Stimulated absorption and emission

Finally, consider the observed intensity of the absorption transition n m. Spontaneous emission from molecules in state m is sent out in random directions and can be ignored. However, emission from m stimulated by the incident light beam can be shown to travel in the same direction as the beam and thus decreases the observed intensity of the absorption line. Stimulated emission and absorption are each proportional to the population of the initial state of the transition and the n—and m—>n transition moments are equal. Hence the observed absorption intensity is proportional to the population difference Nn — Nm [and to dwrt 2 and... 

The black body photons can also be absorbed as the atoms in the n state make the transition to a higher lying n t state. Both the stimulated emission and absorption rates are given by... 

At laser intensities sufficient to saturate the le-2e transition, the stimulated emission and absorption processes which couple the levels are fast relative to collisional transfer processes, and a quasi-equilibrium balance (e)/Np(e)] is quickly established. If the total population of levels le and 2e is approximately constant during the laser pulse, the upper level population 112(e) can be reliably related to Np(e)0 using an analysis similar to a two level atomic model (1, 2, 3). ... 

In Eq. (3), 039 and 023 are the cross sections for stimulated emission and absorption. For narrow-line absorption and emission spectra, these two cross sections are equal. For broadband spectra with emission bandwidth greater than kT, the cross sections are connected by a generalized Einstein relation (6J. The final term in Eq. (3) accounts for possible excited-state absorption from the upper laser level to higher excited-states indicated by the dashed level in Fig. 1. If aesa > a32> absorption from level 3 dominates stimulated emission and laser action is not possible. 

A B, and B are the Einstein transition probabihties for spontaneous emission, stimulated emission, and absorption, respectively and a, a, and p are the cross sections of the respective processes (which are also a function of the velocity distribution of the particles involved), is the electron density is the radiation density at a given frequency v. 

Einstein transition probability - A constant in the Einstein relation Ay +ByP forthe probability of atransition between two energy levels and y in a radiation field of energy density p. The Ay coefficient describes the probability of spontaneous emission, while By and Bj, govern the probability of stimulated emission and absorption, respectively (By =... 

Optical spectroscopy of Er " doped into bulk AIN ceramics has been reported [296]. The material was prepared by using hot press sintering of AIN with Et203 and (NH4)(ErE4), which yielded fully dense, translucent, hexagonal AIN. The Er concentration was a small fraction of a percent, and resided in multiple sites, with one type of center dominant. A number of the energy levels of Er " were identified for this center. The temperature dependent fluorescence lifetime was probably radiative, with which the stimulated emission and absorption cross section spectra were derived for the " I... 

The Einstein coefficients prove to be useful for understanding the relationships among the probabilities for spontaneous emission, stimulated emission, and absorption. They are thus valuable for understanding the criteria for achieving laser action, where the competition between spontaneous and stimulated emission in the laser medium is crucial. The Einstein coefficients also lead to important insights into the relationships between the absorption and fluorescence properties of molecules, relationships that are often taken for granted in the chemical physics literature. 

A simple relation will be derived between the probabilities for spontaneous and stimulated emission and absorption of radiation using well-known statistical distribution laws. Consider a system such as that illustrated in Fig.4.3 with two energy levels, E and E2, populated by and N2 atoms, respectively. Three radiative processes can occur between the levels, as discussed above. In the figure the processes are expressed using the so-called Einstein coefficients 6 2, B21 and A21, which are defined such that the rate of change in the population numbers is... 

The coefficients Asi, B i, and Bu. came to be known as the Einstein coefficients for spontaneous emission and for stimulated emission and absorption of radiation, respectively. The rates of spontaneous and stimulated emission and Wei are connected by the expression... 

Fig. 2.3 Radiative processes of spontaneous emission and stimulated emission and absorption between quantum levels e) and i), which control the equilibrium (Boltzmann) population of levels due to radiative interaction with the equilibrium (Planck) distribution J(uj) of the photon energies of black-body radiation. Spontaneous emission happens in all directions, but stimulated emission occurs in the direction of the incident radiation.

Mollow, B. R. (1969). Stimulated emission and absorption near resonance for driven systems. Physical Review A, 5, 2217-2222. 

Stimulated emission and absorption phenomena are described by quantum mechanics on the basis of the interaction between an incident sinusoidal perturbation like an electromagnetic wave, ytcos(o>0, and a physical (atomic, molecular, etc.) system. The state of the system can be written as a superposition, Y) CkYVk), of eigenstates of the unperturbed Hamiltonian, and in the initial state one... 

This method relies on the dependence of stimulated emission and absorption on the coherence between molecular states. Its spectral resolution is... 

This calculation also shows that spontaneous magnetic dipole emission in the radio or microwave region will be quite unobservable in laboratory experiments. The techniques of radio frequency spectroscopy of atoms and nuclei in solids, liquids, and gases therefore depend on the stimulated emission and absorption processes wliich are discussed in detail in Chapter 9. 

So far in this book we have emphasized the spontaneous emission of radiation. This occurs at a constant rate, independent of any external influences. Now we wish to turn our attention to the processes of stimulated emission and absorption of radiation which are induced by the presence of an external electromagnetic wave. In this chapter we prepare the foundations for an understanding of both the formation of spectral lines, which is considered in detail in Chapter 10, and the physics of gas lasers which is discussed in Chapters 11-13. 

Einstein coefficients for absorption and stimulated emission, denoted by and respectively. The expressions for B j, and Bj are then confirmed by means of quantum mechanics using time-dependent perturbation theory. This enables the probability of stimulated emission and absorption of radiation to be given in terms of the oscillator strengths of spectral lines. Finally we show that there is close agreement between the classical and quantum-mechanical expressions for the total absorption cross-section and explain how the atomic frequency response may be introduced into the quantum-mechanical results. 

We must now consider how the stimulated emission and absorption of radiation are treated in the case of a real atom. The relations between the probability of stimulated and spontaneous transitions were derived by Einstein (1917) using arguments based on statistical mechanics. This paper, which appeared well before the development of a complete quantum theory, is available in translation in ter Haar... 

Fig.9.1. Spontaneous and stimulated emission and absorption of radiation. The rate at which transitions take place between the levels k and i is given for atoms interacting with radiation whose energy density per unit bandwidth is p((o).

As explained in section 13.3, the increase in the hole width at high intensities is the result of an effective reduction in the lifetimes of the upper and lower laser levels caused by stimulated emission and absorption. 

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