Photon density

Figure Bl.18.14. Schematic representation of the increase of absorption with photon density for two- and tliree-photon absorption.

One-photon excitation has lunitations due to the unwanted out-of-focus fliiorophore absorption and bleaching, and light scattering. These drawbacks can be circumvented if multiphoton excitation of the fliiorophore is used. Since it increases with the nth power of the photon density, significant absorption of the exciting light will only occur at the focal point of the objective where the required high photon density for absorption is reached. Consequently, only... 

In the discussion in Section 9.1.6 of harmonic generation of laser radiation we have seen how the high photon density produced by focusing a laser beam into certain crystalline materials may result in doubling, tripling, etc., of the laser frequency. Similarly, if a laser beam of wavenumber Vl is focused into a cell containing a material which is known to absorb at a wavenumber 2vl in an ordinary one-photon process the laser radiation may be absorbed in a two-photon process provided it is allowed by the relevant selection rules. 

For an electrode with high interfacial rate constants, for example, relation (28) can be plotted, which yields the flatband potential. It allows determination of the constant C, from which the sensitivity factor S can be calculated when the diffusion constant D, the absorption coefficient a, the diffusion length L, and the incident photon density I0 (corrected for reflection) are known ... 

Some precautions will be needed for successful measurements. The shorter the time scale the higher the photon densities that will be required. This leads to very high generation of excess charge carriers and to nonlinear phenomena of a complicated nature. 

Here, L total is the depth of the etched hole per pulse and is assumed to be the sum of photochemical and photothermal contributions, Tphoto and Thermal, respectively 0Ceff is the effective photon absorption coefficient of the medium and can vary with laser emission characteristics, e g., photon density Fis the incident laser fluence Fth is the medium s threshold fluence A and F are the effective frequency factor with units of pm/pulse and the effective activation energy with units of J/cm2, respectively, for the zeroth-order thermal rate constant F0, comparable in magnitude to Fth, is important only at low fluences.64 Equation (5) is obtained after assuming that the polymer temperature T in the laser-exposed region of mass mp and the thermal rate constant k are given, respectively, as... 

As carried out above for the Lindemann mechanism, application of the steady-state approximation gives the apparent unimolecular rate constant in Equation (24) where [Av] represents the IR photon density. Again two limits may be considered. 

Again the radiative association kinetics described above allow a direct comparison for some realistic values of k and k. For most chemically activated systems at the threshold for unimolecular dissociation, the observed radiative rate constants are of the order of 10-100 s and hence are much below the values expected for k of about 10 s . Therefore, the first limit is most likely to be valid, with the interesting conclusion that the observed unimolecular dissociation rate constant will depend only on the photon density and the absorption cross section (rate constant) at a given wavelength. 

V cm- ) Toper (K) Photon density Sensitivity Response time Toper (K) ... 

Purcell has demonstrated theoretically that the photon density of states in a cavity having volume V and quahty factor Q increases on resonance in... 

Here n is the photon density [photons/cm3] and c is the velocity of light in the medium, so that nc is the intensity of the laser light expressed in photons/cm2 - sec. 

The above relationship between 0 and the rate constants is derived based on the conventional formulation of the rate equations. The unit to measure the amount of electrons and holes in the particle is density, the same as in bulk semiconductors. When the particle size is extremely small or the photon density is very low, only a few pairs of electron and hole are photogenerated and recombine with each other in the particle. This means that photon density does not take continuous values as suitably used in the conventional rate equations, but takes some series of values whose unit is the inverse of the particle volume. Taking into account this deviation, we proposed a new model in which particles are assigned by two integers, n and m, which represent the numbers of... 

Figure 7. Spectral response of polycrystalline, thin-film, painted CdSeo.esTe0.3.-, photoelectrode in 7M KOH, S", S solution. Corrected for photon density wavelength...

A trace which only accounts for CC and solvent states yields the reduced photon density operator... 

These systems suffer from photo-bleaching at relatively low photon densities. 

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