Electric linear electrooptic effect

Nonlinear second order optical properties such as second harmonic generation and the linear electrooptic effect arise from the first non-linear term in the constitutive relation for the polarization P(t) of a medium in an applied electric field E(t) = E cos ot. 

Non-linear second-order optical properties such as second harmonic generation (SHG) and the linear electrooptic effect are due to the non-linear susceptibility in the relation between the polarization and the applied electric field. SHG involves the... 

The linear electrooptic effect is tlie change in the index of refraction of a medium due to the presence of a dc or low-frequency electric field, in such a manner that the change in the index of refraction depends linearly in the strength of the low-frequency electric field. The linear electrooptic effect is tlie mechanism behind optical intensity modulators that are used in optical switching and fiber-optics communications, where the optical signal is modulated at high frequencies (out to 110 GHz) [7-9],... 

Piezoelectrics. In the neutral-polar classes there are polar directions (not axes), which can be described by several vectors with their vector sum equal to zero. Such crystals do not possess spontaneous polarization and do not manifest polar properties (such as pyroelectric, photogalvanic or linear electrooptical effects) however, the polarization can be induced not only by an electric held but also by a pure mechanical stress. These crystals are called piezoelectrics. Examples are crystals of quartz or ZnS having cubic symmetry with four polar direction but no polar axis. Fig. 13.1b. Such crystals are used in technics as microphones, mechanical micro-motors and sensors, etc. 

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... 

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). 

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) ... 

The structure of the smectic A phase when it is composed of optically active material (i.e., smectic A ) remains the same as that for the achiral phase. The molecules are arranged in diffuse disordered layers, and there is no long-range periodic order. However, because of the molecular chirality, the environmental symmetry is reduced to [10]. As a consequence, when an electric field is applied to a chiral smectic A= phase there will be a coupling of the electroclinic susceptibility to the field and the long axes of the molecules will tilt with respect to the layer planes. The tilt angle, for relatively low applied fields, varies linearly with the field. This linear electrooptic phenomenon is called the electroclinic effect. 

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

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... 

A fast linear electrooptic light modulatkm effect, which can be employed in waveguiding structures, b the Pockek effect. In contrast to ferroelectric switching in SSFLC structures, the Pockek effect b basically a pure NLO effect, whereby a small refractive index change An, b induced along the opti axb by an applied electric field E, which acb along the polar axis [83] ... 

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