Refractive index nonlinear

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.

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. 

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... 

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. 

For all-optical signal processing (based on pure y nonlinearities) the important quantity is the nonlinear refractive index n2. The resulting refractive index change can be induced either by the beam at the frequency co1 itself (self-phase modulation) or by a beam at another frequency to2 (cross-phase modulation). 

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. 

For wavelengths shorter than 500 nm the electronic contribution from the resonance in the UV has growing importance and the above reference value is too small. For wavelengths further in the infrared the reference values are still adequate unless a vibrational resonance is met. At the wavelength A=10.6 pm the nonlinear refractive index 2=(3.9 1.6)xl0 5 cm2/GW is obtained [6] in agreement with the above values at shorter wavelengths. 

The nonlinear refractive index n2 of fused silica has been measured by different methods and a standard value has recently been reported [ 11 ] for the wavelength A=1053 nm. 

To implement an all-optical switch based on the nonlinear refractive index n(I)= n0+n2-I a nonlinear phase (f>MI shift of 2 n or a multiple of 27ris required, depending on the geometry of the switch [1]. As the absorption of the material attenuates the intensity and consequently diminishes the nonlinear phase shift, low absorption is advantageous. To determine the net nonlinear phase shift over the propagation distance the signal depletion by absorption has to be included. 

As large intensities are necessary to induce a nonlinear refractive index change, not only linear but also multiple photon absorption processes have to be considered. The intensity I and the induced nonlinear phase shift NL are coupled differential equations as a function of the propagation direction z. 

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... 

Neglecting the absorption processes in this section the nonlinear phase shift nonlinear refractive index, the intensity, and the interaction length. Keeping dimensions of centimeters in mind, either the nonlinearity n2 or the intensity I can be increased to create the necessary nonlinear phase shift. 

For the continuous-wave semiconductor (AlGaAs) distributed feed back lasers (DFB) used in telecommunication technology today a nonlinear refractive index n2=S cm2/GW would be necessary for all-optical switching, which is presumably impossible to reach. Including an Erbium doped fiber amplifier (EDFA) the needed nonlinearity drops only by a factor of ten. 

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... 

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