Chapitre 4 Propagation des ondes électromagnétiques

~
E~ B
div ~ E= 0
div ~ B= 0
−→
rot ~ E=−∂~
B
∂t
−→
rot ~ B=µ0ε0
∂~ E
∂t
~
E~ B
∆~ E−1
c2
∂2~ E
∂t2=−→
0
∆~ B−1
c2
∂2~ B
∂t2=−→
0
c=1
√µ0ε0
= 3 ×108m·s−1
~
E(~r, t) = ~ E0ei(ωt−~
k·~r)

~
k
∆~ E=−k2~ E
−k2+ω2
c2~
E=~ 0
k=ω
c
ρ= 0
div ~ E= 0
div ~ E=−i~ k·~ E= 0
~
k·~ E= 0 ~ E
~
k
−→
rot ~ E=−∂~
B
∂t
−→
rot ~ E=−i~ k×~ E
−i~ k×~ E=−iω ~ B
~
B
~
B=~
k×~ E
ω
~
k, ~ E

~
k, ~ E, ~ B
ω=kc
k~ Bk=kEk
c
~
E
~
E=~ E0cos ωt −~ k·~r
~
E0=
ω
~
k k =ω/c
ωt −~ k·~r
c=1
√µ0ε0
~
B=~
k×~ E
ω
z0z
~
E=~ E0cos (ωt −kz)
z
T=2π
ω

f=1
T=ω 2π
f
t
z
λ=2π
k=λ k
λ
λ
~
E~ B
Ex=E0xcos (ωt −kz −φ1)
Ey=E0ycos (ωt −kz −φ2)
φ1φ2~
E z = 0
z=cte
Ex=E0xcos (ωt −φ1)
Ey=E0ycos (ωt −φ2)
Ez= 0
Ex
Ex
E0x
= cos (ωt)
Ey
E0y
= cos (ωt −φ)
φ=φ2−φ1
2E0x2E0yEy
E0y
Ey
E0y
= cos (ωt) cos (φ) + sin (ωt) sin (φ)
Ey
E0y
=Ex
E0x
cos (φ) + s1−Ex
Ey2
sin (φ)

Ey
E0y−Ex E0x
cos (φ)2 ="1−Ex
E0x2#sin2(φ)
Ex
E0x2
+Ey
E0y2
−2Ex
E0x
Ey
E0y
cos (φ) = sin2(φ)
φ
φ=mπ(m= 0,1,2, . . . )
E0x=E0yφ= (2l+ 1)π/2
w
w=
w=1
2ε0E2+B2 µ0
τ(S)
W=ZZZ
(τ)
w dτ
dt (τ)dW
p0
p0=dW
dt =ZZZ
(τ)
∂w
∂t dτ
−→
rot ~ E=−∂~
B
∂t −→
rot "~
B
µ0#=ε0
∂~ E
∂t