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IEEE Journal of Quantum Electronics

A semiclassical model for noise propagation in depleted-pump optical amplifiers

Valerio Annovazzi-Lodi, Sabina Merlo

Published Jan 1, 1998• 5 citations
Publisher

Abstract

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.

DOI
10.1109/3.720213

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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.
We present a semi-classical approach for predicting the quantum noise properties of fiber optical parametric amplifiers. The unavoidable contributors of noise, vacuum fluctuations, loss-induced noise, and spontaneous Raman scattering, are included in the analysis of both phase-insensitive and phase-sensitive amplifiers. We show that the model agrees with earlier fully quantum approaches in the linear gain regime, whereas in the saturated gain regime, in which the classical equations are valid, we predict that the amplifier increases the signal-to-noise ratio by generating an amplitude-squeezed state of light. Also, in the same process, we analyze the quantum noise properties of the pump, which is difficult using standard quantum approaches, and we discover that the pump displays complicated dynamics in both the linear and the nonlinear gain regimes.
We derive an analytical theory for the noise figure of an undepleted and lossless fiber optical parametric amplifier (FOPA). Both the signal and the wavelength converted idler are investigated. Our theory is applicable for both an ideal pump power source, as well as a noisy one. We find that a noisy pump source can severely degrade the performance at high gain due to the stochastic gain-variations the signal and idler will experience. The theory is compared with Monte Carlo simulations of the FOPA and an excellent agreement is obtained. Simulations in the gain-depleted region show the possibility to reach below quantum-limited, phase-insensitive amplification for single channel transmission.
The stagnating increase in data transmission capacity in optical communication systems combined with the ever growing demand of transmission bandwidth is leading to an impending capacity crunch, referring to the point in time after which the available bandwidth of the individual user starts to decrease. To postpone this point in time, existing technologies in terms of data transmission through optical fibers must be optimized and new degrees of freedom must be introduced to continue the exponential increase in available bandwidth; space-division multiplexing is believed to be the strongest candidate for another degree of freedom in transmission fibers. This thesis is two-fold: firstly, starting at Maxwell’s equations and basic principles of quantum mechanics, a semi-classical model of the noise properties of fiber optical parametric amplifiers and frequency converters is presented. The model accounts for multiple effects present in nonlinear fibers such as four-wave mixing, Raman scattering, distributed loss, and dispersion, and it is valid in the depleted pump regime. After validating the model against well-known results of quantum models, the model is used to predict the impacts of Raman noise, loss, and pump depletion on the noise properties of parametric frequency conversion and phase-insensitive and phase-sensitive parametric amplification. An important part of realizing space-division multiplexing is the ability of optical signal processing so the second part of this thesis addresses few-mode Raman fiber amplifiers and parametric amplifiers and frequency converters. A model of weak random linear mode coupling in the pump of a two-mode distributed Raman fiber amplifier is presented and it is shown that an amplification noise figure induced by mode coupling increases with the degree of mode coupling and that this tendency increases as the pump depletes. Also, a very low mode-dependent gain of 0.25 dB per 10 dB gain is experimentally demonstrated in a two-mode distributed Raman fiber amplifier by exciting the pump in a combination of two modes. A comprehensive model of four-wave mixing in two-mode fibers acvi counting for six simultaneous processes is derived, and the conversion efficiency from signal to idler in the four-wave mixing processes of phase conjugation and Bragg scattering in two two-mode fibers with different phase matching properties are experimentally investigated. A conversion efficiency of > −2.70 dB is demonstrated for Bragg scattering in the conversion of a signal in the LP01-mode to the idler in the LP11-mode; the signal-to-idler separation is ∼ 25 nm. Good qualitative agreement between experiments and theory is found for both processes in both fibers.
"Doping a part of the optical fiber core by (Er3+ ) ions in presence of external pumping power will lead to form the erbium-doped fiber amplifier (EDFA).The performance of this optical amplifier depends on (the power and the wavelength of the pumping laser, the power and wavelength of the input signal, amplifier length, ion concentration). These parameters will affect the characteristics of EDFA such as amplifier gain, gain saturation, noise figure and output power. However, these characteristics can be determined by solving the EDFA propagation and rate equations. The solution of these equations of two-level laser medium can be done numerically. In this paper, we are proposed a novel method to solve these equations. The reconstructed results are perfectly coincided the well known numerical results.
We explore the potential of a combination of two fiber parametric wavelength converters and an erbium-doped fiber amplifier to serve as a hybrid amplifier for S-band. We experimentally confirm the validity of a simple quantum model of the wavelength-converter noise figure (NF) and use it to extrapolate the measurement results and find the optimum hybrid amplifier settings. We find that the total NF can be below 6 dB, if the wavelength conversion efficiency of the first stage is above 4 dB. Furthermore, the total NF can be as low as 4 dB, if the conversion efficiency of the first stage is 10 dB or higher. Finally, we estimate the potential impact of pump relative noise on the NF.
Semi-classical noise characteristics are derived for the cascade of a non-degenerate phase-insensitive (PI) and a phase-sensitive (PS) fiber optical parametric amplifier (FOPA). The analysis is proved to be consistent with the quantum theory under the large-photon number assumption. Based on this, we show that the noise figure (NF) of the PS-FOPA at the second stage can be obtained via relative-intensity-noise (RIN) subtraction method after averaging the signal and idler NFs. Negative signal and idler NFs are measured, and <2 dB NF at >16 dB PS gain is estimated when considering the combined signal and idler input, which is believed to be the lowest measured NF of a non-degenerate PS amplifier to this date. The limitation of the RIN subtraction method attributed to pump transferred noise and Raman phonon induced noise is also discussed.