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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Modeling output-photon-statistics of erbium-doped fiber-amplifiers and amplifier-chains

Malin Premaratne, Iven Mareels, Kai Song

Published Nov 11, 2002• 0 citations
Publisher

Abstract

Summary form only given. We present a quasi-analytical model for characterizing the output-field photon-statistics of nonlinear erbium-doped fiber amplifiers and amplifier-chains with arbitrary input-field statistics. All the available results on output-photon-statistics of linear amplifiers can be derived as a special case of the present nonlinear theory.

DOI
10.1109/cleoe.2000.910277

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Summary form only given. We present a quasi-analytical model for characterizing the output-field photon-statistics of nonlinear erbium-doped fiber amplifiers and amplifier-chains with arbitrary input-field statistics. All the available results on output-photon-statistics of linear amplifiers can be derived as a special case of the present nonlinear theory.
Erbium-doped fiber amplifiers (EDFA) are gaining increasing importance in the lightwave communications arena due mainly to their low insertion loss and easy manufacturability. Consequently there is significant motivation in obtaining the photon number distribution at the output of an EDFA taking finite bandwith and line shape of the signal lasers into account. In this paper the photon number distribution at the output of an EDFA resulting from an input wave packet having an arbitrary photon number distribution is evaluated. Previously the output photon number distribution was derived [1] for input fields having Poisson photon number distributions, i.e. for coherent sate input fields. Our treatment is more general in the sense that the input field can be in an arbitrary quantum sate. This generality will enable researchers to evaluate EDFA photon number distributions resulting from non-monochromatic incident fields [for example laser sources with phase and/or intensity noise] simply by using the appropriate input photon number distributions in the equations that will be derived below [see for example [2] for several photon number distributions corresponding to various laser line shapes].
We studied the quantum-statistical properties of pulse amplification in erbium-doped fiber amplifiers (OFAs), including saturation of the atomic population inversion and pump depletion. We use a fully quantum theory to describe the atom-field interaction as wed as the light propagation. The generating function of the output photon number distribution (PND) is determined as a function of time during the course of the pulse, with an arbitrary input PND assumed. For input light with Poisson PND, the output PND is shown to be the Laguerre distribution with parameter 1 at all times smaller than the coherence time /spl tau//sub c/, even in the presence of nonlinear effects. An expression for the photon count moment generating function is found for counting times T/spl Gt//spl tau//sub c/. The mean pulse shape is shown to be altered by the nonlinear amplification. The variance is similarly altered, and the excess amplifier noise is greater at the leading side of the pulse.>
"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.
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.
In a fiber-optic link, the continuous semiclassical and discrete photon statistics models are widely used to characterize the output probability distribution of an optical amplifier. The semiclassical model describes the output as a chi-square distribution while the discrete photon statistics model describes it through the noncentral negative binomial (NNB) distribution. In this paper, we present a way of understanding the discrete photon statistical distribution at the output of the amplifier and the convergence of the same to its semiclassical counter part. We highlight this convergence through the relation between the NNB and chi-square distribution demonstrated through deviation analysis and simulations. The penalty incurred in bit error rate analysis due to semiclassical approximation over NNB is also discussed.