Électromagnétisme TD 5 : Ondes électromagnétiques (suite) Faire le

1018
vφvg
k
λ= 633
1,35.103
a
(Oz)
(Oz)
−→
E(M, t) = f(x, y)ei(ωt−kz)−→ uy

f z
f x
d2f
dx2+K2f= 0 K2=ω2 c2−k2
f(0) = f(a)=0
K2<0∀x∈[0, a], f(x)=0
K2>0
f(x) = Bsin (Kx)K=nπ
an∈N∗
B f(x)n= 1,2,3
n= 1
ω=f(k)
fc
2,45
ρ= 0
r= 80 σ= 6,23 −1
00r
−→
∆−→ E−r
c2
∂2−→ E
∂t2=µ0σ∂−→
E
∂t
k2=r
ω2
c2−iωµ0σ
f= 1
L
λV= 380 λR= 780
n(λ) = A+B
λ2A= 1,4764 B= 3,7416.10−3µ−2
∆t
L nR=n(λR)nV=n(λV)c
f L = 1000 fmax
fmax

∆x∆k
∆x∆k≈1
g(ω) = 1
σ√2πexp −(ω−¯ω)2
2σ2
s(x, t) =
+∞
Z
−∞
g(ω) exp(i(ωt −kx))dω
ω=ck
∆ω[ωmin, ωmax]
g(ω)≥g(¯ω)
∆ω= 2p2 ln(2)σ
s(x, t) = Re (s(x, t)) = exp −2σ2t−x
c2cos(¯ωt −¯
kx)¯ k=¯ω
c
t= 0 δω << ¯ω
∆x[xmin, xmax]
∆x=p2 ln(2) c
σ
t= 0
∆k
∆x∆k= 4 ln(2) ≈2,77
+∞
Z
−∞
exp(−Ax2+Bx +C)dx =rπ
Aexp −C−B2 4AA, B, C ∈C