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Optics Communications

Analysis of amplified spontaneous emission: some corrections to the Linford formula

O. Svelto, Stefano Taccheo, C. Svelto

Published Apr 1, 1998• 49 citations
Publisher
DOI
10.1016/s0030-4018(98)00054-6

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Journal of the Optical Society of America B•Apr 1, 1993•5 citations
We demonstrate a fundamental breakdown of the photonic spontaneous emission (SE) formula derived from Fermi's golden rule, in absorptive and amplifying media, where one assumes the SE rate scales with the local photon density of states, an approach often used in more complex, semiclassical nanophotonics simulations. Using a rigorous quantization of the macroscopic Maxwell equations in the presence of arbitrary linear media, we derive a corrected Fermi's golden rule and master equation for a quantum two-level system (TLS) that yields a quantum pumping term and a modified decay rate that is net positive. We show rigorous numerical results of the temporal dynamics of the TLS for an example of two coupled microdisk resonators, forming a gain-loss medium, and demonstrate the clear failure of the commonly adopted formulas based solely on the local density of states.
A model is presented for erbium-doped fiber amplifiers that operate by an upconversion process in which two pump photons at ~800 nm are absorbed and can provide an inverted population and hence the ability to amplify signal photons at ~850 nm. The most important spectroscopic features of the amplifier are identified and used to formulate a theory that predicts how the amplifier gain varies with fiber length and doping density, as well as with launched pump and signal powers. The limitation that amplified spontaneous emission imposes on the gain is investigated, and useful approximate formulas are derived in the limit where amplified spontaneous emission is negligible.