## Fokker-Planck and Langevin analyses of noise accompanying the amplification of optical pulses in semiconductor optical amplifiers

JOSA B, Vol. 22, Issue 8, pp. 1632-1639 (2005)

http://dx.doi.org/10.1364/JOSAB.22.001632

Acrobat PDF (325 KB)

### Abstract

The Fokker-Planck approach is used to study the statistics of an optical pulse propagating in semiconductor optical amplifiers in which the amplified spontaneous emission noise dominates. The probability density functions (pdfs) of the pulse peak sample are calculated for different saturation levels. Analytical results are possible for an ideal linear amplifier and when the simplest first-order approximation for nonlinear amplification is used. In other cases, we solve numerically the Fokker-Planck equation and the appropriate Langevin equation. Multicanonical Monte Carlo simulations ensure efficient calculations of the pdfs whose high- and low-power tails deviate from noncentral chi-square statistics for moderate and deep saturation levels, thus implying that the electric field process is not Gaussian.

© 2005 Optical Society of America

**OCIS Codes**

(250.5980) Optoelectronics : Semiconductor optical amplifiers

(270.2500) Quantum optics : Fluctuations, relaxations, and noise

**Citation**

Alberto Bilenca and Gadi Eisenstein, "Fokker-Planck and Langevin analyses of noise accompanying the amplification of optical pulses in semiconductor optical amplifiers," J. Opt. Soc. Am. B **22**, 1632-1639 (2005)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-22-8-1632

Sort: Year | Journal | Reset

### References

- Y. Yamamoto and K. Inoue, "Noise in amplifiers," J. Lightwave Technol. 21, 2895-2915 (2003).
- C. H. Henry and R. Kazarinov, "Quantum noise in photonics," Rev. Mod. Phys. 68, 801-853 (1996).
- Y. Yamamoto and T. Mukai, "Fundamentals of optical amplifiers," Opt. Quantum Electron. 21, S1-S14 (1989).
- E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley, 1994).
- T. Mukai and Y. Yamamoto, "Noise in an AlGaAs semiconductor laser amplifier," IEEE J. Quantum Electron. 18, 564-575 (1982).
- M. L. Dakss and P. Melman, "Amplified spontaneous Raman scattering and gain in fiber Raman amplifiers," J. Lightwave Technol. 3, 806-813 (1985).
- D. Dahan and G. Eisenstein, "The properties of amplified spontaneous emission noise in saturated fiber Raman amplifiers operating with cw signals," Opt. Commun. 236, 279-288 (2004).
- N. A. Olsson, "Lightwave systems with optical amplifiers," J. Lightwave Technol. 7, 1071-1082 (1989).
- P. O. Hedekvist and P. A. Andrekson, "Noise characteristics of fiber-based optical phase conjugators," J. Lightwave Technol. 17, 74-79 (1999).
- K. Inoue and T. Mukai, "Experimental study on noise characteristics of a gain-saturated fiber optical parametric amplifier," J. Lightwave Technol. 20, 969-974 (2002).
- Y. Yamamoto, "Noise and error rate performance of semiconductor laser amplifiers in PCM-IM optical transmission systems," IEEE J. Quantum Electron. 16, 1073-1081 (1980).
- A. D'Ottavi, E. Iannone, A. Mecozzi, S. Scotti, P. Spano, R. Dall'Ara, J. Eckner, and G. Guekos, "Efficiency and noise performance of wavelength converters based on FWM in semiconductor optical amplifiers," IEEE Photonics Technol. Lett. 7, 357-359 (1995).
- M. Shtaif and G. Eisenstein, "Calculation of bit error rates in all-optical signal processing applications exploiting nondegenerate four-wave mixing in semiconductor optical amplifiers," J. Lightwave Technol. 14, 2069-2077 (1996).
- K. Obermann, I. Koltchanov, K. Petermann, S. Diez, R. Ludwig, and H. G. Weber, "Noise analysis of frequency converters utilizing semiconductor-laser amplifiers," IEEE J. Quantum Electron. 33, 81-88 (1997).
- M. Shtaif, B. Tromborg, and G. Eisenstein, "Noise spectra of semiconductor optical amplifiers: relation between semiclassical and quantum descriptions," IEEE J. Quantum Electron. 34, 869-878 (1998).
- M. Shtaif and G. Eisenstein, "Noise properties of nonlinear semiconductor optical amplifiers," Opt. Lett. 21, 1851-1853 (1996).
- A. Bilenca and G. Eisenstein, "On the noise properties of linear and nonlinear quantum-dot semiconductor optical amplifiers: the impact of inhomogeneously broadened gain and fast carrier dynamics," IEEE J. Quantum Electron. 40, 690-702 (2004).
- D. Hadass, A. Bilenca, R. Alizon, H. Dery, V. Mikhelashvili, G. Eisenstein, R. Schwertberger, A. Somers, J. P. Reithmaier, A. Forchel, M. Calligaro, S. Bansropun, and M. Krakowski, "Gain and noise saturation spectra of wide band InAs/InP quantum dash optical amplifiers: model and experiments," IEEE J. Sel. Top. Quantum Electron., submitted for publication.
- K. Inoue and T. Mukai, "Spectral hole in the amplified spontaneous emission spectrum of a fiber optical parametric amplifier," Opt. Lett. 26, 869-871 (2001).
- M. Shtaif and G. Eisenstein, "Experimental study of the statistical properties of nonlinearly amplified signals in semiconductor optical amplifiers," IEEE Photonics Technol. Lett. 9, 904-906 (1997).
- F. Öhman, B. Tromborg, J. Mørk, A. Aurelius, A. Djupsjöbacka, and A. Berntson, "Measurements of non-linear noise re-distribution in an SOA," in Conference of Lasers and Electro-Optics, Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2004).
- B. Chan and J. Conradi, "On the non-Gaussian noise in erbium-doped fiber amplifiers," J. Lightwave Technol. 15, 680-687 (1997).
- M. Shtaif and G. Eisenstein, "Noise characteristics of nonlinear semiconductor optical amplifiers in the Gaussian limit," IEEE J. Quantum Electron. 32, 1801-1809 (1996).
- C. Xie and P. Ye, "Noise characteristics of four-wave mixing between short pulses in semiconductor optical amplifiers," J. Opt. Soc. Am. B 16, 1909-1914 (1999).
- A. Mecozzi and J. Mørk, "Saturation effects in nondegenerate four-wave mixing between short optical pulses in semiconductor laser amplifiers," IEEE J. Sel. Top. Quantum Electron. 3, 1190-1207 (1997).
- G. P. Agrawal, "Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE J. Quantum Electron. 25, 2297-2306 (1989).
- H. Risken, The Fokker-Planck Equation, 2nd ed. (Springer, 1989).
- B. A. Berg and T. Neuhaus, "Multicanonical ensemble: a new approach to simulate first-order phase transitions," Phys. Rev. Lett. 68, 9-12 (1992).
- R. Holzlhner and C. R. Menyuk, "Use of multicanonical Monte Carlo simulations to obtain accurate bit error rates in optical communications systems," Opt. Lett. 28, 1894-1896 (2003).
- A. Bilenca and G. Eisenstein, "Statistical noise properties of an optical pulse propagating in a nonlinear semiconductor optical amplifier," IEEE J. Quantum Electron. 41, 36-44 (2005)
- T. C. Gard, Introduction to Stochastic Differential Equations (Marcel Dekker, 1988).
- A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, 1991).
- G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (Dover, 2000).
- C. Andrieu, N. De Freitas, A. Doucet, and M. I. Jordan, "An introduction to MCMC for machine learning," Mach. Learn. 50, 5-43 (2003).
- P. Duchateau and D. Zachmann, Applied Partial Differential Equations (Dover2002).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.