Nonlinear optical effects Pockels effect

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,... 

X quantifies all second-order NLO effects such as SHG, electro-optic effect (Pockel) and frequency mixing, x is representative of third-order NLO effects such as THG, optical Kerr effect and two-photon absorption (TEA). The real part of 7 describes the nonlinear refractive index and its imaginary part the two-photon cross section (<72). 

Since the discovery of SHG, NLO has attracted increasing interest, and scientists all over the world have carried out research in this important field. Further nonlinear optical effects were discovered, such as sum-frequency generation (SFG), third-harmonic generation (THG), two photon absorption (TPA), Kerr effect, Pockels effect, and so on. 

The arrival of practical fiber optic communication networks has strengthened the need for more-efficient devices which are capable of routing or modulating optical signals. Such devices often rely on nonlinear optical effects such as the Pockels and Kerr effects which are second- and third-order phenomena, respectively. These effects arise as a result of the electric-field expansion for the electric polarization in a nonlinear medium ... 

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). 

Pockel s effect -for electrooptic materials [CERAMICS - NONLINEAR OPTICAL AND ELECTROOPTIC CERAMICS] (V ol 5) - [NONLINEAROPTICAL MATERIALS] (Vol 17)... 

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) ... 

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 Pockel s effect [3] refers to an electro-optical process wherein the application of large electric fields onto crystals lacking a center of symmetry can lead to nonlinear polarization effects and optical rotation. Pockel cells can be used in place of photoelastic modulators and can achieve very high modulation frequencies but often have the undesirable property of a nonzero birefringence in the absence of an applied field. 

Many of the different susceptibilities in Equations (2.165)-(2.167) correspond to important experiments in linear and nonlinear optics. x<(>> describes a possible zero-order (permanent) polarization of the medium j(1)(0 0) is the first-order static susceptibility which is related to the permittivity at zero frequency, e(0), while ft> o>) is the linear optical susceptibility related to the refractive index n" at frequency to. Turning to nonlinear effects, the Pockels susceptibility j(2)(- to, 0) and the Kerr susceptibility X(3 —to to, 0,0) describe the change of the refractive index induced by an externally applied static field. The susceptibility j(2)(—2to to, to) describes frequency doubling usually called second harmonic generation (SHG) and j(3)(-2 to, to, 0) describes the influence of an external field on the SHG process which is of great importance for the characterization of second-order NLO properties in solution in electric field second harmonic generation (EFISHG). 

In the literature however, other related parameters, besides x are often used to describe the macroscopic second-order NLO properties of materials. The SHG nonlinear coefficient d and the linear electro-optic coefficient r are the parameters commonly used for second-harmonic generation and the Pockels effect respectively [3, 5]. They are related to x according to Eqs. (4) and (5). 

Summation over repeated indices is implied and is the th-order susceptibility tensor that describes the interaction between the electric fields and the material. The first two terms on the right-hand side of Equation 8.A1 give the spontaneous polarization and linear optics effects. The last two terms lead to various phenomena in nonlinear optics. They include SHG and EO Pockels and Kerr effects. The EO susceptibilities are obtained by combining optical and static fields therefore, the susceptibilities that describe the EO Pockels and Kerr effects are (-co, co, 0) and x% respectively. In a... 

From the two descriptions of the Pockels effect in the frameworks of electro-op-tics and nonlinear optics, one can show that the electro-optic tensor elements and the second-order nonlinear susceptibility elements are related by... 

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... 

Some of the relevant applications of nonlinear optics are currently used in laser technology and fiber communications, such as optical frequency conversion, optical parametric oscillation and amplification, the linear electrooptic effect (Pockels... 

As an infrared YAG laser beam of wavelength 1.06 p,m impacts a nonlinear optical (NLO) medium, a green light of A = 0.53 pm is observed. This is the second harmonic generation (SHG) effect. The medium is the NLO sample. In addition to the second harmonic generation, the NLO effects include the Pockel effect, the Kerr effect, the third harmonic generation and the four-wave mixing. 

Table 4.1-149 Electro-optical constants of zinc compounds. Under the influence of an electric field, the refractive index changes in accordance to the nonlinearity of the dielectric polarization (Pockels effect). Crystals with hexagonal symmetry have three electro-optical constants rsi, 733, 751 crystals with cubic symmetry have only one electro-optical constant 741...

Like solid ferroelectrics, the ferroelectric liquid crystals, particularly the FLCPs, show a pyroelectric effect and a piezoelectric effect and are capable of switching polarization direction (dielectric hysteresis). Moreover, they can switch propagating or reflected polarized light. Finally, the polar symmetry of the phase leads to nonlinear optical properties of the FLCPs such as second-harmonic generation, the Pockels effect, and the Kerr effect. These physical properties of the ferroelectric LC polymers are discussed in the following sections. 

The strong interest in nonlinear optical (NLO) properties of organic materials in the past two decades is due to the electronic nature of the nonlinearity and the related fast response. Possible applications are for second-harmonic generation (SHG) and for electro-optic modulation due to the Pockels effect. The advantage of polymeric materials is easy processibility (especially to obtain thin films), which allow the realization of integrated optical elements and higher flexibility in molecular engineering [15,129]. 

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