Absorption three-photon

Three-photon absorption has also been observed by multiphoton ionization, giving Rydberg states of atoms or molecules [36]. Such states usually require vacuum ultraviolet teclmiques for one-photon spectra, but can be done with a visible or near-ultraviolet laser by tluee-photon absorption. 

In a two-photon absorption process the first photon takes the molecule from the initial state 1 to a virtual state V and the second takes it from V to 2. As in Raman spectroscopy, the state V is not an eigenstate of the molecule. The two photons absorbed may be of equal or unequal energies, as shown in Figures 9.27(b) and 9.27(c). It is possible that more than two photons may be absorbed in going from state 1 to 2. Figure 9.27(d) illustrates three-photon absorption. 

U 2 - JI density matrix is second-order and the initial state I) can evolve after the second scattering caused in both bra and ket states caused by the applied field. Further, three-photon absorptions with frequencies uj, 0J2, and can be described by p t) = ///dwidw2dw3/2(a i,u 2,W3)e= ( i+ 2+" ), which obeys a third-order equation of motion,... 

Figure 8.2e shows the dependence of the fluorescence intensity on the excitation power of the NIR light for the microcrystals measured with a 20x objective. In this plot, both axes are given in logarithmic scales. The slope of the dependence for the perylene crystal is 2.8, indicating that three-photon absorption is responsible for the florescence. On the other hand, slopes for the perylene and anthracene crystals are 3.9 for anthracene and 4.3 for pyrene, respectively. In these cases, four-photon absorption resulted in the formation of emissive excited states in the crystals. These orders of the multiphoton absorption are consistent with the absorption-band edges for each crystal. The four-photon absorption cross section for the anthracene crystal was estimated to be 4.0 x 10 cm s photons by comparing the four-photon induced fluorescence intensity of the crystal with the two-photon induced fluorescence intensity of the reference system (see ref. [3] for more detailed information). 

Sutherland RL, Brant MC, Heinrichs J, Rogers JE, Slagle JE, McLean DG, Fleitz PA (2005) Excited-state characterization and effective three-photon absorption model of two-photon-induced excited-state absorption in organic push-pull charge-transfer chromophores. J Opt... 

The intensity of the upconverted beam as a function of the intensity of the exciting radiation for Er3+ doped into CeC>2 is given in the following table. Determine whether the up-conversion is likely to be a two- or three-photon absorption process. 

Two-photon excitation fluorescence is currently the most widely nsed nonlinear contrast mechanism for microscopic investigations. The first experimental demonstration of two-photon excitation fluorescence was provided in 1961 (Kaiser and Garrett 1961), even though the first theoretical description of two-photon excitation flnorescence stems back to 1931 (Goppert-Mayer 1931). Three-photon absorption was demonstrated a few years later by Singh and Bradley (1964). Two-photon absorption is a third-order nonlinear effect, whereas three-photon absorption is a fifth-order nonlinear effect. The transition rate for two-photon absorption, R, depends on the square of the intensity, /, as follows (see Boyd 1992) ... 

Singh, S., and Bradley, L. T. 1964. Three-photon absorption in napthalene crystals by laser excitation. Phys. Rev. Lett. 12 612-14. 

Figures 9A and 9B are photofragment images of D+ following irradiation of D2 with 532-nm light. All of the features can be assigned to dissociation of different vibrational levels of D2 by nominally either one-, two, or three-photon absorption. Because two-photon absorption to the 2p

Laser spectroscopy of the 1S-2S transition has been performed by Mills and coworkers at Bell Laboratories (Chu, Mills and Hall, 1984 Fee et al, 1993a, b) following the first excitation of this transition by Chu and Mills (1982). Apart from various technicalities, the main difference between the 1984 and 1993 measurements was that in the latter a pulse created from a tuned 486 nm continuous-wave laser with a Fabry-Perot power build-up cavity, was used to excite the transition by two-photon Doppler-free absorption, followed by photoionization from the 2S level using an intense pulsed YAG laser doubled to 532 nm. Chu, Mills and Hall (1984), however, employed an intense pulsed 486 nm laser to photoionize the positronium directly by three-photon absorption from the ground state in tuning through the resonance. For reasons outlined by Fee et al. (1993b), it was hoped that the use of a continuous-wave laser to excite the transition would lead to a more accurate determination of the frequency interval than the value 1233 607 218.9 10.7 MHz obtained in the pulsed 486 nm laser experiment (after correction by Danzmann, Fee and Chu, 1989, and adjustment consequent on a recalibration of the Te2 reference line by McIntyre and Hansch, 1986). 

This rule is analogous for any number of photons thus, in a three-photon absorption process the allowed states are the p and f states, which allows even-to-odd or odd-to-even parity. This means that transitions can be divided between states of either the same or different parity corresponding to absorption of either even or odd numbers of photons. Hence the selection rules are the same for one and three photons and for two and four photons, respectively [49]. 

Figure 7.7 Linear (Xa = 337 nm) and three-photon absorption induced f-f emission (Xa = 800nm) of complexes 2 and 3.

Figure 7.11 Three-photon absorption induced f-f emission spectra (left) of 5 in the infrared region with its corresponding power dependence plot (right).

Our present focus is on correlated electronic structure methods for describing molecular systems interacting with a structured environment where the electronic wavefunction for the molecule is given by a multiconfigurational self-consistent field wavefunction. Using the MCSCF structured environment response method it is possible to determine molecular properties such as (i) frequency-dependent polarizabilities, (ii) excitation and deexcitation energies, (iii) transition moments, (iv) two-photon matrix elements, (v) frequency-dependent first hyperpolarizability tensors, (vi) frequency-dependent polarizabilities of excited states, (vii) frequency-dependent second hyperpolarizabilities (y), (viii) three-photon absorptions, and (ix) two-photon absorption between excited states. 

An analytical solution for simultaneous inclusion of one-, two-, and three-photon absorption Oq, a2, a3 is not possible. In reality, one absorption process is usually dominating for a chosen wavelength and the differential equations can be solved by neglecting the other absorption terms, dominating one photon absorption (oq [Pg.137]

For a dominating one-photon absorption the nonlinear phase shift grows asymptotically to a maximal value of (f>NL=2n-n2I0/phase shift does not saturate but deviates significantly from the linear behaviour as expected for absence of absorption (dashed line). 

Fig. 1a-c. Absorption and nonlinear phase shift as a function of the propagation distance for a dominating a one-, b two-, and c three-photon absorption process. The dashed line indicates the nonlinear phase shift without any absorption... 

Here the matrix elements Hi , = (e Hul e ) are operators with respect to nuclear = wave functions in the ground and excited electronic states and At, g = e dE g, and so forth. The two-and three-photon absorption operators D and T are defined by the r bove, identities. 

Recently, Wong and coworkers reported an emissive Tb(III) complex [Tb(L73)(N03)3] (Tb-73, Figure 13.34) based on a ligand of 7V-[2-(bis 2-[(3-methoxybenzoyl)amino]-ethyl amino)ethyl]-3-methoxybenzamide) (L73) as a three-photon luminescence probe with low cytotoxicity [109]. The three-photon process of Tb-73 under excitation at a femtosecond 800 nm laser was confirmed by a power dependence experiment. The three-photon absorption cross section of Tb-73 is around 1.9 GM. Furthermore, the interaction of three selected cells with Tb-73 over different durations of time (from 0 to 60 min and 24 h) was investigated. As shown in Figure 13.34, intracellular luminescence increased as the exposure time increased. At an exposure time of 60 min, more than 95% of the cells under 800 nm excitation exhibited green luminescence, as was observed in the cytoplasmic foci around the cell nucleus. 

Due to its relevance to the next section, we observed and analyzed the fluorescent emission of Tryptophan in water solution excited by one, two, and three-photon absorption. For that, three different light sources were used a UV (180-375 nm) lamp, the second harmonic of a Q-switched Nd YAG laser (with 8 ns pulse duration at 532 nm) and a Ti-Sapphire laser delivering pulses at 76 MHz, with 150 fs pulse duration and 500 mW average power at 800 nm. 

Figure 18.4 Fluorescence spectrum of the Tryptophan solution excited by a) one, b) two and c) three-photon absorption process. Insets show the excitation intensity dependence of the fluorescence.

Figure 18.8 Fluorescent peak intensity of Tryptophan-Ag colloid excited by three-photon absorption process...

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