Two-photon cross section

The transition probability for absorption of two photons can be described in tenns of a two-photon cross section 5 by... 

Kim HM, Cho BR (2009) Two-photon materials with large two-photon cross sections. Structure-property relationship. Chem Commun 2 153-164... 

The term 2PA spectrum will be used here and in the rest of the chapter to indicate the variation of the two-photon cross section as a function of wavelength, even when the data were obtained by monitoring the intensity of the fluorescence emission induced by two-photon absorption (that is when, strictly speaking, the two-photon induced fluorescence excitation spectrum was obtained). Also, unless otherwise specified, the spectra are reported as a function of the wavelength of the excitation beam and are degenerate 2PA spectra. 

Restricting the sum-over-states equations, which in general cases need to include all states of the system [91,92], to include only terms relating to three states of a quadrupolar molecule, the groimd state (g), the lowest one-photon allowed excited state (e), and the lowest two-photon-allowed state (f), which are the states depicted in Fig. 1 when / = e, the maximum two-photon cross section can be expressed as follows [93,94] ... 

The purple membrane is harvested semiindustrially from halobacteria mutants which are bred in fermenters. The BR is then embedded into a polymeric matrix of poly(vinyl alcohol) or polyacrylamide. The BR films manufactured in this way are used for different applications, preferably in holography, for example, as a reversible transient data storage system for optical information processing (159). Another example is real-time interferometry by using the property of BR films to integrate over time (160). BR has been proposed also as a two-photon memory material because of its unusually large two-photon cross section. 

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. 

Since this chapter is focused on electrooptic materials and two-photon absorption, we will not consider measurement techniques for y and y(31 in detail, but refer the interested reader to Ref. [19]. In this section, we will briefly describe some of the techniques that have been used for the measurement of the two-photon cross-section, d. We first recall that the 2PA behavior of a molecule is characterized by a spectrum entirely analogous to a one-photon absorption (1PA) spectrum. Although, from the point of view of an application at a particular wavelength, measurements of d at only that wavelength may contribute to a figure-of-merit for that application, more generally, to understand structure-property relationships, it is helpful to acquire 2 PA data over as wide a frequency range as permitted by the lasers available and by the onset of 1PA. 

Essential-state Models for Two-photon Cross-section... 

Fourier components of the electric field strength two-photon cross-section molar extinction coefficient local field factor... 

Information storage in polymeric media based on phenoxynaphthacenequinones was permanent at room temperature. This property suggests that these media may be suitable for use as materials for 3D optical memory.63 66 In this connection, photofluorochromic quinones providing large two-photon cross sections, high fluorescence quantum yields for the photoinduced form, and relatively low ones for the initial form are of chief interest.67,68... 

Fig. 3 Trigonal bipyramid Dsh) Fe(CO)5 (a) simulated pure electronic one-photon absorption spectrum CCR(3) excitation energy, CCSD oscillator strength, ANO-3 basis, (b) Simulated pure electronic two-photon absorption spectrum CCR(3) excitation energy, CCSD two-photon cross-section, ANO-3 basis...

Zhou. Y.-F., Wang, X.-M, Zhao, X., Jiang, M,-H, A quantum-chemical INDO/CI method for calculating two-photon cross sections. J. Phys, Chem. Sol. 62, 1075—1079 (2001)... 

Abstract The first part of this review presents the state of the art on two-photon absorbing molecules. Early works concerned the optimization of dipolar push-pull molecules. Recently, the synthesis of linear and branched centrosymmetrical quadrupolar molecules led to higher nonlinearities, but still far from reaching the fundamental limits of molecular two-photon cross-sections. 

In the second part of this work we review our theoretical and experimental works to obtain enhanced two-photon cross-sections by using the super-linear response of centrosymmetric monomers that are coherently coupled. In this alternative approach, the nonlinear material consists of an assembly of nonsubstituted /r-electron systems that are coupled by dipole-dipole interactions. The monomer two-photon term is a pure transition dipole term ( UQ,jU,2). Typical materials can be molecular aggregates, nanocrystals, oligomers, and dendrimers. The dipole-dipole interactions determine the size dependency of optical properties, and in particular of two-photon cross-sections. 

Enhancement of two-photon cross-sections by two-dimensional and three-dimensional arrangements of monomers has been demonstrated with fluorene V-shapes and dendrimeric structures. Such multidimensional structures lead to lower two-photon absorptions than Hnear oUgomers, but they have better one-photon transparencies. An accurate calculation of large exitonic systems is obtained by diagonalizing the Hamiltonian operator on a reduced basis set. 

X quantifies all second-order NLO effects such as SHG, electro-optic effect (Pockel) and frequency mixing, x is representative of third-order NLO effects such as THG, optical Kerr effect and two-photon absorption (TEA). The real part of 7 describes the nonlinear refractive index and its imaginary part the two-photon cross section (<72). 

Ozkabak et al. [33b] demonstrated, in connection with the f 2u force constants, that fundamental frequencies provide a poor criterion for the accuracy of a force field. Even good frequency pr ctions do not ne< ssarily indicate accurate force constants. They suggest that eigenvector-dependent quantities, such as two-photon cross sections, provide a more stringent test. 

Table 11.1 Two-photon cross sections of common fluorophores...

A further example of photo-uncaging of MSNs is based on the detachment of a coumarin unit linked through an ester group to the functionalized silica surface (Fig. 22). The mesoporous particles had a size of ca. 100 nm and a pore diameter calculated to be about 2.5 nm. The photolabile protecting group has a two photon cross-section of ca. 1.07 GM at 740 nm and 0.13 GM at 800 nm. When excited by one or two... 

The scattering cross section depends on the matrix element (3.9) of the polarizability tensor and furthermore contains the (o frequency dependence derived from the classical theory of light scattering. One obtains [309] analogously to the two-photon cross section (Sect. 2.5)... 

The modification should introduce the ability to absorb NIR light effectively [ie., a high molar extinction coefficient or two-photon cross-section). 

Two-photon absorption is certainly the main process in coordination complexes with organic chromophores. A tuning of the two-photon cross section can be apprehended by a derivatization of the ligands. By the two-photon excitation process, the excited ligand transfers the energy onto the lanthanide ion similar to a downconversion mechanism. 

The selection rules for two-photon transitions are different and many dyes that have a large coefficient for one-photon absorption exhibit two-photon cross sections in the order of at most a few GM [14]. Correspondingly, a two-photon emission (excited state two photons) is observed as a weak emission, since only the total energy is conserved, not the energy of each individual photon. Thus, emission is a weak continuum of interest more of astrophysicists than of chemistry practitioners, but advancement in the field has been remarkable [15]. 

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