Nonlinear index coefficient

In Chapter 5 where we discussed light scattering, such nonlinear response associated with director axis perturbation is traced back to the extreme sensitivity of the nematic phase to the optical electric field. In fact, the estimate made in Section 5.5.9 for the interaction geometry as shown in Figure 8.7 demonstrates that it is possible to get nonlinear index coefficient ri2 I cm /W. 

In Table 12.1, we list the effective nonlinear index coefficients 2 of these NLC materials along with other well-known classes of nonlinear optical materials 1. Note that is the equivalent third-order nonlinear susceptibility ot is the absorption... 

For the application of QDs to three-dimensional biological imaging, a large two-photon absorption cross section is required to avoid cell damage by light irradiation. For application to optoelectronics, QDs should have a large nonlinear refractive index as well as fast response. Two-photon absorption and the optical Kerr effect of QDs are third-order nonlinear optical effects, which can be evaluated from the third-order nonlinear susceptibility, or the nonlinear refractive index, y, and the nonlinear absorption coefficient, p. Experimentally, third-order nonlinear optical parameters have been examined by four-wave mixing and Z-scan experiments. 

J. Rams, F. Agullo-Rueda, J.M. Cabrera, Structure of high index proton exchanged LiNb03 waveguides with undegraded nonlinear optical coefficients, Appl. Phys. Lett. 71. 3356-3358 (1997). 

In particular, the third-order nonlinear susceptibility is a complex quantity, (ty) = Re[ f (real part of X s related to the to the nonlinear refraction index, [20], and its imaginary component — which is the component of interest to our work - is associated to the material nonlinear absorption coefficient, 02 [20], through... 

Mo and Qq e the linear refractive index and absorption coefficient, respectively ( 2) y is the nonlinear refraction coefficient, while (3 is the nonlinear absorption coefficient. By developing the relation between the electric displacement and the electric field and neglecting the terms proportional to ff, one easily obtains the link between these coefficients and the complex third-order nonlinear susceptibility,... 

Change in the refractive index can be induced by either a resonant or a nonresonant process. For a resonant process, the frequency of the incident light overlaps with an electronic absorption band, by either a one-photon or a multiphoton process. The energy is absorbed by the sample and an excited state population is generated. This induces a transient change in the absorption spectrum of the material due to the bleaching of the ground state absorption and/or the appearance of the excited state absorption. A nonlinear absorption coefficient a2 can be defined similarly to Eq. (15) ... 

In this equation, A is the polarizability, B is the hyperpolarizability, and Xo1, %jui3) are the 1st, 2nd, and 3rd order susceptibilities, respectively. These are tensors, where i,j, k, l correspond to the space coordinates (x, y, z) and crystal axes. The refractivity is related to Xij"-The occurrence of birefringence in anisotropic media is a direct consequence of the fact that X,fu is a tensor. Susceptibilities of order higher than one are called nonlinear susceptibilities. The nonlinear refractive index, n2, and the nonlinear absorption coefficient, a2, both depend on the intensity of light, /. They are defined by Eqs. (5.10) and (5.11),... 

Note that ri2 is a differently dehned nonlinear index that relates the refractive index change to the square of the electric held amplitude]. The nonlinear absorption coefficient is related to the imaginary part of through [13] ... 

Second-order nonlinear index of a absorption coefficient... 

Doping with active species (e.g., Au or Ag NPs, and CdSe or PbS QDs) can result in new NLO materials, such as those with significant third-order NLO susceptibility. The Z-scan method is used to characterize NLO effect in nanocomposite sol-gel films. Z-scan measures the nonlinear refiactive index and nonlinear absorption coefficient of a material [22]. The measurement setup is shown in Figure 22.3. A standard open-aperture Z-scan apparatus is used to measure the nonlinear extinction coefficients of materials, using a laser with a pulse duration of fs, ps, or at least ns as an excitation source, to avoid thermal effects. All the Z-scan measurements described in this chapter were carried out at room temperature. Sol-gel films doped with noble metal NPs (e.g., Au, Ag, and Cu) or QDs (e.g., CdS and PbS) have been investigated by Z-scan measurements [23,24]. 

Nanosized noble metal gold nanoparticles (AuNPs 10 nm)-doped dielectric composite titania films [323] with large third-order nonlinear susceptibility were reported to be applied to optical information processing devices, such as optical switch or all optical logical gates. The third-order nonlinear refractive index and nonlinear absorption coefficient of the films were on the order of 10 cm and 10 cm with nonlinear susceptibility = 6.88 x 10 ° esu. 

An interesting and important point is that, at low optical power, the orientational effect actually is the dominating one, even in such highly absorptive material. In other recent studies " of dye-doped nematic liquid crystals, observed nonlinearities have approached the so-called supranonlinear scale characterized by refractive index coefficients n2 1 cm /W. The observed nonlinearity is orders of magnitude larger than the so-called giant optical nonlinearity of pure liquid crystals. In particular, methyl-red dye-doped nematic liquid crystals were first observed to have a nonlinear index... 

The thermal optical nonlinearity of TM74A under short laser pulse excitation has also been studied by a dynamic grating technique. For visible laser pulses (the second harmonic of a Nd YAG laser at 0.53 pm) and an absorption constant a 2 cm (determined by the absorbing dye dopant concentrationX the measured nonUnear index coefficient 2 is on the order of about -2 X10 " cm AV. 

Table 12.1. Refractive Index Coefficients of Some Nonlinear Optical Materials...

Real part of third-order susceptibility nonlinear refractive index coefficient [Re... 

Consider the reflection of a normally incident time-harmonic electromagnetic wave from an inhomogeneous layered medium of unknown refractive index n(x). The complex reflection coefficient r(k,x) satisfies the Riccati nonlinear differential equation [2] ... 

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