Shot-noise formula for time-varying photon rates: A general derivation

Journal of the Optical Society of America B: Optical Physics

Volumn 14, Issue 10, 1997, Pages 2424-2429

  Winzer, Peter J ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031500293     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.14.002424     Document Type: Article

References (23)

1. N. R. Campbell, "The study of discontinuous phenomena," Proc. Cambridge Philos. Soc. 8, 117 (1909); "Discontinuities in light emission," Proc. Cambridge Philos. Soc. 15, 310 (1909).
2. N. R. Campbell, "The study of discontinuous phenomena," Proc. Cambridge Philos. Soc. 8, 117 (1909); "Discontinuities in light emission," Proc. Cambridge Philos. Soc. 15, 310 (1909).
3. B. M. Oliver, "Thermal and quantum noise," Proc. IEEE 53, 436-454 (1965).
4. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
5. T. M. Niebauer, R. Schilling, K. Danzmann, A. Ruediger, and W. Winkler, "Nonstationary shot noise and its effect on the sensitivity of interferometers," Phys. Rev. A 43, 5022-5029 (1991).
6. B. J. Meers and K. A. Strain, "Modulation, signal, and quantum noise in interferometers," Phys. Rev. A 44, 4693-4703 (1991).
7. A more detailed description can be found in, e.g., Refs. 3, 7, 8, and 9.
8. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, England, 1995).
9. B. E. A. Saleh, Photoelectron Statistics (Springer-Verlag, New York, 1978).
10. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
11. The expression script O sign (Δt) stands for all terms in the series converging to zero faster than Δt.
12. 2.
13. H. A. Steinberg and J. T. La Tourette, "A note on photon-electron converters with reference to a paper by A. Arcese," Appl. Opt. 3, 902 (1964).
14. E. A. Lee and D. G. Messerschmitt, Digital Communication, 2nd ed. (Kluwer Academic, Boston, Mass., 1994).
15. The weight of Dirac impulses is denoted by a hat [e.g., Σ̂(0)]; the spectrum Σ(jω) thus equals Σ̂(0)δ(ω) + Σ̃(jω).
16. x ≥ 1/2: (Equation Presented) In these relations, X(jv) stands for the Fourier transform of x(t).
17. R. Müller and W. Heywang, Rauschen (Springer-Verlag, New York, 1989).
18. As h(t) is real, the magnitude of its spectrum is even and the phase is odd; this means |H(0)| = H(0).
19. 0 is defined to be the direct current before the filter f(t) according to Eq. (12).
20. This definition is not the only reasonable one; another well-motivated definition could be (Equation Presented) which does not yield the same results as Eq. (20), however.
21. This is the case in a heterodyne detection arrangement, for instance, if the detector works well below its cutoff frequency, resulting in |H(jω)| ≈ e, and if|F(jω)|, representing a fairly narrow bandpass filter, equals unity in the passband.
22. 2.
23. The procedure of making the signal x̃(t) periodic for the definition of a time average may look strange at a first glance. However, it is seen in the main text that it in fact unifies the derivations for time-limited and time-unlimited signals.