8bB5B5?0O,363.’afV/f
}e‚NDB8„0O3.•eQ8EAoD‹0
8„0O,3634Ž0;DNDI F04U.;z
'
>>
L
p
α

‡
peff
L
α
p'
≈
"`0U.z
m
p
µλ
CC '=
h`0U.zy68B4‚•3.Mz.@3B
{EOK /enpN6k‡ 
/KkmL
eff
=
 709? 
eff
A
š
/
CK m
µ
‡8„0O
,363ONB|HKK6X n4?8BTF7.E237
<345BO'
mW'K÷
VN7`„|0`:,: 8B4‚
.?E@
eff

A
š'K
/
/K m
µ
÷
‡8„7.E0O
WP
th
o
'K
4UTf@8@A
eŽmš'K6 \7.E45B`y4U8„0O‡7.E`16@Œ5
7.E:BNi8E3z 8BTF‡.z:BNi.’Bb06b.z
`1645.83.z:BNiE/F07.E23z2fUŒB|6†01
8?h' !Ck \F<|f5F7.E`16fU‡`V8B.;.838EA.z
:BNi45.f0;.z:BNiQb45B7.E45B
1.2.3 Ảnh hưởng của các chất phụ gia trong sợi thuỷ tinh
:;R0;BŠ•;BIeiz|@ $BIei5@B836b4l
f6UzE8‹6S•fVNF•; 709.;R
0;3;EN34DeQ0
‡
C/
OP
/
GeO
Œ3@M6b.DE
23R0€.F.E‡..ƒ $EQ35@ˆf563@
M<3MI,36323.;R
?' Jw>3MI,36323fBRBIei0;

.•eQ8B.;<3.
?' JŒ<3MI,36323.;<3RBIei R
z51`|f5eBIei.fzb8bM8E8bhNB|=K•k4U
6b€D8BN4TŠ==KF=JK6
'−
UE3f5i•
/
b8b
Mž1009b.If61 UL
/
•
C
N7‰
09b.Ia65‘IE4‚M6Uz€'!JK6
'−

4UNB|e„8EfU
1.2.4 Ảnh hưởng của phân cực ánh sáng
LST.z|08EfUFN|aI|@83I,363 .
N@F,363Qb8EA45B.T01<3‰3.`1645
.D >8?I,363I|@838E6N.`1645.D
ST \.`1645.DzST8T3B<
8?II|@83@F18EA YBz6daDTF`yM8„a
D.B.B45aD8T3B 4U.;R8bi•
/
‡aD<3z
Œ0;I„iB7d









−= L
KA
P
LgdBG
s
eff
effR
α
K
!= =kh
h' Kk
8Bz\f5.ST .STl8„v'xN.`1645
.DST45l8„v/xN3.5@8T3B
?' 'KP02301<3ST
‰3.D45.`16
1.3 Ảnh hưởng của tán xạ Raman kích thích trong thông tin quang
1.3.1 Ảnh hưởng của SRS đối với hệ thống đơn kênh
>8?8@A6bI8B.;<3zŒ0;67|`y018?
:8Bei8@Fhm:wBfi38:8Bei8i<3Bk–'—(
AAiA
t
Ai
t
A
z

A
/
/
/
/'
//
γ
α
ββ
=+
∂
∂
+
∂
∂
+
∂
∂
h' Kk
8Bz
A
f5`VbI†0;“B˜3f5
/
A
Df57.E
<3 
α
f5..@3B23.;<3‡
‡
'

β
/
β
f5.8BN38Œ3@fB8
23
β

L018?m:†`3B6.@3B7<3
α
‡.ƒ657<3
/'
‡
ββ
45
.@F
γ

..ƒY<34Uy.f38@A
/'
‡
ββ
iB018?(
/
/
/
/
'
/
λ
λ

β
λ
π
λ
β
d
nd
c
c
d
d
D ≈−==
h' Kk
8Bzf54l.8BSN7‡
λ
f5`0U.z‡f5F.Ef•
.;
}e‚018?h' !Gkf5N@2Œd6Ad@F
08VTFz|z.T3@M n4?8B018?h' !GkN7
`3B6d@FfV<3FINDDN750:,:45
:n: F€7.E23D45B40;<8„0O:,:?<8?
I:,:.’f56`FMaf0;23.z`165.z:BNih‚8@A4U
.z`16`V8B.;<3iB|30Ul450;k $I.’b
fŽ37<3N@F,36301T033@A.zz`0U.z
N3‚8@A8B.;<3
1‰3018?h' !Gk€IS@eTBIzb8bfU1'.‡eB
z|A€4UITƒ{1'KK. \Izb8b
{1'KK.‡`A8bM
ω
∆

23zzŒ.B.4U.63
K
ω
V‰
oD‹ŒIS@eT018?h' !Gkˆ|Ii6Iof
Bb23:,:8B.;<3.’1|8EAF|.•8y
d2367809f5d9 8Š809;Izb8bO'Kj.‡f‹5@
d2367809l68D‘l61|dI
\zŠ018?h' !GkD||023:,:‡.T01‰3I
`1645I:BNi0;NF`}018?(
[ ]
ps
p
psppp
pp
p
p
gp
p
AA
g
AAAiA
t
A
i
t
A
vz
A
///

/
/
/
ŸŸ
/
ŸŸ/ŸŸ
//
'
−+=+
∂
∂
+
∂
∂
+
∂
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