Ondes électromagnétiques dans le vide

u(x, y, z, t)
∇2u=1
c2
∂2u
∂t2
c
x
∂2u
∂x2=1 c2
∂2u
∂t2
x
u+(x, t) = F(x−ct)
F(x)
c
x
u−(x, t) = G(x+ct)
u(x, t) = F(x−ct) + G(x+ct)

F(x) = Acos(2πx
λ)
u+(x, t) = Acos(kx −ωt)
k λ
k=2π
λ
ω T
ω=2π
T
k=ω
c
X
−→
k=2π
λ
−→
u
−→
u
X
kX =−→ k·−→ r
−→
r=x−→ ux+y−→ uy+z−→ uz
u(x, t) = Aei(−→
k·−→ r−ωt)
A A
.
k=ω/c
φ(x, t) = −→ k·−→ r−ωt

c
∂u
∂t =−iω u
∂2u
∂t2=−ω2u
P
F(x) =
P
X
n=1
Anei(nk1x)
u+(x, t) =
P
X
n=1
Anei(nk1x−nω1t)
ω1=2π
T
k1=ω1
c=2π λ
Ann
N N + 1
N

N
10−15 s
∇2−→ E=1
c2
∂2−→ E
∂t2
−→
E(−→ r , t) = −→ E0ei(−→
k·−→ r−ωt)
k=ω
c
λ=cT
Vφ=ω
k=c

−→
E(−→ r , t) = −→ E0ei(kxx+kyy+kzz−ωt)
div −→ E=∂Ez
∂z =i(E0xkx+E0yky+E0zkz)ei(−→
k·−→ r−ωt)=i−→
k·−→ E
−→
k·−→ E= 0
∂−→ B
∂t =−−→
rot−→ E=−i−→ k∧−→ E
−→
B(−→ r , t) =
−→
k∧−→ E
ω
−→
B=
−→
u∧−→ E
c
.
.(−→ E , −→ B , −→ k)
. B =
E/c
X Y