The Dielectric Electrooptic Effect

It is well established that the phase transition temperature TC of ferroelectric oxygen perovskites is strongly affected by the presence of impurities and defects. For example, the replacement of a Ta ion in potassium tantalate niobate (KTN) by an Nb ion will cause a change in TC of magnitude: δTC≈8.5 K° /1% per mole of Nb. A similar effect can be achieved by replacing a K ion in KTN by Li. Here the effect is more dramatic and results in certain cases in δTC≈50 K° /1% per mole of Li [KLTN]. Thus, at the paraelectric state where the dielectric constant is given by the Curie law, a spatial variation in the composition that causes a correlated modulation in the Curie temperature (designated by δTC(x)) will yield a change in the dielectric constant given by: 


where is the relative static (and low frequency) dielectric constant, C is the Curie-Weiss constant, and T is the temperature. Applying a uniform electric field E to a crystal in which δTC is modulated will generate a modulation in the induced polarization that is spatially correlated with δε(x) and is given by:


where it is assumed that the crystal is slightly above TC so that εr>>1. At the paraelectric phase where the electrooptic effect is quadratic, the electric field induced birefringence is given by:


where n0 is the index of refraction at the paraelectric phase, geff is the effective quadratic electrooptic coefficient, and P is the induced (low frequency) polarization. Note that for a KTN crystal at T=TC+7K where εr=104, geff=0.2m²/C² , and applied field of E = 3 kV/cm, equation (3) yields induced birefringence of Δn≈0.01!
Finally, combining (1), (2) and (3) will yield the spatially modulated induced birefringence:


In summary: a permanent spatial modulation in TC is created by periodic changes in the composition introduced during the growth of the crystal. This generates a correlated modulation in the static dielectric constant. Under the application of an electric field the latter induces a correlated modulation of the refractive index. This feature, namely a refractive index grating activated by the application of an electric field is the dielectric electrooptic effect [REF16].

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