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Keywords
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Spontaneous emission rate, Fermi’s golden rule, Vector potential operator, Electric field correlation function, commutation relations, singlet and doublet polarization states
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Abstract
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By using the vector potential operator commutation relations, for a molecule (or generally an emitter) placed between two infinite identical dielectric slabs and with the given transition frequency and electric dipole moment, the spontaneous emission rate is evaluated via Fermi golden rule. Molecules with the electric dipole moment parallel and perpendicular to the slabs are considered separately, and for each orientation, a typical variation of the emission rate in the space of the cavity is demonstrated. In the used quantization scheme, the dielectric functions of the slabs can be an arbitrary complex function of frequency (satisfying Kramers–Kronig relations) and thus, slabs generally can be dissipative and dispersive. By showing the agreement of this quantization approach with two previous green function approaches, in evaluating the spontaneous emission rate in a Fabry–Perot cavity, the consistency between field quantization and Green function approaches is shown.
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