Photon-absorption probability

The concentration of liberated iodine, as measured by its absorbance at 5000 A, is proportionalato the two-photon absorption probability, since no reactants have absorption bands at the single... 

The other probabilities of photon emissions or absorptions are negligible. During the process, we remark that small transient 001 and 002 photon absorption probabilities arise. An early 002 photon absorption is observed, coinciding exactly with the (negative) shift of the transfer eigenvector. The first effects of the ( 2 pulse are indeed to (i) split the unpopulated dressed states connected to 2) and 3) and (ii) produce a Stark shift of the dressed state connected to 1) (the early part of the transfer state), which is equivalent to a partial absorption of a 002 photon. Symmetrically, a late 001 photon absorption occurs. It is due to a (positive) Stark shift of the dressed state connected to 3) (the late part of the transfer state). Arising near the end of the process, for which one 001 photon has already been absorbed, it leads to a partial absorption of a second 001 photon. At the end of the process the complete population transfer from state 1) to state 3) is accompanied by the loss of a 001 photon and the gain of a 002 photon. Thus the final result is not different from the semiclassical result. 

We therefore obtain from (2.66) for the two-photon absorption probability... 

It is remarkable that the transitions 4s S -> 4p S and 4s S Ap D of the Ca atom do not represent allowed dipole transitions and are therefore forbidden for the isolated atom. Regarding the photon-absorption probability, the absorption by a collision pair with subsequent energy transfer to the atom is therefore called collision-induced absorption or collision-aided radiative excitation [1093], where a dipole-allowed transition of the molecular collision pair A B or AB takes place. 

The excimer XeBr(B,Q fluorescence was obtained by optical-optical double excitation of the complex Xe-Br2 (excitation of the B state of Br2 by the first harmonic of the laser and followed by the excitation of the valence state by the second harmonic [12]). The action spectrum, excitation of the complex and observation of the XeBr(B->X) fluorescence, is structureless and starts at the energetical threshold. The fluorescence spectrum ob ned with an excess of energy of 3800 cm is characteristic of a cold XeBr(B,Q, and presents a small emission assigned to the Br2(D - A0 transition. As the reaction occurs at the energetical threshold, then no barrier to the reaction was found. However, when the Rydberg states of the Br2 are excited no fluorescence is observed (direa two UV photon absorption). Probably... 

Photon absorption probability per unit time charge carrier scattering probability per unit time Cadmium molar fraction in Hgi- Cd Te x-coordinate... 

In 1931 in her doctoral dissertation supervised by Max Bom, Maria Goppert-Mayer proposed the concept of the simultaneous absorption of two photons by a molecular system in one elementary action,(English translation Ref ). This prediction was based on the principles of the quantmn theory of radiation " as well as the concept of the intermediate energy level. Based on the formalism of summation over all eigenstates of the system, Maria Goppert-Mayer derived an expression for the two-photon absorption probability which, however, occurred to be too low to be experimentally observed in the incoherent light excitation regime. Hence, the unquestionable experimental confirmation took over thirty years. ... 

If this expression is then multiplied by the equilibrium probability pi that the moleeule is found in the state i and summed over all sueh initial states and summed over all final states f that ean be reaehed from i with photons of energy h co, the equilibrium averaged rate of photon absorption by the moleeular sample is obtained ... 

If cof i is positive (i.e., in the photon absorption ease), the above expression will yield a non-zero eontribution when multiplied by exp(-i cot) and integrated over positive covalues. If cOf j is negative (as for stimulated photon emission), this expression will eontribute, again when multiplied by exp(-i cot), for negative co-values. In the latter situation, pi is the equilibrium probability of finding the moleeule in the (exeited) state from whieh emission will oeeur this probability ean be related to that of the lower state pf by... 

That is, the semi-classical approximation to the photon absorption rate is equivalent to a Landau-Zener treatment of the probability of hopping from Vj -i-hco to Vf induced by the electronic coupling perturbation p, f (s,0,Q). 

At heart, this greater intensity may be explained as follows. The ease with which an electron may be photo-excited depends on the probability of successful excitation, which itself depends on the likelihood of photon absorption. If the probability of excitation in the woad was 20 per cent, then 20 from every 100 incident photons are absorbed (assuming each absorption results in a successful electron excitation). By contrast, cobalt blue is more intense because it has a higher probability of photon uptake, so fewer photons remain to be seen, and the absorbance increases. 

The probability of two-photon absorption depends on both spatial and temporal overlap of the incident photons (the photons must arrive within 10 18 s). The cross-sections for two-photon absorption are small, typically 10 so cm4 s photon-1 molecule 1 for rhodamine B. Consequently, only fluorophores located in a region of very large photon flux can be excited. Mode-locked, high-peak power lasers like titanium-sapphire lasers can provide enough intensity for two-photon excitation in microscopy. 

Because the excitation intensity varies as the square of the distance from the focal plane, the probability of two-photon absorption outside the focal region falls off with the fourth power of the distance along the z optical axis. Excitation of fluorophores can occur only at the point of focus. Using an objective with a numerical aperture of 1.25 and an excitation beam at 780 nm, over 80% of total fluorescence intensity is confined to within 1 pm of the focal plane. The excitation volume is of the order of 0.1-1 femtoliter. Compared to conventional fluorometers, this represents a reduction by a factor of 1010 of the excitation volume. 

Two-photon absorption occurs when the energy of a molecular transition matches the combined energy of two photons. Quantum mechanically, the absorption probability is proportional to the two-photon transition moment from the ground state, g, to the excited state, n, via intermediate state, m, and can be expressed as follows (Boyd 1992 Abe 2001) ... 

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