Rate of Spontaneous Emission
The rate of spontaneous emission (i.e., the radiative rate) can be described by Fermi's golden rule. The rate of emission depends on two factors: an 'atomic part', which describes the internal structure of the light source and a 'field part', which describes the density of electromagnetic modes of the environment. The atomic part describes the strength of a transition between two states in terms of transition moments. In a homogeneous medium, such as free space, the rate of spontaneous emission in the dipole approximation is given by:
where is the emission frequency, is the index of refraction, is the transition dipole moment, is the vacuum permittivity, is the reduced Planck constant and is the vacuum speed of light. (This approximation breaks down in the case of inner shell electrons in high-Z atoms.) Clearly, the rate of spontaneous emission in free space increases with . In contrast with atoms, which have a discrete emission spectrum, quantum dots can be tuned continuously by changing their size. This property has been used to check the -frequency dependence of the spontaneous emission rate as described by Fermi's golden rule.
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