Cascaded stochastic processes in optics
Processus stochastiques en cascade d'importance en optique
OPEN ACCESS
Thirty years ago, Bernard Picinbono and his colleagues carefully addressed an important problem : how an optical field is converted into a sequence of photoelectrons upon detection. Their choice of problem could not have been better, nor their timing more judicious. In a paper entitled "Photoelectron Shot Noise", published in the Journal of Mathematical Physics in 1970, when quantum optics was in its infancy, they obtained results that were to serve as an important building block in analyzing and generating many different forms of Tight. We present some variations on the theme of cascaded stochastic processes in optics.
Résumé
Il y a trente ans, Bernard Picinbono et ses collègues ont traité rigoureusement un problème important : comment un champ optique est converti en une suite de photoélectrons après détection. Leur choix de ce problème ne pouvait pas être meilleur et a révélé un caractère pionnier. Dans un article intitulé « Photoelectron Shot Noise », publié dans le Journal ofMathematical Physics en 1970, alors que l'optique quantique n'était encore qu'à ses débuts, ils obtinrent des résultats qui constituèrent un important point de départ pour analyser et générer de nombreuses et diverses formes de lumières. Nous présentons des variations sur le thème des processus stochastiques en cascade, en optique.
Poisson process, shot noise, self-exciting process, doubly-stochastic process, compound Poisson process, doubly-Poisson, triggered optical emissions, multiply-Poisson, cascaded-Poisson, correlated-Poisson, nonclassical light, sub-Poisson light
Mots clés
Processus de Poisson, processus stochastique en cascade
[1] B . Picinbono, C. Bendjaballah, J. Pouget, "Photoelectron shot noise", Journal of Mathematical Physics, Vol . 11, #7, 1970, p . 2166—2176.
[2] L . Mandel, "Fluctuations of photon beams : The distribution of the photo - electrons", Proceedings of the Physical Society (London), Vol. 74, #3, 1959, p . 233—243.
[3] B . Picinbono, "Tendance vers le caractère gaussien par filtrage sélectif" , Comptes Rendus de l'Académie des Sciences (Paris), Vol . 250, #1, 1960, p . 1174—1176.
[4] D. Snyder, Random Point Processes (Wiley-Interscience, New York, 1975).
[5] N . Campbell, "Discontinuities in light emission", Proceedings of the Cambridge Philosophical Society, Vol. 15, 1909, p. 310—328.
[6] W. Schottky, "Über spontane Stromschwankungen in verschiedenen Elek trizitätsleitern", Annalen der Physik, Vol . 57, 19l 8, p . 541—567.
[7] S . O. Rice, "Mathematical analysis of random noise", Bell System Technical Journal, Vol. 23, 1944, p . 282—332.
[8] E. N . Gilbert, H . O . Pollak, "Amplitude distribution of shot noise", Bell System Technical Journal, Vol . 39, 1960, p. 333—350.
[9] S . B . Lowen, M . C . Teich, "Power-law shot noise", IEEE Transactions on Information Theory, Vol . 36, #6, 1990, p . 1302—1318.
[10] B . I. Cantor, M . C . Teich, "Dead-time-corrected photocounting distributions for laser radiation", Journal of the Optical Society of America, Vol. 65, #7 , 1975, p . 786–791.
[11] M . C . Teich, G . Vannucci, "Observation of dead-time-modified photocounting distributions for modulated laser radiation", Journal of the Optical Society of America, Vol . 68, #10, 1978, p. 1338–1342.
[12] D. R. Cox, "Some statistical methods connected with series of events" , Journal of the Royal Statistical Society, Series B, Vol. 17, 1955, p. 129–164.
[13] B . E . A. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978) .
[14] G . Bédard, "Photon counting statistics of Gaussian light", Physical Review, Vol . 151, #4, 1966, p . 1038–1039.
[15] O. Macchi, "Distribution statistique des instants d'émission des photoelectrons d' une lumière thermique", Comptes Rendus de l'Académie des Sciences (Paris), Vol. A272, #6, 1971, p. 437–440.
[16] J. Pefina, "Superposition of coherent and incoherent fields", Physics Letters , Vol . 24A, #6, 1967, p . 333–334 .
[17] B. Picinbono, "Quasistationary optical fields", Physics Letters, Vol . 29A, #10, 1969, p. 614–615.
[18] B. Picinbono, M. Rousseau, "Generalizations of Gaussian optical fields" , Physical Review A, Vol . 1, #4, 1970, p . 635–643 .
[19] G . Vannucci, M. C . Teich, "Dead-time-modified photocount mean and variance for chaotic radiation", Journal of the Optical Society of America , Vol . 71, #2, 1981, p . 164–170.
[20] B . E . A. Saleh, J . T. Tavolacci, M . C . Teich, "Discrimination of shot-noisedriven Poisson processes by external dead time : Application to radioluminescence from glass", IEEE Journal of Quantum Electronics, Vol . 17, #12 , 1981, p . 2341–2350 .
[21] E . Jakeman, "On the statistics of K-distributed noise", Journal of Physics A, Vol . 13, 1980, p . 31–48 .
[22] M. C . Teich, P. Diament, "Multiply stochastic representations for K distributions and their Poisson transforms", Journal of the Optical Society of America A, Vol . 6, #1, 1989, p . 80–91 .
[23] B . E. A. Saleh, M . C . Teich, "Multiplied-Poisson noise in pulse, particle, and photon detection", Proceedings of the IEEE, Vol . 70, #3, 1982, p . 229–245 .
[24] B. E. A . Saleh, M . C. Teich, "Statistical properties of a nonstationary Neyman–Scott cluster process", IEEE Transactions on Information Theory, Vol . 29, #6, 1983, p. 939–941 .
[25] S . B . Lowen, M. C. Teich, "Doubly stochastic Poisson point process driven by fractal shot noise", Physical Review A, Vol. 43, #8, 1991, p. 4192–4215.
[26] S . Thurner, S . B . Lowen, M . C . Feurstein, C . Heneghan, H . G . Feichtinger, M . C . Teich, "Analysis, synthesis, and estimation of fractal-rate stochastic point processes", Fractals, Vol . 5, #4, 1997, p . 565–595 .
[27] J. Neyman, "On a new class of `contagious' distributions, applicable in entomology and bacteriology", Annals of Mathematical Statistics, Vol . 10, 1939, p. 35–57.
[28] M . C . Teich, B . E . A . Saleh, "Approximate photocounting statistics of shotnoise light with arbitrary spectrum", Journal of Modern Optics, Vol. 34, #9 , 1987, p. 1169–1178.
[29] G. Bédard, J. C. Chang, L . Mandel, "Approximate formulas for photoelectric counting distributions", Physical Review, Vol. 160, #5, 1967, p . 1496–1500.
[30] C. W. Helstrom, S . O. Rice, "Computation of counting distributions arising from a single-stage multiplicative process", Journal of Computational Physics, Vol . 54, #2, 1984, p . 289–324 .
[31] M . C. Teich, "Role of the doubly stochastic Neyman type-A and Thomas counting distributions in photon detection", Applied Optics, Vol . 20, #14, 1981, p . 2457–2467 .
[32] M. C . Teich, B . E . A. Saleh, "Fluctuation properties of multiplied-Poisson light : Measurement of the photon-counting distribution for radioluminescence radiation from glass", Physical Review A, Vol. 24, #3, 1981, p. 1651–1654.
[33] M . C . Teich, T. Tanabe, T. C . Marshall, J . Galayda, "Statistical properties of wiggler and bending-magnet radiation from the Brookhaven vacuum-ultraviolet electron storage ring", Physical Review Letters, Vol . 65, #27, 1990, p. 3393–3396.
[34] M . C. Teich, P. R. Prucnal, G. Vannucci, M . E . Breton, W. J. Mc Gill, "Multiplication noise in the human visual system at threshold : 1 . Quantum fluctuations and minimum detectable energy", Journal of the Optical Society of America, Vol. 72, #4, 1982, p . 419–431 .
[35] M . C. Teich, B . E . A. Saleh, "Interevent-time statistics for shot-noise-driven self-exciting point processes in photon detection", Journal of the Optical Society of America, Vol . 71, #6, 1981, p . 771–776 .
[36] K. Matsuo, M. C . Teich, B . E . A . Saleh, "Thomas point process in pulse, particle and photon detection", Applied Optics, Vol . 22, #12, 1983, p. 1898 –1909 .
[37] M . Thomas, "A generalization of Poisson's binomial limit for use in ecology" , Biometrika, Vol. 36, 1949, p . 18–25 .
[38] B . E . A. Saleh, D . Stoler, M . C . Teich, "Coherence and photon statistics for optical fields generated by Poisson random emissions", Physical Review A , Vol . 27, #1, 1983, p . 360–374 .
[39] M. C . Teich, B. E . A. Saleh, "Photon bunching and antibunching", Progress in Optics, Vol . 26, 1988, p . 1–104 .
[40] M . C . Teich, B . E . A . Saleh, J . Pefina, "Role of primary excitation statistics in the generation of antibunched and sub-Poisson light", Journal of the Optical Society of America B, Vol . 1, #3, 1984, p . 366–389 .
[41] M . C . Teich, B . E . A. Saleh, "Observation of sub-Poisson Franck-Hertz light at 253 .7 nm", Journal of the Optical Society of America B, Vol. 2, #2, 1985 , p. 275–282 .
[42] M . C . Teich, B . E . A . Saleh, "Squeezed states of light", Quantum Optics, Vol . 1, #2, 1989, p . 153–191 .
[43] M . C . Teich, B . E . A. Saleh, "Squeezed and antibunched light", Physics Today, Vol . 43, #6, 1990, p . 26-34 .
[44] M . C . Teich, B . E. A . Saleh, F. Capasso, "Generation of photon-numbersqueezed light by semiconductor incoherent light sources", Coherence, Amplification, and Quantum Effects in Semiconductor Lasers, Chap. 12, 1991 , Wiley, New York, p. 539–560.
[45] K. Matsuo, B . E. A . Saleh, M . C . Teich . "Cascaded Poisson processes" , Journal of Mathematical Physics, Vol . 23, #12, 1982, p . 2353–2364 .
[46] K . Matsuo, M . C . Teich, B . E. A . Saleh, "Poisson branching point processes", Journal of Mathematical Physics, Vol. 25, #7, 1984, p . 2174–2185 .
[47] T. S . Larchuk, M. C. Teich, B . E . A . Saleh, "Statistics of entangled - photon coincidences in parametric downconversion", Annals of the New Yor Academy of Sciences, Vol . 755 (Fundamental Problems in Quantum Theory), 1995, p. 680–686.
[48] M .M. Hayat, B .E.A . Saleh, M .C. Teich, "Effect of dead space on gain and noise of double – carrier – multiplication avalanche photodiodes", IEEE Transactions on Electron Devices, Vol . 39, #3, 1992, p . 546–552.