cours optique ondulatoire smp3 smc3

7/22/2019 Cours Optique Ondulatoire SMP3 SMC3

1/60

3 3

2013 2014


2/60


3/60


4/60


5/60


6/60


7/60

n= c

v,

v

c

c=299792km/s

1(vide)< n


8/60

[AA] = [AMA] = [AM] + [M A] =n.AM+n

.MA,

[AA

] = A

A n(M)dlM,


9/60

r

r= i0

i1

i0

n.sin(i0) =n

.sin(i1)


10/60

S

=[SM] = [SM]

K

[MK] = [MK]

(P)

K


11/60

19

(M, t)

(x , y, z, t)

(M, t) =(x, t)


12/60

+(M, t) =f(t xc )

(M, t) =f(t+ xc

)

(x, t) =A.cos(t kx)

(x, t) =A.exp[j(t kx)]

1/r

er +(M, t) = 1r

.f(t rc

)

c

er (M, t) = 1r .f(t +

rc)

c

(r, t) = A

r.cos(t k.r)

(r, t) = A

r.exp[j(t k.r)]

A= Cste

(M, t) =0.cos(t k. OM+0)

0

0

T = 2

= 2

k

v=

k


13/60

2

x2 1

c22

t2 = 0,

c

2

x2 1

c22

t2

2

c2 = 0,

2

x2 1

c22

t2

2

c2 1

c2= 0,

(x, t)

2

x2 1

c22

t2 = 0,

f(t xc

)

c

x

g(t +xc

)

c

x

(x, t) =f(t xc

) +g(t+x

c),


14/60

c

x

(r, t) =1

r

f(t r

c) +g(t+

r

c)

,

(x, t) =A.cos(k.x+).cos(t+),


15/60


16/60

s(M, t) =s0(M).cos(t

(M)),

s0(M) M

T = 2

0=cT

(M)

M

s(M, t) =Re[s(M, t)]

s(M, t) =s0(M).exp[j(t (M))]


17/60

Div B = 0,

rot E= B

t,

Div E= 0,

rot B =00E

t

,

rotrot= grad(div)

B =00rot E

t = 00

2 B

t2 ,

B 002 B

t2 = 0,

1c2

=00

E

B

E 002 E

t2 = 0,

E(M, t) = E0cos(t k0. OM) B = 1 ( k0 E) k0

k0=

20

= c

n

k= nk0 = n

20

=n c

= v


18/60

E= E0exp[j(t

k0z)],

E0

E= E0xcos(t k0z+x) + E0ycos(t k0z+y),

E0x E0y x y

E

yx = y x


19/60

yx = y x= 2

E0x=E0y

yx =

2

yx = 2


20/60

E

E(z.t)

n

yx = 0(2)

ux E

E=E0cos(t

k0z) ux,

Ex = E0xcos(t k0z+x) ux, Ey =E0ycos(t k0z+y) uy,

(z?ct)

Ex< x < Ex Ey < y < Ey


21/60

yx = 0

E=cos(t k0z+x)[E0xux+E0yuy],

ExE0x

EyE0y

= 0,

yx =

E=cos(t k0z+x)[E0xux E0yuy],

ExE0x

+ EyE0y

= 0,


22/60

yx = 2

E=E0xcos(t k0z+x) ux E0ysin(t k0z+x) uy,

(ExE0x

)2 + (EyE0y

)2 = 1,

Oy

Ox

E0x E0y

yx = 2

E=E0xcos(t k0z+x) ux+E0ysin(t k0z+x) uy,

(ExE0x

)2 + (EyE0y

)2 = 1,

Oy

Ox

E0x E0y

E(M, t) =s(M, t)u

u

(M)

(M) = 0+ k.

OM

OM = r

0

O

0 = 0

S

0=

k.OS


23/60

I(M, t) =|s(M, t)|2

I(M) =s(M, t)s(M, t)

I(M) = [s0(M)]2

1v2

22 = 0

(M, t)

r= OM

(r, t) =

A

rcos(t kr)

O

kr

O

+kr

k= 2

(r, t) =A.cos(tkr)

k

k=

k

=2

(M)

(M) =(S) +2

0.[SM],


24/60

n(M)

(M) =(S) +2

0

MS

n(M)dlM,

0

R

120s 104ou5s

S1 S2

s1(r1, t) s2(r2, t)


25/60

1 2

1 2

k1= 21

u1 k2= 22

u2 u1 u2 S1M S2M

I1

I2

1 s1(0, t) =s01exp[j(1t)]

2 s2(0, t) =s02exp[j(2t+(t))]

1 s1(r1, t) =s01exp[j(1t k1.r1)]

2

s2(r2, t) =s02exp[j(2t+(t) k2.r2)]

1

I1=s1s

1

2 I2=s2s2

M

s(M, t) =s1(r1, t)+s2(r2, t) =s01exp[j(1tk1.r1)]+s02exp[j(2t+(t)k2.r2)],

1= 1t+k1.r1 2= 2t (t) +k2.r2

s(M, t) =s01exp(j1) +s02exp(j2)

I=s.s

I(M, t) =I1+I2+ 2

I1I2cos((t))

(t) =2 1= (1 2)t k1.r1+k2.r2 (t)

I(M) = I(M, t) =I1+I2+2

I1I2 cos((t))

I(M) =I1+I2


26/60

S1 S2

M

S

(t)

(t) = = Constante

1 =2 = k1 =k2 =

2

k1.r1+k2.r2 = 2 (r2 r1) =2,

= r2 r1

n

S2M =nr2 r1

= 2

= Cste= 0= 2

cos() =cos(2

)

I(M) =I1+I2

I(M) =I1+I2+ 2

I1I2cos(

2

),

p

M

p=

I(M) =I1+I2+ 2

I1I2cos(2p),

p

entier

I =Imax= (

I1+

I2)

2

p entier+ 12

I=Imin= (

I1 I2)2


27/60

C

V

C=Imax IminImax+Imin

=2

I1I2I1+I2

[0, 1] ,

C

1

C

0

C= 1

I(M) = 2I0[1 +cos(2

)],

I0=

I1+I22

C= 0.8


28/60

C


29/60

108s

c= 1

M

M

Lc=cc


30/60

S

l

d

Ls Ls = dl

s s=

l

1996


31/60

2, leslaserssemiconducteurs...etc


32/60

S1 S2

S

S1 S2 S


33/60

S1 S2

M

M

I(M) =I1+I2+ 2

I1I2cos(2

.),

= [S2M]

[S1M]

I(M) =Cstecos(2

.) =Cste

[S2M] [S1M] =constante

S1 S2

a

D


34/60

y= 0

S1M=

(x a

2)2 +D2,

S1M D[1 +12

(x a

2

D )2],

S2M=

(x+

a

2)2 +D2,


35/60

S2M D[1 +12

(x+ a

2

D )2],

S2M S1M= x.aD

p= x.aD

H

S1

S1M=H M,

S2M S1M=S2H,

O M

S2M S1M a= axD

p= 1

p= x.aDi= x= D

a

I0

I(M) = 4I0cos2(

x

i ),

i


36/60

qme

M

r

r

D

S2

S1 S2M H

HM=S1M

=S2M S1M=S2H,

=a.cos()

=

r

D

p= a

(1

2

2) =

a

(1 r

2

2D2),

p0 =

a

p0 p1=p0 0


37/60

S

S1 S2

S

S1 S2

S

S

S

S1 S2 S1 S2

(E)

D >> a

M(x, y)

O

x y


38/60

a/D x/D y/D

2/1(M) =D[1 +1

2(

x+ a2

D )2 +

1

2(

y

D)2] D[1 +1

2(

x a2

D )2 +

1

2(

y

D)2] =

ax

D,

(E)

i= 0D

a i

S S1 S2 Oy

S

D

a

0

i

dI(M)

M

x

dI(M) = 2dIs.[1 +cos(2

0.],


39/60

dIs

dx

dI(M) =dx.[1 +cos(2

0.],

= 2I0

b

= a.(x

d + x

D)

I(M) =

+ b2

b

2

dI=

+ b2

b

2

[1 +cos(2

0(a

x

d +a

x

D))]dx,

I(M) = 2I0.[1 +0d

absin(

ab

0d)cos(

2ax

0D)],

sincx= sinx

x

I(M) = 2I0.[1 +sinc(ab

0d)cos(

2ax

0D)],

V =sinc( ab0d

) =sinc(u),

u= ab

0d

C

D = d

b

b = 0d

a = 0D

a V = 0


40/60

= 1

c

=2 1

dI(M) =d.[1 +cos(2ax

D0],

=

2I0

I(M) =

21

dI=

[1 +cos(

2ax

cD .)]d,

u = ax

cD = c c

=c c

I(M) = 2I0.[1 +V(u).cos(2ax

0D)],

V(u) =sinc(u) = sin(u)

u


41/60

= c

V = 0,

R


42/60

O

R

D

a

M

I(M) =I1+I2+ 2

I1

I2Cos(),

D >> a

2

.ax

D,

2 aR

,

a 2R,

2

.2Rx

D ,

i= D

2R,


43/60

x= C te

i

D

p+D

h

p

p

p = pf

p+f,

a

a= hp

p,


44/60

M

I(M) =I1+I2+ 2

I1

I2Cos(),

D >> a

=2

.ax

D =

4

.

hpx

pD,

i=Dp

hp

,

x


45/60

h

a= 2h

D

M

I(M) =I1+I2+ 2

I1

I2Cos(),

D >> a

=2

.ax

D,

i=D

2h,

x = Cste

i

S1 S2 S

s1=s0.ejts2 =s0.e

j(t),

s= s1+s2=a.ejt[1 +ej],

M

I(M) =s.s = 4s20cos2

2 =I0cos

2

2,


46/60

=2

.=

2

.

ax

D,

I(M) =I0cos2ax

D,

ax

D =k,

x= k.

D

a ,

i=D

a ,

S1S2=a tg() = a2d a= 2d= 2d(n 1)A

A

= (n 1)A

i= D

2d.(n 1)A ,


47/60

0.4m 0.75m

O

x= 0= 0

= p

= (2p + 1)2

= 3m


48/60


49/60

n0 n

r

t

r1=n0 nn0+n

,

t1 = 2n0n0+n

,

n

n0

r2=n n0n+n0

,

t2 = 2n

n+n0,

r1 = r2 r= |r1|

r2 +t1t2= (nn0)2

(n+n0)2+ 4n0n

n+n0= 1

R= r2

T =t1t2 R T

R+T = 1


50/60

A= A0.cos(t )

A1A0

=rA2A0

=rt1t2A3A0

=r3t1t2

n0 = 1

n = 1, 5

r= 0.2 t1 = 0.8 t2= 1.2

A1A0

= 0.2

A2A0

= 0.192

A3A0

= 0.0076

A4A0

= 0.0003

A1 A2


51/60

A1A0

=t1t2A2A0

=r2t1t2A3A0

=r4t1t2

A1A0

= 0.96

A2A0

= 0.038

A3A0

= 0.0015

A1A0

= 0.1

A2A0

= 0.09

A3A0

= 0.081

= geo+sup,

geo = [IJK] [IH] ,


52/60

[IJK] = 2n.IJ= 2n. e

cos(r),

[IH] =IK.cos(

2i) = 2e.tg(r)sin(i),

geo = 2n.

e

cos(r) 2e.tg(r)sin(i),

sin(i) =n.sin(r)

geo = 2ne.( 1

cos(r) sin

2r

cos(r)) = 2ne.cos(r),

sup = 2

= 2ne.cos(r) +

2,

=4ne.cos(r)

+,


53/60

= [IJKL] [IJM] = 2ne.cos(r),

=

4ne.cos(r)

,

f

ik = constante

Rk


54/60

p

p=

=

2ne.cos(r)

+

1

2,

p

p0 = 2ne

+ 12

n >1

i

r

n0 = 1 cos(r) = 1 r22 i= nr

p=en

i2 +2ne

+

1

2=en

i2 +p0,

en

i2 =p0 pi=

ne .(p0 p)

p0

ik= ne .k

Rk =f

ik =f

ne .k

e = 0

p = 1

2 Rk +


55/60

p=

=

2ne.cos(r)

,

p0 = p0 12

S

M1 M2 M1 M2

S

M1 M2

n= 1 r= i


56/60

p=

=

2e.cos(i)

,

e

M1 M

2

i = 0

r= 0cos(i) =cos(r) = 1

= 2ne+

2 = 2nx+

2 = 2x+

2,


57/60

I=I1+I2+ 2

I1I2cos(),

I=Cste

= 2

.= Cste

e= Cste

i

= x=

2

i=

2,

x= 0

=

2

= 2ne,

= 2ne+

2 = 2e+

2,

2 + (R e)2 =R2,

2 +e2

2eR= 0


58/60

e2

=2

R+

2,

= Cste = Cste = Cste

=k.,

k

=

(k 1

2)R,

=

kR,

e

2

L1 L2


59/60

A1 =t1t2A0 A2 = r2.ejA1 A3=r

2.ejA2

2

1

= 2necos(r).= 2ecos(r). 2

,

R= r2

T =t1t2

A

A= A1+A2+A3+...,

=t1t2A0(1 +r2.ej +...),

=A0. t1t2

1

r2.ej

,

=A0. T

1 R.ej ,

=A0. 1 R

1 R.ej ,

I

I=A.A =A0.A0

(1 R)2(1

ei)(1

ei)

=I0. (1 R)2

1 +R2

2RCos()

,


60/60

=I0. (1 R)2(1 R)2 + 2R(1 Cos()) =I0.

11 + 4R

(1R)2.sin2(

2))

,

M= 4R

(1R)2

I=I0. 1

1 +M.sin2(2

))=I0. (),

=

1

1 +M.sin2(2

))

2

I= I0

2 M.Sin2(

2) = 1

Sin2(

2) =

1

M

Sin(2

) =

1M

= 2M

= 2=

4M

= 4

M=

2(1 R)R

,

M

cours optique ondulatoire smp3 smc3

Documents