FibreOptique Aluminium

DS SCIENCES PHYSIQUES MATHSPÉ
calculatrice: autorisée
durée: 4 heures
Sujet
!" 
#!$ 
%& ' 
()*+,-
!."-
#/ 0
!).), 1
!""2
3)""4,"" 2
%5
67-

Fibre optique
)) "8  9: ),
"; :<.(*
=>:):  "8
=,0µ""8'),6µ"
I. Loi de Snell-Descartes pour la réfraction
A. Principe de Fermat
  8          '  "'    $")8>  :  
n6
n
'
A6
A
 '9
A6
"":
n6
+
x6
A
      "  :
n
  +    
x
O
H
)?
A6
A
I
(
A6
>
A
I
"@"*
OI =z
OH =h
?"8
A6
+
A
I
"?)
A6I
"
6
?)
I A
"
6 &,'.
v
"8",
n
c
n
("8.
c
*
 A'"
tz
? 
n6> n> z , h , x6> x> c
 $$
I
""
•". 
z
 ?'"
•B .""""
•/?.
z
B. Approche ondulatoire
7-
A1
A2
I
O
H

-     "   :
n
   8     "     "
='[jt –  kr]
&,'"
k
k
): "
0 A,'
k
 ), .:
n
"
;.,
k6
"
6
. 
'"',
n6
n
<
xOz
:)
:
i6
.,
k
" :)
O
+ 
yOz
,
O
6O ,t =6 '[j t – 6O]
,  
O
O , t= '[jt – O]
( >  
>: $*.
8
I
 (
xI=
*
1 3
6I , t
I , t
""
k6
>
k
>
r= OI
 $):: @
I
$
 3$).
k> z=k6> z
(
k> z
k6> z
.:
z
*
2 3
k> x
>
k> z
> >
n
k> x
>
k6> z
>
>
n
":"" ).
<"''). )):
i6
i
) )"."
5 &.* 
C. Réflexion totale
:."" )(
nn6
*>:
" :?).
7-
O
z
I
i1
i2
x

6 :)"
i6>"
<::'< 
 '       C.  :)  "
 :'D
6=6 ' jt−k6xi6– k6z i6
    "
6
x , y , z 
       :)
i6
    +  :)  "
66A *2*.
k
"
k
"'
'
:+:""
x , y , z 
%.:)
6""" 
x
>"'9
= '−x/' jt−k6zi6
    :'  
, n6> n>i6
6C):"D".$
A +."8"D
6-&
x
(+
z
*  +       %""  
$"8
x
II. Fibre optique (ou guide) à saut d'indice
 :=<<
a
:
n6
>
:):
n
 +
n6
 :
<:'
Oz
" :"> :>
.":
n
""
:
n=6
A. Ouverture numérique
60;<"'
SI
.
I
 : ! (*
(*:<> >?D
>>" >)""98 
$(=*: >:
n6
"")):
n
?8<
SI
=
Oxz
i
:):
i
:).
Ox
"
:
n6
61C). :)
i
<"'
 ': =)D.'"
i
)
iL
6A 
n
>
n6
n
 i
< )) '+$ :
=)
62.'"
i
 )
m
() :  *
-7-

."(
O.N.
*)
O.N.=n m
•A'"
O.N.
n6
n
•%
iL
m
()*
O.N.
 :
n6
E6>-01(*
n
E6>-6(*
•C.)):+:)"
n6
E>5
n
E>D%""
θ
i
B. Modes
""( 9
m
* "
) A>= >:
" $
I
>
I6
>
I
F",.$) ', 
7)
65
H
H ’
<
II6
(. )*
! $
=H ’−H
H
H ’
$D
%<
H
H ’
( >
07-
6
4
4: