Third nonlinear absorption

Rao reported measurement of third-order optical non-linearity in the nanosecond and picosecond domains for phosphorus tetratolyl porphyrins bearing two hydroxyl groups in apical position [89]. Strong nonlinear absorption was found at both 532 nm and 600 nm. The high value of nonlinearity for nanosecond pulses is attributed to higher exited singlet and triplet states. Time resolved studies indicate an ultra-fast temporal evolution of the nonlinearity in this compound. 

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. 

The term nonlinear optical property refers to an optical property, which can be modified by exposing the material to intense light irradiation. In this section, we focus on the cascaded first- (/ 1 ) and third-order ( / ) susceptibilities describing nonlinear absorption (ESA and 2PA) and nonlinear refraction (n2) processes. Z-scan, pump-probe, and two-photon upconverted fluorescence techniques are among the most used experimental methods for determining optical nonlinearities. 

A quantitative description of giant pulse generation is again given by a set of rate equations in the simplest case one for the inversion, another for the population density mo of the dye in the ground state So and a third for the laser light intensity nc. If excited state absorption has to be taken into account, additional rate equations would have to be added as described above in the section on nonlinear absorption. 

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... 

In a composite material, as described here, the effective third-order nonlinear susceptibility should depend linearly with the concentration of the inclusions in a low filling fraction regime. In that way, the nonlinear absorption coefficient of the medium, associated to the Im[ (ru)] and consequently to the two-photon absorption processes, should also be a function of the inclusions concentration. 

However, the figure of merit presented in Eq. (78) is not useful in characterizing third-order nonlinear materials because it is not dimensionless and it does not separate between linear and nonlinear absorption. More appropriate dimensionless figures of merit have been proposed by Stegeman [55, 56],... 

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,... 

Samoc, M., Humphrey, M.G., Cifuentes, M.P., McDonagh, A.M., Powell, C.E., Heath, G.A., Luther-Davies, B. Third-order optical nonlinearities of organometallics influence of dendritic geometry on the nonlinear properties and electrochromic switching of nonlinear absorption. Proc. SPIE—Int. Soc. Opt. Eng. 4461, 65-77 (2001)... 

Copper nanoparticles have been synthesized in silica by 50 keV Cu ion implantation with doses of 8.0x10 ion/cm. N anoparticles were c haracterized by absorption band of surface plasmon resonance in the visible range. Metal nanoparticle composite glasses were analyzed by the Z-scan method at the IR wavelength of NdiYAG laser radiation 1064 nm. The third order nonlinear susceptibility in the analyzed medium with simultaneous nonlinear refraction and absorption were considered as complex values. It is suggested that the samples with nonlinear absorption is perspective ones for optical applications. 

In order to understand the origin of the high values of the third-order nonlinearity observed, we picked polybenzidine for more detailed study. The real and imaginary components of the third-order susceptibility x are measured separately. The real part Rex leads to nonlinear refraction, and the imaginary part Imx ) is responsible for nonlinear absorption. The nonlinear-optical measurements were made using dilute solutions of the polymer in DimethyLsulfoxide/Methanol in the ratio 4 1 (DMSO MeOH). 

Another solution to restore the Ramsey fringes, which are generally washed out in the second field, is based on the introduction of a third field at the distance 2L downstream from the first field. The idea of this arrangement was first pointed out by Chebotayev and coworkers [1257]. The basic idea may be understood as follows In Sect. 2.2 it was discussed in detail that the nonlinear absorption of a molecule in... 

In the preceding discussion the effect of nonlinear absorption was neglected. However, in materials with large nonlinear refractive responses it is not uncommon to find an absorption component due to the presence of a single or multiphoton resonance, saturation of the single-photon absorption, or free carrier dynamic absorption. All of these can have a strong effect on the Z-scan profile. If we consider only the effects of two-photon absorption (TPA) the third-order nonlinear susceptibility can be considered complex, represented by a real and an imaginary part as follows ... 

The symmetrical valley-peak or peak-valley closed-aperture Z-scan profile occurs only for materials with a third-order nonlinear susceptibility that is purely refractive (jS = 0) or for which the imaginary component is negligible (jS/y < 1). When the nonlinear absorption is significant the closed-aperture Z-scan transmittance will be distorted (in some cases the peak will be suppressed and the valley enhanced). One could still deduce the values of y and j8 by performing a detailed... 

The functionalities of the second-order nonlinear optical susceptibility, generally called second-order optical nonlinearity, are second harmonic (SH) generation, optical rectification and generation of addition and subtraction of two incident radiation beams. On the other hand, those of the third-order nonlinear optical susceptibility, which is called third-order optical nonlinearity, are the optical Kerr effect, nonlinear absorption, third harmonic generation and so on. 

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. 

Nonlinear Absorption. In theory, any of the above measurement techniques could be applied to materials in the presence of nonlinear absorption and interpreted to provide the two-photon absorption coefficient or the two-photon cross-section The study of multiphoton absorption is, of course, inherently spectroscopic, probing the multiphoton resonances that impact various nonlinear phenomena. Third-harmonic generation in thin films has been used to characterize the phase of the complex x and thus but the experimental technique requires additional steps and interpretation may be complicated by excited state absorption and three-photon resonances (282). The presence of an imaginary component of x significantly complicates DFWM measurements by adding... 

Jiang s group [68] prepared fluorinated hb-PAEK end-capped with nickel phtha-locyanine and checked the material for NLO applications. The third-order nonlinear coefficient was found to have a value of 0.98 x 10 " esu, which the authors attributed to the dual contributions of nonlinear absorption and refraction of the molecules. Moreover, the obtained value was found to be almost five times larger than that of other metallophthalocyanines [314] due to presence of the hyperbranched structure, the aromatic backbone, and the number of end-functionalities. 

Two-photon Absorption, a Third Nonlinear Optical Phenomenon... 

All nonlinear (electric field) spectroscopies are to be found in all temis of equation (B 1.3.1) except for the first. The latter exclusively accounts for the standard linear spectroscopies—one-photon absorption and emission (Class I) and linear dispersion (Class II). For example, the temi at third order contains by far the majority of the modem Raman spectroscopies (table B 1.3.1 and tableBl.3.2). 

Third-order nonlinear optical properties of CdTe QDs were examined by Z-scan and FWM experiments in the nonresonant wavelength region. We found that the two-photon absorption cross section, a, is as high as 10 GM, although this value decreases with decreasing size. In addition, the nonlinear response is comparable to the pulse width of a fs laser and the figures of merit (FOM = Re Xqd/ Xqd)... 

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