Resonance two-photon

Figure Bl.5.3 Magnitude of the second-order nonlinear susceptibility x versus frequency co, obtained from the anliannonic oscillator model, in the vicinity of the single- and two-photon resonances at frequencies cOq and coq 2> respectively.

The SHG/SFG technique is not restricted to interface spectroscopy of the delocalized electronic states of solids. It is also a powerful tool for spectroscopy of electronic transitions in molecules. Figure Bl.5.13 presents such an example for a monolayer of the R-enantiomer of the molecule 2,2 -dihydroxyl-l,l -binaphthyl, (R)-BN, at the air/water interface [ ]. The spectra reveal two-photon resonance features near wavelengths of 332 and 340 mu that are assigned to the two lowest exciton-split transitions in the naphtli-2-ol... 

Brueck S. R. J. Vibrational two-photon resonance linewidth in liquid media, Chem. Phys. Lett. 50, 516-20 (1977). 

Experiments on the sky. Two experiments have been carried out at the sky, using two laser installations built for the American and French programmes for Uranium isotope separation, respectively AVLIS at the Lawrence Livermore Nat l Lab (California) in 1996 and SILVA at CEA/Pierrelatte (Southern France) in 1999. The average power was high pa 2 x 175 W, with a pulse repetition rate of 12.9 and 4.3 kHz, a pulse width of 40 ns and a spectral width of 1 and 3 GHz. Polarization was linear. The return flux was < 5 10 photons/m /s (Foy et al., 2000). Thus incoherent two-photon resonant absorption works, with a behavior consistent with models. But we do need lower powers at observatories ... 

The first two terms in (5) are called D-terms or dipolar terms, which are nonzero only if Ape =/= 0. The two-photon resonance denominator, ( leg — 2hco), indicates that an electron is excited into the lower excited state e. If we consider a near resonance condition hco = %imaginary part of the D-terms can be written in SI units as ... 

Ref. 31 Xs=0 87 x 10- esu for CHCI3 and Xs=l 06 x 10 esu for hexane. There are no two-photon resonances in the solvents in the frequency range of interest here (31). The resulting values of Y t and y"t> with 90% confidence limits expressed as error bars, are shown in Fig. 9. Each data pair is determined from the... 

When the surface was covered with trimethyl acetate (TMA), which has no resonance with the pump and probe wavelengths, no molecular vibration was observed. When adsorbates were replaced by p-nitrobenzoate (pNB), which has two-photon resonance, the SH intensity showed a modulation at a fifth frequency assigned as a molecular vibration [76]. The study thus provided a first successful application of TRSHG to organic adsorbates. 

At a fundamental wavelength of 1064 nm, large and anisotropic optical nonlinearity was also observed. The values of X (3) and are 4.5 x 1010 esu and 1.0 x 10 10 esu, respectively. The large values are due to the two photon resonance, because the harmonic wavelength of 355 nm is near off-resonance region. From the two-photon fluorescence measurement, we confirmed that a two-photon absorption band, which is origin of the enhancement effect, exist around 532 nm, half of the fundamental wavelength. 

The spectral line shape in CARS spectroscopy is described by Equation (6.14). In order to investigate an unknown sample, one needs to extract the imaginary part of to be able to compare it with the known spontaneous Raman spectrum. To do so, one has to determine the phase of the resonant contribution with respect to the nonreso-nant one. This is a well-known problem of phase retrieval, which has been discussed in detail elsewhere (Lucarini et al. 2005). The basic idea is to use the whole CARS spectrum and the fact that the nonresonant background is approximately constant. The latter assumption is justihed if there are no two-photon resonances in the molecular system (Akhmanov and Koroteev 1981). There are several approaches to retrieve the unknown phase (Lucarini et al. 2005), but the majority of those techniques are based on an iterative procedure, which often converges only for simple spectra and negligible noise. When dealing with real experimental data, such iterative procedures often fail to reproduce the spectroscopic data obtained by some other means. 

Figure 6.9 Generic five-state system for ultrafast efficient switching. The resonant two-state system of Figure 6.6 is extended by three target states for selective excitation. While the intermediate target state 4) is in exact two-photon resonance with the laser pulse, both outer target states 3) and 5) lie well outside the bandwidth of the two-photon spectrum. Therefore, these states are energetically inaccessible under weak-field excitation. Intense femtosecond laser pulses, however, utilize the resonant AC Stark effect to modify the energy landscape. As a result, new excitation pathways open up, enabling efficient population transfer to the outer target states as well.

The third line describes oscillation of a wave packet in an anharmonic potential (phase term omitted). Eq. (1) would be valid also in the presence of an intermediate resonance. In Eq. (2), the Apl dependence is only in the Plon terms. The fundamental arises from the sin terms (hence from dPion/dx) and the overtone from the sin2 terms. A phase jump of the fundamental is expected at a Tpr where dPlnn/dx and hence dPloir/dIE change sign. From these derivatives (proportional to the fundamental amplitude in Fig. 3) we can infer that Ploa has a maximum at 680 nm and a minimum near 405 nm. The maximum could reflect either an intermediate resonance or a two-photon resonance with an autoionizing state. The minimum is likely to announce a further rise of PIon at shorter Apr due to the lower order of ionization. 

The intensity dependence of molecular chromophore ion R+ yield for the femtosecond MPI of the tryptophan is shown in Fig. 3. Two-photon resonance-enhanced MPI requires an absorption of the five visible (620-nm) photons. 

Figure 3. Intensity dependence of chromophore molecular ion R+ yield for two-photon resonance-enhanced MPI of tryptophan.

Fig. 9.7 Fourier transforms of two photon, resonant, excitation spectra of the H atom Balmer series around the ionization limit in a magnetic field of strength B = 6 T, excited through individually selected magnetic substates m = 0 and m = +1 of the n = 2 state to final m states of even parity, (a) m = 0, (b) m = +1 (c) m = +2, plus some admixture ( 25%) of m = 0. The resolution is =0.3 cm-1 (from ref. 22).

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. 

In consequence, any dominating two-photon resonance has to be avoided to maintain a small phase of the third-order susceptibility yf3). 

The second-order hyperpolarizabilities in oligothiophenes measured by THG showed an exponent a=2.8 [78]. DFWM and EFISH data revealed an exponent a= 4.05 [79] and a=4.6 [80],respectively, for these oligomers. These larger exponents, however, can be explained by a two-photon resonance enhancement in the DFWM and EFISH experiments. 

For any application, resonant contributions to the second-order hyperpolarizability have to be strongly avoided. It is possible to retrieve huge values in the two-photon resonances but they are useless if all-optical signal processing applications are in mind. 

The side-chain polymers DANS and DAN2 exhibit two-photon figures of merit T 1 below unity at 1064 nm as the nonlinearity is still in a two-photon resonance. At 1319 nm the two-photon resonance is left for DANS and the figures of merit are fulfilled. A nonlinear phase shift of 0wf=O.57rin a 1.65 cm longMach-Zehnder interferometer was demonstrated [96]. 

Here, as noted above, E/) denotes Ei Jh M,) and the j summation indicates a sum overall bound states )) of the ground A 1 Er potential surface. Computationally, of all the bound eigenstates of X Xq, the contribution to (E, n, q T Et) is dominated by those states with energy E, that nearly satisfy the two-photon resonance condition Ej E, + 2fe ,. 

Stokes pulse (labeled S), is in near resonance with the transition from [Eq) to E2). In most applications one chooses the two frequencies to fulfill the two-photon resonance condition,... 

The discovery of the 25 — 2P Lamb shift has led to the development of the theory of quantum electrodynamics. Today, radio frequency measurements of this splitting have reached the uncertainty limits imposed by the 100 MHz natural linewidth of the 2P state. The considerably sharper optical two-photon resonances used in optical experiments leave significant room for future improvements. 

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