Third-order nonlinear refractive index

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. 

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. 

Thus, the linear polarizability a (responsible for the value of the refractive index n) can be treated as an electric field amplitude-dependent quantity, i.e., aeff = a + (3-yEo)/4. Remembering that the light intensity is proportional to the square of the field amplitude, this means that the third-order nonlinearity leads to the linear dependence of the refractive index on the light intensity and that, for example, the phase of the propagating beam is modified at high light intensities due to this dependence. 

Sulfur heterocycles, including those with more than two sulfur atoms, are used for optical materials <2000JPP2002040201>. The molecular third-order optical nonlinearity 7R (Second hyperpolarizability or nonlinear refractive index) was measured for pentathiepinethiafulvalene <1999PCA6930>. 

Some authors are using the same relations between the third-order susceptibility and the nonlinear refractive index and the two-photon absorption coefficient for the self- and cross-phase modulation process. 

No external parameter occurs in the two-photon figure of merit T. It is a function of the material only without any possibility to tune the figure of merit by external means. With the nonlinear refractive index n2 and the two-photon absorption coefficient a2 proportional to the real and imaginary part of the complex third-order susceptibility 3 >= 3 > -et<>>< 3 1 the two-photon figure of merit T 1 can be rewritten as a function of the nonlinearity phase (p< VK... 

In the degenerate four wave mixing (DFWM) experiment the third-order susceptibility 3)(-tt>,tt>,-CL>,CL>) with degenerate frequencies can be determined [22]. This nonlinear susceptibility is directly proportional to the nonlinear refractive index n2, which is used to describe optically induced refractive index changes. An advantage of this technique is the possibility to record the temporal shape of the third-order nonlinear optical signal. 

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... 

The second and third terms of the right hand side of Eq. (25) constitute the second- and third-order nonlinear contributions to the total polarization. These corrections to the polarization are responsible for numerous nonlinear optical processes such as the generation of light beams with new frequencies or an intensity dependent refractive index. 

An extremely useful feature of the third-order nonlinear optical response is the intensity-dependent refractive index, where the refractive index of the medium changes due to the interaction with a light beam. This optically-induced change in the refractive index is essential for all-optical switching applications. 

In order to successfully substitute the role of the electron by the photon in photonic applications, it is necessary to achieve high processing speeds. For applications of the intensity-dependent refractive index, one could define the following figure of merit that evaluates the optical switching performance of a third-order nonlinear optical material [24] ... 

The measurement of third-order nonlinear response, characterized by is simplified because no geometrical condition in the material is required. The intensity-dependent refractive index, a unique feature of the third-order nonlinear response, allows to characterize by smdying the change in the refractive index of the nonlinear material. This effect is exploited in numerous technical applications, and results in different experimental techniques that determine x - However, the absence of a geometrical condition in the material results in an extra complication when measurements are performed, since all materials (cell walls, glass, air,...) contribute to ... 

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. 

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,... 

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). 

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. 

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