When we study Pockel's effect (as linear electro optic effect) it starts with anisotropic material, birefringence, O-ray, E-ray, index ellipsoid, & change in optical impermeability when electric field is applied (using index ellipsoid), which is directly proportional to Electric field. Later on, we got an expression with Pockel's coefficient "rij" connects change in r.i. with applied electric field, which is a linear relationship and finally some devices i.e. waveplate, modulator etc.
Since Pockel's effect is a linear eletcro optic effect but it occurs in those materials which are having no inversion symmetry, material should be asymmetric, Which is concerned with second order non linear coefficient (chi2) & it should be non zero. I could not interpret these two terminologies (two coefficient) at the same time.
Thank you
At optical frequencies, electrons in an asymmetric potential wells give us the second order nonlinear coefficient. At low frequencies, there is an additional contribution from the motion of ions in the crystal. The linear electro-optic effect comes from both sources below the resonance frequency of the ion in its potential well.
There is also an indirect linear electroptic effect due to the piezo-electric effect coupled with the acousto-optic effect, which must also be modified for local rotations of the index elipsoid as shown in the Nelson and Lax publications
I think its essentially the same, however in different frequency regimes. As Robert pointed out, this leads to additional contributions of ionic movements etc. for smaller frequencies and therefore the electrooptic effect is usually larger than second order nonlinearity in the optical regime.
For some (probably historical) reasons, the notation is different, but you can transform r and chi into each other if you want to compare them.
Please find attached the relation between Pockels coefficient and second order susceptibility.
Dear Patrick Steglich, it would be possible to make exactly the same comparison but now between the E-O Kerr and third order nonlinearity to obtain the relation between the E-O Kerr coefficient and the third-order susceptibilty. Thank you very much in advance.
Hello Patrick,
Can you add a reference to this relation between the electro-optic coefficients and the second order susceptibility?
Thanks a lot
Dear Yedidya Lior,
please find here a link to a open-access reference to the relation between the electro-optic coefficients and the second order susceptibility:
https://iopscience.iop.org/article/10.1088/1361-6463/ab6059/meta
Best regards,
Patrick
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