Dielectric electroholographic gratings are electrically controlled Bragg gratings implemented by periodic striations that were produced during the crystal growth. The striations gratings are periodic modulation in the composition. In **electrooptic paraelectric crystals** these induce a periodic spatial modulation in the static (low frequency) dielectric constant, which upon the application of an external field induce a refractive index grating through the (quadratic) electrooptic effect.

**Figure 1:** Images of a striation grating with a period of Λ = 4.21 μm scanned by an input beam polarized at 45° to the grating vector, and the output polarizer aligned to maximize the contrast. (a) When the applied electric field is zero. (b) Under an electric field *E *= 1.53 kV / cm.

It is well established that the phase transition temperature T_{C} of ferroelectric oxygen perovskites is strongly affected by the presence of impurities and defects. For example, the replacement of a Ta ions in potassium tantalate niobate (KTN) by x % per mole of Nb ions will cause a change in T_{C} given by Tc [K] ≈682*x*+33.2 [REF1]. 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 : δT_{C}≈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 : δT_{C} (x)) will yield a change in the dielectric constant given by:

(1)

where ε 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 δT_{C} is modulated will generate a modulation in the induced polarization P that is spatially correlated with *δε*(x) and is given by:

(2)

where it is assumed that the crystal is slightly above T_{C} so that ε_{r}>>1. At the paraelectric phase where the electrooptic effect is quadratic, the electric field induced birefringence is given by:

(3)

where n_{o} is the index of refraction at the paraelectric phase, and *g _{eff}*

_{ }is the effective quadratic electrooptic coefficient. Note that for a KTN crystal at T=T

_{c}+7K where ε

_{r}=10

^{4}, g

_{eff}=0.2m²/C² , and an 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:

(4)

_{C}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.

Dielectric EH gratings are described in detail in [REF16].