Pockels, effects

Quadratic NLO effects arising from (3 and x(2) include SHG, the electro-optic (EO, Pockels) effect and frequency mixing (parametric amplification). SHG is actually just a special case of a three-wave... 

The proportionality constants a and (> are the linear polarizability and the second-order polarizability (or first hyperpolarizability), and x(1) and x<2) are the first- and second-order susceptibility. The quadratic terms (> and x<2) are related by x(2) = (V/(P) and are responsible for second-order nonlinear optical (NLO) effects such as frequency doubling (or second-harmonic generation), frequency mixing, and the electro-optic effect (or Pockels effect). These effects are schematically illustrated in Figure 9.3. In the remainder of this chapter, we will primarily focus on the process of second-harmonic generation (SHG). 

Electro-optic modulation (Pockels effect) using a poled polymer is shown schematically in Figure 5.33, where an optical signal confined in a wave-guide is modulated by the application of an external voltage, known as a Mach-Zender Interferometer. 

Show the Pockels effect (electro-optic modulation)... 

A second type of behavior existing in the PLZT s is the linear (Pockels) effect which is generally found in high coercive field, tetragonal materials (composition 3), This effect is so named because of the linear relationship between An and electric field. The truly linear, nonhysteretic character of this effect has been found to be intrinsic to the material and not due to domain reorientation processes which occur in the quadratic and memory materials. The linear materials possess permanent remanent polarization however, in this case the material is switched to its saturation remanence, and it remains in that state. Optical information is extracted from the ceramic by the action of an electric field which causes linear changes in the birefringence, but in no case is there polarization reversal in the material. 

Changing the Propagation Characteristics of Light The Pockels Effect. 

The applied voltage in effect changes the linear susceptibility and thus the refractive index of the material. This effect, known as the linear electrooptic (LEO) or Pockels effect, modulates light as a function of applied voltage. At the atomic level, the applied voltage is anisotropically distorting the electron density within the material. Thus, application of a voltage to the material causes the optical beam to "see" a different... 

Comments on NLO and Electrooptic Coefficients. Typically, the Pockels effect is observed at relatively low frequencies (up to gigahertz) so that slower nonlinear polarization mechanisms, such as vibrational polarizations, can effectively contribute to the "r" coefficients. The tensor used traditionally by theorists to characterize the second-order nonlinear optical response is xijk Experimentalists use the coefficient dijk to describe second-order NLO effects. Usually the two are simply related by equation 31 (16) ... 

This tutorial deals with nonlinear optical effects associated with the first nonlinear term in expression for the polarization expansion described in the next section. The first nonlinear term is the origin of several interesting and important effects including second-harmonic generation, the linear electrooptic or Pockels effect,... 

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. 

The most useful of the known photorefractives are LiNbC>3 and BaTiC>3. Both are ferroelectric materials. Light absorption, presumably by impurities, creates electron/hole pairs within the material which migrate anisotropically in the internal field of the polar crystal, to be trapped eventually with the creation of new, internal space charge fields which alter the local index of refraction of the material via the Pockels effect. If this mechanism is correct (and it appears established for the materials known to date), then only polar, photoconductive materials will be effective photorefractives. However, if more effective materials are to be discovered, a new mechanism will probably have to be discovered in order to increase the speed, now limited by the mobility of carriers in the materials, and sensitivity of the process. 

The T(3) rtjk gives the linear electro-optic (Pockels) effect, while the 7(4) ptjkl is responsible for the quadratic electro-optic (Kerr) effect qtjkl is the photoelastic tensor. 

Example 15.4-3 Both the piezoelectric effect and the Pockels effect involve coupling between a vector and a symmetric 7(2). The structure of K is therefore similar in the two cases, the only difference being that the 6 x 3 matrix [rqi is the transpose of the 3x6 matrix [diq where i 1, 2, 3 denote the vector components and q= l,. .., 6 denote the components of the symmetric 7(2) in the usual (Voigt) notation. Determine the structure of the piezoelectric tensor for a crystal of C3v symmetry. 

PNA, bioorganometallic studies, 1, 902 P2N2 dianionic macrocycle, in organometallic synthesis, 1, 69 7yV,P-tridentate ligands, in platinum(II) complexes, 8, 537 Pockels effect, and second-order non-linear polarization,... 

We note from Eq. (15) that the space-charge field is shifted in space by n/2 with respect to the intensity pattern [Eq. (11)], which corresponds to a distant shift of Ag/4 in the x direction (Fig. 3d). This space-charge field induces an index volume grating via the Pockels effect (Fig. 3e). The refractive index including the fundamental component of refractive index modulation with magnitude of An can be written as... 

The linear susceptibility yy1 1 is related to optical refraction and absorption. The most common effects due to second-order susceptibility x(2) are frequency doubling x (-2co co, co) and the EO (Pockels) effect x(2)(- 0, co). The third-order susceptibility y 3) is responsible for such phenomena as frequency tripling and the Kerr effect. 

Both the amplitude and the direction of the total poling field are functions of position x. The dipole chromophore will align in response to the field Et(x), and a periodic refractive index modulation will be formed due to both molecular anisotropy and the Pockels effect [37], The contribution from molecular anisotropy is an important, sometimes even dominant, mechanism. 

This is called the linear electro-optic effect, also called the Pockels effect . 

Thus, the applied field, E2, changes the effective linear susceptibility (i.e. the dependence of the polarization on the light field, Eft. Since the linear susceptibility is related to the refractive index, the refractive index of the material is also changed by the applied field. This is known as the linear electrooptic (EO) or Pockels effect and can be used to modulate the polarization or phase of light by changing the applied voltage. 

In 1875 John Kerr carried out experiments on glass and detected electric-field-induced optical anisotropy. A quadratic dependence of n on E0 is now known as the Kerr effect. In 1883 both Wilhelm Rontgen and August Kundt independently reported a linear electro-optic effect in quartz which was analysed by Pockels in 1893. The linear electro-optical effect is termed the Pockels 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. 

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