Resonance one-photon

A complex 7THG can result from one-, two-, or three-photon resonances. One-photon resonance occurs when the fundamental frequency co is close to an allowed electronic transition. Two-photon resonance occurs when 2co is close to a two-photon allowed electronic transition. For centrosymmetric molecules the two-photon selection rule couples states of like inversion symmetry, e.g. g <- g. For acentric molecules one-photon transitions can also be two-photon allowed. Three-photon resonance occurs when 3co is close to the energy of an electronic transition the same symmetry rules apply as for one-photon transitions. 

We are faced with the important problem to elucidate the competition between resonant (here tliree-photon) absorption and off-resonant one-photon absorption for pumping of the excited state. From previous work on two-photon excitation [9, 10, 35] we learnt that the balance is most delicately dependent on factors like pulse lengths, excited state lifetimes and saturation. The transition dipole moment,... 

Applying the estimations (52) to our model we found the saturation intensities to be equal to 35GW/cm for off-resonant one-photon transitions 1 4,... 

MW/cm for resonant one-photon transitions 3 -> 2 and 169 GW/cm for resonant three-photon transitions 1 4. For comparison, Are saturation intensity for... 

Figure 8.3 Photoelectron spectrum of NO obtained by resonant one-photon excitation of N = 21 of the A2E+(u = 0) state (from Wilson et al., 1984).

As already stated, the "velocity" operator (p = —/ftV) expresses the EDA to the interaction operator V (f) (Eq. 16), while the "length" operator ( ) expresses the EDA to the interaction operator V ° (f) (Eq. 19). These two operators are directly connected via the Heisenberg equations of motion and so is related a third form, the "acceleration" operator, which, for Coulomb interactions, is /r . These expressions are expected to give the same answers when exact wavefunctions and an exact treatment in terms of complefe sefs are carried out. On the other hand, when approximations are made, as is necessary when dealing with real systems with many electrons, the issue arises as to which expression is more appropriate. This holds even for the calculation of the formulae representing the rates for the on-resonance one-photon transitions [107]. 

The line center does not give exactly the 2S-8D energy because of the small light shifts due to the non-resonant one-photon irradiation 1381. For each transition, the center frequency has to be extrapolated at null light power to eliminate these systematic shifts, whose the maximum value is 0.30 MHz. 

These equations assume that the optical field is strong and can be treated classically, a perturbative interaction with the sample that begins and ends with the vibrational ground state, and that there are no levels directly resonant with any of the individual frequencies in the pulse (resonant one-photon interactions do not occur). Near-infrared light (800-1400 nm), which is only weakly absorbed by biological tissues, contains frequencies typically well above the vibrational frequencies of molecular bonds, but below the electronic excitation frequencies, and so is suitable for NIVI. These equations give the time evolution of a CARS/CSRS process involving many possible simultaneous Raman-active... 

The Goeppert-Mayer two- (or multi-) photon absorption, mechanism (ii), may look similar, but it involves intennediate levels far from resonance with one-photon absorption. A third, quasi-resonant stepwise mechanism (iii), proceeds via smgle- photon excitation steps involvmg near-resonant intennediate levels. Finally, in mechanism (iv), there is the stepwise multiphoton absorption of incoherent radiation from themial light sources or broad-band statistical multimode lasers. In principle, all of these processes and their combinations play a role in the multiphoton excitation of atoms and molecules, but one can broadly... 

In contrast to the ionization of C q after vibrational excitation, typical multiphoton ionization proceeds via the excitation of higher electronic levels. In principle, multiphoton ionization can either be used to generate ions and to study their reactions, or as a sensitive detection technique for atoms, molecules, and radicals in reaction kinetics. The second application is more common. In most cases of excitation with visible or UV laser radiation, a few photons are enough to reach or exceed the ionization limit. A particularly important teclmique is resonantly enlianced multiphoton ionization (REMPI), which exploits the resonance of monocluomatic laser radiation with one or several intennediate levels (in one-photon or in multiphoton processes). The mechanisms are distinguished according to the number of photons leading to the resonant intennediate levels and to tire final level, as illustrated in figure B2.5.16. Several lasers of different frequencies may be combined. 

Figure 9.50 Processes involved in obtaining (a) an ultraviolet photoelectron spectrum, (b) a zero kinetic energy photoelectron (ZEKE-PE) spectrum by a one-photon process and (c) a ZEKE-PE spectrum by a two-photon process in which the first photon is resonant with an excited electronic state of the molecule...

More commonly, the resonant two-photon process in Figure 9.50(c) is employed. This necessitates the use of two lasers, one at a fixed wavenumber Vj and the other at a wavenumber V2 which is tunable. The first photon takes the molecule, which, again, is usually in a supersonic jet, to the zero-point vibrational level of an excited electronic state M. The wavenumber of the second photon is tuned across the M to band system while, in principle, the photoelectrons with zero kinetic energy are detected. In practice, however, this technique cannot easily distinguish between electrons which have zero kinetic energy (zero velocity) and those having almost zero kinetic energy, say about 0.1 meV... 

Shoute, L. C. T, Bartholomew, G. P., Bazan, G. C. and Kelley, A. M. (2005) Resonance hyper-Raman excitation profiles of a donor-acceptor substituted distyrylbenzene one-photon and two-photon states./. Chem. Phys., 122,184508. 

The fourth-order coherent Raman spectrum of a liquid surface was observed by Fujiyoshi et al. [28]. The same authors later reported a spectrum with an improved signal-to-noise ratio and different angle of incidence [27]. A water solution of oxazine 170 dye was placed in air and irradiated with light pulses. The SH generation at the oxazine solution was extensively studied by Steinhurst and Owrutsky [24]. The pump and probe wavelength was tuned at 630 nm to be resonant with the one-photon electronic transition of the dye. The probability of the Raman transition to generate the vibrational coherence is enhanced by the resonance. The efficiency of SH generation is also enhanced. 

On the other hand, we cannot ignore drawbacks in observing fourth-order responses. The desired response is always weak due to the high optical order. The damage threshold of the interface to be analyzed is severe with intense irradiation. The difficulty has been overridden by one-photon resonant enhancement of Raman-pump efficiency. The observable range of materials is somewhat limited as a result. There is still much room for technical improvements and the author is optimistic for the future. 

Figure 8. Phase lag spectrum of HI in the vicinity of the 5d(n, 8) resonance. In panel (a), the circles show the phase lag between the ionization and dissociation channels. The diamonds and triangles separate the phase lag into contributions from each channel, using H2S ionization as a reference. Panels (b) and (c) show the conventional one-photon (m3) and three-photon (3a>i) photoionization spectra. (Reproduced with permission from Ref. 45, Copyright 2002 American Institute of Physics.)...

Figure 9. Phase lag spectrum of HI and DI in the vicinity of the 5sa resonance. The top panel shows the phase lag between photoionization and photodissociation of HI (filled circles) and DI (open circles), the phase lag between the photoionization of HI and DI (squares), and the phase lag between the photoionization of HI and H2S (triangles). The bottom two panels show the one-photon ionization spectra of HI and H2S. (Reproduced with permission from Ref. 30, Copyright 1999 American Physical Society.)...

Fig. 1 (Left) Schematic of frequency degenerate 2PA (1) into the first allowed singlet state, (2) above the first allowed singlet state, and (3) a double resonant condition, with a small intermediate state resonance energy difference, A, and a transition into an allowed final 2PA state. (Right) Photograph illustrating the much sharper contrast of two-photon (b) versus one-photon excitation (a) (taken from [2])...

In order to extend the range of 2laser excitation, both CARS (Coherent Anti-Stokes Raman Scattering) and CSRS (Coherent Stokes Raman Scattering) are used. In both cases <03 = 2003 -U2 In the CARS mode 0)3 > wj > (03 in the CSRS mode <02 > (1)3. One-photon resonance effects are the same in both cases as described later. Phase matching is also the same in both cases with 3 = 2 ... 

The two-photon state as determined by the fit to the yellow-solution data has =30 500 cm l. The effect of the one-photon resonance enhancement on yt can be seen if we consider the form of the solid curves in Fig. 9 under conditions that no one-photon resonance is present. In this case, y t would be a dispersive type curve with inversion symmetry around the y t O point at 30 500 cm-l and y"t would be an absorptive like curve centered at 30 500 cm l. The large increase in the magnitudes of y t an Y t on the high-energy side of the spectrum is therefore attributed to one-photon resonance. The peak expected for y"t at 30 500 cm l is barely discernible as a broad shoulder, since it is almost completely obscured by the one-photon resonance. 

The simplest version of REMPI uses a two photon (1-1-1) process, namely resonant two photon ionization (R2PI). In this, the species M is first promoted from its electronic ground state So to the electronic excited state Si via a resonant absorption step. Then, the non-resonant absorption of a second photon takes the species into the ionization continuum. If the frequencies of the excitation and ionization photons are equal, the process is named one color R2PI (lcR2PI), otherwise two colors R2PI (2cR2PI) (Fig. 1). 

One-color resonant two photon ionization (lcR2PI) spectroscopy... 

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