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Chapter I Brief Introduction...
important NLO phenomenon is the second-harmonic-generation (SHG). In the
similar manner the third order susceptibility, a fourth-rank tensor and the third
order coefficients are responsible for the third harmonic generation,
parametric conversion, stimulated scattering, etc. there are 81 possible third
order terms.
The net polarization of a material depends on its symmetry properties
with respect to the orientation of the applied field. A careful examination of the
symmetries in a material is indispensable in understanding its nonlinear
optical properties. For instance, 11 of the point groups are “centrosymmetric”,
meaning that the structure of the crystal remains unchanged along a direction
reversed 180º. No second order effects can take place in centrosymmetric
crystals as all components of even order of are zero. Obviously, an
important criterion for a material to exhibit SHG is that it should be a non-
centro-symmetric material.
At the molecular level equation (1.2) is expressed as [14],
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(1.3)
Where, α ij = Polarizability, β ijk = First hyper-polarizability (second order
effects), γ ijkl = Second hyper-polarizability (third order effects) and i,j,k,l
corresponds to the molecular coordinates.
A medium exhibiting such a NLO response might consist of a crystal
composed of molecules with asymmetric charge distribution. If the medium (or
molecule) is centro-symmetric, then first order hyper-polarizability (β) is zero,
indicating that centro-symmetric media do not show second harmonic
generation. If a field +E is applied to the medium, equation (1.3) predicts the