cours optique ondulatoire smp3 smc3
TRANSCRIPT
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3 3
2013 2014
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n= c
v,
v
c
c=299792km/s
1(vide)< n
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[AA] = [AMA] = [AM] + [M A] =n.AM+n
.MA,
[AA
] = A
A n(M)dlM,
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r
r= i0
i1
i0
n.sin(i0) =n
.sin(i1)
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S
=[SM] = [SM]
K
[MK] = [MK]
(P)
K
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19
(M, t)
(x , y, z, t)
(M, t) =(x, t)
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+(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
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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),
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c
x
(r, t) =1
r
f(t r
c) +g(t+
r
c)
,
(x, t) =A.cos(k.x+).cos(t+),
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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))]
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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
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E= E0exp[j(t
k0z)],
E0
E= E0xcos(t k0z+x) + E0ycos(t k0z+y),
E0x E0y x y
E
yx = y x
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yx = y x= 2
E0x=E0y
yx =
2
yx = 2
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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
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yx = 0
E=cos(t k0z+x)[E0xux+E0yuy],
ExE0x
EyE0y
= 0,
yx =
E=cos(t k0z+x)[E0xux E0yuy],
ExE0x
+ EyE0y
= 0,
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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
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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],
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n(M)
(M) =(S) +2
0
MS
n(M)dlM,
0
R
120s 104ou5s
S1 S2
s1(r1, t) s2(r2, t)
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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
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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
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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
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C
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108s
c= 1
M
M
Lc=cc
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S
l
d
Ls Ls = dl
s s=
l
1996
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2, leslaserssemiconducteurs...etc
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S1 S2
S
S1 S2 S
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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
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y= 0
S1M=
(x a
2)2 +D2,
S1M D[1 +12
(x a
2
D )2],
S2M=
(x+
a
2)2 +D2,
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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
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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
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S
S1 S2
S
S1 S2
S
S
S
S1 S2 S1 S2
(E)
D >> a
M(x, y)
O
x y
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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.],
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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
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= 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
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= c
V = 0,
R
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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,
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x= C te
i
D
p+D
h
p
p
p = pf
p+f,
a
a= hp
p,
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M
I(M) =I1+I2+ 2
I1
I2Cos(),
D >> a
=2
.ax
D =
4
.
hpx
pD,
i=Dp
hp
,
x
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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,
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=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 ,
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0.4m 0.75m
O
x= 0= 0
= p
= (2p + 1)2
= 3m
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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
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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
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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] ,
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[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)
+,
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= [IJKL] [IJM] = 2ne.cos(r),
=
4ne.cos(r)
,
f
ik = constante
Rk
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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 +
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p=
=
2ne.cos(r)
,
p0 = p0 12
S
M1 M2 M1 M2
S
M1 M2
n= 1 r= i
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p=
=
2e.cos(i)
,
e
M1 M
2
i = 0
r= 0cos(i) =cos(r) = 1
= 2ne+
2 = 2nx+
2 = 2x+
2,
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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
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e2
=2
R+
2,
= Cste = Cste = Cste
=k.,
k
=
(k 1
2)R,
=
kR,
e
2
L1 L2
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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()
,
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=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