nonlinear fiber optic

7/29/2019 Nonlinear Fiber Optic

1/25

1

............................................................................................................... 2

....................................................................................... 21.2 ............................................................. 2

...................................................................................... 2 ................................................................................................. 2 ........................................................................................... 21.2. ...................................................................... 2

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2/25

2

CHNG

1GII HI

I CNH CH

CC C I C I NG

Mode

I HI N

1.3.1

NG N

CC N

I I H HO


3/25

3

CHNG

2 N N NGNG I

CC HNG NH MAXWELL

I

HNG NH N N NG

HNG H

-step Fourier Medthod)

-difference Methods)

CC N

I I H HO


4/25

4

CHNG

3N N C NH

CC CH N N HC NHAU

222

2,

2 2

A i Ai A A A

z T

(3.1.1)

.g gv T t z v

0 0 D NL D, LNL

0:

0 0,

gt z vT

T T

(3.1.2)


5/25

5

U:

0, exp 2 , ,A z T P z U z (3.1.3)

P0

2 222

sgn exp,

2D NL

zU Ui U U

z L L

(3.1.4)

2sgn 1 2

2

0

2 0

1, .

| |D NL

TL L

P (3.1.5)

D NL

NL D 2 2 1.U ( , ) (0, )U z T U

n thng quang. Cho L ~ 50km, LD NL 0 0 2 . = 1.55m,

2

2 20 ps km 1 13W km

0 0 ~ 1mW.Tuy nhin LD NL D LNL 0 0

NL D

2

0 0

2

1.D

NL

P TL

L

(3.1.6)

P0 2 = 1.55m.


6/25

6

D NL 2 2 1.U )

2

0 0

2

1.D

NL

P TL

L

(3.1.7)

0 0

D

NL

-dispersion) (2 -dispersion) (2

NG NG C NG N (DESPERSION-INDUCEDPULSE BROADCAST)

2

2

2.

2

U Ui

z T

(3.2.1)

2 /(2 (disper- -inducedspatial).


7/25

7

~1

, , exp ,2

U z T U z i T d

(3.2.2)

~

~21

22,Ui U

z

(3.2.3)

~ ~

2

22, 0, exp ,iU z U z (3.2.4)

~

2

22

1, 0, exp ,

2iU z T U z i T d

(3.2.5)

~

0, 0, exp ,U U T i T dT

(3.2.6)

3.2.1 Xung Gaus

2

2

0

0, exp ,2

TU T

T

(3.2.7)

T0 0

1 2

0 02 ln 2 1.665 .FWHMT T T (3.2.8)

ta

2

0

1 2 220 20 2

, exp .2

T TU z T

T i zT i z

(3.2.9)

1


8/25

8

1 2

2

1 0 1 ,DT z T z L (3.2.10)

20 2D

L T

D

i z = 2LD D

D

2

,U z T 0, 2LD D.

( ) ( ) [( )] (3.2.11)

22 1

2 2

0

sgn 1, tan .

21

D

DD

z L T zz T

T Lz L

(3.2.12)

,z T

0. Sai phn T 0exp i t

2

2 2

0

sgn 2.

1

D

D

z L TT

T Tz L

(3.2.13)


9/25

9

2 2 > 0), 2 < 0).

2 > 0)

2 < 0).

3.2.2 Chirped Gaussian Pulses

2. D c (3.2.7)]

2

2

0

10, exp ,

2

iC TU T

T

(3.2.14)

- -

0,U

1 22 2 2

0 020, exp .1 2 1

T TU

iC iC

(3.2.15)

-

1 2

2

01 / .C T (3.2.16)


10/25

10

2

0

1 2 220 20 2

1, exp .

2 11

iC TTU z T

T i z iC T i z iC

(3.2.17)

1/22 2

1 2 2

2 2

0 0 0

1 .T C z z

T T T

(3.2.18)

min 2.

1D

Cz L

C

(3.2.19)

min 01 1 2

2

.

1

TT

C

(3.2.20)

2

2

0 0

0, sech exp ,2

T iCT U T

T T

(3.2.21)

0 02ln 1 2 1.763 .FWHMT T T (3.2.22)


11/25

11

2

0

10, exp ,

2

m

iC TU T

T

(3.2.23)

0 0(ln 9) .2

r

T TT

m m (3.2.24)

1/222 ,T T

(3.2.25)

2

2

,.

,

p

pT U z T dT

TU z T dT

(3.2.26)

1/2

2 22 2

2 2

0 0 0

1/ 2 2 1/ 21 1 ,

3 / 2 3 / 2

m mC z zm C

m T m T

(3.2.27)

3.2.4 Super-Gaussian Pulses

N C C A

2 3

32

2 3.

2 6

iU U Ui

z T T

(3.3.1)

~

2 3

2 3

1, 0, exp ,

2 2 6

i iU z T U z z i T d

(3.3.2)

' 3

0 3/ .DL T (3.3.3)

2

, , exp ,I z U z T i T dT

(3.3.4)

2

0lim ( , ) , .

nn n

nI z i T U z T dT

(3.3.5)

~

0lim , ,

n nn

n

c

iT I z

N

(3.3.6)

2 2

, 0, .cN U z T U T dT

(3.3.7)

~ ~ ~

, , ' * , ' '.I z U z U z d

(3.3.8)


12/25

12

~ ~

* , , .

n nn

n

c

iT U z U z d

N

(3.3.9)

1/2

2 22~30 0

2 3

2, exp .

1 2 1 6

T iTi iU z z z

iC iC

(3.3.10)

1/22 2 2

22 32 2

2 2 3

0 0 0 0

11 1 ,

2 2 2 4

zC z zC

(3.3.11)

1/2

1/2 22 '

0 1 1 / 2 / ,D D DC L L z L

(3.3.12)

2 2 2

22

2 2 2 32 2

2 2 2 3

0 0 0 0

11 1 1 ,

2 2 2 4

zC z zV C V

(3.3.13)

-Shape Pulses)

,U

i HUz

(3.3.14)

2 3

32

2 32

.! 2 6

nn

n

iiH

n T T T

(3.3.15)

, ,

d T

i H Tdz (3.3.16)

2

, , ,d T

H H Tdz

(3.3.17)

0 1 ,T a a z (3.3.18)

2 2

0 1 2 ,T b b z b z (3.3.19)

*

0 0 0

,a U T TU T dT

(3.3.20)

*1 0 0, ,a i U T H T U T dT

(3.3.21)

* 20 0 0 ,b U T T U T dT

(3.3.22)

* 21 0 0, ,b i U T H T U T dT

(3.3.23)

* 22 0 01

, , ,

2

b U T H H T U T dT

(3.3.24)


13/25

13

2 2 2 20 0 2 2 012 , 3 .b T b T (3.3.25)

1/2

2

2

0 0

1 ,6

z

(3.3.26)

-Pulses Measurements)

N N C

3.4.1 - -Induced Limitations)

1/2 1/2

2 22 2

0 2 0 ,L DL (3.4.1)

1 4.BL D (3.4.2)

1/222

0 2 02 .L (3.4.3)

1/2

2 1/4.B L (3.4.4)

1/2

22 210 3 02

4 .L (3.4.5)

1/3

3 0.324.B L (3.4.6)

2 21 1 22 21

, 0, exp ,2 2

m

iU L t U L L i t d

(3.4.7)

1 1 2 2 0.D L D L (3.4.8)

21 1 22 2 31 1 32 20 0,L L L L (3.4.9)

CC N I I H HO


14/25

14

CHNG

4I IN NG HM

-

-steepening.

NG H C NG T0 LD LNL LD >> L > LNL T0 P0 > 1W).

Trong ( , )U z T

2

2| | ,

z

NL

U ieU U

z L

(4.1.1)

Chi

1

0( ) ,NLL P

(4.1.2)


15/25

15

P0 n2 exp( )NLU V i

20;

z

NL

NL

V eV

z z L

(4.1.3)

V L

( , ) (0, )exp[ ( , )],NLU L T U T i L T (4.1.4)

U(0,T)

2( , ) | (0, ) | ( / ),NL eff NLi L T U T L L (4.1.5)

Leff

[1 exp( )] / ,effL L (4.1.6)

NL

L D Leff L. = 0,Leff =L.

max T = U U(0,0)| = 1.

max 0/ ,eff NL eff L L P L (4.1.7)

LNL max =1. = 2 W-1

km-1

m LNL P0 0

2( ) ( ) | (0, ) | ,

effNL

NL

LT U T

T L T

(4.1.8)

2 1 2

0 0 0

2( ) ( ) exp[ ( ) ,

eff m m

NL

Lm T TT

T L T T (4.1.9)


16/25

16

max

0

( )( ) ,

mf mT

T (4.1.10)

1 1 21 1

( ) 2 1 exp 1 ,2 2

m

f mm m

(4.1.11)

max 0 max0.86 , (4.1.12)

2

0( ) (0, ) exp ( , ) ( ) ,

NLS U T i L T i TdT

(4.1.13)


17/25

17

max

1,

2M

(4.1.14)

222

0 0 ,rms (4.1.15)

0

0 ,

n

n S dS d

(4.1.16)

1 2

2

max

0

41 ,

3 3

rms

(4.1.17)


18/25

18

, exp ,S z i d

(4.1.18)

, * , , ,z U z T U z T (4.1.19)

2

2 2, 0, 1 1 | 0, | ,Z Z

(4.1.20)

2 20, exp 2 ,cT (4.1.21)

Partial Coherence)

4.2 NH HNG C N N C NHM

4.2.1 Pulse Evolution

2

222 2

1sgn ,2

zU Ui N e U U

(4.2.1)


19/25

19

0, = ,Dz L T T (4.2.2)

22 0 0

2

.D

NL

PTLN

L

(4.2.3)


20/25

20

1 22

2

max max 2

0

41 2 1 ,

3 3D D

L L

L L

(4.2.4)

2 2

2

2 2

** ,

2

p

pd T i A A

T A A dT dz W T T

(4.2.5)

2,

2

pSd

zdz

(4.2.6)

41

0, ,pS A T dT W

(4.2.7)

2 2 210 22 ,pz S z (4.2.8)

22

2,

2

U d Ui U U

Z

(4.2.9)


21/25

21

0( , ) , exp , ,T

U z T z T i v z T dT (4.2.10)

4.2.3 Optical Wave Breaking


22/25

22

3 __

22

3 3sgn ,

' 6

zU i Ui N e U U

(4.2.11)

3'__2 0 0

3

.D

NL

P TLN

L

(4.2.12)

2 3 max / 2 , (4.2.13)

HI NG HI N C CAO

22 3

2 22 3

2 ' 3

sgn sgn,

2 6

z

R

D D NL

UU U U ei i U U is U U U

z L L L

(4.3.1)

2 3'0 0

2 3 0

1, , ,

D D NL

T TL L L

P (4.3.2)

0 0 0

1, ,RR

Ts

T T

(4.3.3)

-Steepening)

2 2

.

U

s U U i U U z

(4.3.4)


23/25

23

3 0,I I

sIZ

(4.3.5)

,sI IZ

(4.3.6)

, 3 ,I Z f sIZ (4.3.7)

20, exp .I f (4.3.8)

2

, exp 3 .I Z sIZ (4.3.9)

1 2

20.39 .

3

NLes NL

Lz L s

s (4.3.10)

2

1 2

0, exp , .S I z i z i d

(4.3.11)


24/25

24

4.3.3 Intrapulse Raman Scattering


25/25

CC N

I I H HO

nonlinear fiber optic

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