Affiliation:
1. School of Mathematics , Sichuan University , Chengdu , Sichuan, 610064 , P. R. China
Abstract
Abstract
This paper considers a class of nonlinear time-harmonic Maxwell systems at fixed frequency, with nonlinear terms taking the form
X
(
x
,
|
E
→
(
x
)
|
2
)
E
→
(
x
)
\mathscr{X}(x,\lvert\vec{E}(x)\rvert^{2})\vec{E}(x)
,
Y
(
x
,
|
H
→
(
x
)
|
2
)
H
→
(
x
)
\mathscr{Y}(x,\lvert\vec{H}(x)\rvert^{2})\vec{H}(x)
such that
X
(
x
,
s
)
\mathscr{X}(x,s)
,
Y
(
x
,
s
)
\mathscr{Y}(x,s)
are both real analytic in 𝑠.
Such nonlinear terms appear in nonlinear optics theoretical models.
Under certain regularity conditions for 𝒳 and 𝒴, it can be shown that boundary measurements of tangent components of the electric and magnetic fields determine the electric permittivity and magnetic permeability functions as well as the form of the nonlinear terms.
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