Transition Rates and Optical Properties

We analyse the absorption and emission of photons for radiative transitions between states at energies and 2, involving photons with energy in the range from hw to hv + d(tho). The rate of upward transitions from states at 

Stimulated emission is a process in which a photon is duplicated, producing one additional photon in exactly the same state as the incident photon initiating the transition. It follows that these photons cannot be distinguished 

This important relation allows us to replace the matrix element and the combined density of states in the spontaneous emission rate by the absorption coefficient a(fkj) and makes this treatment applicable to real materials once the absorption coefficient is known  

Inserting f(ei) and /(e2) from (4.8) and remembering that the energy difference e2 — i over which the transitions occur equals the photon energy tko, equation (4.16) becomes 

Equation (4.17) is a generalisation of Kirchhoff s and Planck s laws and is valid for materials that are neither black nor have a single Fermi distribution over all states. 

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