## Evolution of the Statistical Properties of Photons Passed through a Traveling-Wave Laser Amplifier (1992)

Venue: | IEEE J. Quantum Electron |

Citations: | 2 - 1 self |

### BibTeX

@ARTICLE{Diament92evolutionof,

author = {Paul Diament and Malvin C. Teich},

title = {Evolution of the Statistical Properties of Photons Passed through a Traveling-Wave Laser Amplifier},

journal = {IEEE J. Quantum Electron},

year = {1992},

volume = {28},

pages = {1325--1334}

}

### OpenURL

### Abstract

We 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 travelingwave amplifier are always broader than those at the input, and they can take many forms. Our most general solution can be applied when the input distribution to the amplifier takes the form of a negative-binomial transform. The results are expected to be useful in calculating the performance characteristics of lightwave systems using optical amplifiers in which the object is to detect light with a broad range of statistical properties, including scattered light, spontaneous-emission light, and light emitted from a laser. In the latter case the input is Poisson, and the output distribution assumes the form of a non-central-negative-binomial (Laguerre) distribution which is usually associated with a multimode (phase-preserving) superposition of coherent and chaotic fields.

### Citations

43 |
Inference and stochastic processes
- Bartlett
- 1967
(Show Context)
Citation Context ...epartment of Electrical Engineering, Columbia University, New York, NY 10027. IEEE Log Number 9106853. birth-death-immigration (BDI) process, which is well known in the theory of stochastic processes =-=[7]-=--[9]. Various versions of the BDI model have been used to represent the processes of absorption, stimulated emission, and spontaneous emission taking place in a cavity [10]-[14]. In particular, Schell... |

8 |
Radiation and noise in quantum electronics
- Louisell, H
- 1964
(Show Context)
Citation Context ...ribed by the noncentral-negative-binomial with one degree of freedom. Light amplifiers have been examined in the context of quantum optics by a number of authors. Louisell and his collaborators [15], =-=[16]-=- developed an early quantum model of a linear single-mode phase-insensitive intensity amplifier. The spatial propagation of the optical field through the amplifying medium was replaced by a timedepend... |

4 | Multiply stochastic representations for K distributions and their Poisson transforms
- Teich, Diament
- 1989
(Show Context)
Citation Context ... medium when the input distribution is a negative -binomial transform of an arbitrary continuous probability density function. We previously discussed the significance of negative-binomial transforms =-=[24]-=-. One particular example of interest in the current context is the noncentral-negative-binomial (NNB) distribution, which can be viewed as a modified negative-binomial transform. This provides an exce... |

4 |
Neural counting and photon counting in the presence of dead time
- Teich, McGill
- 1976
(Show Context)
Citation Context ... abbreviations s = k/h and u = No/k have been used. This distribution, also denoted [24] L(n, k/h, N(t)), often arises in the statistical description of superimposed coherent and chaotic fields [25], =-=[26]-=-. Its mean is N(t) = No/h + (v/X)k/h and its variance is o2(0 = (No/h)[2(k/h) + 1] + (v/X)(k/h)[(k/h) + 1]. (46) In terms of our general notation, this PDF is p(n, o0, No, X, , v, N), as indicated in ... |

2 |
Coherence properties of the linear photon amplifier
- Friberg, Mandel
- 1983
(Show Context)
Citation Context ... [3]-[5], [17]-[22]. Several of these quantum-mechanical models provided solutions for the photon-number distribution at the output of the amplifier in terms of the distribution at the input [3]-[5], =-=[20]-=--[22]. The relationship between the quantum model of Louisell and the population -statistical approach of Shimoda, Takahasi, and Townes [6] has been elucidated by Shepherd and Jakeman 141. One of the ... |

2 |
Fundamentals of optical amplifiers
- Yamamoto, Mukai
- 1989
(Show Context)
Citation Context ...tical field through the amplifying medium was replaced by a timedependent growth of the optical intensity. This model has provided the point of departure for a number of generalizations [3]-[5], [17]-=-=[22]-=-. Several of these quantum-mechanical models provided solutions for the photon-number distribution at the output of the amplifier in terms of the distribution at the input [3]-[5], [20]-[22]. The rela... |

1 |
Noise in resonant optical amplifiers of general resonator configuration
- L, Goldstein, et al.
- 1989
(Show Context)
Citation Context ... semiconductor laser amplifiers are being used increasingly in optoelectronic systems. Such amplifiers are typically operated either as travelingwave or resonant devices, depending on the application =-=[1]-=-, [2]. The amplification is the result of the interaction of light with a large number of atoms for which a population inversion is externally maintained. Them are several theoretical formulations of ... |

1 |
Properties of the optical quantum amplifier," Opt
- Loudon, Shepherd
- 1984
(Show Context)
Citation Context ...h a population inversion is externally maintained. Them are several theoretical formulations of the laser amplification process that are useful for dealing with amplifiers of different configurations =-=[3]-=--[$]. The population -statistical approach first used by Shimoda, Takahasi, and Townes [6] generally provides a suitable point of departure for characterizing the photon statistics associated with las... |

1 |
Stochastic Theo O, and Cascade Processes
- Srimvasan
- 1969
(Show Context)
Citation Context ...tment of Electrical Engineering, Columbia University, New York, NY 10027. IEEE Log Number 9106853. birth-death-immigration (BDI) process, which is well known in the theory of stochastic processes [7]-=-=[9]-=-. Various versions of the BDI model have been used to represent the processes of absorption, stimulated emission, and spontaneous emission taking place in a cavity [10]-[14]. In particular, Schell and... |

1 |
Maser noise considerations," Phys. Rev
- Weber
- 1957
(Show Context)
Citation Context ...eory of stochastic processes [7]-[9]. Various versions of the BDI model have been used to represent the processes of absorption, stimulated emission, and spontaneous emission taking place in a cavity =-=[10]-=--[14]. In particular, Schell and Bamkat [11] examined the approach to equilibrium of the photon-number distribution for a single radiation mode in a cavity, given a variety of initial photon-number di... |

1 | Noise and error-rate perfbrtnance of semiconductor laser amplifiers in PCM IM optical transmission systems - Yamanmto - 1980 |

1 | A model lbr photodetect,on of single-mode cavity radiation - Shepherd - 1981 |

1 |
Point Process Models of Cavtty Radiatton and Detection
- Srinivasan
- 1988
(Show Context)
Citation Context ...of stochastic processes [7]-[9]. Various versions of the BDI model have been used to represent the processes of absorption, stimulated emission, and spontaneous emission taking place in a cavity [10]-=-=[14]-=-. In particular, Schell and Bamkat [11] examined the approach to equilibrium of the photon-number distribution for a single radiation mode in a cavity, given a variety of initial photon-number distrib... |

1 |
Iouisell, "Quantum statistics of masers and attenuators
- Walker, H
- 1963
(Show Context)
Citation Context ...n described by the noncentral-negative-binomial with one degree of freedom. Light amplifiers have been examined in the context of quantum optics by a number of authors. Louisell and his collaborators =-=[15]-=-, [16] developed an early quantum model of a linear single-mode phase-insensitive intensity amplifier. The spatial propagation of the optical field through the amplifying medium was replaced by a time... |

1 | Quantum statistics of light after one-photon interaction with molter - Carosotto - 1975 |

1 | Evolution of the quantum statistics of light," Phys - Smith - 1978 |

1 |
Bit-error rate for a lightwave communication s3*stem incorporating an erbium-doped fiber amplifier." Elec tron
- Li, Teich
- 1991
(Show Context)
Citation Context ...or properly calculating the performance characteristics of a digital lightwave communication system incorporating an ideal laser and a traveling-wave optical amplifier (e.g., Er3+-doped silica fiber) =-=[23]-=-. Performance calculations can also be carded out using the more general distributions dcvcloped here. These should enable us to determine whether optical amplifiers are useful devices for detecting o... |

1 |
Superposition of coherent and incoherent fields
- Pevina
- 1967
(Show Context)
Citation Context ...re the abbreviations s = k/h and u = No/k have been used. This distribution, also denoted [24] L(n, k/h, N(t)), often arises in the statistical description of superimposed coherent and chaotic fields =-=[25]-=-, [26]. Its mean is N(t) = No/h + (v/X)k/h and its variance is o2(0 = (No/h)[2(k/h) + 1] + (v/X)(k/h)[(k/h) + 1]. (46) In terms of our general notation, this PDF is p(n, o0, No, X, , v, N), as indicat... |

1 |
Performance of a lightwave system incorporating a cascade of crbium-doped fiber amplifiers," Opt. Cornmum
- Li, Teich
- 1992
(Show Context)
Citation Context ...here are applicable to a cascade of optical amplifiers as well as a single alnplifier, even in the presence of intervening loss, provided that the normalized bandwidth is the salne for all amplifiers =-=[27]-=-, [28]. In addition to being used in inodeling the evolution of the photon statistics of a source of light as it passes through an optical amplifier, the particle-based travelingwave model considered ... |

1 |
Theory of noise accumulation in linear optical-atnplifier chains
- Loudon
- 1985
(Show Context)
Citation Context ...re applicable to a cascade of optical amplifiers as well as a single alnplifier, even in the presence of intervening loss, provided that the normalized bandwidth is the salne for all amplifiers [27], =-=[28]-=-. In addition to being used in inodeling the evolution of the photon statistics of a source of light as it passes through an optical amplifier, the particle-based travelingwave model considered here m... |

1 | Quantum Statistics of Linear and Nonlinear Optical Phenomena - Peb, 'ina - 1984 |

1 |
Quantum theory of a saturable optical amplifier," Phys
- Abraham
- 1980
(Show Context)
Citation Context ... intensity-based models. Finally, we note that it would be useful to incorporate the results of amplifier saturation in the general case; there are a number of ways in which this might be carried out =-=[30]-=--[33]. APPENDIX DERIVATION OF PDF AND PGF INPuT-OUTPUT RELATIONS This Appendix reviews the developlnent of the relationship between the probability density functions (PDF's) and probability generating... |

1 | Comparison of statistical properties of two models for saturated laser-light amphfier," Phys - Bendjaballah, Oliver - 1980 |