Refraction, nonlinear

Nonlinear refraction phenomena, involving high iatensity femtosecond pulses of light traveling in a rod of Tfsapphire, represent one of the most important commercial exploitations of third-order optical nonlinearity. This is the realization of mode-locking ia femtosecond Tfsapphire lasers (qv). High intensity femtosecond pulses are focused on an output port by the third-order Kerr effect while the lower intensity continuous wave (CW) beam remains unfocused and thus is not effectively coupled out of the laser. 

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. 

Figure 9.2 illustrates a typical example of normalized transmittance, T(z), of CdTe QDs against the sample position z from the focusing point vdth and vithout aperture [17]. Since the peak ofthe normalized transmittance for the closed aperture precedes the valley, the sign ofthe nonlinear refractive index of CdTe QDs is negative. 

Figure 9.2 Normalized transmittance measured by the Z-scan with and without the collecting aperture for CdTe QDs with the diameter of 4.1 nm excited at 803 nm (0.4 pj pulse ). The open aperture Z-scan corresponds to the nonlinear absorption and the closed aperture Z-scan to the nonlinear refractive index.

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. 

The Z-scan technique, first introduced in 1989 [64, 65], is a sensitive single-beam technique to determine the nonlinear absorption and nonlinear refraction of materials independently from their fluorescence properties. The simplicity of separating the real and imaginary parts of the nonlinearity, corresponding to nonlinear refraction and absorption processes, makes the Z-scan the most widely used technique to measure these nonlinear properties however, it does not automatically differentiate the physical processes leading to the nonlinear responses. 

The discussion in this chapter is limited to cyanine-like NIR conjugated molecules, and further, is limited to discussing their two-photon absorption spectra with little emphasis on their excited state absorption properties. In principle, if the quantum mechanical states are known, the ultrafast nonlinear refraction may also be determined, but that is outside the scope of this chapter. The extent to which the results discussed here can be transferred to describe the nonlinear optical properties of other classes of molecules is debatable, but there are certain results that are clear. Designing molecules with large transition dipole moments that take advantage of intermediate state resonance and double resonance enhancements are definitely important approaches to obtain large two-photon absorption cross sections. 

Sheik-Bahae M, Hutchings DC, Hagan DJ, Van Stryland EW (1991) Dispersion of bound electronic nonlinear refraction in solids. IEEE J Quantum Electron 27 1296-1309... 

Balu M, Hales J, Hagan DJ, Van Stryland EW (2005) Dispersion of nonlinear refraction and two-photon absorption using a white-light continuum Z-scan. Opt Express 13 3594-3599... 

Two redox states of one complex, (168) and (169), exhibit very similar respective values of ca. 0.6 J cm-2 and 0.7 J cm-2 with 32 ps pulses at 532 nm (in benzene).452 A 532 nm OL study of the two neutral complexes (170) and (171) using ns and ps pulses has also been reported.453-455 Low values of ca. 0.3 Jem-2 are observed with ps pulses in benzene, and both ps time-resolved pump-probe and Z-scan measurements reveal that RSA and nonlinear refraction are responsible for the OL behavior.453-455 Because (170) and (171) are transparent in the region 400-900 nm, their OL responses should cover a wider range than those of fullerenes and MPcs.453-455 Dai et al. have applied ps 532 nm DFWM to the tetrahedral Zn11 or Cd11 complexes (172) and (173), the modest 7 responses of which are resonance enhanced by the n- 7r transition at 512nm.456 The dimeric square pyramidal Zn11 complex (174) exhibits a broad n —> tt absorption with Amax = 497 nm in DMF and is shown by 532 nm Z-scan to exhibit SF behavior.457... 

Other less definite yet important effects such as profile changes due to nonlinear refractive index alteration in spatially nonuniform high power beams must be carefully considered. As example, the use of nonidentical liquids and optical paths prior to and in, say, EFISH cells and the usual quartz calibration cells could cause potentially inaccurate x determinations. Obviously these types of considerations are important when precise experimentation to test fine models of molecular behavior are intended, but have not stood as obstacle to uncovering the important general trends in molecular nonlinearity enhancement. 

X in most strong Kerr, nonlinear refraction, etc. media. For use in extremely high bandwidth applications, such as totally optical processing, predominantly electronic responding media are needed (M). 

Part C Demonstration of a Nonlinear Refractive Index Calibration Curve... 

Boling, N. L., Glass, A. 1., and Owyoung, A. 1978. Empirical relationships for predicting nonlinear refractive index changes in optical solids. IEEE J. Quant. Electron. 14 601-8. 

Z-scan8 is a technique used to derive the nonlinear refractive index intensity coefficient n2 (from which 3) and y can be determined) by examining self-focusing or self-defocusing phenomena in a nonlinear material. Using a... 

Data in Table IX are given as nonlinear refractive indices n2 other experimental parameters are needed to derive y values that are required for comparison to the results given earlier. As with data in Table VIII,... 

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>. 

The nonlinear refractive index, r, linear absorption, a, and two photon absorption coefficient, jS, of metal dithiolenes and rare earth metallocenes have been measured at 1064 nm using 100 ps and 10 ns pulses. These measurements have shown resonance enhanced molecular nonlinearities of 10M05 times those of carbon disulphide can be obtained. Figures of merit based on the nonlinear refractive index and the linear and two photon absorption coefficients are within the limits required for devices. 

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