IEEE Journal of Quantum Electronics

Evolution of the statistical properties of photons passed through a traveling-wave laser amplifier

Paul Diament, Malvin Carl Teich

Published May 1, 1992• 41 citations

Abstract

The authors determine the evolution of the photon statistics of a light beam as it passes through a traveling-wave laser amplifier, modeled as a birth-death immigration (BDI) medium. The relationship between the input and output probability distributions and probability generating functions with given (but possibly varying) birth, death, and immigration rates for arbitrary input statistics is obtained. The case of constant birth, death, and immigration rates is considered in particular detail. The photon statistics at the output of a general BDI traveling-wave amplifier are always broader than those at the input, and they can take many forms. The most general solution can be applied when the input distribution to the amplifier takes the form of a negative-binomial transform.>

DOI: 10.1109/3.135273

Related papers

Photon point process for traveling-wave laser amplifiers

T. Li, Malvin Carl Teich

The authors determine the evolution of the photon point process of a light beam as it passes through a traveling-wave laser amplifier (TWA). In particular, when coherent light is presented to the input of the amplifier, the output photon statistics are characterized by a marked-Poisson (MP) point process, which has a noncentral-negative-binomial (NNB) output photon-number distribution (PND). Using this distribution we calculate the probability of error (PE) for an ON-OFF keying (OOK) direct-detection photon-counting communication system, and show that the results differ somewhat from those obtained when the Gaussian-PND approximation is used. It is shown that receiver performance is optimized by filtering the amplifier output. Analysis of the point process is of interest because it permits the time response of the amplifier to be determined; this, in turn, allows the effects of intersymbol interference to be calculated.>

IEEE Journal of Quantum ElectronicsJan 1, 199336 citations

Stochastic characterization of amplified photons in lightwave systems with optically bistable elements

Hooman Abediasl, Ali Naqavi, Khashayar Mehrany +1 more

An optical amplifier followed by a bistable element is statistically analyzed. To this end, the birth-death-immigration model and the coupled mode theory are used to characterize the amplifier and the bistable element, respectively.

International Symposium on Communications, Control and Signal ProcessingMar 1, 20101 citation

Strict calculation of the light statistics at the output of a travelling wave optical amplifier

Jordi Guitart, Sergio Ruiz‐Moreno

A new method for calculating the probability density function of the photon number propagating through a travelling wave optical amplifier with no restriction on its working regime (linear and nonlinear) is reported. The Letter shows that the widely used Gaussian approximation of the probability density function does not match the real statistics if the incident optical power is small.

Electronics LettersAug 19, 19935 citations

Quantum description of light propagation in generalized media

Teppo Häyrynen, Jani Oksanen

Abstract Linear quantum input–output relation based models are widely applied to describe the light propagation in a lossy medium. The details of the interaction and the associated added noise depend on whether the device is configured to operate as an amplifier or an attenuator. Using the traveling wave (TW) approach, we generalize the linear material model to simultaneously account for both the emission and absorption processes and to have point-wise defined noise field statistics and intensity dependent interaction strengths. Thus, our approach describes the quantum input–output relations of linear media with net attenuation, amplification or transparency without pre-selection of the operation point. The TW approach is then applied to investigate materials at thermal equilibrium, inverted materials, the transparency limit where losses are compensated, and the saturating amplifiers. We also apply the approach to investigate media in nonuniform states which can be e.g. consequences of a temperature gradient over the medium or a position dependent inversion of the amplifier. Furthermore, by using the generalized model we investigate devices with intensity dependent interactions and show how an initial thermal field transforms to a field having coherent statistics due to gain saturation.

Journal of OpticsJan 5, 20163 citations

Spectral gain modeling of optical amplifiers

Stefano Bottacchi

Introduction In this chapter we will present the theory of spectral gain in optical amplifiers and the related optical power distribution. The concepts are general, as they apply to every optical amplifier configuration, independent of the specific architecture and implementation technology. We will configure the optical amplifying medium as a traveling-wave device, where the optical field undergoes optical amplification as it propagates from the input to the output sections. Generally speaking, optical amplification is achieved by a net stimulated emission process. Referring to a generic section z of infinitesimal thickness dz , optical gain is determined by the imbalance between net stimulated emission and cavity losses, including extrinsic absorption, reflection and radiated fields. As we know from the theory of light amplification in the three-level atomic system presented in Chapter 5, stimulated absorption of photons is governed by the same transition rate as stimulated emission, and is included in the net stimulated emission process. With this in mind, we note the identity between stimulated emission and the stimulated absorption rates, Γ 12 = Γ 21 , and the net stimulated photon term Γ[ j 2 ( t ) – j 1 ( t )] p ( t ) in the rate equation. In order to develop the traveling-wave model, the photon density becomes a function of the longitudinal position 0 ≤ z ≤ L along the amplifier medium. Accordingly, we will set p ( t , z ) as the relative density of stimulated photons per unit volume (0 ≤ p ( t , z ) ≤ 1) at time t and section z . When photons with appropriate energy proceed along the amplifying medium, they are amplified by means of net stimulated emission. At some section z = z 0 , the steady-state photon density P ( z ) can approach the saturation density P sat ( z ).

Cambridge University Press eBooksSep 6, 20140 citations

Quantum Fluctuations and Noise in Parametric Processes. II

J. P. Gordon, W. H. Louisell, L. R. Walker

In this paper we consider further the quantum-statistical properties of radiation in nondegenerate parametric-type amplifiers. In particular we find moment-generating functions and probability distribution functions for the field variables at the output of an amplifier for various input conditions. We find that a classical description of the input fields and of the amplification process is completely valid provided we take correctly into account the response of the amplifier to the input zero-point noise fields. This result is valid for inputs of arbitrarily small power.

Physical ReviewJan 1, 1963143 citations