Quadratic electro-optic coefficient , effect

Potassium tantalate-niobate [K(Ta Nbi jc)03, KTN] is one of the ferroelectric materials with the perovskite structure, and is a sohd solution of potassium tantalate (KTaOs) and potassium niobate (KNbOs). The Ciuie temperature of KTN for the cubic to tetragonal transition varies with Ta/Nb ratio, and is lowered with increasing Ta substitution (Triebwasser, 1959). The ferroelectric properties of KTN, therefore, can be controlled by the Ta/Nb ratio. The nonferroelectric cubic phase of KTN atx= 0.65 is known to show photorefractive effect based upon a large quadratic electro-optic coefficient at room temperature (Gausic, 1964 Orlowski, 1980). 

Photonics is playing an ever-increasing role in our modern information society. Photon is gradually replacing the electron, the elementary particle in electronics. Several hooks and reviews have appeared dealing with the theory of nonlinear optics and the structural characteristics and applications of nonlinear optical molecules and materials [1—18]. Tlie earliest nonlinear optical (NLO) effect discovered was the electro-optic (EO) effect. The linear EO coefficient defines the Pockel effect, discovered in 1906, while the quadratic (nonlinear) EO coefficient s,i relates to the Kerr effect, discovered 31 years later (1875). Truly, all-optical NLO effects were not discovered until the discovery of lasers. Second harmonic generation (SHG) was first observed in a single crystal of quartz by Franken et al. [1] in 1961. They frequency doubled the output of a ruby laser (694.3 nm) into the 383... 

Ceramic PLZT has a number of structures, depending upon composition, and can show both the Pockels (linear) electro-optic effect in the ferroelectric rhombohedral and tetragonal phases and the Kerr (quadratic) effect in the cubic paraelectric state. Because of the ceramic nature of the material, the non-cubic phases show no birefringence in the as-prepared state and must be poled to become useful electro-optically (Section 6.4.1). PMN-PT and PZN-PT are relaxor ferroelectrics. These have an isotropic structure in the absence of an electric field, but this is easily altered in an applied electric field to give a birefringent electro-optic material. All of these phases, with optimised compositions, have much higher electro-optic coefficients than LiNb03 and are actively studied for device application. 

There are two common types of electro-optic birefringent effects within the PLZT compositional phase diagram, i.e., (i) nonmemory quadratic (Kerr effect) and (ii) memory hnear (Pockel effect). The respective electro-optic coefficients for these effects are calculated by using the following relationships ... 

In Equation (14.7), the linear term vanishes and only the Kerr effect term survives. The electrooptic tensor for the Kerr effect varies with different molecular stmcture. For an isotropic Uquid, its quadratic electro-optic effect coefficients can be represented by the following matrix ... 

FIGURE 7.1.5 Birefringence induced by the electro-optic effect and the electric field, (a) Linear electro-optic effect. Linear electro-optic coefficient gradient, (b) Quadratic electro-optic effect. Coefficient of is proportional to (Rn — Rn) value. 

Historically, the earliest nonlinear optical (NLO) effect discovered was the electro-optic effect. The linear electro-optic (EO) coefficient rij defines the Pockels effect, discovered in 1906, while the quadratic EO coefficient sijki relates to the Kerr effect, discovered even earlier (1875). True, all-optical NLO effects were not discovered until the advent of the laser. 

In non-polar, isotropic crystals or in glasses, there is no crystallographic direction distinguished and the linear electro-optic effect is absent. Nevertheless a static field may change the index by displacing ions with respect to their valence electrons. In this case the lowest non-vanishing coefficients are of the quadratic form, i.e. the refractive index changes proportionally to the square of the applied field Kerr effect . 

Whether or not the dependence is expressed in terms of E or P is a matter of choice it seems customary in the literature relating to single crystals to use the r coefficient for the linear Pockels effect and g for the quadratic Kerr effect. In the case of electro-optic ceramics r and R are most commonly used. 

Under the conditions used for the electro-optical measurements on the various device structures that are reported in sections S and 6, we will expect to see a substantial electric field applied across at least a fraction of the polyacetylene layer, and we need to characterise the modulation of the %-n absorption edge with electric field. This electromodulation response is the Franz-Keldysh effect, and arises through modulation of the electron states near the band edge in the applied field. It is found to be very large in Shirakawa polyacetylene [54,55] and it has been pointed out that this is due to the strong non-linear electronic response that characterises the conjugated polymers [55]. In the low field limit, we expect to see a response that varies quadratically with the applied electric field, and that is proportional to the second differential of the absorption coefficient, a, 92a/aE2 [54]. 

---