126
L. Parameswar
Like all electromagnetic phenomena, the propagation of optical fields through a nonlinear photorefractive medium is governed by Maxwell’s equations. These equations
are
∇. ˜
D = 4πρ
(20)
∇. ˜
B = 0
(21)
∇ × ˜
E = −
1
c
∂ ˜
B
∂t
(22)
∇ × ˜
H =
1
c
∂ ˜
B
∂t
+
4π
c
˜
J
(23)
Putting
˜
ρ = 0, ˜
J = 0, ˜
B = ˜
H
(24)
Using Eqs. (24), (23) becomes
∇ × ˜
B =
1
c
∂ ˜
D
∂t
(25)
Taking curl of Eq. (22) and using Eq. (25), the optical wave equation obtained is
∇
2 ˜
E −
1
c 2
∂
2 ˜
D
∂t 2 = 0
(26)
Introducing Fourier Transforms
˜
E(z, t) =
∞
−∞
E(z, t)e
−iωt dω
2π
(27)
and
˜
D(z, t) =
∞
−∞
D(z, t)e
−iωt dω
2π
(28)
where the Fourier amplitudes are related by
D(z, ω) = ω)
(29)
and is the effective dielectric constant that describes both the linear and nonlinear
contributions to this response. Using Eqs. (27), (28) and (29) in (26), the equation
obtained is
∂
2 E(z, ω)
∂z 2
+ (ω)
ω
2
c 2 E(z, ω) = 0
( 3 0 )
Writing the Fourier transform of A(z, t)as