Propagacion en FO

8/15/2019 Propagacion en FO

1/43

F


2/43

I

I , . C A

E

, . D : , ,

I ,

E : F , ,

, .


3/43

G


4/43

G C

x z y

E

yx


5/43

n r

n r a

n r a( ) =

≤

≥

1

2

L

≥=∆−≈∆−

≤

∆−≈

∆−

=

ar nnn

ar a

r n

a

r n

r n

21

2 / 1

1

1

2 / 1

11

)1()21(

121)(

α α

121

2

1

2

2

2

1

/ )(

2 / )(

nnn

nnn

−≈∆

−=∆

A


6/43

ϕ 1 ϕ r

ϕ 2

n n

n n

1 1 2 2

1 2 2 1

sen senϕ ϕ

ϕ ϕ

=

> ⇒ >n1

n2L

ϕ 1=ϕ

r

ϕ 2= /2

ϕ

ϕ ϕ

c Arcn

n

sic

=

>

sen 2

1

1


7/43

G


8/43

C A

C 2

C

1

L

o sen =

= n 1sen θ = n 1 cosϕ E α =α m →ϕ =ϕ c = ar sen (n 2 / n 1)

n o sen α m = n 12− n 2

2= AN


9/43

E

(θ )=o

cosθ

θ

P 0 = I (θ ) 2π sen θ d θ = π I 00

π / 2

∫

P = I (θ ) 2π sen θ d θ = π I 0sen 2α m ( )

0

α m

∫ = P 0AN

2

n o 2

F


10/43

ϕ c

Lcsenϕ

L

∆T = n

1

c

L

sen ϕ c − L

=

L

c

n 1

2

n 2

∆D

.∆ < 1→B .L ≤ n

2

n 12

c

∆= 2

n 2c

AN 2


11/43

1−

100

101

102

103

∆ = 0.01

∆ = 0.001

B L Gbit s xKm. ( / )

L

d 2r

dz 2=

1 dn

dr E

r (z ) = r 0 cos pz ( ) + r 0′

p sen pz ( )

p = 2n 1∆ / a

Limitación de ancho de banda

∆T

L=

n 1∆2

8c BL ≤

8c

n 1∆2

1 1 5. 2 2 5. 3

α

10 2−

= 2


12/43

G


13/43

∇×E = −∂ B

∂ t

E

∇×H = ∂ D

∂ t ∇⋅D = 0 ∇ ⋅B= 0

D = ε 0E+P B = 0H +M

2 % w 2

%

E Hε = n1

2

H ,

F

,

c 2

=

C ( )ε = n 22

Ẽz (r ,θ ,z )

H̃ z (r ,θ ,z )

=ψ (r )e

± j l θ e − j β z

%E(r ,θ ,z )

= %

E r (r ,θ , z )ˆr + %

E θ (r ,θ , z )ˆ

θ + %

E z (r ,θ , z )ˆ


14/43

E r t AJ hr e e

H r t BJ hr e e

z l

jl j wt z

z l

jl j wt z

( , ) ( )

( , ) ( )

( )

( )

=

=

−

−

θ β

θ β :

h = n 1w

c

2

− β 2

C:

A,B,C,D ,

=.

E z (r , t ) = CK l (qr )e jl θ e j (wt − β z )

H z (r ,t ) = DK l (qr )e jl θ e j (wt − β z )

β

q = β 2 − n 2w

c

2


15/43

V 2 = (ha )2 + (qa )2

qa = V 2 − ha ( )2

L , :

F

L , ,

V = 2π a

λ n

1

2− n

2

2= ak o n 1

2− n

2

2

λ


16/43

ECACI DE DIEI.

+

=

+

+

′′′′ 222

2

2

2

1 11

)(

)(

)(

)(.

)(

)(

)(

)(

haqak

l

qaK

qaK

q

n

ha J

ha J

h

n

qaqK

qaK

hahJ

ha J

ol

l

l

l

l

l

l

l β

E

2

, :

qa = V 2

− ha ( )

2

β =

a

1

c −

ha ( )

2

A H :

HE, EH,

E0, 0,

E z ≠ 0, H z ≠ 0, H z > E z E z ≠ 0, H z ≠ 0, E z > H z

E z ≠ 0, H z = 0 E z = 0, H z ≠ 0

H


17/43

C ()

HE 11

TE 01

TM 01

EH 11

HE β

k o n 1

b = β / k o ( )− n 2

n 1 − n 2

1

V = 2.405

HE 22

HE 12

HE 12 EH 21HE

41

TM 02

TE 02

0k o n 2

V

0 1 2 3 4 5 6

c

wn

k nk nc

wn 10102

2

=≤≤= β b (V )→ β λ ,a ,n 1,n 2( )

F (=0, =)


18/43

C G


19/43

L ,

.

E ,

A

.

E : H ().

.

.

β


20/43

G D E

C

%E(r ,θ ,z ) = %E r (r ,θ ,z )r̂ +

%E θ (r ,θ , z )θ̂ + %E z (r ,θ ,z )ẑ

%E(r ,θ , z ) = %E x (r ,θ , z )x̂ o

%E(r ,θ , z ) = %E y (r ,θ , z )ŷ


21/43

Designaciónmodos exactos

que lo componenFactor de

degeneración

LP01 HE x11 2 2

LP TE TM HE x01 01 21 2, , 4

L

LP21 EH x HE x11 312 2, 4

LP02 H E x1 2 2 2

LP31 EH x HE x21 412 2, 4

LP12 TE TM HE x02 02 22 2, , 4


22/43

E

E AJ hr e e

E

E

x l

jl j wt z

y

z

=

=

=

≈

−( ) ( )θ β

0

0

E

E BK qr e e

E

E

x l

jl j wt z

y

z

=

=

=

≈

−( ) ( )θ β

0

0

CLE CBIEA

F

E

E

E AJ hr e e

E

x

y l

jl j wt z

z

=

=

=

=

−

0

0

( ) ( )θ β E =

E x = 0

E y

= BK l

(qr )e jl θ e j (wt − β z )

E z ≈ 0

CBIEACLE


23/43

,

ha l −1(h )

J (ha )= −qa l −1

(q )

K l (qa )

C

LPlm

variación radial


24/43

0.5

0.6

0.7

0.8

0.9

1

01

11

21 02

31 12

a g a c i ó n N o r m a l i z a d a b ( V )

C () L

0 2 4 6 8 10

0

0.1

0.2

0.3

0.4

4122

51

03

32

61

13

Frecuencia Normalizada V

C o n s t a n t e d e P r o p


25/43

C . E 2

. E 2.

F

E

(=0) 2 4


26/43

G


27/43

LP01

E L (L01 L02)

LP01

H

LP02 LP02

H


28/43


29/43

LP 21(variación coseno)

LP 21(variación coseno)

E L (L21)

H

LP 21(variación seno)

LP 21(variación seno)

H


30/43

F : L33

LP33


31/43

0.5

0.6

0.7

0.8

0.9

1

o r m a l i z a d a

Ditribuc ión de potenc ia en el nucleo de la fibra

F : L33

0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

Variable radial (mic ras)

P o t e n c i a


32/43

F : L11


33/43

2.12 A III


34/43

(


35/43

>6 :

SI IGSI M M V

M 2

=≈ α

E: F =10 50

F =10 25


36/43

( )∫ ∫ −=a

x y y xnucleo drd H E H E r P

0

2

0

**

2

1 π

θ CLE

F

( )P r E H E H drd cubierta x y y xa= −∫∫

∞1

20

* *

θ CBIEA

P nucleo P

= 1− h 2

V 2

1− J l

2

(ha )J l +1(ha )J l −1(ha )

P cubierta P

=1− P nucleo P

E


37/43

- C

F

V )


38/43

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

01

s t a n t e d e P r o

p a g a c i ó n N o r m a l i z a d a b ( V

V=0.7

V=2

V=8

0 2 4 6 8 100

0.1

Frecuencia Normalizada V

C o


39/43

G


40/43

C


41/43

b V V

01

2

114280 996

( ) ..

= −

L L 01 1.5


42/43

)()(

0

2

)( zwt jW r

zwt j e Aeehr AJ E β β −

−

−≈=

E C , . D

1 2 / e 1 2 2 4. .≤ ≤V

E .

C , G :

W

a = 0.65 +1.619V −3/2 + 2.879V −6

< 1% :

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

0

2

4

6

8

10

12

14

W (V )

a

V

2

2

0

2

0

2

1

−

∞ −==

∫

∫W

a

x

a

x

nucleo e

dr rE

dr rE

P

P

C:

B


43/43

L . D, .

B n n x y

= −01 01

B = −− −10 106 5

β 01 01

x y≠

B

y

y

B

z L B=

z L B

=2

z L B

=3

4

z L B=4 z = 0

y

y

y

x

x

x

x

x

L :

L B B =

λ

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