Nonlinear Optical Probes and Processes in Polymers and Liquid ...

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ear electro-optic effect P ω
i = χ (2)
ijk (−ω; ω, 0)Eω j E0 k . For the nonlinear susceptibility
χ (n) with even n (which for most practical purposes is limited to n = 2) to have a
nonzero value, and thus for the second order effects such as SHG and linear electro-
optic effect to exist, a noncentrosymmetric medium is required. The reason is that in
a centrosymmetric medium, if we change the sign of the electric field E, then the sign
of the induced polarization density P must also change due to inversion symmetry. In
second order processes this leads to the relation for the nonlinear polarization density
P = −P which suggests that χ (2) = 0. So, second order nonlinear optical effects
can be observed only in noncentrosymmetric media which includes crystals of certain
symmetry groups that do not possess inversion symmetry, nonlinear optical polymers
in which the symmetry is broken by an applied electric field or some other way, media
with interfaces and other systems.
These requirements for media do not exist for the effects due to χ (n) with odd
n. The studied odd n nonlinear effects are mostly limited to n = 3, although re-
cently a phase-conjugation experiment by nondegenerate six-wave mixing that in-
volves χ (5) was performed [2]. Examples of the third order optical susceptibility
χ (3)
ijkl (−ω; ω1, ω2, ω3) include third harmonic generation
P 3ω
i
= χ (3)
ijkl (−3ω; ω, ω, ω)Eω j E ω k E ω l ,
electric field induced second harmonic generation (EFISHG)
P 2ω
i
= χ (3)
ijkl (−2ω; ω, ω, 0)Eω j E ω k E 0 l ,