Multiphoton resonance

Surface Analysis by Laser Ionization Post-Ionization Secondary Ion Mass Spectrometry Multi-Photon Nonresonant Post Ionization Multiphoton Resonant Post Ionization Resonant Post Ionization Multi-Photon Ionization Single-Photon Ionization... 

Measurements made by DFWM on Group 10 metal bis(acetylide) complexes are listed in Table VIII. Although results cannot be directly compared to those cited earlier, internal comparisons within the series are valid. These reveal that hyperpolarizability decreases progressing down the group for phenylacetylide examples (as observed with other acetylide complexes see earlier), but that larger nonlinearities are observed for butadiynide complexes of the heavier metals. The complexes exhibit a high-order intensity dependence, characteristic of multiphoton resonant enhancement for these complexes this is possibly due to three-photon resonant enhancement, as Amax is, in all cases, close to 3o>. 

Fig. 10.10 Multiphoton resonant transition at an avoided crossing from the photon and field points of view. The solid curves are the avoiding levels and the dashed lines are the levels which cross when the coupling is ignored. The static field Es gives rise to a six photon resonant transition, indicated by the stacked arrows. The range of the electric field variation is shown for the case in which the peak field + mw exactly reaches the crossing...

Having considered the connection between the multiphoton resonances and the microwave threshold field for the K (n + 2)s —> (n,k) transitions, it is now interesting to return to the analogous n — n + 1 transitions which are responsible for microwave ionization and consider them from this point of view. We start with a two level description based on the extreme n and n + 1 m = 0 Stark states, a description which is the multiphoton resonance counterpart to the single cycle Landau-Zener model presented earlier. The problem is identical to the problem... 

Due to the n(n + 1) possible n— n + 1 transitions it is in general difficult to observe resonance effects in microwave ionization as obvious as those shown in Fig. 10.9. Nonetheless several experiments show clearly the importance of multiphoton resonance in microwave ionization. In Ba and in He the observed microwave ionization thresholds are structured by resonances3,6. An excellent example is the microwave ionization probability of the He 28 3S state shown in Fig. 10.14. In He the 3S states intersect the Stark manifold at fields approaching l/3n5, and as a result making transitions from the energetically isolated 3S state requires a field comparable to the field required to drive n — n + 1 transition. The structure in Fig. 10.14 is quite similar to the structure in Fig. 10.8, which is not... 

In alkali atom experiments no explicit resonances have been observed in microwave ionization. However, there are indirect confirmations of the multiphoton resonance picture. First, according to the multiphoton picture the sidebands of the extreme n and n + 1 Stark levels should overlap if E = 1/3n5. In the laser excitation spectrum of Na Rydberg states from the 3p3/2 state in the presence of a 15 GHz microwave field van Linden van den Heuvell et al. observed sidebands spaced by 15.4 GHz, as shown in Fig. 10.15.18 The extent of the sidebands increases linearly with the microwave field, as shown in Fig. 10.15, and the n = 25 and n = 26 sidebands overlap at microwave fields of 150 V/cm or higher, matching the observation that the 25d state has an ionization threshold of 150 V/cm in a 15 GHz field. 

The ionization curve of Fig. 10.18 is obtained in the same way as the data shown in Fig. 10.14, by exciting atoms in zero field and then exposing them to a strong microwave field. When atoms are excited in the presence of a static field, to a single Stark state, and held in single Stark state by the continued application of the field, resonances became more apparent when a microwave field in the same direction is applied. Bayfield and Pinnaduwage have observed transitions from the extreme red H n = 60, m = 0 Stark state to other nearby extreme Stark states in static fields of 5-10 V/cm.29 As shown by Fig. 10.19 resonances corresponding to the four photon transition to the extreme red n = 61 Stark state and four and five photon transitions to the extreme red n = 59 Stark state are visible. These experiments are similar to the K and He multiphoton resonance experiments described earlier, but are inherently simpler because the extreme red n = 60 Stark state is only coupled to the extreme n = 59 Stark state. In contrast, the K (n + 2)s state is coupled to all the (n,k) Stark states. 

The interaction of keV particles with solids has been characterized by the measurement of the angle and energy distribution of sputtered secondary ions and neutrals. The results are compared to classical dynamics calculations of the ion impact event. Examples using secondary ions are given for clean Ni 001), Cu 001) reacted with 0>, Ni 001 and Ni 7 9 11 reacted with CO, and Agllll) reacted with benzene. The neutral Rh atoms desorbed from Rh 001 are characterized by multiphoton resonance ionizaton of these atoms after they have left the surface. 

Two mechanisms have been proposed to account for the formation of protonated ammonia clusters under multiphoton resonant ionization conditions. They are absorption-ionization-dissociation (AID) (Echt et al. 1984, 1985 Shinohara and Nishi 1987 Tomoda 1986) and absorption-dissociation-ionization (ADI) (Cao... 

Multiphoton resonant processes with simplest fundamental quantum systems exposed to sufficiently strong laser fields attracted conspicuous attention over last years. Currently, this interest is being especially strongly stimulated by dramatic improvements in the precision of measurements presently attainable in spectroscopic experimental studies of hydrogenic and few-particle atoms. Using methods of ultra high precision Doppler-free spectroscopy, particularly impressive results have been recently obtained in studies of fundamental bounded systems such as hydrogen (H) and its natural isotopes deuterium (D) and tritium (T) [1,2,3,4,5,6,7], positronium [8,9], denoted Ps = (e+ — e ), muonium [10,11,9,12,13,14,15], denoted (M = — e ), and the helium atom (He) [16[... 

When the static field brought the two states into multiphoton resonance a sharp increase in the detected signal was observed, as shown in Fig. 7, which is a sequence of field scans showing the K 18s - (16, transitions with different microwave field amplitudes. In Fig. 7 the sequence of N photon 18s - (16,3) transitions, separated by 28 V/cm is quite apparent. At higher microwave fields transitions to other (16, fe) states are also present, cluttering the spectrum. From the data of Fig. 7 it is evident that the highest number of photons, N, which can be absorbed increases with the microwave field. In fact, it increases approximately linearly with the microwave field, and a linear fit of N to the microwave field yields... 

The zero-field resonances can be identified with respect to the system energy levels and the field frequency when the field is off. They are usually one- or two-photon resonances. The one-photon resonance is of first order with respect to the field amplitude in the sense that the degeneracy of the eigenvalues is lifted linearly with the field amplitude. The two-photon resonance is of second order since the degeneracy of the eigenvalues is lifted quadratically with the field amplitude. Multiphoton resonances (more than two-photon) are more complicated since they are generally accompanied by dynamical shifts of second order... 

For very small field amplitudes, the multiphoton resonances can be treated by time-dependent perturbation theory combined with the rotating wave approximation (RWA) [10]. In a strong field, all types of resonances can be treated by the concept of the rotating wave transformation, combined with an additional stationary perturbation theory (such as the KAM techniques explained above). It will allow us to construct an effective Hamiltonian in a subspace spanned by the resonant dressed states, degenerate at zero field. 

First we identify a set of atomic (or molecular) essential states, connected with the initial condition, whose population will be appreciable during the dynamics. This means that these states are in multiphoton resonance (or quasi-resonance). This allows us to split the Hilbert space into two orthogonal subspaces = and thus the enlarged Hilbert... 

P. N. Prasad and G. S. He, Multiphoton Resonant Nonlinear Optical Processes in Organic Molecules. In Nonlinear Optical Materials. Theory and Modeling, Vol. 628, S. P. Kama and A. T. Yeates, Eds., American Chemical Society, Washington, DC, 1995, p. 225. 

G. Grynberg, B. Cagnbac, F. Biraben, Multiphoton resonant processes in atoms, in Coherent Nonlinear Optics, ed. by M.S. Feld, V.S. Letokhov. Topics Curt Rhys., vol. 21 (Springer, Berlin, 1980)... 

Figure 5.4 Charged particle detection methods multiphoton resonances in photon-particle interaction processes, here exemplified for a (2 -I- 1)-REMPI process...

Therefore, a nonresonant third-order process can be overcome by a resonantly enhanced higher order process. Strong two-photon excitation or absorption saturation at 2ct), would generate strong fifth or higher order nonlinearities. Therefore, a careful characterization of a nonlinear optical response necessitates the investigation of the possible roles of higher order nonlinearities enhanced by multiphoton resonances or saturation processes. 

In the preceding discussion the effect of nonlinear absorption was neglected. However, in materials with large nonlinear refractive responses it is not uncommon to find an absorption component due to the presence of a single or multiphoton resonance, saturation of the single-photon absorption, or free carrier dynamic absorption. All of these can have a strong effect on the Z-scan profile. If we consider only the effects of two-photon absorption (TPA) the third-order nonlinear susceptibility can be considered complex, represented by a real and an imaginary part as follows ... 

Resonant Nonlinear Phenomena. The susceptibility tensors x and X may be complex, indicating the presence of multiphoton resonances and nonlinear absorption effects. The effects of nonlinear absorption are of significant interest in polymer device applications and are typically expressed in a power series in the incident intensity with the transmitted intensity 7i given by (44)... 

Reports of photodegradation in Raman spectroscopy are indeed numerous. In many cases, however, these are due to multiphoton resonances at high intensities in Optical tweezers or CARS experiments. In a study of photodegradation in Raman spectroscopy of living cells and chromosomes Puppels reported that... 

Fig. 10.5 Schemes for resonance molecular photoionization via high-lying vibrational states by way of multiphoton resonance vibrational excitation with IR laser radiation (a) multiphoton IR + VUV excitation, (b) IR multiphoton excitation, and (c) IR multistep + VUV excitation.

Our goal is to model quantitatively 7r-electronic contributions to both vibrational and electronic spectra. The general e-ph analysis introduced in Section II combines the microscopic AM formalism [18,19] with the spectroscopic ECC model [22]. The reference force field F for PA provides an experimental identiHcation of delocalization effects. Transferable e-ph coupling constants are presented in Section III for polyenes and isotopes of trans- and a s-PA. The polymer force field in internal coordinates directly shows greater delocalization in t-PA, while coupling to C—C—C bends illustrates V(/ ) participation and different coupling constants a(/ a) and a(Jis) in Eq. (3) support an exponential r(/ ). NLO spectra of PDA crystals and films are presented in Section IV, with multiphoton resonances related to excited states of PPP models and vibronic contributions included in the Condon approximation. Linear and electroabsorption (EA) spectra of PDA crystals provide an experimental separation of vibrational and electronic contributions, and the full tt-tt spectrum is needed to model EA. We turn in Section V to correlated descriptions of electronic excitations, with particular attention to theoretical and experimental evidence for one- and two-photon thresholds of centrosymmetric backbones. The final section comments on parameters for conjugated polymers, extensions, and open questions. 

Cubic NLO data for selected group 10 metal bis(alkynyl) complexes are listed in Table XVII. Hyperpolarizability decreases progressing down the group for phe-nylalkynyl examples, the same observation as with group 4 metal alkynyl complexes (see above). For these complexes is, in all cases, close to 3co, and a high-order intensity dependence was observed this is characteristic of multiphoton resonant enhancement, so it is possible that three-photon effects exist. 

In the technique of multiphoton-ionization spectroscopy, two or more photons excite atoms or molecules from the ground state to an excited state which may be ionized by several methods (see Sect.8.2.5), e.g., field ionization, photoionization, collisional, or surface ionization. If the laser is tuned to multiphoton resonances, ionization signals are obtained if the upper level is ionized which can be, for instance, monitored with the setup shown in Fig.8.42. The ionization probe is a thin wire inserted into a pipe containing the atomic vapor. If the probe is negatively biased relative to the walls of the pipe, thermionic emission will lead to space-charge-limited current. Ions produced by the laser excitation partly neutralize the space charge, thereby allowing an increased electron current to flow (see Sect.8.2.4). 

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