Quadratic electrooptic effect

Three common types of electrooptic effects are illustrated in Figure 8 i.e, quadratic and linear birefringence and memory scattering. Also included in the figure is a typical setup required for generating each effect along with the observed behavior shown in terms of light intensity output (I) as a function of electric field (E). 

DIRK AND KUZYK Quadratic Electrooptic Effect in Small Molecules... 

We report the largest known useful microscopic NLO susceptibilities for the linear and quadratic electrooptic effects. The QEO susceptibility of 9 might be large enough to explore simple primitive QEO modulation experiments, though perhaps is not nearly large enough to be of commercial importance. 

X(3) ( — (1) 0), 0,0) Quadratic electrooptic effect Variable-phase retardation, liquid-crystal displays... 

As shown in previous sections of this chapter, when an external perturbation is applied to the polymer film (such as irradiation), the ATR guided modes shift their angular positions and the reflectivity is modulated (Fig. 31b). These angular shifts are very small in the case of electrooptic experiments they correspond to refractive index variations of the order of 10 . One has then to modulate the measuring electric field at a low frequency Q( = cos fit) and to detect the modulated signal with lock-in amplifiers. The lock-in signals detected at the modulation frequency and its second harmonic give, respectively, the linear (or Pockels) and the quadratic (or Kerr) electrooptic effects. The amplitude of the modulation of the thickness and the refractive indices is evaluated by a computer fit, and allows the determination of Pockels (r) and Kerr (s) coefficients (Eqs. 28) ... 

In electric-field-induced birefringence (or electrical birefringence, quadratic electrooptic effect, Kerr effect), an isotropic transparent substance becomes birefringent when placed in an electric field . The sample assumes the characteristics of a uniaxial crystal, the optical axis of which is parallel to the direction of the applied field. When the sample is illuminated normal to , the resulting two indices, and wj (which can be thought of as He and ), are associated with the parallel and perpendicular orientations, respectively. 

Combination with Static Fieids. A common technique, useful for optoelectronic devices, is to combine a monochromatic optical field with a DC or quasistatic field. This combination can lead to refractive index and absorption changes (linear or quadratic electrooptic effects and electroabsorption), or to electric-field induced second-harmonic generation (EFISH or DC-SHG, 2 > = > - - third-order process. In EFISH, the DC field orients the molecular dipole moments to enable or enhance the second-harmonic response of the material to the applied laser frequency. The combination of a DC field component with a single optical field is referred to as the linear electrooptic (Pockels) effect co = co + 0), or the quadratic electrooptic (Kerr) effect ( > = > - - 0 -I- 0). These electrooptic effects are discussed extensively in the article Electrooptical Applications (qv). EFISH is... 

For every nonlinear optical effect, one would expect that there is a measurement technique to characterize it. Not all of NLO effects, however, are subject to measurements that are convenient or informative for comparative purposes or device applications. This section highlights a few of the more common test methods for NLO organic molecules and polymers, and provides references for more detailed explanations of these techniques. Significant omissions here are techniques based on the linear and quadratic electrooptic effect, which are discussed in the article Electrooptical Applications. 

Optical Kerr Effect. Another important method used to characterize polymers is the optical Kerr effect (OKE). The optical Kerr effect differs from the quadratic electrooptic effect in that the birefringence effects are induced solely by an optical field (37). In this measurement, an intense linearly polarized pump pulse induces birefringence in the nonlinear sample through an intensity-dependent refractive index change. The sample is placed between crossed polarizers and a weak, typically tunable, continuous wave (cw) probe laser (usually at a different wavelength and polarized at 45° to the pump pulse) overlaps the pumped region. The increased transmission of the probe beam when the pump pulse arrives is proportional to (Xeff), a combination of elements of the tensor. Many... 

The first observation of natural optical anisotropy was made in 1669 by Bartolinius in calcite crystals, in which light travels at different velocities depending on the direction of propagation relative to the crystal structure. The electrooptic effect, electric-field-induced anisotropy, was first observed in glass in 1875 by J. Kerr. Kerr found a nonlinear dependence of refractive index on applied electric field. The term Kerr effect is used to describe the quadratic electrooptic effect observed in isotropic materials. The linear electrooptic effect was first observed in quartz crystals in 1883 by W. Rontgen and A. Kundt. Pockels broadened the analysis of this relationship in quartz and other crystals, which led to the term Pockels effect to describe linear behavior. In the 1960s several developments... 

These relationships describe the quadratic Kerr electrooptic effect. 

In Fig. 62 this linear electrooptic effect is compared with the quadratic effect controlling the state of a twisted nematic device. 

Broussoux and Mkheron [17] reported electrooptic and elastooptic effects in stretched PVDF. The linear EO coefficients in PVDF were measured at room temperature and constant stress at the He-Ne laser wavelength. The refractive indices n, 1.444. A = 1.436, and n, 1.42S and electrooptk coefficients rn = 0.10 pmA, 0.21 pm/V were OKasured. The secondary electrooptic effect estimated for the longitudinal configuration was ZS% of the measured free electrooptic coefficient. The quadratic electrooptic coefficients at constant strain and stress were gu 0.02 m /C and ga s 0.01 m /C. ... 

NLO organic molecules and polymers, and provides references for more detailed explanations of these techniques. Significant omissions here are techniques based on the linear and quadratic electrooptic effect, which are discussed in the article Electrooptical Applications. 

Optical Kerr Eftect. Another important method used to characterize polymers is the optical Kerr effect (OKE). The optical Kerr effect differs from the quadratic electrooptic effect in that the birefringence effects are induced solely by an optical field (37). In this measurement, an intense linearly polarized pump pulse induces birefringence in the nonlinear sample through an... 

Second-order materials which exhibit quadratic effects such as SHG or electrooptic (EO) switching (in which the refractive indices of EO materials can be modulated by application of an electric static field). The materials must be non-centrosymmetric at both microscopic and macroscopic levels. 

The second-order NLO properties are of interest for a variety of NLO processes [1-3]. One of the most relevant is the SHG, originated by the mixing of three waves two incident waves with frequency co interact with the molecule or the bulk material with NLO properties, defined by a given value of the quadratic hyperpolarizability, fi, or of the second-order electrical susceptibility, respectively, to produce a new electrical wave, named SH, of frequency 2co. Another important second-order NLO process is the electrooptic Pockels effect which requires the presence of an external d.c. electric field, E(0), in addition to the optical E co) electrical field. This effect produces a change in the refractive index of a material proportional to the applied electric field, and can be exploited in devices such as optical switches and modulators [1-3]. 

Quadratic Response (3rd rank tensors) (1) electric field effects Linear electrooptic (Pockels) effect, three-wave mixing, SHG. (2) radiation/magnetic field Faraday Effect. 

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 ... 

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