Optical cross section excited states

Fig. 21.5 Plots of (a) the spectral density, (b) the square of the overlap integral between initial and final states, and (c) their product which is proportional to the optical cross section a. All are calculated for the third laser excitation from the 6sl5d (q, = 12.35) state to the (6p3/2nd)j = 3 channel (from ref. 6).

We have previously pointed out that, under the appropriate conditions, the sigmoidally shaped fluorescence induction curves should also be observed when the PS II reaction centers are partially closed by short, pulsed light flashes and when the fluorescence yield is measured with a weak probe light flash delivered at some time 6t (30 - 100 ps) after the variable - intensity pump flash (3). This follows from the assumption that under either steady-state or flash-excitation conditions, the fraction of closed reaction centers q should depend simply on the number of photons absorbed by PS II In both cases. However, using pump flashes of less than 1 /is in duration, the fluorescence induction curves measured by the pump-probe technique have been shown to be exponential in shape [3.4]. Similar obsenrations have been made by Mauzerall and his co-workers [5.6] who concluded that the probability of escape of an exciton from a PS II unit with a closed reaction center to a unit with an open one. is less than 0.25 and that the apparent optical cross-section of PS II with open and closed traps is constant to within + 10 % [7]. The exponentiaiity of the pump-probe fluorescence Induction curves implies that the variable fluorescence Fy = (F[l ] - Fo)/(Fmax " Fq) is proportional to q under these conditions, where 1 represents the fiuence of the pump flash expressed in units of incident photons/cm. ... 

Optical resonance excitation fi-om the atomic ground state up to final ionization can follow a number of different pathways (O Fig. 54.7). Typical ionization potential is 6 eV for all the alkaline earths, rare earths, and actinides. Due to the high optical cross section (cr = l2n) of the order of 10 cm, all resonant optical excitation steps between bound atomic states (typical excited state hfetime of 10 s) can be saturated with continuous-wave as well as pulsed laser systems. Nomesonant ionization into the continuum has a relatively low cross section in the range of cm and is thus difficult to saturate with continuous-wave lasers. 

The dendritic effect evidenced for 1-8 might be useful to optimize the optical hmiting properties characteristic of fullerene derivatives. Effectively, the intensity dependant absorption of fuUerenes originates from larger absorption cross sections of excited states compared to that of the ground state [32], therefore the... 

In conclusion, we stress that the complementary NLO characterization techniques of pump-probe, Z-scan, and 2PF allow for the unambiguous determination of nonlinear optical processes in organic materials. The important molecular parameters of 2PA cross section, fluorescence efficiency, reorientation lifetimes, excited state cross sections, etc. can be determined. 

The discussion in this chapter is limited to cyanine-like NIR conjugated molecules, and further, is limited to discussing their two-photon absorption spectra with little emphasis on their excited state absorption properties. In principle, if the quantum mechanical states are known, the ultrafast nonlinear refraction may also be determined, but that is outside the scope of this chapter. The extent to which the results discussed here can be transferred to describe the nonlinear optical properties of other classes of molecules is debatable, but there are certain results that are clear. Designing molecules with large transition dipole moments that take advantage of intermediate state resonance and double resonance enhancements are definitely important approaches to obtain large two-photon absorption cross sections. 

Let N(j,Ni,N2, and Nj, be the equilibrium population densities of the states 0, 1,2, and 3, respectively (reached under continuous wave excitation intensity Iq), and let N = NQ + Ni+N2 + N3he the total density of optical absorbing centers. The up-converted luminescence intensity ho (corresponding to the transition 2 0) depends on both N2 and on the radiative emission probability of level 2, A2. This magnitude, which is dehned below, is proportional to the cross section a20 (called the emission cross section and equal to the absorption cross section ao2, as shown in Chapter 5). Thus we can write... 

Fig. 10 shows the relation between the experimental values ctm and the theoretical predictions cross sections previously reported for the de-excitation of He(3 P) [146,147]. The difference between the values for He(2 P) and He(3 P) is explained by the difference in the optical oscillator strengths for the two states. The experimental values can generally be explained by ct-wk based on the long-range... 

It must be emphasized that these cross sections are only valid for an electron excitation into free-electron like final states (conduction band states with parabolic band shape) and not for resonance transitions as f — d or p - d excitations. If too low excitation energies (< 10 eV, see Table 1) are used in UPS, the final states are not free-electron like. Thus the photoemission process is not simply determined by cross-sections as discussed above but by cross-sections for optical transitions as well as a joint density of states, i.e. a combination of occupied initial and empty final states. 

The simplest description of compoimds of this type is obtained limiting the siun-over-state equations to terms depending only on the properties of the groimd state g and the first excited state e (two-state model) [93]. This is analogous to the two-level model introduced to describe other nonlinear optical properties, for example the nonlinear polarizability pS - co coi,co2) [ 104]. In the case of 2PA, this two-state, or dipolar, contribution to the cross section is, on resonance ... 

For a molecule in the excited, state, direct contact between two interacting partners may not be necessary and effective cross-section for optical... 

For a molecule in the excited state, the effective cross-section for coil os can be much greater than those for kinetic collision. The optical collisions nay be defined as the minimum distance of approach over which the excited mole-cule can interact with another molecule to bring about a physical or chemical change. 

In the experiment, the transmission intensities for the excited and the dark sample are determined by the number of x-ray photons (/t) recorded on the detector behind the sample, and we typically accumulate for several pump-probe shots. In the absence of external noise sources the accuracy of such a measurement is governed by the shot noise distribution, which is given by Poisson statistics of the transmitted pulse intensity. Indeed, we have demonstrated that we can suppress the majority of electronic noise in experiment, which validates this rather idealistic treatment [13,14]. Applying the error propagation formula to eq. (1) then delivers the experimental noise of the measurement, and we can thus calculate the signal-to-noise ratio S/N as a function of the input parameters. Most important is hereby the sample concentration nsam at the chosen sample thickness d. Via the occasionally very different absorption cross sections in the optical (pump) and the x-ray (probe) domains it will determine the fraction of excited state species as a function of laser fluence. 

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