Basis of Non-linear Optics

For an organic material to show electro-optical activity it must exhibit high second order non-linear behaviour. This is one of the terms in the equation that defines the polarisation (u) of an organic molecule as shown below, where E is the perturbing electric field. 

In this equation a is the usual linear polarisability, whilst the others are the hyperpo-larisability terms, P, y etc. Macroscopically this equation turns into 

Where P is the polarisation and the others the linear (1) and non-linear, second (2) and third order (3) terms. Examples of important second order effects are frequency doubling and linear electro-optic effects (Pockles effect), third order effects are third-harmonic generation, four-wave mixing and the quadratic electro-optic effect (Ken-effect). 

Each term can converted into a bulk response as follows 

Where is the bulk second order NLO property, N is the number of molecules and / the local field factors. Erom this equation it can be readily seen that the target must be for molecules with a high f] in order to achieve high bulk activity, although in practice the relationship is not quite so simple. 

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What has been presented above is based on the interaction of electrons or atoms with the electric field through a quadratic harmonic potential. When potentials including higher-order terms are used, the polarization, electric dipole moment, and optical susceptibility include, in turn, higher order terms whose contributions are the basis of non-linear optics and anharmonic effects. 

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