Electromagnétisme dans les milieux diélectriques

z= 0 n1n2
−→
ki=ki
sinθi
0
cosθi
ωiz > 0
−→
Ei(−→ r , t) = −−→ E0,ieiωit−
−→
ki.−→ rωr,−→
kr
ωt,−→
kt
ωi, ωrωt
−→
ki,−→ kr
−→
kt
ωi=ωr=ωt
−→
kr
−→
kt
−→
kr=kr
sinθr
0
cosθr
−→
kt=kt
sinθt
0
cosθt

z= 0 n1n2
−→
ki=ki
sinθi
0
cosθi
ω
z > 0−→ Bi(−→ r , t) = B0,ieiωit−
−→
ki.−→ r−→
uy
ω, −→
kr=kr
sinθr
0
cosθr
ω, −→
kt=kt
sinθt
0
cosθt
n1sinθi=n2sinθtθi=−θr
ωi, ωrωt
−→
ki,−→ kr
−→
kt
−→
B E
−→
Bi
−→
Br
−→
Bt
−→
Ei
−→
Er
−→
Et
r=E0,r
E0,i t=E0,t E0,i

ω n
z= 0 z=e−→ E=E−→ ux
−→
B=B−→ uyz= 0−−→ E0=E0−→ ux
−→
B0=B0−→ uyz=e+E0cB0E cB
M0E0
cB0=M0E cB 
2N e1
n1e2n2n1e1=n2e2=λ
4
M1M21
2
E0
cB0x= 0 Et cBt
x= 0 Ei
cBi
Er
cBr
E→⇒ E1→
E2←
⇒E0→B=E
cB1=nE1 cB2=−nE2 cB0=E0 c
0E=E1+E2
cB =cB1+cB2⇔cB =n(E1−E2)⇔E1= (E+cB/n)/2 E2= (E−cB/n)/2
L
E0=E1eink0L+E2e−ink0L
cB0=cB1eink0L+cB2e−ink0L⇔cB0=n(E1eink0L−E2e−ink0L)⇔
E0=Ecos (nk0L) + icB
nsin (nk0L)
cB0=niEsin (nk0L) + cB
ncos (nk0L)
E0
cB0=cos (nk0L)i
nsin (nk0L)
in sin (nk0L)cos (nk0L) E
cB k0−k0
nL =λ
4E0
cB0=0i
n
in 0 E
cB 
M2M1=0i
n2
in20 0i
n1
in10=−n1
n20
0−n2
n1

ET=E0−n1
n2N
cBT=cB0−n2
n1N⇔
ET= (Ei+Er)−n1
n2N
ET= (Ei−Er)−n2
n1N
⇔
τ= (1 + r)−n1
n2N
τ= (1 −r)−n2
n1N
⇔
τ−r−n1
n2N
=−n1
n2N
τ+r−n2
n1N
=−n2
n1N
⇔
τ=2−n1
n2N
1+n1
n22N
r=1−n1
n22N
1+n1
n22N