Induced emission probability

The kinetic energy of charge earners in a solid increases with increasing temperature and therefore the probability that a charge carrier passes a given potential barrier also increases. The thermally induced current flow of the charge earners from a metal contact into a polymer film can be derived from the Richardson equation, which describes the temperature-induced emission of hot charge carriers from a metal surface... 

The Einstein coefficients characterize the probability of transition of a molecule between two energy levels Ei and E2 (Scheme B3.2). Bu is the induced absorption coefficient (see Chapter 2), B21 is the induced emission coefficient and A21 is the spontaneous emission coefficient. The emission-induced process E2 —> Ei occurs at exactly the same rate as the absorption-induced process Ei —> E2, so that B12 = B 21. 

Equation (A3.7) shows the equality between the probabilities of absorption and stimulated emission that we have already established for monochromatic radiation in Equation (5.15). Equation (A3.8) gives the ratio of tlie spontaneous to the induced transition probability. It allows us to calculate the probability A of spontaneous emission once the Einstein B coefficient is known. 

The procedure is to extract by deconvolution from the measured emission probabilities the surface density of occupied states for energies between the Fermi level and about 10 eV below that, and to predict the relative atomic positions from that information about the electronic structure of the surface for example, adsorbate-induced peaks will occur, that depend on the adsorbate and its position, as in UPS. This technique is primarily sensitive to the outermost atoms of the surface, in particular adsorbates, since the emitted electrons originate from those regions only. The difficulties in deconvoluting and interpreting the density-of-states information have limited the use of INS. 

The use of lanthanides are common for optical purposes because of their narrow and sharp bands, and distinguishable long lifetimes, accomparied by low transition probabilities due to the forbidden nature of the transitions [10-13]. Thus chromophoric sensitization of ligand to metal has been subjected to numerous theoretical and experimental investigations [14—16]. However, only limited classes of organic-lanthanide complexes have been developed and shown to display nonlinear processes [17-19]. Common nonlinear processes from lanthanide complexes include harmonic generation, photon up-conversion and multiphoton absorption induced emission. 

P+ and P are the probabilities for absorption and emission, respectively B+ and B are the coefficients of absorption and of induced emission, respectively A- is the coefficient of spontaneous emission and p v) is the density of radiation at the frequency that induces the transition. Einstein showed that B+ = B, while A frequency dependence, spontaneous emission (fluorescence), which usually dominates in the visible region of the spectrum, is an extremely improbable process in the rf region and may be disregarded. Thus the net probability of absorption of rf energy, which is proportional to the strength of the NMR signal, is... 

Mercuiy in the Arctic cycles with the seasons between the atmosphere and snow on the ground. In the spring, as the sun reappears after the winter darkness, mercury levels in the troposphere decline for about 3 months. At the same time, the level of mercury in the snow increases 100-fold, both as methylmercury and as inorganic compounds of mercury. Later in the year, as the snow melts, the levels in the snow drop and mercury reappears in the troposphere. The elemental mercury in the atmosphere is converted to particulates or reactive species, parallelling a decrease in atmospheric ozone, and is then deposited in the snow. Later in the summer, the mercury levels in the atmosphere increase, probably due to temperature- or sunlight-induced emission of volatile mercury species from the surface. 

To proceed further, we now assume that, because of Franck-Condon factors, only a> can combine in absorption from the initial state g. That is, a> is an absorption doorway state.29 (The assumption that only a few out of many S, vibrational levels have any appreciable dipole-induced transition probability to or from any given S0 vibrational level is a good approximation for a large number of molecules.) This, with the definition of the fiHm and Eqs. (3.1), gives nlg = (xnag and fi2g = PHag- We also assume, for similar reasons, that either a> or i>> combines in emission with the final state /> (i.e., a> or f > is a doorway state in emission to / . If a> is the emission doorway state,... 

Here, ijJ v)) is the mean and angle averaged value of the local radiation field, weighted with the profile function of the local absorption coefficient. The Aij and Bij are the Einstein coefficients for spontaneous and induced transitions, while denotes the probability for a collisional transition from state j —> i. Accordingly, the first row in eq. (10.20) accounts for spontaneous emission and collision of the molecule considered with H2, whereas in the second row induced emission processes are described. This system of rate equations has to be solved simultaneously with the generalized radiative transfer equation for every point in physical and velocity space. 

Einstein coefficients Coefficients used in the quantum theory of radiation, related to the probability of a transition occurring between the ground state and an excited state (or vice versa) in the processes of induced emission and spontaneous emission. For an atom exposed to electromagnetic radiation, the rate of absorption is given by... 

If the laser pulse applied to the sample molecules is sufficiently long and intense, a molecule (represented by a two-level system) will be driven back and forth between the two levels at the Rabi flopping frequency (Vol. 1, (2.96)). The time-dependent probability amplitudes ai (t) and 02 (0 are now periodic functions of time and we have the situation depicted in Vol. 1, Fig. 2.23. Since the laser beam is alternately absorbed (induced absorption E E2) and amplified (induced emission 2 i). the intensity of the transmitted beam displays an oscillation. Because... 

Since we are interested mainly in the roots of spontaneous emission, we shall quantize the electromagnetic field because we know that the semi-classical description where the atom is quantized and the field is classical, does not provide aity spontaneous emission it is introduced phenomenologically by a detailed balance of the population of the two-states atom and comparison with Planck s law. This procedure introduced by Einstein gave the well-known relationship between induced absorption (or emission), and spontaneous emission probabilities, the B12, B21 and A21 coefficients, respectively, but caimot produce the coherent aspect and its link with spontaneous emission. 

Equation (2.21) states that for levels 1), 2) with the equal statistical weights g2 — g y the probability of induced emission is equal to that of induced absorption. 

When the excited molecule A( /) is exposed to an intense radiation field, the induced emission may become noticeable. It contributes to the depopulation of level Ei in a transition i) -> k) with the probability... 

This shows that a stationary inversion AA stat > 0 can only be maintained for R > A21. The relaxation probability R of the lower laser level 1) must be larger than its refilling probability A21 by spontaneous transitions from the upper laser level 2). In fact, during the laser operation the induced emission mainly contributes to the population A i and therefore the more difficult condition R >A2 - -B2ip must be satisfied. Continuous-wave lasers can therefore be realized on the transitions 2) I) only if the effective lifetime reff=l// i of level 1) is smaller than (A2 + B2ip) ... 

Regarding transitions from ground to excited state and vice versa, the interaction of the radiation with the molecules are in principle the same. For this reason, the Einstein coefficients, which are a measure of probability of the two transitions, are the same for both (induced) absorption and induced emission [II], (12). (I4J. [15]. Which of the two transitions is more effective for the interaction with radiation depends only on the relative distribution of the molecules between the two states. 

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