Two-photon absorption TPA

The simultaneous absorption of two photons of equal energy can occur if a laser beam (ps or fs pulses) is focused within a material [31, 32]. The process, depicted schematically in Fig. 3.6, is related to the excitation of a molecule to an energy level hvi = 2 hv2 by the simultaneous absorption of two photons of energy hv2 (v = co/2n). 

Two-photon absorption is possible, provided that both photons are spatially and temporally coincident. It occurs with a probability proportional to the square of the light intensity. 

TPA can be measured by the transmission method or by the Z-scan technique. Moreover, two-photon fluorescence can serve to measure TPA absorption cross-sections, provided that a fluorescent excited state is reached by TPA. In nonlinear 

L is the sample thickness and 2 is the absorption coefficient for the pure two-photon absorption process. 

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Winter, Underhill, and co-workers have published extensively on the cubic NLO properties of complexes of DT and related ligands,411 22 particularly those containing formally Ni11 centers. For example, time-resolved 1,064 nm DFWM was used to obtain resonantly enhanced values for group 10 complexes such as (157).411 15 The smaller of (157) compared with (156) is largely due to resonance effects since the absorption maximum of (157) is somewhat removed from the laser fundamental. However, figures of merit derived from measurements of 2 and linear and two-photon absorption (TPA) coefficients show that low optical losses render complexes such as (157) superior to (156)413 for potential all-optical switching applications.411 14... 

In the case of SHG in waveguide nonlinear crystals, we describe a theoretical model which accounts for the temporal behavior of the interacting pulses and the possible z-dependence of the phasematching condition. The model also describes the observed saturation and subsequent decrease in SHG conversion efficiency in the waveguide samples, as a result of two-photon absorption (TPA) of the second harmonic (SH) wave. The results of this model are later compared with experimental data from SHG experiments using femtosecond pulses in the waveguide nonlinear crystals of periodically-poled potassium titanyl phosphate (ppKTP) and appKTP. This model is presented in section 2.3. 

When using the waveguide ppKTP crystal experimentally, the dependence of internal SHG efficiency on input power is characterized by a maximum efficiency of 37 %. A further increase in fundamental pulse energy then leads to a saturation and subsequent decrease in the efficiency of the SHG process (figure 18). This behavior was also observed in the waveguide appKTP crystal (figure 18), and has been reported elsewhere" ". As we have suggested previously, two-photon absorption (TPA) of the second-harmonic (SH) wave is the most likely explanation for this behavior. 

The most widely employed material characterization techniques in third-order nonlinear optics are third-harmonic generation (THG) [21], degenerate four wave-mixing (DFWM) [22], Z-scan [6], and optical limiting by direct two-photon absorption (TPA) and fluorescence spectroscopy induced by TPA [23]. All of them will be discussed in the following. Further measurement techniques such as electric-field induced second-harmonic generation (EFISH) [24], optical Kerr... 

The two compounds 121 and 122 were studied for applications in two-photon excitation fluorescence microscopy (TPEM). The corresponding Zn complexes showed an enhanced efficiency and a significant increase of the two photon absorption (TPA) cross section <07JA11888>. 

In the present contribution the discussion of the NLO response is restricted to off-resonant case. The only exception is the purely resonant quantity, namely imaginary part of second-order hyperpolarizability in the resonant regime (Im-y(-tt> tu, —w, w)). This quantity describes the process of simultaneous absorption of two quanta. The two-photon absorption (TPA) process is much better understood than the three-photon absorption. The basic quantity associated with the two-photon absorption process is the two-photon absorption tensor (S ). In the most general case referring to two different photons (different polarizations and different energies is given by [75, 81] ... 

Though experimentally verified already in 1964 by Singh and Bradley [128], three-photon absorption (3PA) is far less examined than the two-photon absorption (TPA) analog. However, the increased attention directed toward non-linear optical... 

This article is devoted to Are methodology of predicting the direction of the changes of molecular (hyper)polarizabilities values as a function of tire solvent polarity. Since the environmental effect on the two-photon absorption (TPA) is still poorly understood, we will consider the two-level approximation to describe the influence of the solvent effects on TPA from the ground to the CT excited state of the D-tt-A type chromophores. Only electronic contributions will be taken into account. In contrast to the TPA process, the substantial progress in theoretical description of the solvent influence on the vibrational (hyper)polarizabilities has been observed recently [64-67],... 

The existence of even parity states lying above the have been identified by two-photon absorption (TPA), two-photon fluorescence excitation [31], and electroabsorption (EA) spectroscopy. We measured the TPA spectrum of DOO-PPV by Z-scan [32] showing both the real and imaginary components of Figure 7-13 compares the linear absorption spectrum of DOO-PPV to the spectra of the real and imaginary molecular second hyperpolarizability. The imaginary component, y", is proportional to the TPA coefficient a2, while the real component, y, corresponds to the non-linear dispersion, 2- The y" spectrum shows a clear peak at % 3.2,5 eV, 0.5 eV above the peak of the l.B absorption band, and a shoulder at se3.5 eV, which may correspond to a second TPA band. The y spectrum clearly indicates dispersion near the two y" peaks, as expected from Kra-mers-Kronig analysis, and permits us to identify two distinct TPA bands. 

Since its theoretical prediction by GOppert-Mayer in 1931 [1], the nonlinear optical (NLO) process of two-photon absorption (TPA) has received considerable attention, owing to numerous relevant applications in several fields [2], such as optical limiting [3-5], three-dimensional microfabrication [7-15], up-converted lasering [16-18], photodynamic therapy [19-22], data storage [23-28], and biomedical imaging [29-33]. 

For sufficiently high power intensities, non-linear effects can give rise to two-photon absorption (TPA) where simultaneous absorption of two photons... 

The possibility of two-photon absorption (TPA) due to non-linear effects has been mentioned in Sect. 4.1. The magnetic-field-tuned LHeT absorption by n-type GaAs of a laser line at 20.2 cm-1 (2.50 meV) has been reported by [28] for B = 1.15 T and attributed to a two-photon Is —> 2s transition at 40.4cm 1 (5.00meV). The fact that the initial and final states of this transition have the same parity can be explained by assuming an odd-parity... 

In Sect. 2.5,1 pointed out that the auyu and 7i yu configurations differ mainly in the density of their excited states. The former should create 16 states, the latter 32. Polarised absorption spectroscopy only detects 12 excited states, so both configurations remain possible. The cynic can claim that many more states are present but are undetected. This argument can never be completely overturned, but can be undermined by increasing the number of observables characterising the states, and by reducing the probability that some states are not detected. Two-photon absorption (TPA) is very helpful in this regard. 

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