Two-photon absorption coefficient

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. 

Figure 4. Spectrum of the two-photon absorption coefficient P in cm/MW for PDN6S, calculated from birefringenece growth curves as a function of two-photon energy ( ) compared with single-photon absorption spectrum (- - -). Solid line is a least-squares fit to p using the sum of two Gaussians, one broad ( 412 meV), the other narrow ( 33 meV). (Reproduced with permission from Ref. 8. Copyright 1990 Elsevier Science Publishers.)...

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... 

An analogous consideration leads to the dotted line for n2<0 (Fig. 10a). An identical z-scan experiment without the aperture allows the determination of the two-photon absorption coefficient a2 (Fig. 10b). In principle, this method also allows to determine nonlinearities of higher order (e.g. n3 and a3) [33]. 

Fig. 10a,b. a Typical Z-scan curves for n2>0 (solid line) and n2<0 (dotted line), b If the aperture is removed the two-photon absorption coefficient a2 can be determined... 

For 3D recording, the large two-photon absorption coefficient is preferred because 3D memory uses basically a two-photon process to access a point in a volumetric medium. In the following sections, typical photochromic compounds used for 3D memories are described. 

Calculated using the equation cr2 = hcop/lTrN, where p is the two-photon absorption coefficient [58]. 

Table I. Two photon absorption coefficients (P) and nonlinear refractive coefficients (n2) for PDA solutions from z-scan measurements at 532 nm (near...

Near resonant z-scan studies provide both nonlinear refractive coefficients, ni, and two photon absorption coefficients, p. Results for a selection of PDAs in solution at 532 nm are given in Table 1. Diethylamino-PDA (lid) and the related quatemized polymer (15a) show comparable magnitudes of nonlinear absorption and refraction to those of poly-4-BCMU, with figures of merit, T, which satisfy the requirement for nonlinear optical switching devices. The metal-containing PDAs... 

This applies when esu units are used for both H2 and It is interesting to note that the set-up shown in Fig. 3.5 a can also be used to determine the two-photon absorption coefficient a2. In this case, the Z-scan experiment is performed without the aperture. 

Z-scan experiment was carried out for some amorphous PDAs using wavel gth of 1064 nm A typical exanople is own in Figure 4. Two photon absorption coefficient, P, was found to be 2.7 cm/GW. 

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... 

TPA cross-section (ajPA) values were determined from experimentally measured two-photon absorption coefficient, p, which is obtained by measuring the nonlinear transmissivity (Ti) of chromophores in solution for a given input intensity, / , and a given thickness of a sample solution, lo, from the following relationships (23,24) ... 

The two-photon absorption coefficients, p, for the solutions and films were determined by the intensity-dependent transmission technique that has been described earlier. As before, the laser beam used was obtained from a frequency-doubled Nd YAG laser (of 532 nm wavelength) that was mode locked to produce 30-picosecond pulses. 

On the other hand the number of photons absorbed may be evaluated from two photon absorption coefficient 3 dl /I ( 3 I )ndx, with... 

General optical properties IVansparency range (iLm) Refractive index n Two-photon absorption coefficient fi (10- cm/W) Nonlinear dielectric susceptibility Xini (10-22 m2/v2)... 

As is the case with molecular quantities, Fourier components of E and P are accompanied by frequency-dependent, complex susceptibilities % The macroscopic susceptibilities are used in the physical description of NLO effects, such effects typically being analyzed using wave equations in which the nonlinear polarization produced by a given type of interaction constitutes a source term. Quantities other than the susceptibilities are often used for describing specific NLO interactions. The most useful of these are the electro-optic coefficient r related to co ca,0), the nonlinear refractive index ti2, related to the real component of the degenerate third-order susceptibility Re(x —m,ai)), and the two-photon absorption coefficient jSg, related to the corresponding imaginary component Im(x —[Pg.66]

In work of some potential import for practical waveguides, Halvorson and Heeger [864] measured the two-photon absorption spectrum of oriented trans-P(Ac)y and found that the two-photon absorption susceptibility ruled out waveguiding devices in this CP. They then cautioned that any CP must be characterized for its two-photon absorption coefficient before attempting to fabricate waveguides from it. 

Cha et al. [33] reported open aperture Z-scan experiments which demonstrate enhancement of the effective two photon absorption coefficient, j eff (the non-linear absorption coefficient 4a(/) = Petr, where / is the intensity), for the conjugated polymer/ [6,6]PCBCa composites, by more than two orders of magnitude at 760 nm compared with the components alone [33]. Fitting the non-linear absorption data to kinetic equations for the population of the photoinduced charge transferred state, one obtains the excited state cross section shown in Figure 8.38. The peak at 760 nm (1.63 eV) indicates a resonance in the excited state absorption which is correlated with the photoexcited absorption data as shown in Figure 8.38. 

Nonlinear Optical Properties 235 Table 3.15 Two-photon absorption coefficients for a variety of materials. 

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