Microlasers : Dynamique de Couplage et de Polarisation

HAL Id: tel-00083926

https://tel.archives-ouvertes.fr/tel-00083926

Submitted on 4 Jul 2006

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Microlasers : Dynamique de Couplage et de Polarisation

Géraud Bouwmans

To cite this version:

Géraud Bouwmans. Microlasers : Dynamique de Couplage et de Polarisation. Physique Atomique [physics.atom-ph]. Université des Sciences et Technologie de Lille - Lille I, 2001. Français. �tel-00083926�

! " #

$ %

&

'

& !

& !

( ! ) "*

+,,-

) !&

""

!

. " !

'/

.

0/

& ! 1

2/ /

!

"

/

%

!

#

'/

3 !

$%& $' ( )

$*

/

+ '

( $

$*

"

" !&

+ % , -. ) *( # * # / 0 1 # * * 2 . 3 / 4 . 5 # ' + 6 7 1 + . * * ! 5 $%& $' ) * . # # , ( -* + 1 8 6 9( ! ( ( 0 ( / ( 0 ( * ( ( ( ( . 9 9 : . # $ *( ( # :

SOMMAIRE

'

...

-4 '

/////////////////////////////5

- 6 7 6 8 ; ! " # $ ! - ! <= - $ << % & - 6 :::::::::::::::::: <> '( ) * " ) *+#," % - " >?8@65A <B - @65A <; - * <; - ! <C - + D< ) * +&-- " >?8@%) D; - " >?8@%) DC " ) *./"* +&-- " >?( A?8@%) >D - " >?₍ A?_{8@%) >A}

4 '

9

6

'

:///;<

- ' 0 =' AD 0 " - 0+ # AD - A> - ! A> 1 "2 - * AB - %1 A; - $0 '%'0 $E $ $"'% E F= 3 %4 - 5 F< - % F< - F< 5 $$ % - $ ∆ν FD - FA - ! FF - F; - $ + BD - BF ' $$ 3 6 2% ) 3 22 - * BB - $ BC

& & - $ BC - 6 ϕ0 ;= - ) ;D - ;> - $ ;G 6- =' 6 : ::::::::::::::::::::: :GD / $ 7 (6 89 $$ ! - ! GC - 3 C< - + # CD - $ CD - ! + # CA " : $ $ 6 !% 6- =' 9 6 00 ' C; 5 ( ! & $ 3 4 / $$ 6 6 4" - <=A - <=G

4 '

9

6

'

9

///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////---- ;> 9 <<A / 6 " $ 6 / ; ! - / <<C - <D= - <D< - $ <DA - 3 <DB " 0 - # * <DG - # <DC - % # <DC - <>D - $ + <>B - 3 <>B - <>G % β' β " - % <A< - 6 <A< - 5 <A< - <A< - <AD 2 / $ 3 6 / " - 0 # <AD - ' # <AA - ! <AF / < =56 "% - / <AB - / <A; ? ;>@ A>9 <AC &; %4 : % 56 = % " 56 %

- 0 :::::::::::::::::::::::::: <FA - H 4 <FA % 0 %% - ! <FF - ! : <FC 2 ) %! - 0 <B= - H 4 <B< / 2

?

=

;>

@

A>

9

'

//////////////-BA

0 6 " / ; % - + <;B - 0+ <;; - 0+ <;G

::::::::::::::::::::::::::////-C-'4

::::::::::::::::::::::::://-C5

<

'

!& & !

! ( 8 ( ( ( ( ( : ( # , ≤< -( I ( + ( 0 # * * ( * ( J<KJDKJ>K , # -( * , * -* 7 JAKJFK L * 7 * ) ) . ) + * * M N 7 * * JBKJ;KJGKJCK( + ( O + ( + (

& D & O * # * ( * @%) , + - + ,@65A-( * * + " >? ! @%)( * * ( 7 # + + * @%) + ," >? 8@%)-," >?( A?8@%)- $ 7 + , * ( :-J<<KJ<DK L J<>K * # J<K&J<=K + # * J<AK + # * % # ( 7( * # # 1 * * * ( ( 6 * #

> # * * * 7 + # ( # 7 * # @%) + " + ( * ( " >?8@%) ( " >?( A?8@%) 2 P # + * * * + #

F

3 $ &

; 7 + $ ( ( Q , - ,

-?

6

&7

#

! "

8

1) Présentation générale

( , - ! ( + &3 + + # 0 % D- ( = 3 &< λ , -( λ * ( + ( '

' "$

λλλλ

'

"

!

λλλλ

& #

3

E

#

"$ F &

$

F *

G- ""

""

G ( * λ * , *- λ R , ( & ( :-# ," + ( $ ( ' :-9 ( 9 , -( ( , ( :-( + , & -( # ( ( ( ( # % * ( CCS G=G B== T + D S + ," >?8@65A- + L U ( 7 % " , + -( 7 <G= T J<FK +

2) Fonctionnement monomode longitudinal

&3 + J<BK # , 0 - ∆ν > ' V # J<BK & ∆ν ( * ( V 0 > ∆ν J<;K * (

C ( ∆ν ∆ν 7 * ( @%)( F== T ( <S " + ( ∆ν ∆ν * <F= )W9 , & - % ( ( ( *( M N J<GK( # *

3) Fonctionnement monomode transverse

+ & ( J<CK % 1 ( ( < , > < X =- * @%) @65A ( ( 0 * + 9 ( ( W Y 4 JD=K ' 3 JD<K ( * $ ( % ( # 7

4) Variation de la fréquence émise

" # (

' ( ( (

(

<=

ν

'

ν

∆ν

'

ν

'

∆

' ,' ? ' -( # ,' ≤< - <=BA ( =(< L FF W9 ! * 8

?

F &

F

Q* ,3 &D-& 0 % D+88 ( $ $ $ $ 6 $$ . ( @ $ 7 $ ( * * * ( + <= ( ( δ( =(=F T D δδδδ ≈≈≈≈ ,@,5 H" ∆∆∆∆

νννν

≈≈≈≈ +5 4I J$ K + ""? δδδδ ≈≈≈≈ ,@,5 H" ∆∆∆∆

νννν

≈≈≈≈ +5 4I ' ! & ≈≈≈≈

λλλλ

L-, - J

νννν

-? + J

νννν

+? ≈≈≈≈ 5,, H" ' "$ -' "$ + F & $ " ≈≈≈≈ -,

<< λZ<=( ( δ [ =(=F T DF )W9 F== T <(=B T

*?

FF& &3 " #

* * * '

ν

'

ν

( ( 8 ' ' D = =

ν

ν

, \<-V ν 8 + − = < ' ' < < < <

ν

ν

_, \D-" ( (

ν

+ (

ν

> < # ( * (

& <(BA )W9ZY @65AJDDK

0 ( ( *

! @65A(

& =(F> )W9ZY JDDK

( L

5) Avantages des microlasers

+ ,'$ ==

<D ( R * JDFKJDBKJD;KJDGK Z R 1 JDCKJ>=K 7 ] JDDK J><K % ' ' JDDK + <=; )W9 R * I ( ( <= B=S J>DKJ>>K R + 9 P R ( * ( @%) , A?- * " >?8@%) J>AKJ>FK + * 9 4 9 7 4 P + ( J>BK ! ( 1 # I $ ( ( < # # ( # ( ( + # , ? - # I ! ( # * ( + ( * # ( *& ( ( $ ( + ( ( I U ( + (

<> + ( * ( ( ( ( : 1 % # * ( + #

?

&

& #

"

&

% ( $%& $' ,) -! ( " + ," >?- 7 + ,@65A- + ,@>%F5<D @%)-! ( ! @%)( * 8 , 0%- 1 @%) , A? -" ( ( # + * $ ( " >?8@65A( + * " " >?8@%) " >?( A8@%)

<A

1) L’ion Nd

3+

" >? ( $ ,$ -' ,' -( * JDFKJ>;KJ>GK J>CKJA=KJA<K ] ! * ( + + @>? 3 &> * J<BK A & * 7 A ( # * . D0?< . V0 0 % D; " 6 ($$ ( ) *

λ

A

λ

- ( A .

σ

A

σ

- $$ 4= A = . < B 2C A CZD , =- * R λ A 3FZD ,>-σ # R A 3>ZD ,D- λ) A 3>ZD A <<ZD ,<- σ) $ ( * # * > ,'>- < ,'<- D ,'D- /

λ

λ

)

D

=

>

<

'

>

'

<

'

D

σ

σ

) A

3

FZD A

3

>ZD A <<ZD A CZD

<F " >? ,@%) @65A-( + '>( '<^^ 'D 0 ( * ( *A3>ZD A <<ZD JADK σ) * . JADK & * A F A 5 * & * # , 0 4- % ( # JA>K ' ( @%) @65A( <=BA ( * * ( G=G % # # (

2) Nd

3+

_:YVO

4 ,@65A- + * " * ! # ( # ! ( *

?

&

& #

&

;>

9

A

@65A + !A + 9 ,_ 0 5A- JAAK * ( + * * , - * , -' &< @65A + * , - ( ( σ)

<B σ ( λ) λ ( ∆ν) ∆ν 3 D ,'D- < ,'<-( α " * ,<S DS -* '> ( * # ,'> ^^ 'D -* <=BA ( * > < $ ( ( α * # , -( D.

&

& #

&

;>

9

A

J 7

&?

λλλλ'J!"? G=G(F JDGKJAFK λλλλ J!"? <=BA J>;K 0 σσσσ'J-,7-< "+? D(; JDGKJABK 0 σσσσ J-,7-< "+? _{<D&<B JDGKJA;K} & _∆ν ∆ν∆ν ∆ν'J 4I? BC= JABKJAGK & ∆ν ∆ν ∆ν ∆ν J 4I ? DF;&DBF _J>;KJAGK ! +JH ? ;A&<== ,! <S->=&>> ,! DS-JAFK JA;KJACK ! 1 1 1 1 J$ ?M G;= ,!_{>>= ,!} <S-_DS- JACKJF=K αααα * J "7-? DG&>= ,! <S-;D&G= ,! DS- JDGKJ>>K <=BA _D(<BG JDGKJABK ' * J-,7(N7-? > JF<KJFDK αααα J-,7( N7-? A(A> JF<KJFDK J L"/N? F(<&F(D JF<KJFDK * D- < ; $ ( +#," 7 6

<; F G ] ( F== T G=G C=S( * <=BA CC(FS ( G=G ( # CFS <=BA

*?

&

& #

"

"

9

A % ( + ( * i) Montage expérimental * 3 &A 0 % DA8 1 +#," ' A' $ $ A$ ".% A ( 4. A4.% ' '" 6 3 " 4 $ TuARu ; (6 A ,0! D>BD-* ;== H # U F= T ( # <DF T

=(A & DA`

R ( # * , D < A >

*

+

9

!

3

@65

A

D

0

Tx, Ty, Tz Tx, Ty, Tz Rx, Ry

E ? 4F

<

<G [ G=G(F - D 1 1 7 L # ( , ( - ] , L -F= W9 ( <D6 * + # >! 1 ( ( O * * # R * * * 1 ( # ] 1 * , AF`-, > A- <D= < # <A(F =(DG( D G + , &D- >= FG T + + # # * ( ( * ( * ,=(A- $ ( + JF<K , F=S-,F -( & 7 * + # >! ( * *

<C

( (

* (

ii) Détermination des caractéristiques du milieu amplificateur * * @65A " >?, ' \<- ! V * ( % + , G=G -( O " ( ! ( <=BA a $ a ( ;F &< DS ( JF>K # * ,D- ,<-D , - * 'D( * ( ( ( ,' !$' A<=( <F= W9- ,' 4 * '!0 AD=% <==

W9-D= 3 \F * , <- ,≈<T -< D , D- L * ( DG T ( * > 1 * ( * ( DFS # 0 % D585 $ ' ; A ( A $ $ ' ; 6 . G ; 6 F 'D # ,>= >> T -, ' \<- DS( D M & N JFAK 1 R " + + FCF

-;

+

0 50 100 150 200 Temps (µs) In te ns ité (u ni té a rb itr ai re )

D< ! # JFAK( * * A3>ZD ( * ,D <ZD- ! ( * A <FZD + # FC= # * ( 'D L

iii) Caractéristiques du rayonnement émis et de la cavité

0 * 3 \B , <=BA -, G=G -B= H O DFS * * & , -F F= H 0 % D(8 A7 42" $ A7 4 $ + ( 1 & 9 $ & ( * 0 10 20 30 40 50 60 0 50 100 150 200 250 300 Puissance de pompe (mW) P ui ss an ce é m is e (m W )

DD , *- , -<=== * ,<S-( + @65A 0 ( 3 DB * D== H C= @65A 1 * # &D <D(B 0 % DB 5 $ $ ; 7!4 ' 6 . ; E? .2 G 6 6 * a * * ( 7 7 ( ( 6 A=6 JFFK 6 A=6 # ( 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 15 20 25 30 35 40 x (mm) In te ns ité (u ni té a rb itr ai re )

D> + ,P - # O + ; A> T 3 + * # + + ,' !$' A<=( <F= W9- ,'!0

AD=%- + ,% ' A<><$ <= 4W9&>(F

)W9-( /( , * - J<BK * * ,κ -,γbb -* O ( 7 JAFKJACK 3 \G( <;= H ,D(G -( * ( B(> W9 * , #-0 % DC 56 $ ( A 4 H> 5 . I 72. 0JK 7 $ 6 A ? 4 L & ? . 0 2 4 6 8 10 Fréquence (MHz)

DA 3 \C * * + <== W9 8 D= S FS * ( % ( 0 % D<85 ( $ ( $ (6 3 . &= * ! * * ν * J<BK 8

(

<

)

D < D D _{= −} & 8

π

ν

κ γbb , \>-# κ γbb * κ 3 \<= 0 20 40 60 80 100 120 0 1 2 3 4 5 A-1 A m pl itu de r el at iv e de s flu ct ua tio ns (% )

DF

* # &&<

( * ( R ,, \>--

κ

<(D <=<= &< γbb[<Z'D[ >G <=> &<

γ

⊥ G(D <=<< &<, #

' \<-( 1 # + /

γ

_⊥XXγbb(κ 0 % D-, 5 $ 6 $ (6 3 A&= ' 6 6 ; ( G 6 6 A ? 0JK

.

$ 1 ( ( # * * ( + + &3 + <F W9 ," P ( 0 + 0&DF=- 0 ,%≈ F-9 # ( + ' = D= A= B= G= <== = < D > A 7-F # ! . & ! J 4 I + ?

DB % + & ( $ , > <X= @65A -ν , \D- & 8 + − = < ' ' < < < <

ν

ν

! @65A( [ D(<;( > < [ > <=&B Y&< >'M '> <

A(A> <=&B Y&<, ' \<-

ν / Τ

\<(BA )W9ZY c!

V J<BK( ( ,

γ

⊥XX κ

)

( * & , &3 +-3 \<< 0 % D-- # $ $ ' 6 ; G 6 6 -20 -16 -12 -8 -4 0 0 50 100 150 200 250 300 Puissance de pompe (mW) V ar ia tio n de la fr éq ue nc e op tiq ue (G H z)

D; ! ( L \C= W9Z H # ' % , \D-( FF YZH ( ( <;`( >== H D= 4H Z D % # @65A( * , -( ( @%) ( @%)

3) Nd

3+

:YAG

@65A( ( ( # @%) + #

?

&

& #

&

;>

9

" + @ @%)( @65A <S " + 8 @D(C;" =(=>%F5<D JA>K @65A # * + , -( @%) J>GK + " >?8@%) @%) 1 ' \D

DG

&

& #

&

;>

9

$ O-P

λλλλ'J!"? G=G(; JDGK λλλλ J!"? <=BA(<G JA>K 0 σσσσ'J-, 7-< "+? =(; JDGK 0 σσσσ J-, 7-< "+? >(>&G(G JA>KJABK JA;KJFBK

& ∆ν∆ν∆ν∆ν'J 4I? >;= JABKJAGK

& ∆ν∆ν∆ν∆ν J 4I ? <>D&<GF JABKJAGK ! +JH ? D>=&DF= JA>KJABK ! _{1 1 1 1} J$ ?M DDF JF=K αααα * J "7-? ;(<&G(> J>>KJABK <=BA _{<(GD&<(GA JDGKJF;K} ' * J-,7(N7-? ;(> JF;KJFGK αααα J-,7( N7-? B(;&;(C JF;KJFGK JFCK J L"/N? <=&<> JDGKJFCK * D+ < ; $ ( +&-7 N $ ' \< @65A( @%) @65A( ( * @%) <(<S >S @65A( " >?8@65A " >?8@%) σ @%) @65A L % ( @%) F== T >= S

DC @%) G=G @65A 'D @65A,DA= T >= T -( # '< # B D # < = ( * J<<<K( # # FD= T # CFS G=G ( * <=BA * CGS <=BA CFS G=G R

*?

&

& #

"

"

;>

9

+ ] * B(F =(B<F G ] + , * G=G 8<=?A- λZD = G=G ( * * >== H # ;= T " & $ * ( # * @65A + A= T

>= 0 * 3 \<D ;F H GS * * A( <G H 0 % D-+ $ ! * @65A( @%) * @65A % * ( * ,&- A( <FS( FS @65A * * , 3 &<>- * 5 >(> <=C &<( 'D[ DA= T 0 4 8 12 16 20 0 50 100 150 200 250 300 Puissance de pompe (mW) P ui ss an ce é m is e (m W )

>< 0 % D-; 5 $ 6 $ (6 3 ) * +&- ' 6 6 ; (G % + & ( * ( * ( * < , ' \D-( \>(D )W9ZY( * @65A L O * D= W9Z H C= W9Z H @65A * B(> YZH

4) Nd

3+

,Cr

4+

:YAG

! ( A? @%) ( 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 3 A-1 C ar ré d e la fr éq ue nc e de r el ax at io n (M H z 2 )

>D

?

&

& #

;>

@

A>

9

@%) + ,≈ <S - ;== T ( @%) , A?-( <== T ( 1 ] 0 C ] * J<(<(<K % ( A? %>? * , B=S % - JB=KJB<K * # A? 1 & , D?- JB=KJBDK >? ( A? & JB<KJB>K " >?8@%)( + " >?( A?8@%) I A? 8@%) # $ JB<K ] * ( + 0 % D-A 6 ( (; / "* +&-# 1 * 3 \<A * < * > & * > %D >'D J>AKJBDKJB>KJBAKJBFK( A >'< J>AKJBAK( D <$ JBDKJB>K( &

A

>

D

σ

σ

'

'Q

'd

<

>> > 'D J>AKJBAK 0 @%) 0 @ JBFK # ' * > A * # D( * * D < D ,') D(C A(< T J>AKJB<KJB>KJBBK * * > ,' - A ,'d-# ( ( # ' 0 _ / JBDK ) E JB>K 'd =(F =(< < * > + <=BA * * D A * ( ( ( A? 8@%) JB=KJBDK ( 7 ( ( A? ( ( ' \> O σ , <e >- <C ;= <=&<C D σ , De A- D D= <=&<C D A? ( '= , - * ' , - $' ;;(FS C;S σσσσ% J-,7-< "+? 5B±±±± +, B,±±±± C -<±±±± 5 ;,±±±± ,@5 +5±±±± ; σσσσ J-,7-< "+? C±±±± + +,±±±± ; 5±±±± - +±±±± ,@5 ;±±±± ,@; F ! JB<K JBDK JB>K JBAK JB;K * D;8< ; $ $$ 6 A

σ

6 " A

σ

" >?( A?8@%)( * <=BA CC(FS( ,G=G

->A

C=S G=G # ;S

<=BA #

( <C;

*?

&

& #

"

"

;>

@

A>

9

* 0 &' , GCC -<F H , A==- G=G + D H F== 4W9 , ^=(<-" >?( A?8@%) D== ,<F - + &D <>(F T D= T <D(A ( + D;(A T 0 * " + 3 \<F 0 % D-5 5 $ = F <= <F D= DF = <== D== >== A== F== ' ! $ "$ J" ? ' ! " J" ?

>F <F= H ( ;S * * A( ' * + A== , & - ,<=&C=S- DG= ( BF= * # ,3 \<B- $ B= 4W9 * # D(< , AB= H -J>BKJABKJBGK $ 7 * + O 0 % D-( 5 $ $ (6 3 % + & &3 + & <F )W9 D=( < D )W9 + D== W9 + &3 + 0 10 20 30 40 50 60 70 0 0.5 1 1.5 2 2.5 A-1 F ré qu en ce ( K H z)

>B " >?8@%)( " >?( A?8@%) (

α

# * " >?( A?8@%) " >?8@%) \>(D )W9ZY 3 \<; * * ( L 1 * D=F W9Z H ( * BA YZH @%) ( ( I , -0 % D-B85 $ $ ' ; 4% 0JK> L G 6 6 -40 -35 -30 -25 -20 -15 -10 -5 0 150 200 250 300 350 400 Puissance de pompe (mW) V ar ia tio n de la fr éq ue nc e ém is e (G H z)

>;

7 (

*

* * " >?8@65A

>C

3 $ &

! " #

$ %

!&

A< * ! ( * # U + * # * + * " + " # + # # $ + # # * * + # * * ! # ( + # # " + * * * # # + + # $ # # * + *

AD

?

$

& F .$

" !&

* + * " * L *

1) Montage

& *

?

&Q"

$ "$ %

* ( ( * 7 R + # ( & 7 * 1 ,3 \<- 7 + # * * * ( ( # <DF T ( ( * * 7 * R O 7 & 7 * + # * ( * ( ( 7 1 <A= D=== T

A> J ? J*? 0 % D-8 $ $ ; . A ; . A; O 3

*?

'

& !! " !&

"

9 V + O *

?

%! &

+ # * ( + $ ( JBKJ;KJGKJCKJBCK( # ( * 3 \D + # + , < D- % ( * * # ( , [ <F - 1 * O *& M N % D(F * > # D *( , ['[F=S-< D

AA # < * + ,!< !D -<F= W9 ,' !$'A<=-,' 4 * '!0 AD=% <== W9 + >>A% F== W9-* 0 % D+ 8 6 ( 6 * ,F=== F= T '!0 AD=% DF=== F= T >>A%-4 ( ( 3 +

-:

,

4

0

^ < )W9

1

,

3

+

"

>R "

8

≈

%4N

<

≈

%4N

8

≈

4N

<

≈

4N

8

≈

%4N

<

≈

%4N

AF 0 * # , 3 \D-( * * ,!>- < )W9 ," P G<G&//&>=-( + ( * " < )W9( &3 + ,0 + 0&DF= " P -# + * &3 + 5 # # + + ( ! ,0 + - 9 , - 9 * , - , * -,) f 3 &GG=( D= /- # 7 ! ( 7 ( L , ( ( ( &3 +:-# Z 1 7 & <=BA I * * ( 1 & 7 * ( a D= / " *

AB

2) Stratégies retenues

* ( ( 1 1 * ( # , ( ( * - ( * 1 $ ( # @65A " 1

?

3 .

&

" + + 8 " >?8@%)( " >?8@65A " " >?8@%) 1 + * , -+ # # + + " * JF>K 7 ! ( + U " @%) @65A % ( + " <= >= * * J;=K ( 7 ( $ ( CCS <G= T # * (

A; * @65A ) R ( + * , - * / # C;S + ( " * , &

-*?

S & " !&

F #

!

!&

+ * # # 9 * I $ ( , -, -1 . E JGK " 8@%) # O ( & JBCK & $ ( O 7 # 9 & + # ( ( * # 1 $ ( * 5 ] Z 0 7 * ( * ! (

AG ! ( V 1 ] * # , D== T -O # $ & ( V 0 # $ ( * ( # + # 8 * ' ( * * ( # # + D== T ( + ( * A= W9Z H + D== H 9( * & ( ! V * & V * * ( * 7 1 ( ( % ( ( O ( * * \A= W9Z H ( < W9 D # P <=&A D== H , + - ! Y , ( # :- $ ( * ( 9

AC 9 ,=(< W9-* ( ∆ν [ ν D& ν < * " ∆ν [ νD& ν< * * ∆ν ∆ν8 I a * & 7 / ,κ^^γ⊥-( # ( ( ,

ν

κ

γ

γ

ν

∆ + = ∆ ⊥ ⊥ _{- J<BK} ! V ( !> # * ( ( * ( # ( ( ,

6-F=

?

& &

.$

" !&

.

1) Dynamique temporelle du système

+ + O + ( ,<A= T ^ ^ DF= T - * ,<(F ^& ^ A-% ( * ( * * <=S ( 7 * + * " * * ( * ! * ( * * $ ( ( ( * * * 7 * * ! ( $ ( * V * 0 ( D

,& ≥ & V&

-0 (

* > + +

*

F<

?

& ! #

!

$ !

!&

( &3 + , 3 \D-* * + ( R ( Q 3 Q + , !< !D -* % ( 1 # 9

*?

3 %

$3

% ( ( * 7 Q* Q &3 + !> ! ( + + # # ( * Q * # * 7 *

?

% "

! & *

( ( + + ( b∆

ν

b + + Q $ * + # ( ( V *

FD

% # O (

* *

2) Etudes détaillées des différents régimes dynamiques

?

&

!& ! &

"

$

3 #

! F! & !

∆∆∆∆νννν

∆ν( * + ?? 3 ( ( * * ( * + * $ * , # * -( # 3 \> Q ∆ν ( 3 \>& 7 7 + 3 \>& * * * V *&

<CA±F T ( * & , <- & , D

-* D(F >(F ( ∆ν * ( ∆ν * * *& 7 ( L( + # * ( " ∆ν ( ! ( , -* * $ ( ( (

F> * + < D b∆ν b , 6-0 % D; 5 $ ( @ 7 @ ( A ; $ 6 A; P . Q . R 6 6 A ? !" F ,3 \>& - , -Q ?DF W9 1 \>= W9 Q = F== <=== <F== D===

&F= &A= &>= &D= &<= = <= D= >= A= F=

" $ & & ) & ! JP ? D > A F B ; G C

&F= &A= &>= &D= &<= = <= D= >= A= F=

∆ν ∆ν∆ν ∆ν J 4I? 0 # ! & ! J 4 I? -+ ; J*? J ?

FA

Q J\>( ?> K W9( *

Q &DF W9 &A W9

?A W9 ?DD W9

i) Lasers quasi indépendants

! ( * ,F(F W9 <( ;(A W9 D -( ( ( Q <FS , 0- * Q Q 3 ( Q* Q * ( " ] Q * 0 Q ( Q ( * ( ( 7 Q " O * 3 &A 3 &A& 3 &A& ( D * 0 3 &<A& ( * a , * -a 5 * D <, -7 * 5 ( ( 7 * " ( ( # # 7 + + # 5 * * 3< 3D F(A ;(A W9( ,F=(>

W9-FF

0 % DA 56 ; A 5

( A; ; $

0@ 6 ::S

ii) Domaine d’accrochage

3 &F * 7 3 \> ( D = = < = D = > = A = F "$ JH ? ! & ! & J / /? 0 10 20 30 40 50 60 Fréquence (MHz) + -+ -0+ 0 -0 J ? J*?

FB 0 % D5 56 5 ( ; ; $ 0@ 6 ::S ,3 &F& - # ( >S + 3 &F& ( ,3<[ 3D[ B(B W9-* 9 ,F(A ;(A W9- ! ( 9 ! * ( * =(GG( * # =(CF 0-K 0+K (@( 4I = B = ; = G = C < = D A B G <= "$ JH ? ! & ! & J / /? = F <= <F D= 0 # ! J 4I? + -+ -J ? J*?

F; iii) Régimes instables

! ( + " * , <= W9- ! ( * # ( & * ] ] , 3 \>& -+ $ ( ( * ( ,3 \>& g-( * < D * &G W9 3 &B ( * + # + <<B=S , <- <<C=S , D -+ DF & ( < F D * ,3 &B& - 7 A(FC W9( * (

FG 0 % D( 5 ( ; ; $ 0@ 6 ::S $ S 0JK ' 6 ' ; ( 6 ( ( < * * D * # * ( ( J ? J*? = < D > A = < D > A F "$ JH ? ! & ! & J / /? = F <= <F D= DF >= >F A= 0 # ! J 4I? + -+ -0-K 0+K A@5< 4I + 0+ ; 0+

FC 3 \; * 0 % DB856 ; $ 5 ( ; ; $

∆ν

? . 0JK 0@ 6 ::S * 3< ,A(> W9- 3D ,;(= W9-* * 3/ ,<G(G W9- & 7 ,3/±3<( 3/±D3<:- < 0 D = = F < < F D D F > = < D > A F "$ JH ? ! & ! & J / /? = F <= <F D= DF >= >F A= 0 # ! J 4I? J ? J*? + -+ -0 -+0 -0 >-0 -0 7 -0 -0 7 +-0 -0 7 ;-0 -0+ 0 K -C@C 4I

B= a 3D( D3< 3/&>3< 7 % ( ( ! ( ! ( * * 3 \G 0 % DC 56 ; $ 5 ( ;

∆ν

? = !. 0JK 0@ 6 ::S = < D > A = < D > A F "$ JH ? ! & ! & J / /? = F <= <F D= DF >= >F A= 0 # ! J 4I? J ? J*? + -+ -0 K -<@- 4I

B< * ( 7 7 <=(; < <<(< D # ( * A(D W9 < * F(D W9 D ,3/[ <C(< W9- ( <( # ( * ( <F=±F T ( \B= ? F= W9 9 1 <D= W9 % ( [ D>G±F T ( D= W9 ( * 9 ( 1 Q , -( + + L O ( ( * ( ( $

BD

*?

)

& !

&

&

! 3 "$

!& !

!! " !& "

+ R 3 \D ( + 3 \C * # * * 3 \C * 3 \> 7 ( 9 ( <F= T O + # ( ( ! ( , *& -Z, *? - V * , - * , - + # + # * * @ J;<K # ! * ( 0 3 \C( ( * \B= W9( = W9 ?F= W9 " # " 3 \C & ( =(;π ! ( + 3 \> G W9 , # <- 0 + # * * 0

B> V ( 7 + # 7 , Dπ -0 % D<81 $$ = ? %4 F . 7S24 0JK . 4 0JK ; %4 0JK ' $ 3 $ =$ ; ? !"F A$ 3 ::S . =$ ; A$ 3 ::S

J ?

J*?

J ?

J ?

J ?

JF?

BA ! ( # * \>= W9 \A= W9 , # D > 3 \>- 0 ( # νD D # 7 νD < + # 7 * + # ( νD ν< * ( + # 7 % , * - * * + # ( + ( 7 * ( ( + # # π , D -$ ( * * + 8 - ( - ( -+ 8 + ( 1 + #

BF

?

& !

( ( # * * / ( # * * * * * # * + * ( * % # ( #

<-

Les différents modèles existants

0 1 ( # 0 ( 8 & ( 1 L , - J;DKJ;>KJ;AK( M + N & # M N J<K & * + + # J;FKJ;BKJ;;K & , - J;GKJ;CKJG=K( * & & J;BKJ;;KJG<KJGDK J;KJG>KJGAKJGFKJGBK # ( * * *( +

BB

2) Notre modèle

?

FF

!&

$ %

"$ .

# Y $ * JG;K 8

(

)

5 T5G 5 + − − = <

δ

, &<-+ − =

γ

& < 5 D ,

&D-γ

?

γ

||>

κ

V [ < D G [ >& 5 * ( & *

γ

|| *

κ

*

δ

ZDπ ( *

κ

&< T 9 Y $ * * ,T = T + T = D −θ - ( 1 ( T , &<- 7 5

ϕ

D < 8

(

)

(

ϕ

( )

G

θ

)

G D5 5 5 < < + + − − = _,

&>-(

+

)

+

(

−

)

− ∆ =

ϕ

θ

ϕ

θ

ϕ

D < < D 5 5 5 5 D , &A-V5 =5 −ϕ ( ∆=

δ

_D −

δ

_<

ϕ

=

ϕ

_D −

ϕ

_< * * + , - + + , &D-, &A-( + * 5 A=

∆

?5GA

∆

5 A=

∆

?5 A

∆

VG[>&

B; + # 8 ' 8 ] ,5→5G. → G -,

ϕ

→ &

ϕ

- ,∆→ &∆) ' 8 ,

ϕ

→ &

ϕ

- ,∆→& ∆), ,5→5 . → -' 8 ,∆→ &∆-h ,

ϕ

→

π

=

ϕ

-( ( V ,& [ & -( + # , - " 5 A

∆

? 5GA=

∆

+ L #

+ ,& X & - 2 & & * (

8 • ! ( T [ = ,

θ

[ =

π

), + # , - 5 A

∆

? 5 A=

∆

• ! ,T [ =-( , -+ # 1 5 A

∆

? 5 A=

∆

• ( * ( 5 A

∆

? 5 A=

∆

1 + * , -( * 7 < D( V ( 1 5 A

∆

? 5 A=

∆

% + ( 1 + * 7 1 O 2 * ( JBK % ( 7 (

BG JFFK 0 7 ( + , -* 3 * ( V * * ( * " 1 * + , 6-0 ( + # ,: =

(

5_< +5_D

)

×, - V + * 1 * - % , &<- 8

(

ϕ

)

θ

ϕ

- D D ( ( ,5 D 5_<D 5_DD 5_<5_D $ : + + × + = ∂ ∂ V $,5( (

ϕ

- ( * 0 ,

θ

= =(

π

-( ( L D

π

θ

=± , -( # $ ( * ( # % ( * $ 7 * # 5 ( V ( JFFK # # ( + # + # , &D- ,

&A-BC

*?

& & & & !!

( + # F 8

(

+

)

+

(

−

)

− ∆ = = ∂ ∂ϕ _{ϕ θ ϕ}1 _θ 1 1 1 1 1 1 5 5 5 5 D = D < < D ,

&F-(

)

1

(

ϕ1

( )

Gθ

)

G 1 1 1 D5 5 5 < < == − + + − = ∂ ∂ _, &B-+ − = = ∂ ∂ 1 1 1 5 & < D =

γ

, &;-V * 0 * + + # * + # * % # ,

&F-i) Etude de la plage de verrouillage

, &F- 8 = = + + ∆ _/

ϕ

1

ϕ

1 _{, &G&} -8

(

)

= D D + +Φ = + ∆ 1 /

ϕ

, &G& -V =− + 1 1 1 1 5 5 5 5 T / < D D < ( =− − 1 1 1 1 5 5 5 5 T < D D < _Φ= / &

&&

#

& ! !

" &

& ! #

D D / + ≤ ∆ , &C-5(

ϕ

7 V M N * % 9 ( * 7 ( + ₁ 1 1 1 5 5 5 5 < D D < ₁ − 1 1 1 1 5 5 5 5 < D D < ₍

;= ( /( ! V ∆ ( + 5 ( ,T [ =-,T [ =-( + ,5 ,∆) = 5 ,&∆)-+ , ∆- 0 ( * ,& ?& -( D * ∆ T , - AbT b T 9 * ( # ! ( = D ,51 =5= = & −< -+ ∆ D = D = D / + V − − + − − − = < < < < < D D < = & & & & T / − − − − − − = < < < < < D D < = & & & & T " ( ( AbT b * *

ii) Valeurs stationnaires du déphasage entre les lasers

ϕ

S

% * , = D -(

ϕ

1 , &G& - * ( & 8 = D = D = Φ − + ∆ + = / 1 π ϕ , &<=-V

Φ

=[ , =Z/=

-;< ∆ T 1 ϕ −Φ D >π = , =D D = / + − = ∆ - −Φ D π = , =D D = / + = ∆ -( π * ( ,θ = -(π

Φ

= [ = * ( D >π D π _π = = ∆ ϕ1 $ ( ϕ1 * ! * ( ,ϕ1[ π-+ # ( V =( # * # , =≅ =-* + T ( T $ ( 4 9 ( , &G- φ0≅&∆>/4 ( VT ,/4^=-( φ1[ = ∆[= ! ,T ^=-( ∆ $ ( + # , &D-, &A- ∆ 8 + V 4^^ /4

;D ( + + # , &D- , &A-∆

?

!

, < ∆ D -( *

ϕ

* ∆ , &A- ! , &>-( L O a ∆ $ ( * O D ! ( O * ,± -(θ Dθ % ( ( ∆ = D

ε

( )

D = _{+ +Ο}ε = 5 5 ,

&<<-( )

D = _{+ +Ο}

ε

= , &<D-V5= = ,5= = & −<( = = -< , &D- , &>- + # 8

(

G

θ

)

G D5 5= + = ∆ +,−< -=

[

& +D5=

]

− =

γ

8

(

G

θ

)

G D5 -< , = − + ∆ ∆ =

;> V ( [<(D 1[>& # ( γ ,≈<=&B - * + # ( < DZ∆, 8

( )

(

∆ + −

)

∆ + = = G Gθ 5 D5 5 5 : < D < = = D = D , &<>-∆ ∆ < bΨb D < ∆( ∆

(

Ψ=−D

( )

∆ ×

θ

)

*

?

FF

!&

$ %

5 JBK

•

( ( ( *

•

M N % 1 # 9

•

9 # , -( , &<>- T( * *

;A 8

( )

(

∆ + −

)

∆ + =

θ

ν

ν

_G 8 8G D : : = < D < $ O <Zb∆b ( 8 8G D

ν

ν

D * * ( <, -D,ν <^ν D -! * ( * * * ( Q 1 ( * # * 3 &<= <;>± F T 3 &<=&

ν

D&

ν

< V

ν

D&

ν

< ∆

ν

D&

ν

< [∆κZ,Dπ- * + 1 * * L + ( # ( <, - D,

ν

D[ ;(DC W9(

ν

<[ F(GA

W9-;F 0 % D-,8 & ( 7 $ ; 6 AP' .Q' . . . ; G 6 ; $$ ' ' 0 3 \<<( * * * = = D = A = B = G <

&D== &<F= &<== &F= = F= <== <F= D==

νννν+7νννν-J 4I? " $ & & ) & ! O F # ! * && " ! & &< &= ;F &= F &= DF = = DF = F = ;F <

&D== &<F= &<== &F= = F= <== <F= D== νννν+7νννν-J 4I? ' 3 & ) & ! O F # ! * && " ! & J L ππππ ? J ? J*?

;B 7 * ! * ( =(=<D± =(==< ,κ&<- C= 0 % D-- 5 7 $ ; $ ( i j 6 ' ' ' ; Ψ ,3 &<=& - L ( $ # ,=(BFπ - # ,b

ν

D&

ν

<b- G= W9 θ (

( )

∆ − = Ψ D

θ

Ψ 7 Dπ #( θ π #( 5 7 ! * ( ,&=(>D;± =(==;-π π # ( + + # 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.005 0.01 0.015 0.02 0.025 1/|νννν2-νννν1| (µs) A m pl itu de r el at iv e de s os ci lla tio ns à la fr éq ue nc e de b at te m en t

;; ( 3 \<D ϕ1 , &<=- ∆ * T ( # * ,T ZT [ =(G( 5_D= =< 5(D _<= -T T $ ( ∆ ϕ1 \=(43π =(F;π =(=7π T T ϕ1 =(57π <(F;π π, T T ( Φ= π T ( % ( T ! * ( * ,ϕ1 ≅ π- k T θ ,=(B;>±=(==;-π " * T [ ,&=(==BD± =(===G-& ,=(=<± =(==<-( * ( [ <;>± FT 0 % D-+ 5 6 $ ' ; ; T >T ? 4. . 5_D= =< 5(D _<= T U4 ; $ ; @ 3 $ T V4 -1 -0.5 0 0.5 1 1.5 2 -1 -0.5 0 0.5 1 ∆∆∆∆/(C02+D02)0,5

ϕϕϕϕ

S /

ππππ

;G

?

)

& !

FF

!&

$ %

! F! & !

& !

!&

! V * , - ( " + <A= DA= T DA= T ( 7 % ( ( ( # , -( 1 # L $ ( <A= T ( T ,X D== W9- ∆ * I * ( * + * & * 3 \> $ ( * + 7 * " $ ( * 0 * # , <=S- O 1 3 \<> ( ( D ,3 \<>& - ( ( &θ ,3 \<>& -! * ( D L O ( D D(FF <=&D >(F <=&A( ( D >= <;= T DA= T ( D <A=&<;= T ,&θ

-;C \=(Gπ \=(B;π <F= T <;= T 0 % D-; 5 D A ( SθA; $$ $ -1 -0.9 -0.8 -0.7 -0.6 -0.5 140 160 180 200 220 240 & ! !& JH"? −θ ( /π ) −θ ( /π ) −θ ( /π ) −θ ( /π ) 0.0001 0.0010 0.0100 0.1000 140 160 180 200 220 240 J ? J*?

G= T T L * V * T T 3 \<A 0 % D-A 5 T A T A; $ " * %

O \<(A <=&D \F(< <=&A L(

* , \=(=<>- [ <BF T = * * ( * T ( J ? J*? -0.02 -0.015 -0.01 -0.005 0 140 160 180 200 220 -0.02 -0.015 -0.01 -0.005 0 140 160 180 200 220 & ! !& JH"?

G< T T * 0 W JBK R ( 1 9 # ( 1 % ( # * +

GD

?

.$

" !& & ! ! "

#

" O * & " # * * * # $ ( + + # * + #

1) Présentation du programme

* * # ( ?? + # ( + ; * ( # * ,& & -( * ,κ- ,γbb-( ,T T -, ∆

ν

- , -ϕ * *( 7 7 ( + + # # 3 * + # I * V + # * Θ

G> * * + ,<ZF= - 5 + + 8 Θ − + Θ −

₊

+

+

=

Θ

5

5

5

5

5

5

:

_{1 2} < ₂ ϕ < ₂ ϕ D D

-,

(

)

5

5

5

5

:

,

Θ

-

=

₁D

+

₂D

+

D

_{< 2} −ϕ

Θ

−

ϕ

V + + ϕ =−

(

5_<5_D −ϕ

)

+ ( + * Θ=ϕ 8 D D <

D

2 1 2

5

5

5

5

#

+

=

−ϕ + ϕ # 5 A ( 5 A ϕA + F= ( ( # ' ( + ( + # , ≈<=S-+ ( L $ ( + # *

2) Confrontation des résultats numériques à l’expérience

" (

(

* 3 \>

* & [ D(A; & [ >(F>

* C= DB T

&=(==<> &=(==DC 3 &<B

GA 0 % D-5 5 ( ( 6 A . $ ( A; $ $ 1 ::S T ? =4.44 . T ?=4.44 !. & ? ." . & ? .% .γ||−1? 2 F .κ= ? !4 P .Q . R 6 6 3 &<F& 7 7 , + - 3 &<F& ( ( * * O ( = F== <=== <F== D=== DF== >=== >F== A===

&F= &A= &>= &D= &<= = <= D= >= A= F= ∆ ∆∆ ∆νννν J 4I? " $ & & ) & ! JP ? = D A B G <= <D

&F= &A= &>= &D= &<= = <= D= >= A= F= ∆∆∆∆νννν J 4I? 0 # ! & ! J 4 I ? J ? J*?

GF + # ( * * ( ( # * * 5 # 8 - * + 8 ( 9 - + - * 9 * & % * 9 ( * 7 ( , + -! O ( * ( + 8

•

! *

•

* ;

•

< D

•

# ( < # * D ] ]

•

! ( $ ( < D 9

GB * * # 9 $ ( * \>= ?DF W9 * \A= ?>F W9 7 * * + # # , + # D *( /( 8 6- * + # M N 9 # 9 + " 7 * # 9 ( * * ( # 1 k # ( * ( # 0 3 \<B 3 &<F 0 % D-( / $ ; A♦ ; A A ::= % 0 10 20 30 40 50 60 -50 -40 -30 -20 -10 0 10 20 30 40 50 ∆ν ∆ν∆ν ∆νc (MHz) Fr éq ue nc e de B at te m en t ( M H z)

G; ( L , -( 1 ( , -* # 1 > W9 1 + # + # * 3 \<; 0 % D-B8 W ; 3 $ $ A ::= % 9 ,−>(F ?> W9- * * ,X=(;-\<F W9 G W9 + # * + ( * # * * % & ( L # , - A= W9 =(<F( 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -50 -40 -30 -20 -10 0 10 20 30 40 50 ∆ν ∆ν ∆ν ∆νc (MHz) V is ib ili té d es F ra ng es

GG 5 + $ # V # \A \ <F W9 * * ,3 \B- ,3 &<F-+ # * + # +

ϕ

3 \<G (

ϕ

ϕ

,♦-( ( ( a * + , &<=-# \F(F ?F(F W9 5 \>(F W9 ?> W9 M N * ( 0 % D-C W $ $ A ::= % -2 -1.75 -1.5 -1.25 -1 -0.75 -0.5 -0.25 0 -50 -40 -30 -20 -10 0 10 20 30 40 50 ∆∆∆∆ννννc (MHz) P ha se r el at iv e en tr e le s la se rs (r ad /ππππ )

GC + 3 \<G ( ( \<(=Dπ \=(BFπ, + # ( * * 3 \C , −A \<F W9-(

ϕ

* ( , 3 \<;-(

ϕ

\<(>>π \=(>>π 5

ϕ

π, & * V =(A & * * ( ( ] T T + + # 1

3) Rôle des parties réelle et imaginaire du coefficient de couplage

" + 7 ( ( # ( + T T ( * 3 &<F 0 ( T T * &=(==><;G =

?

" !

3 %

&

! & * &

3 &<C

, ,

-C= 0 % D-< 5 $ A A; P .Q A ::= % $ T T # L + ,3 &<C& - + + 7 + ( 5 A∆ ?5 A=∆ 7 , - , - $ ( + + + + + # * + # 0 2000 4000 6000 8000 10000 12000 -30 -20 -10 0 10 20 30 ∆ν ∆ν ∆ν ∆νc (MHz) A m pl itu de r el at iv e de s os ci lla tio ns (% ) 0 100 200 300 400 500 600 700 -30 -20 -10 0 10 20 30 ∆ν ∆ν∆ν ∆νc (MHz) A m pl itu de r el at iv e de s os ci lla tio ns (% ) J ? J*?

C< * # 9 7 + * 3 &<F. 1 * + # $ ( L ! ( <G W9( # D>(A W9 * + , &C- ! ( B W9( * ( * + $ # ( * $ ( & ( * a L , - ( * # ( ( + $ ( * 9

*?

0 #

!

* && " !&

3 \D= * L T T ,

-CD 0 % D+, 5 $ ; $ ♦ . R A ::= ! 5 ( + * 6 _ JGGKJGCK( M + N M + N 5 ( ( , - ] 7 ,

-?

&

& #

&Q"

F !%

( + + #

! #

+ i) Etude de la visibilité des franges.

3 &D< + , - * 1 L VT [ = V T [ = ( 9 # L # =(A 0 10 20 30 40 50 -30 -20 -10 0 10 20 30 ∆ν ∆ν ∆ν ∆νc (MHz) Fr éq ue nc e de b at te m en t ( M H z)

C> * ( ( ( D= W9 =(<F 0 % D+- 5 ; $ $ A . A; A ::= ! ( < * ( 1 ( ,X=(F =(C -0 0.2 0.4 0.6 0.8 1 -30 -20 -10 0 10 20 30 ∆ν ∆ν ∆ν ∆νc (MHz) V is ib ili té 0 0.2 0.4 0.6 0.8 1 -30 -20 -10 0 10 20 30 ∆ν ∆ν∆ν ∆νc (MHz) V is ib ili té J ? J*?

CA

ii) Déphasage au centre du système de franges

ϕ

3 \DD (

ϕ

&π , -, - \πZD , - 0 9 0 % D++ 5 $ ( $ $ A . A; A ::= ! ] + ( ( 9 -1.25 -1 -0.75 -0.5 -0.25 0 0.25 -10 -5 0 5 10 ∆ν ∆ν∆ν ∆νc (MHz) ϕϕϕϕ m (/ππππ ) -1.75 -1.5 -1.25 -1 -0.75 -0.5 -0.25 -30 -20 -10 0 10 20 30 ∆ν ∆ν∆ν ∆νc (MHz) ϕϕϕϕ m (/ππππ ) J ? J*?

CF * 9 V * ! ( 9 $ ( 9 T [ = T [ = 0 + M N ] 9 % ( M N( 7 * + + # V * + # +

4) Influences des fréquences de relaxation sur la dynamique

* + + # ( 1 # + # ( * * ,κ, γZZ( & & - * , 3 &<C-3 \D> F= ,T [ &=(====BF. T [=- * ,F(AB W9 < ;(A W9 D- 9 ,=(DF W9- + + * 3 &<C ! ( 9 * * 9 V *

CB * ,≈<> W9- ,≈<(G W9-* O 8 O , -O JC=K( 7 & D(G W9 7 * O + * * 0 % D+; 0 3 6 $ 6 ν8 ? %.2" 0JK.ν8 ? ."4 0JK. T [ &=(====BF. T [= ( + # 9 + * ,3 \G- 7 O + # 9 $ ( 9 * * ( + * 0 100 200 300 400 500 -15 -10 -5 0 5 10 15 ∆ν ∆ν∆ν ∆νc (MHz) A m pl itu de r el at iv e de s os ci lla tio ns (% )

C;

?

.$

! ! & #

FF

!&

$ %

# * # * ( *P &/ ( # ( * + ( # * JBK ' ( + # * ( ( 1

1) Equations d’évolution des champs

( V ( 1 ] + + # % & * / ( *P ( JFFK 8 D D = D = = D D < < ∂ ∂ − = ∇ − ∂ ∂ E _E P ε ε µ , &<A-Vε4 F4 E P P * 8 P P P= + , &<F-VP , -( P , + - " A JFFK 8

(

)

E P D < = − ε = A , &<B-V V P 0 * P * ( + # O 1 " + @65A ! ( * + 8 + =

CG ,≅ D(<; <=BA -* 8 -, -, -, = ₌ +∆ _< +∆ _D , &<;-V∆ A + ( O ω ( % # ( 8

( )

₊ = ⊥ − -( , D < -( , D Z < bb 5 ω

µ

γ

γ

E

( )

₋ = ⊥ − -( , D D < -( , D Z < bb D = = ω µω γ γ κ ε t P V 4 F ] , &<A- 8

(

)

₍

_{) (}

)

(

)

D D D = D D D D = = D D _D < -, < 5 5 5 ∂ ∂ − ∂ ∂ − − = ∇ − ∂ ∂ −ω −ω −ω −ω

ω

κ

ε

µ

, &<G-! V ω ( * 8 5 5 _<<ω ∂ ∂ _<<ω ∂ ∂ 5 5 ∂ ∂ << ∂ ∂ _ω D D ∂ ∂ << ∂ ∂ _ω D D , &<G- 8

.

A

A

.

A

5

.

A

5

A

.

A

5

.

A

5

D D = D D D

D

D

−

_ω

∇

+

κ

=

−

κ

ω

−

∂

∂

, &<C-V O κ5

CC ( , - 5A ( -JBKJGCK8 -, -, -, -, -( , _< 5_{< D} 5_D 5 = + , &D=-V W 9 JBK -, -, D D T − = ∇ , &D<-% ( A * T O * * ω 8 T =ω ₌Z , &DD-A * 8 < -, -, = k , - _G, - =

η

≠= ≠1 , οVη * * # 1 ] * 5A A ( 8 A A 5 A = − V A , &D-# * A # $ ω # " + # # ( 8 -, -, -, -, -( , = _{< <} + _{D D} , &DA-V , - , - * * A ( * *

<== ! V * ∆ A 4. = D < D D = _{< D} A A A ∆ + ∆ − ≅ * ( , &<C- 8

(

< < D D

)(

< < D D

)

= D < = D < D D D D D D = D < < < < < < < D < 5 5 5 5 A 5 5 5 5 A 5 5 + + ∆ + ∆ − κ = ∆ + ∆ ω − ω − ω + κ + + ∆ + ∆ ω − ω − ω + κ + , &DF-$ 1 ( 5 8

(

< < D < <

)

<

(

< < D < <

)

D < _{< 5 $ ; 5} 5 + + + − − + = _, &DB-V κ&< <( ;<( <( <( < $< 8

(

−

)

− ∆ + ∆ − − = η ω η ω ω κ < < < D = D < D < < _< < <

(

)

(

)

; ∆ +∆ − − = < D D D = D < D < < η κ η ω

(

−

)

∆ + ∆ − − = < < < < < D = D < D < < D < < _η η

(

−

)

∆ + ∆ − − = _{D < < D < D} = D < D < < D < < _η η

(

−

)

∆ + ∆ − − = < D < < D D = D < D < < D < < η η

(

)

$ − ∆ +∆ − − = _{D D < D D D} = D < D < < D < < _η η 5

<=<

2) Analyse des résultats et confrontation avec le modèle initial

7 # ( ( , , &<-- 8

(

< <

)

<

(

)

D < _{< 5 T T 5} 5 + + − − =

δ

, &D;-* , &DB- , &D;- ( * ,&5<-( <5<( ,∼& 5<-( ,∼5D -* , &DB- # $ ( L D ,∼ D5< -$ ( , < * D$<- * *& 7 # # $ + ( 7 * + * # ( ] , &DB-*

•

# δ 8

(

− −

)

∆ + ∆ − − > = D < D < < _η η ω *

•

* ;<( ( # 0 ;< ;D ∆ 7

•

* < ( < . < $< , &DB-, - *

<=D a ( , - 7 * # < < + , _{G T} −

η

_{′ G′ T′}- ( = D <, -+∆ , -∆ , <=&F- 7 A 8

(

<<< <<D

)

D < < < : :

η

η

− − = k

(

_{D<< D<D}

)

D < < < : :

η

η

− − =

(

<D< <DD

)

D < < < : : η η − − = k

(

_{DD< DDD}

)

D < < < : : $ η η − − = V :_GT = _{G T} * * * ( * η( ,η≠=- $ * , &DB- 5< ,η- 5D ( & 7 ( 5< 5 3 \DA <<< < < < < < < < 5 : 5 = 5 < D<< D < < < D D < 5 : 5 = 5 D <D< < D < D < < D 5 : 5 = _{5 <} DD< D D < D D D D 5 : 5 = _{5 D} 0 % D+A / ; 7 ( 5 # * < ,:<<<

-<=> ( L 1 % ( ( 7 # , - ( L : ?: * M N ,l5 - , &DB- 8

(

)

(

D<< D<D

)

D < D < < <<D <<< D < D < < < < < < < < 5 : : 5 : : 5 5 η η η η − + − − − = + :<<< D. # ( L 7 $ :<<<( # D <<< <−η : < :14 , T<- 8

(

)

(

DD< DDD

)

D D < <DD <D< D < < < < < : : : : T η η η η − + − − − = 7 # ( ( ( $ ( & # <( 7 ( 1 A===S ! γ , <=&B- ! ( L < * * # 1 ( #

<=A % ( * + ( 8

(

)

[

<D< DD< <DD DDD

]

D < < < : : : : T + − + − = η η , &DG

-(

)

(

)

T ∆ +∆ − − = < D D D = D < D < < η κ η ω , &DG -* -* ( * ( ( ( ( + ,T ? T ? T T ? T ? T - ( ∆ * + * * + ( 1

3) Calcul du coefficient de couplage et comparaison avec les

résultats expérimentaux

?

'

&

( * * * * ( * " * * *& 7 ( 7 + E . ! 7 O ( * * ( 7 + E' " ( ( * * + & # 8

<=F

( )

− + − π = _D D D D < D * D ' ' E 6 E k −

( )

+ + π = _D D D D D D * D ' ' E 6 E V 6 = < = = − D D D < D * ' E 6 η < < D <<< ₌ η − :

( )

− + − αα + η − = D D D D < < < * D D E 6 k = −η +_αα −

( )

+ + D D D D D < < * D D E 6 V D D ' E E =

α

+ :14 8 D DDD <<< = : = <−η : k

(

)

α α η η ++ − = = = = < D D D<D DD< <D< <<D : : : < : k

(

₋

_η

)

_η

+α = = < A D <DD D<< : < : 8 α α αα _{η η} η ++ _{− −} ++ = < F < D D T , &DC-* ( T E' E FA(F T F= T 3 \DF

<=B 0 % D+5 5 $$ $

♦

6 X (6 , &DC- E'? %".% F E ? %4 F + E' E 1 O # T * ,♦- E >= FG T , - ( E' >=S A>± F T & *

η

1 ] * T $ ( # V # % ( * 7 ( ( * ∆ , - + + , ( 3 &;-$ ( + # ( * & 9 &= =D &= =<F &= =< &= ==F = <A= <B= <G= D== DD= & ! !& JH"?

<=; 0 * * ( ( , &DC- 1 3 \DB ( # $ ( T O 9 ( <<= T G= T ( * ( # * + :( (>& :<<< ' T . ( * * JBK V ,T ^=- ,T X=-0 % D+( : T AE'? %".% F E ? %4 F $ L 1 1 * & 7 9 &= =F &= =DF = = =DF = =F F= <== <F= D== DF= & ! !& JH"?

<=G

*?

'

&

" % !

( * + ( ( ∆ # $ ( * , - , > <-* , -( , - $ ( # V % * ( 7 7 ( * + T ∆ 8 + ± − ∆ = ∆ = ∆ _D D D D D * -, -, < E 6 < < < < V∆' * E' &D * 8 − − + ∆ − = + + + + β β β β η η η β β κ η ω _<F < D = D D < < < < T , &>=-V

β

[ E'DZE D # ∆' E' 1 * * 3 \D; T E' <<= T * ∆' >>`,E'[ FA(F T

-<=C 0 % D+B 5 $$ R < A

∆

< ? Y. E<? 4 F ( E'? %".% F * ∆'( ( # * ( <F` $ ( # + * 7 ( ( V * E' + * # 0 # * T ( ( -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 100 125 150 175 200 225 250 & ! !& JH") ki

<<= $ ( + # * 1 # + + # * % ( 3 \DG O 0 % D+C 1 A' . ' ' 6 ( % 6 . ' . ' X ' . ' X ' . ' & + # * * + # * J ? J*? J ? J ?

<<<

3 $ &

! " #

$

& !

<<> * " >?8@%) " >?( A?8@%) ( ( * * " >?( A?8@%) * * ( + " >?( A?8@%) # * ( " >?8@%) + 7 8 ( 1 # , -( , ( J<>K:- ( ( , J<<K( J<DK :-] O ( V * L # " >?8@%) $ $ ( * " >?( A?8@%) $ * * * " >?( A?8@%)

<<A

?

&

"

;>

9

! # * + " >?8@%) & + , - , -+ 1 ( # * " >?( A? 8@%) + # % # * ( * , * - # + 7

1) Contexte

1 $ 9 ,W &" * _ JCDK&JCFK- JCBKJC;K( ,@%) J<DKJCGK&J<=DK-J<;KJ<=>KJ<=AK $ # , a -( , - # W &" V + J<=FK ' J<BK( + 1 7 5 + ( V # ( * ( * *

<<F $ ( , a - , -( Z 7 , # -( @65A( + % ( / P ( # + 7 / P J<=BK ! 7 ( # ( @65A( * ( ( * JDDK ! V ( Z * J<=DK + ( ] ( I ( 1 J<DK , ( Z - 1 * * + * J<;K * 7 ( * # ( L + * % / J<=<K * ( * ( + ( & # # # ( * @%) # ( , -(

<<B + V ] I * ( ( + + ,J<<KJ<>KJDAKJ><KJ<=;K&J<<DK-Z , * - , -$ 7 ( # *& 7 ( * * ,JDAKJ><KJ<=;KJ<=CK- $ ( ( # ( @%) 8 & * ∆ν + 9 9 J<<KJ<<=K&J<<DK ( J<>K J<<DK * ( 7 ∆ν J><K & 7 J<>K J<<=K @%) 8 ∆ <=&B <=&G # ( ( ( 1 * 7 J<<=K ! V ( ( * * ( * J<<=K ! ( ( ∆ν J<>K J<<=KJ<<>K

<<; ! ( @%) * 0 * ( ( *

2) Dispositif expérimental

* 3 \< * + @%) + ] + , 6 ( * * <=?A- 7 1 λZD = G=G + + <=BA , 0 <=BA- λZD = # a * , 9 - * !< !D ,!$'A<= ' - , + >>A%- ! M N , - < D , ≈ F=S( ' ≈ F=S- # + ( + , &3 + 8 " P 0 +

0&DF=-,P # 8 5 !&>==&>H - + # 0 <=BA( λ/D <=BA

P # ( + JC<K ! ( * * 0 <=BA λZD <=BA 0 1 &3 + ,) f 3 &GG=( D=

/-<<G 0 % D- $ 6 ( ) * +&- $ ? . ? K % ( ' ( * # ,^ FS-( , m

&>-"

λλλλ

L

+ O-,(A !"

₊ ;> 9

&

$& #

!&

+

!&

;

-≈≈≈≈5,P @ -≈≈≈≈5,P

'

-,(A

'

$

&L

!

$ &

&

! #

F*

"

λλλλL+ OC,C !"

!&

-'

!

'

&70 *

+ -;

0 &

C,C !"

$ &

$& #

<<C a " ∆ν * , - + < <== W9 , J<<KJ<<=K&J<<DK-* B <=&C B <=&; J<<K $ ( ∆ν 9 * ( W Y J<>K( 1

3) Comportements observés

! V # ( + * 8 * * 8 V ( # ( + * * ( * " ( # ( O

?

F !% !

"$

& !&

<D= + ∆ν 9 9( * GB W9 * Z *

θ

* * , -5 * ! # ( &

θ

! ( * 7

θ

i) Puissance de pompe élevée

! # * ( , - D(C , - " (

θ

( ( ,j- ; ,n-( 3 \D = < D > A F B ; G C <= = AF C= <>F <G= θθθθ'JT? ' ! " J" ? θθθθ JU?

<D< 0 % D+8 5 $ Q . Z ;.

×

A 6 > ? .!.

≈

2 0JK L * *

θ

* a ( ; . =(B H G(A H ,×- ,C H - * # ,≈ FS- ! O ( *

θ

a * * , -1 + ? 4*

∆

A

θ

*

ϕ

ϕ

?4

ϕ

;?

π

θ

> 8 > ? . 5 * , -5 # * ,G(A H 3 &D- 7 ! * 1 * J<<AK # ! ( A

θ

*

ϕ

L # V O " # * _ 3 J<=GK _ + P 4 J<=CK * # , <=- ! 44 ! P J<<=K # *

<DD * , > U . -( *

θ

* , - # , > ; ;> X F=- θ * * 3 \> * > <(A 3 \D( 5 + k ,>=`^

θ

^ B=`-( ,=` ^

θ

^ >=`-. ; ,B=`^

θ

^ C=`- C=`^

θ

^ <G=` + 0 % D; 5 Aj ; An $ $ 3 A > ? .".

≈

2 0JK A

×

5 + λZD <=BA O 0 <=BA + * + &3 + + = = = D = A = B = G < = < D < A < B = >= B= C= <D= <F= <G=

θθθθ

JT? ' ! " J" ? θθθθ JU?

<D> 3 \A V , ;- 9 V * * * 3 \> 0 % DA 5 $$

θ

, >

≈

." X

≈

% 0JK-( * * V * ,

θ

[ AF`-( ( *

θ

( 8 1

θ

$ 6 , ;-( (

θ

! 44 ! P J<<=K

θ

[ =`

θ

[ AF` -,, 4I ! " θ [ <A;o θ [ <A>o θ [ <>Fo θ [ <D;o θ [ <D>o

<DA

+

iii) Evolution temporelle en fonctionnement bimode

$ ( ,>(G -,CD W9- * 3 \F 0 % D5 56 7 $ 7! 0JK A > ? . .

θ

? "%Y. ? L ! * 8 − − − − α- ! ,ν ≤ D W9- * * + # * , J<;K( * J<<FKJ<D=K:- * * , <(; W9-, * -0 0.1 0.2 0.3 0.4 0.5 Temps (µs) In te ns ité (u .a .) " !

<DF * , - L * AF` * , -* * A , <=S #-

θ

[ AF` & β- ( V <<S( 7 1 , 0 <=BA- a * * $ ( # * ! 3 \F( AF` * ( * 3 \B V * *

θ

0 % D(8 5 6 AQ ; AZ 7 $ A! 0JK $ 0@ :::S% 0% 10% 20% 0 30 60 90 120 150 180 Ta ux d e m od ul at io n θθθθ JU?

<DB + / J<=<K W Y J<>K @%) W (' 8@%) 7 * # W Y J<>K L λZA + ! ( * <<S # =(=D; *Z <=== * & a * J<=<K( # ( 7 & a * L * $ (

θ

* ,p=` C=`-( L 9 $ ( M N , -L # * *& M N * ,

F-*?

0 *

!

&

$

9 V ,∆ν 9 9-( / J<<>K ! 4 ! P J<<=K

<D; 3 \; * ; + & D== * =(B W9 5 * 7 O # ,D W9 > /-( + 0 % DB 56 ( ; ( $ ; A

≈

% 0JK X > ? . .

θ ≈

"4Y , <- λZD ( 5 ( * O / J<=<K @%) ] 0 5 10 15 20 25 30 35 40 Temps (µs) In te ns ité (u .a .) & = & =

<DG $ ( # ( + # ! ( a 7 + 7 # 5 * # * 8 & θ D= A=` * * ,l < W9-3 & % 9 ,∆νl<= W9-( , -(

θ

* , - * * , AF`-J<=<K

θ

9 #

4) Modélisation

# % # 7 ( + # * ( * + +

?

Q

. & !&

# + * # 7 O 8 & # # J<;KJ<=AK

<DC & + ( , -J<<BKJ<<;K & + & 7 / , " >?8@%) @65A -* JCDKJC>KJ<<GK ! * # _ / J<<CK / J<=<K # , /( # - 0 # J<<CK J<=<K( ( * " # * # J<=<KJ<<CK * + ( ( #

*?

Q

)

$$

" * # ! ( * & i) Approche du problème 1 ( & * a J<<BK 1 " >?8@%) ( * ( a , -# $ ( 1 * * ; ( 5 * 5; * ; *

∆

∆

;

<>= 0

∆

∆

; O ( @%) ( + ( + !D J<==KJ<<BK( 7 * 7 " ( ( # 7 J<=AKJ<<BKJ<D<K & * * 5 ( ( 8 5

χ

ε

= = V

χ

! ( + + # 1 # 5 ( ( 5

χ

# ,5(6( (K- ! ( *

χ

₆₆(

χ

(χ_KK

χ

( K 6( ( ( * % ( 7 + ( ( + 5

χ

# * * + J<=AKJ<<BKJ<D<K * ( * 5

<>< * 5 * ( # ( ( B + @%) 7 * ( ( * # * B > J<<BK ( + # * * * JCGKJ<=>KJ<=AK # 1 # D! >! J<=AK * # 7 * , + -# α( α * , * - ( * Σ ,α- Σ ,α- 8 ⊥ = Σ α α σ β σ α ( = = -, ⊥ = Σ α α σ β σ α ' ' ' ' ( = = -, _{, &<} -Vσ σ' α β β' $ ( β β' # & $ 4 JCCK

<>D ' 1 ( # @%) * B ] + $ 8 & % ( * * @%) + ( O B 5 # + J<=>K J<=AKJ<<AK & * ! J<<BK B=`( * B ( # , D`-( 1 + # $ ( ( * ( + ! + # 1 % * * ( # ! J<<BK( > <D #

ii) Mise en équation

% ( 1 * * ; ( 8

(

)

[

+

]

=ℜ ℜ = − − ;; 5 5 5 5 l l ω l ω * * 5l 5l_; 8

(

)

5 5

κ

κ

δ

− + − = l l , &D-V [ ; δ ω κ * , - 1

<>> , = ? ; " 7 O % ( α, )Aα # * # _α ⊥ α β' , ,

&<--(

α β α

)

α π ' ⊥ + = = -, -, V ,α-=),α- _α 5l _{α ⊥},α-=),α- _α⊥ 5l _α⊥ )Aα 8

(

)

(

)

{

+ + +

}

− − = d _⊥d _⊥ ld -, -, l -, -, D < -, -, -, 5 5 ) & ) α β α α β α α α γ α Vγ * &Aα * * _α $ * ,

α

- * ( 8

(

+

)

(

+

)

+

(

−

)

(

−

)

+

(

−

)

+ − =γ α α β β α β α φ α D < D < D < < D < < -, -, -, D D D D ' ; ' ; ' ; 5 5 5 5 5 5 ) & ) , &>-V5 5; * 5 l ; 5l φ 5 5; -* , l 5 5 = −

φ

( 5l_; =5_; * ,−

φ

_;-( φ =φ_; −φ , &A-)Aα . & 3 * J<=<KJ<<CKJ<<AK 8

(

D D D D

)

D -, = ₌ + α+ α + π α ) ) ) ) , &F-$ * , &>-( 3 )4() ( ) 8

(

+

)

(

+

)

−

(

−

)

(

−

)

−

[

(

)(

−

)

]

+ − =γ β < β < β φ D < < D < < D D D D = = = ' ; ' ; ' ; ) 5 5 ) 5 5 5 5 ) & )

<>A

(

−

)

(

−

)

− +

(

+

)

(

+

)

− = & ) 5 5; ' ) 5 5; ' ) β β γ < D < < < A < D D D D =

(

)(

)

[

−

]

− +

(

+

)

(

+

)

− = & ) 5 5; ' ) 5 5; ' ) β φ β γ < D < < < D < _{D D} = V %=( % % 3 * %, α-, , -= D

(

₌+D Dα +D Dα

)

+ π

α & & &

& - 8 = π α α = = , -D < & & ( = π α α α = D -, D < & & = π α α α = D -, D < & & &Aα # _{α α⊥} , , &<--( * ( 8 -, -, -,

α

∝

σ

D Ψ −

α

+

β

σ

D Ψ −

α

&

(

, - , -

)

A -, D

α

β

D

α

π

α

= & Ψ − + Ψ − & Vβ Ψ * & α Ψ 5 %,α-8

(

)

&

&₌ = <+

β

k & = &

(

<−

)

DΨ

D

β

k & = &

(

<−

)

DΨ D

β

, &B-$ * ",α- , , &F--* 8

(

)

(

)

[

]

(

)

{

}

(

)

(

)

[

]

(

)

{

; ' ' '

}

' ; ' ' ; ) 5 ) ) 5 ; ) 5 ) ) 5 ;

β

β

β

β

β

β

− + − − + + − + − + + = + = < l < < l < l < < l = = $ 1 ; , &D-( * * * ; 5 , -* # 8

(

)

(

)

(

)₌ < β_' ) < β_' <

)

5 )

(

< β_'

)

5_; φ 5 − + − − + + = _{, &;&}

-<>F

(

)

(

)

(

₌ <

β

_' <

β

_' <

)

_;

(

<

β

_'

)

φ

; 5 ) 5 ) ) 5 − + − − − + = , &;&

-(

−

)

+ − ∆ =

β

φ

φ

< ; ; ' 5 5 5 5 ) , &;&

-(

+

)

(

+

)

−

(

−

)

(

−

)

−

[

(

)(

−

)

]

+ − =γ β < β < β φ D < < D < < D D D D = = = ' ; ' ; ' ; ) 5 5 ) 5 5 5 5 ) & ) , &;&

-(

−

)

(

−

)

− +

(

+

)

(

+

)

− = & ) 5 5_{; '} ) 5 5_{; '} )

_γ

_β

_β

< D < < < A < D D D D = , &;&

-(

)(

)

[

−

]

− +

(

+

)

(

+

)

− = & ) 5 5; ' ) 5 5; ' )

β

φ

β

γ

< D < < < D < D D = , &;& -V (

∆

(

γ

*

κ

&< *

κ

6 ) , # - # , -, - + + # ,) -# / P 4 J<;K * ( # V # *

β

' # 0 # 9 / J<=<K( $ ! # *

<>B

+ + (

?

&

! & #

#

& !

i) Forte anisotropie de cavité

% * ( * # 0 ∆ 8

(

−

)

+ >> ∆ ; ; ' 5 5 5 5 ) <

β

, &G-* 5 5; (

φ

∆

, , &;& -- $ + ( 8 -, -, -, -, ) ) 5 5 T T T = + + = V ? ;( T ? 4. . 5 )_T

φ

+ # , &;- _T M N , β p<-8 ' ' & 5

β

ρ

ρ

+ − Ψ + = < < D < = D , &C& -' ' ; & 5

β

ρ

ρ

+ − Ψ − = < < D < = D , &C& -' )

β

+ = < < = , &C& -= = ) , &C&

-(

'

)

) Ψ + = D < D

β

ρ

, &C&