Stimulated emission factor

The argument is sometimes given that equation (Al.6,29) implies that the ratio of spontaneous to stimulated emission goes as the cube of the emitted photon frequency. This argument must be used with some care recall that for light at thennal equilibrium, goes as BP, and hence the rate of stimulated emission has a factor... 

The above fomuilae for the absorption spectrum can be applied, with minor modifications, to other one-photon spectroscopies, for example, emission spectroscopy, photoionization spectroscopy and photodetachment spectroscopy (photoionization of a negative ion). For stimulated emission spectroscopy, the factor of fflj is simply replaced by cOg, the stimulated light frequency however, for spontaneous emission... 

G-. Denton, N. Tesslcr, N.T. Harrison. R.H. Friend, Factors influencing stimulated emission from polytp-phcuylenevinylcne), Phys. Rev Ia.ii. 1997, 78. 733. 

The molecule-intrinsic factor in the intensities of emission spectra can be obtained from the well-known Einstein coefficients (see, for example. Refs. [20, 21]). For the two states i and f considered above, whose energies are Ei and Ef, respectively, with Ei < Ef, we define as the Einstein coefficient for absorption, Bfl as the Einstein coefficient for stimulated emission, and Afl as the Einstein coefficient for spontaneous emission. We denote by Ni and Nf the number of molecules with energies Ei and Ef, respectively, and the Einstein coefficients are defined such that, for example, the change in Nf caused by electric dipole transitions to and from i is given by... 

For most treatments, the spectral density, J(a>), Eq. 2.86, also referred to as the spectral profile or line shape, is considered, since it is more directly related to physical quantities than the absorption coefficient a. The latter contains frequency-dependent factors that account for stimulated emission. For absorption, the transition frequencies ojp are positive. The spectral density may also be defined for negative frequencies which correspond to emission. 

Emission and absorption spectra are thus given by the same basic profile, J(co), commonly referred to as the spectral density, times some factors that depend on frequency. The exponential in Eq. 5.2 accounts for stimulated emission (see pp. 48ff.). The factor co of Eq. 5.2 is typical for absorption, just as the factor co3 is typical for the emission probability, Eq. 5.4, see also pp. 49ff. 

In addition to absorption and stimulated emission, a third process, spontaneous emission, is required in the theory of radiation. In this process, an excited species may lose energy in the absence of a radiation field to reach a lower energy state. Spontaneous emission is a random process, and the rate of loss of excited species by spontaneous emission (from a statistically large number of excited species) is kinetically first-order. A first-order rate constant may therefore be used to describe the intensity of spontaneous emission this constant is the Einstein A factor, Ami, which corresponds for the spontaneous process to the second-order B constant of the induced processes. The rate of spontaneous emission is equal to Aminm, and intensities of spontaneous emission can be used to calculate nm if Am is known. Most of the emission phenomena with which we are concerned in photochemistry—fluorescence, phosphorescence, and chemiluminescence—are spontaneous, and the descriptive adjective will be dropped henceforth. Where emission is stimulated, the fact will be stated. 

Furthermore, one can generally use approximation (14b) for the correction factor for stimulated emission. Hence according to Eqs. (16 and 20) the optical depth of radio molecular lines is inversely proportional to the excitation temperature... 

Overtone pumping spectroscopy has the limitation that, because excitation starts in the ground vibrational state, only very specific states can be accessed, e.g., the (ui,0,0) progression in HOCl and only few other states in the vicinity of the (ui,0,0) states. Stimulated emission pumping (SEP) [147], on the other hand, involves a transition to an excited electronic state, whose equilibrium geometry may be quite different from the equilibrium in the ground state. Therefore, Pranck-Condon factors are comparatively large for a wide variety of vibrational states, not just the... 

The factor in Equation 14.4 containing exp -hcVgi/kT) accounts for stimulated emission and is negligible at wavelengths below 2.5 pm and temperatures below 2500 K, and therefore it has been neglected. As Equation... 

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