Optical Kerr effect electric field

Here Xo (2w), x (wiiw2) and Xo (O) are the non-resonant values of the hyperpolarisabilities. Thus second harmonic generation is resonantly enhanced at both the fundamental and the harmonic of the optical transition, sum and difference frequency generation at the fundamentals and the sum and difference frequencies, and the rarely observed optical rectification only at the fundamental frequency. The term 3 in the expansion gives rise to effects such as third harmonic generation, x(3) -3oj oj, oj,u>), electric field induced second harmonic generation, x(3) (- 2w 0,w, oj), the optical Kerr effect, x(3) (-oj oj, oj, -cj), etc. that will display resonances at oj, 2oj and 3u>. 

Experimental Hyperpolarizabilities for Gas and Liquid. The usual sources of hyperpolarizability data are EFISH (Electric Field Induced Second Harmonic), the static and optical Kerr effect (KE and OKE) and hyper-Rayleigh scattering (HRS). The extraction of molecular hyperpolarizabilities from the EFISH signal requires careful analysis of the second harmonic output signal... 

As the local electric field in the particles is enhanced at the SPR, the metal nonlinear optical response can be amplified as compared to the bulk solid one. Moreover, the intrinsic nonlinear properties of metals may themselves be modified by effects linked with electronic confinement. These interesting features have led an increasing number of people to devote their research to the study of nonlinear optical properties of nanocomposite media for about two decades. Tire third-order nonlinear response known as optical Kerr effect have been particularly investigated, both theoretically and experimentally. It results in the linear variation of both the refraction index and the absorption coefficient as a function of light intensity. These effects are usually measured by techniques employing pulsed lasers. 

The first contribution to the polarization induces a modification of the wave propagation in the material, for both its amplitude and phase, but without any frequency change. This phenomenon is known as the optical Kerr effect, by analogy with the magneto-optic and electro-optic Kerr effects where the medium refractive index varies proportionally with the square of the applied magnetic or electric static field. The second contribution corresponds to the third harmonics generation (THG). 

Isotropic media can be made birefringent by application of an electric field. This phenomenon is an electro-optic effect.5 There are in fact several electro-optic effects the Pockels effect, the electro-optic Kerr effect, the Stark effect in atoms and molecules, the Franz-Keldysh effect in semiconductors, etc. (see Table 4.6). We will limit our discussion in this section to the Pockels effect and the electro-optic Kerr effect. 

The tensors and 7 constitute the molecular origin of the second-and third-order nonlinear optical phenomena such as electro-optic Pock-els effect (EOPE), optical rectification (OR), third harmonic generation (THG), electric field induced second harmonic generation (EFI-SHG), intensity dependent refractive index (IDRI), optical Kerr effect (OKE), electric field induced optical rectification (EFI-OR). To save space we do not indicate the full expressions for and 7 related to the different second and third order processes but we introduce the notations —(Ajy,ui,cj2) and 7(—a , o i,W2,W3), where the frequency relations to be used for the various non-linear optical processes which can be obtained in the case of both static and oscillating monochromatic fields are reported in Table 1.7. 

P( P(-o> w,0) P(0 -fa>,w) Y( - Y(-2(i) (i>,tD,0) Y(-o) (i>,0,0) Second harmonic generation (SHG) Electrooptic Pockels effect Optical rectification Third harmonic generation DC electric-field-induced SHG Intensity-dependent refractive index Optical Kerr effect Coherent anti-Stokes Raman pSHG pEOPE pOR. yTHG. EFISH oj DC-SHG. JlDRI or. yOKE. yCARS... 

This intensity-dependent change of the refractive index is caused by the nonlinear polarization of the electron shell induced by the electric field of the optical wave and is therefore called the optical Kerr effect. 

Furthermore, they examined the performance of different density functionals, including a local-density approximation and a generalized-gradient approximation as well as the functional of van Leeuwen and Baerends that has been constructed to have the correct asymptotic behaviour. Moreover, they considered different frequency-dependent processes, including third-harmonic generation [THG, corresponding to y( 3electric-field-induced second harmonic generation (EFISH, y( 2electro-optic Kerr effect [EOKO, y(—ft> optical rectification [OR, /S(0 [Pg.161]

A well-known nonlinear process taking place in the liquid state of anisotropic molecules is the optical-field induced birefringence (optical Kerr effect ). This nonlinearity results from the reorientation of the molecules in the electric field of a light beam. In the isotropic phase the optical field perturbs the orientational distribution of the molecules. In the perturbed state more molecules are aligned parallel to the electric field than perpendicularly to it and as a consequence the medium becomes birefringent. On the other hand in liquid crystals the orientational distribution of the molecules is inherently anisotropic. The optical field, just as a d.c. electric or magnetic field, induces a collective rotation of the molecules. This process can be described as a reorientation of the director. 

Figure 11 shows the change in the refractive indices AWj and Ang as a function of an applied dc electric field for a PLZT (9.5/65/35) ceramic. The dc field was cycled from 0 to +1.1 MV.m+ down to -1.1 MV.m i, and back up to 0. Awj remained near zero while Afig decreased quadratically with the dc field, due to the electro-optic Kerr effect, until a minimum of -... 

In the Kerr effect pattern of Fig. 29, the n 0 and n 1 lines have coalesced in the central region. This obscures the n 0 bright line for a zero field with aligned polarizers. Within the sensitivity of the optical measurement, the electric field is discontinuous across these coincident lines, so the charge at this position is effectively a sheet of surface charge with charge density [Pg.411]

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... 

In the case of third-order nonlinear phenomena the materials can be centrosymmetric in its molecular structure. One example is the optical Kerr effect reported for the first time by J. Kerr in 1877 and 1878 exposing a material to an electric field the refraction index of an optical medium changes, proportional to the square of the applied field. A double refraction can be generated with the difference between Kerr and Pockels effect being that in the latter case the double refraction is linearly proportional to the electric field. 

The argument Rp implies structure relaxation in the field, and P" means the nuclear relaxation part of P, while the subscript oc oo invokes the so-called infinite optical frequency (lOF) approximation. In principle, this procedure allows one to obtain most of the major dynamic vibrational NR contributions in addition to the purely static ones of Eqs.4.5. 7. The linear term in the electric field expansion of Eq. (4) gives the dc-Pockels effect the quadratic term gives the optical Kerr Effect and the linear term in the expansion of beta yields dc-second harmonic generation (all in the lOF approximation). For laser frequencies in the optical region it has been demonstrated that the latter approximation is normally quite accurate [29-31]. In fact, this approximation is equivalent to neglecting terms of the order with respect to unity (coy is a vibrational frequency). In terms of Bishop and Kirt-man perturbation theory [32-34] all vibrational contributions through first-order in mechanical and/or electrical anharmonicity, and some of second-order, are included in the NR treatment [35]. 

A number of optical effects arise out of both the first and second hyperpolarizibilities. However, only some among them have been systematically studied for practical applications. In this chapter, we will discuss the electric field-induced optical birefringence in second-order NLO materials and the light-induced optical nonlinearities including optical Kerr effect and two-photon absorption (TPA) in third-order NLO materials. Molecular design for... 

The electric field of a light beam exerts a torque on anisotropic molecules by coupling to the oscillating dipole induced in the moleeule by the field itself. The resulting light-induced molecule reorientation is the main mechanism for optical nonlinearity in transparent liquids, the so-ealled optical Kerr effect [17]. 

As was proven later by Bishop [19], the coefficient A in the expansion (73) is the same for all optical processes. If the expansion (73) is extended to fourth-order [4,19] by adding the term the coefficient B is the same for the dc-Kerr effect and for electric field induced second-harmonic generation, but other fourth powers of the frequencies than are in general needed to represent the frequency-dependence of 7 with process-independent dispersion coefficients [19]. Bishop and De Kee [20] proposed recently for the all-diagonal components yaaaa the expansion... 

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