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Integrated Photonics Research

Simple theory of optical fiber amplifiers having nonuniform distributions of gain and spontaneous emission factor

Shinji Yamashita, Takanori Okoshi

Published Jan 1, 1991• 1 citation
Publisher

Abstract

The conventional noise theory of an optical amplifier is based on the semiclassical master equation which is known as Shimoda, Takahashi and Towns' (STT) theory. However, this theory deals only with lumped amplifiers. The present paper shows first that the noise formulas for distributed nonuniform amplifiers can be derived in a simple way by using the STT theory.

DOI
10.1364/ipr.1991.mb3

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The conventional noise theory of an optical amplifier is based on the semiclassical master equation which is known as Shimoda, Takahashi and Towns' (STT) theory. However, this theory deals only with lumped amplifiers. The present paper shows first that the noise formulas for distributed nonuniform amplifiers can be derived in a simple way by using the STT theory.
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The authors present a rigorous and self-contained noise analysis of an optical amplifier based on the statistics of the input source field and the amplified spontaneous emission field of the amplifier. The method enables us to obtain the frequency dependence of the output electrical noise power, which has not been derived in previous studies of optical amplifier noise based on the photon-statistics master equation. The authors characterise for the first time the noise of an optical amplifier in combination with a super-fluorescent source, taking into account the frequency dependence of the gain and the presence of optional optical filters.
Erbium-doped and parametric fiber-optic amplifiers can be modeled as a cascade of amplifying beamsplitters, each representing a short fiber section in which the pump is approximately constant. Each beamsplitter obeys simple noise combination relations and its gain is calculated from the standard rate equations. The proposed model allows for the management of pump depletion in a very simple way by numerical analysis, avoiding direct quantum mechanical calculations. Sample noise propagation diagrams are reported for technically significant values of the parameters. For the four-wave-mixing amplifier, it has been found that the 3-dB noise limit can be reached even for a strong gain compression.