5.2.2 Critères de design d`un composant homogénéiseur 5.2.3

2
4
1
I(β) = Zb
a
f(x) exp (ıβφ (x)) dx
Ic(β)∼exp (ı[βφ (c) + µπ/4]) f(c)s2π
β|φ00 (c)|
µ=sign [φ00 (c)] φ0(c)=0 φ00 (c)6= 0 |Ic(β)|2
φ(x)
E(ω) = Z∞
−∞
rect x
αexp (ıb [φ(x/α)−ωx/b]) dx
α b ω/b =β
b
rect (x)

Ic(b)∼exp (ı[bψ (c) + µπ/4]) f(c)s2π
b|ψ00 (c)|
µ=sign [ψ00 (c)] c ψ0(c) = 0
|E(ω)|2=rect (c)2π
b|φ00 (c)|
ψ(x) = φx
α−βx
ψ00 (c) = const
φx
α=x α2
c dψ (c)/dc = 0 c=βα2/2
E≈rπ
bexp −ıω2α2 4b−π 4rect ωα 2b
ω= 2πx/λf W
b=πW α
λf
b·φ(x)φ(x)
b
b
b≥1b
b
b10 100
b b
b=πW α
λf =3.14 ·450µm ·60mm 532nm ·1.3m= 122

P1
P2P1P2
U1U2
U1X1=ρ1X1exp ıφ1X1
U2X2=ρ2X2exp ıφ2X2
z
X1= (x1, y1)X2= (x2, y2)
GX2, X1
U2X2=ZGX2, X1U1X1dX1=b GU1X1
b
G
b
G
b
GU1X1U2X2L2
D(ρ1, φ1, ρ2, φ2) = 
U2−b
GU1
=Zdx2U2(x2)−b
GU11/2
D= 0 U2=ˆ GU1
D2ρ1φ1ρ2φ2
ρ2=
b
GU1
ρ1=
b
G+U2
φ2= arg b GU1
φ1= arg b G+U2
b
G P1P2
φ2(x2) = arg hb Gρ1exp (ıφ1)i
φ1(x1) = arg hb A−1
Dhb
G+ρ2exp (ıφ2)−b AND ρ1exp (ıφ1)ii
b
AD=b Ib AND = 0 b G
φ(0,0)
1
φ(0,0)
2Zdx1φ(0,m1)
1−φ(0,m1+1) 1≤1
φ1φ2

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