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.
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.
The basic equations governing noise phenomena are derived from first principles and applied to examples in optical communications. Quantum noise arises from two sources, the momentum fluctuations of electrons at optical frequencies and the uncertainty-related fluctuations of the electromagnetic field. Shot noise results from the beating of the noise sources with the signal field. In high-gain amplifiers, the spontaneous-emission noise dominates shot noise and results in a noise figure of at least 3 dB. It is shown explicitly how, at high power, both the laser field and the laser noise source become classical. The increase in noise in lasers with open cavities is not due to enhanced spontaneous emission as once thought, but to single-pass amplification. The noise fields and spontaneous currents have Gaussian distributions, while nonlasing modes have exponential photon-number distributions. Low-frequency intensity fluctuations arise from the electric current driving the laser and can be sub-Poissonian, in contrast to shot noise, which has a Poissonian distribution. The calculational tools are a wave equation for the field operator and a rate equation for the carrier-number operator, each containing spontaneous current noise sources. The correlation functions of these sources are determined by the fluctuation-dissipation theorem. [S0034-6861(96)00503-X]
The population-statistical description of a linear optical amplifier, extended to include both a resonant optical cavity and explicit input and output photon fluxes, is shown to yield three useful noise relationships. Despite the treatment's plainly particulate character, it provides an expression for the variance of the time-integrated output-photon-detection process in which terms associated with interferometrically generated beat noise are prominent. For systems whose photodetector electrical bandwidth B is much smaller than the amplifier's optical bandwidth Delta v, as is almost invariably the case for semiconductor amplifiers in lightwave-communication systems, the time-integrated photocurrent variance can be written in a simple, physically intuitive form. Two quotients are of central importance: ( Delta nu /B) and the ratio (/) of mean amplified-signal power to mean amplified-spontaneous-emission power. In the usual case of interest for optical amplifiers in communication systems where>>, the signal-to-noise ratio of the integrated photocurrent, on which the error probability in an on-off-keyed system depends, is approximately=1/2( Delta v/B) ((n/sub S/)/(n/sub ASE/)).>
A field noise spectral density matrix for the noise from a linear optical device, modeled as an optical multiport, is derived semi-classically. The noise is formulated in the scattering parameters, population inversion factor, and internal efficiency of the device. From this noise expression, a new equation for the amplified spontaneous emission spectral density from an optical amplifier is derived. This equation is more general than those previously published. The derivations are accomplished with the aid of methods from ordinary (classical) electrical network theory and only one quantum mechanical result regarding the noise from a conductance. As a result, the first-mentioned noise expression also includes the so-called vacuum field fluctuations. Further, the current noise spectrum of a square-law detector is derived with classical methods. The optical input to the detector includes the vacuum field fluctuations, which are shown to be the cause of the detector shot noise. Here, a second quantum mechanical result has to be employed, viz., that the vacuum field fluctuations cannot be detected alone. The results in this paper agree with the special cases found in the literature. The noise expressions are well suited for examination of the optical noise performance of arbitrary linear optical networks including, e.g., amplifiers, attenuators, isolators, reflections, filters, and couplers.>
The paper presents a comparison between a semiclassical and a quantum description of the output noise spectra of semiconductor optical amplifiers. The noise sources are represented by Langevin noise functions or operators and by the vacuum field operator, and the analysis takes into account the effects of increasing gain saturation along the amplifier waveguide. It is shown that the difference between the semiclassical and quantum descriptions sums up to a shot noise term and to a correction to the semiclassical autocorrelation relation for the carrier noise. A discussion is given of the shapes of the noise spectra, the relative importance of various noise contributions, and their dependence on input power.
Adopting a new classical approach, the additive noise power generated in optical amplifiers is calculated in terms of power spectral density. The classical formalism used combines a coruscular approach to a phase-amplitude description of the optical field. The noise contributions of the input field fluctuations, including zero-point fluctuations, and of the electron momentum fluctuations at optical frequency linked to the amplifier itself, are clearly identified. The excess of noise associated to coupling or built-in losses is determinated. The well-known result of the Amplified Spontaneous Emission (ASE) is obtained for the laser amplifiers. This description is applied to linear phase-insensitive amplifiers and to inhomogeneous, nonlinear phase-insensitive Raman amplifier, pointing out the effects of gain compression and gain distribution. This new approach makes possible the treatment of the squeezed-state of light and the quadrature reduced noise amplifications.
After pointing out some questionable assumptions of the standard beating theory, we formulate a new semiclassical wave theory of the noise in optical amplifiers. The theory is simple yet rigorous and uses a few quantum statements in a classical signal framework. The amplifier is modeled as a 2/spl times/2 port device, and the amplified spontaneous emission and associated noise are shown to be just the amplified coherent state (or vacuum state) fluctuation of the field entering the idler input. The new theory can treat other closely related detection schemes as well, correctly supplying both mean signal and noise.