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Journal of the Optical Society of America B

Convergence of quantum and semiclassical models of erbium-doped fiber amplifiers

A. R. Karthikeyan, Harishankar Ramachandran

Published Feb 25, 2011• 4 citations
Publisher

Abstract

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.

DOI
10.1364/josab.28.000533

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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.
The Bit Error Rate (BER) performance of Erbium Doped fiber amplifiers (EDFA) is analysed in this paper. An analysis of the BER from quantum statistics is compared to the BER obtained from semiclassical approaches. In earlier work [1], the authors showed how the predictions of the two treatments approached each other in the case of ideal amplifiers for large gain. In this paper, the analysis is carried out for non-ideal, i.e., saturated EDFA and it is found that convergence of the two treatments occurs at a lower gain for saturated amplifiers than for ideal amplifiers.
Abstract A model of photon statistics and quantum phase distribution is analyzed for coherent optical communication links in the presence of quantum phase noise, dispersion and phase noise of the radio-frequency (RF) oscillator using an in-line optical amplifier. The quantum analysis of a dual drive Mach–Zehnder modulator and the quantum transfer function for an optical field mode across an in-line amplifier is performed by taking into account both the quantum and the classical phase noises. The resulting photon statistics are compared with the semiclassical model. We analyze the quantum phase distribution by considering the Wigner quasiprobability distribution for a coherent optical link. Here, we investigate the broadening of the quantum phase distribution due to quantum phase noise of the laser, the dispersive optical fiber, the phase noise of the RF oscillator and the inevitable noise coefficient of the optical amplifier for arbitrary amplified spontaneous emission (ASE) field modes. We analytically investigate the quantum analog to the bit error rate (BER) as a function of the laser’s linewidth, the linewidth of the RF oscillator and chromatic dispersion. The results of quantum models are compared with the semiclassical model. Quantum treatment of both the BER and variance is found to agree with prior results for a single-mode ASE field in the absence of phase noise but deviate when the effect of phase noise is considered. Including phase noise effects in the amplitude in the semiclassical treatment of the BER yields a new semiclassical expression that agrees with quantum expressions of machine precision for single-mode ASE fields.
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 report measurement of the photon-number distributions of zeros and ones that emerge from an erbium-doped fiber amplifier (EDFA) in an on-off modulated communication system. Single-mode single-photon resolution was achieved by employing the method of optical homodyne tomography. The measured distributions agree with the quantum predictions of a Bose-Einstein distribution for the zeros and a Laguerre (noncentral negative binomial) distribution for the ones over a dynamic range up to 40 dB. The resulting noise figure of the amplifier compares well to that measured by an optical spectrum analyzer.
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].