Two-photon absorption cross section

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. 

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)... 

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. 

Albota M, Beljonne D, Bredas JL, Ehrlich JE, Fu JF, Heikal AA, Hess SE, Kogej T, Levin MD, Marder SR, McCord-Maughon D, Perry JW, Rockel H, Rumi M, Subramaniam G, Webb WW, Wu XL, Xu C (1998) Design of organic molecules with large two-photon absorption cross sections. Science 281 1653-1656... 

Chung SJ, Zheng S, Odani T, Beverina L, Fu J, Padilha LA, Biesso A, Hales JM, Zhan X, Schmidt K, Ye A, Zojer E, Barlow S, Hagan DJ, Van Stryland EW, Yi Y, Shuai Z, Pagani GA, Bredas JL, Perry JW, Marder SR (2006) Extended squaraine dyes with large two-photon absorption cross-sections. J Am Chem Soc 128 14444-14445... 

Pond SJK, Tsutsumi O, Rumi M et al (2004) Metal-ion sensing lluorophores with large two-photon absorption cross sections aza-crown ether substituted donor-acceptor-donor distyryl benzenes. J Am Chem Soc 126 9291-9306... 

Stabo-Eeg F, Lindgren M, Nilsson KPR, Inganas O, Hammarstrdm P (2007) Quantum efficiency and two-photon absorption cross-section of conjugated polyelectrolytes used for protein conformation measurements with applications on amyloid structures. Chem Phys 336 121-126... 

A quantitative determination of two-photon absorption cross-sections from direct measurements of chemical yield was performed by Speiser and Kimel i ) who studied the two-photon-induced photolysis of iodoform with a Q-switched ruby laser. 

Absolute Two-Photon Absorption Cross Sections and Spectra... 

In conclusion, it should be noted that fluorene derivatives 16 and 22, with large two-photon absorption cross sections, high fluorescence quantum yields and high photochemical stabihty imder one- and two-photon excitation are outstanding candidates for various linear and nonhnear optical apphcations, especially 3D fluorescence bioimaging. 

Table 6 Two-photon absorption cross sections, 32PA> and quantum yields of singlet oxygen generation, under single and two-photon excitation of 57-60 at 775 nm in ACN...

Based on the MCSCF/CM quadratic response method it is possible to calculate the hyperpolarizability tensor and the two-photon absorption cross-sections. The calculated MCSCF/CM properties exhibit for all the individual tensor components substantial shifts compared with the corresponding molecular properties of the molecule in vacuum. 

Similar to the average hyperpolarizability, the two-photon absorption cross-sections are also affected by the interactions with the structured environment. For forbidden transitions we have observed that the structured environment perturbs these transitions significantly. Generally, the results from the MCSCF/CM model including polarization contributions compare very well with the available experimental data on two-photon cross-sections of liquid water. 

Au nanorods are especially appealing as TPL probes due to their high quality factors at NIR wavelengths and their sensitivity to incident polarization, which can provide additional orientational information.217,225 The TPL intensities of Au nanorods have been shown to have a cos4 relation with respect to the polarization of incident light, and are at a maximum when aligned with their longitudinal axes (Fig. 10.10). The two-photon absorption cross-section of individual Au... 

If intrinsic two-photon absorption cross-sections are the subject of investigation short pulses (ps or fs) should be used and two-photon fluorescence (see below) should be measured to verify the Independence of the TPA process. Most often, two-photon absorption is measured either with the Z-scan technique (see above) or with the nonlinear transmission method [38]. 

In TPA induced fluorescence spectroscopy the excited state population for fluorescence is created by the simultaneous absorption of two photons instead of the one-photon absorption in standard fluorescence experiments. The principles of this technique are described in Ref. [23]. It allows an experimental determination of two-photon absorption cross-sections provided the material is fluorescent and that its two-photon fluorescence quantum efficiency is known (which is usually assumed to be equal to the one-photon fluorescence quantum efficiency if the same excited state is reached). In this case the method generally provides high sensitivity. 

Prototype examples of molecules that were developed based on these criteria are shown in Fig. 27. Huge effective two-photon absorption cross-sections with values close to 12,000x10 50 cm4s/photon were obtained with ns pulses. Since the two-photon absorption cross-section was determined at a single wavelength and only with ns pulses excited state absorption may also have contributed to the observed large effects. Detailed studies on heterocyclic chromophores revealed that the molecular environment also plays a role on the two-photon absorption properties if excited state absorption is present [91]. 

Table 6. Experimentally determined two-photon absorption cross-sections 6, the imaginary part of the second-order susceptibility y, single photon absorption maxima Xmax, and the wavelength of maximum two-photon absorption Unless indicated otherwise, the measurements were performed in toluene. For the calculation of Im yC-co, o,-co,co) from 6 (see Eq.(51))a refractive index of n =1.5 was taken. All data originate from Refs.[8] and [41]. 

Fig. 28. Structure of the noncentrosymmetric molecule that was theoretically analyzed for the optimization of the two-photon absorption cross-section 6...

Fig. 29. Two molecules with excellent effective two-photon absorption cross-sections. The increased values (6670x10 50 cm4s/photon for the molecule on the left and 8180xl0 5° cm4s/photon for the one on the right) in comparison with similar molecules of Table 6 indicates that they are enhanced by excited state absorption. The molecule on the right has a large potential for optical limiting in the wavelength range from 675 to 800 nm...

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