Various Sources of Noise in Optical Fiber Communication Systems: A Review
Subject Areas : electrical and computer engineeringAbstract :
This paper reviews different sources of noise in optical fiber communication systems. The most important sources of noise, in such systems, are semiconductor lasers, optical amplifiers, and optical detectors. First, we review the relative intensity noise (RIN) and phase noise in semiconductor lasers. We show that, at low frequencies, RIN is negligible, and reaches its maximum at the damping frequency. RIN decreases with an increase in injection current, while it maximizes for the threshold current, at a certain frequency. The phase noise, which is related to laser line width, is constant below the damping frequency and increases to its maximum at the damping frequency. In semiconductor lasers, both RIN and phase noise decrease with an increase in the output power. Next, Amplified spontaneous emission (ASE) noise in erbium doped fiber amplifiers (EDFA) is reviewed. We show that, while ASE noise increases with an increase in the pump power, it decreases with an increase in the input signal power, for the various pump powers. Then, reviewing the formulation of noise figure (NF) in semiconductor optical amplifiers (SOA), we study the effects of cavity thickness and length on NF in both Fabry Perot (FP) and traveling wave amplifiers (TWA). Then we review sources of noise in an optical detector, and present an equivalent electric circuit model for it, including signal to noise ratio (SNR) and bit error rate (BER). Then, modal noise in a multimode optical fiber is reviewed. Finally, crosstalk as the main limiting parameter in optical multiplexer/demultiplexer units in multiwavelength systems is reviewed.
References:
[1] ابراهيم مرتاضي، وحيد احمدي و محمد كاظم مروج فرشي، "مدل سازي مداري واندازه گيري نويز در ليزرهاي نيمه هادي، " مجله علمي-پژوهشي دانشگاه تبريز، شماره 31،صص83-77،تابستان 1382.
[2] وحيد احمدي، ابراهيم مرتاضي، محمدكاظم مروج فرشي، و عباس ظريفكار، "اندازه گيري و آناليز نويز شدت و فاز در ليزرهاي مخابراتي چند مد،" مجله.علمی پژوهشی امیرکبیر، شماره 53،صص258-249،زمستان 1381.
[3] ابراهيم مرتاضي، انداز هگيري و تحليل مشخص ههاي نويز ليزرهاي مخابراتي، پايان نامه كارشناسي ارشد، دانشگاه تربيت مدرس، تابستان 1380.
[4] عباس ظريفكار، مد لسازي و شبي هسازي نويز د ر ليزرها ي نيمه هادي، رساله . دكتري، گروه الكترونيك، دانشگاه تربيت مدرس، تابستان 1380.
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[6] E. Mortazy, V. Ahmadi, and M. K. Moravvej-Farshi, "Circuit modeling and measurement of noise for a semiconductor laser diode," in Proc 10th Iranian Conf. on Electrical Engineering,ICEE2002, vol. 1, pp. 568-575,Tabriz, Iran, May 2002.
[7] E. Mortazy, V. Ahmadi, M. K. Moravvej-Farshi, and A. Zarifkar, "Mode partition, mode hopping and phase noise in a two-mode semiconductor laser," in Proc Int. Conf. on Advanced Optoelectronics and Lasers, CAOL’2003, IEEE/LEOS proceedings, vol. 1, pp. 245-247, Alushta, Ukraine, Sep. 2003.
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[9] E. Mortazy, F. Shahshahani, V. Ahmadi, A. H. Tehranchi, and M. K. Moravvej-Farshi, "The effect of grating structure on relative intensity noise in DFB laser diode," in Proc. SPIE, Fluctuations and Noise in Photonics and Quantum Optics II, vol. 5468, pp. 154-164, Spain, May 2004.
[10] V. Ahmadi, F. Shahshahani, and E. Mortazy, "Analysis of RIN in DFB semiconductor laser diodes using three rate equations model," in Proc Int. Symposium on Telecommunications, IST2003, pp. 215-218, Isfahan, Iran, Aug. 2003.
[11] A. Zarifkar, A. Falahatpisheh, M. K. Moravvej-Farshi, and E. Mortazy, "Semiconductor laser noise analysis including spatial variations in the lateral direction," in Proc Int. Conf. on Advanced Optoelectronics and Lasers, CAOL’2003, IEEE/LEOS proceedings, vol. 1, pp. 242-244, Alushta, Ukraine, Sep. 2003. [12] Y. Yamamoto, "AM and FM quantum noise in semiconductor lasers-Part I: theoretical analysis," IEEE J. Quantum Electron., vol. 19, no. 1, pp. 34-46, Jan. 1983.
[13] Y. C. Tseng and J. C. S. Woo, "Phase noise characteristics associated with low-frequency noise in submicron SOI MOSFET feedback oscillator for RF IC’s," IEEE Electron Device Letters,vol. 20, no. 1, pp. 54-56, Jan. 1999.
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[17] T. T. Bich-Ha and J. Mollier, "Noise equivalent circuit of a two mode semiconductor laser with the contribution of both the linear and the nonlinear gain," IEEE J. Selected Topics in Quantum Electronics, vol. 3, no. 2, pp. 304-308, Apr. 1997.
[18] T. K. Yee, "Analysis of the intensity noise of nearly single longitudinal- mode semiconductor lasers," IEEE J. Quantum Electron., vol. 22, no. 2, pp. 275-285, Feb. 1986.
[19] W. Strefer, A. Hardy, D. R. Scifres, and R. D. Burnham, "Analysis of diode laser properties-Part II," IEEE J. Quantum Electron., vol. 19, no. 6, pp. 991-1001, Jun. 1983.
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[21] M. Ohtsu and Y. Teramachi, "Analyses of mode partition and mode hopping in semiconductor lasers," IEEE J. Quantum Electron., vol. 25, no. 1, pp. 31-38, Jan. 1989.
[22] M. P. van Exter, M. B. Willemsen, and J. P. Woerdman, "Effect of mode-partition noise on intensity squeezing in a two-mode laser," J. Opt. B: Quantum Semiclass, Opt., vol. 1, no. 6, pp. 637-645,Dec. 1999.
[23] K. Ogawa, "Analysis of mode partition noise in laser transmission systems," IEEE J. Quantum Electron., vol. 18, no. 5, pp. 849-855, May 1982.
[24] T. B. Anderson and B. R. Clarke, "Modeling Mode Partition Noise in Nearly Single-Mode Intensity Modulated lasers," IEEE J. Quantum Electron., vol. 29, no. 1, pp. 3-13, Jan. 1993 .
[25] M. R. Alalusi and R. B. Darling, "Effects of nonlinear gain on mode hopping in semiconductor laser diodes," IEEE J. Quantum Electron.,vol. 31, no. 7, pp. 1181-1192, Jul. 1995.
[26] M. F. S. Ferreira, J. R. F. Rocha, and J. L. Pinto, "Analysis of the frequency noise of tunable multi section DBR lasers," IEEE J. Quantum Electron., vol. 28, no. 4, pp. 833-841, Apr. 1992.
[27] K. P. Ho, "Spectral density of cross-phase modulation induced phase noise," Optics Communications, vol. 169, no. 1-6, pp. 63-68, Oct. 1999.
[28] K. Kikuchi, "Effect of 1/f type noise on semiconductor laser line width residual in high-power limit," IEEE J. Quantum Electron., vol. 25, no. 4, pp. 684-688, Apr. 1989.
[29] Y. Yamamoto, T. Mukai, and S. Saito, "Quantum phase noise and line width of a semiconductor laser," Electronic Letters, vol. 17, no. 9, pp. 327-329, May 1981.
[30] G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed., New York: Van Nostrand Reinhold, 1993.
[31] E. Desurvire, Erbium-Doped Fiber Amplifier, John Wily & Sons Ltd., 1994.
[32] W. Johnstone, B. Culshaw, D. Walsh, D. Moodie, and I. Mauchline, "Student laboratory experiments on erbium doped fiber amplifiers and lasers," SPIE Proceeding in Optics and Photonics, vol. 3831, pp. 259-267, Cancun, Mexico, Jul. 1999.
[33] P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers, Academic Press, 1999.
[34] S. Shimada, Optical Amplifiers and Their Applications, John Wily & Sons Ltd., 1994.
[35] J. H. Franz and V. K. Jain, Optical Communications, Alpha Science International Ltd., 2000.
[36] C. Y. J. Chu and H. Ghafori-Shiraz, "Equivalent circuit theory of spontaneous emission power in semiconductor laser optical amplifiers," J. Lightwave Technology, vol. 12, no. 5, pp. 760-767,May 1994.
[37] H. Ghafori-Shiraz, Fundamentals of Laser Diode Amplifiers, John Wily & Sons Ltd., 1996.
[38] S. M. K. Thiyagarajan and A. F. J. Levi, "Noise in voltage-biased scaled semiconductor laser diodes," Solid-State Electronics, vol. 43, no. 1, pp. 33-39, Jan. 1999.
[39] K. Sato and H. Toba, "Reduction of mode partion noise by using semiconductor optical amplifier," IEEE J. Selected Topics in Quantum Electronics, vol. 7, no. 2, pp. 328-333, Mar./Apr. 2001.
[40] A. A. M. Saleh, "Nonlinear models of traveling-wave optical amplifier," Electronics Letters, vol. 24, no. 14, pp. 835-837, Jul. 1988.
[41] L. Thylen, M. Gustavsson, T. K. Gustafson, I. Kim, and A. Karlsson, "Calculation of photon and current fluctuations in traveling-wave semiconductor laser amplifier," IEEE J. Quantum Electronics, vol. 27, no. 6, pp. 1251-1258, Jun. 1991.
[42] D. Marcuse, "Computer model of an injection laser amplifier," IEEE J. Quantum Electron., vol. 19, no. 1, pp. 63-73, Jan. 1983.
[43] G. Morthier and B. Moeyersoon, "Intensity noise and linewidth of laser diodes with integrated semiconductor optical amplifier," IEEE Photonics Technology Letters, vol. 14, no. 12, pp. 1644-1646, Dec. 2002.
[44] E. S. Bjorlin and J. E. Bowers, "Noise figure of vertical-cavity semiconductor optical amplifiers," IEEE Journal Quantum Electronics, vol. 38, no. 1, pp. 61-66, Jan. 2002.
[45] W. Rideout, E. Eichen, J. Schlafer, J. Lacourse, and E. Meland, "Relative intensity noise in semiconductor optical amplifiers," IEEE Photonics Technology Letters, vol. 1, no. 12 , pp. 438-440,Dec. 1989.
[46] M. A. Summerfield and R. S. Tucker, "Noise figure and conversion efficiency of four-wave mixing in semiconductor optical amplifiers," Electronics Letters, vol. 31, no. 14, pp. 1159-1160, Jul. 1995.
[47] _, Fast Semiconductor Detectors, www.medphys.ucl.ac.uk/research/ borg/homepages/davek/phd/chapter3.pdf, 2002.
[48] A. Yariv, Optical Electronics in Modern Communications, Oxford University Press Inc., 1993.
[49] R. C. Woods, "Noise effects in avalanche photodiodes," IEEE Trans. on Education, vol. 43, no. 3, pp. 321-323, Aug. 2000.
[50] B. K. Ng, J. P. R. David, R. C. Tozer, M. Hopkinson, G. Hill, and G. J. Rees, "Excess noise characteristics of Al0.8Ga0.2As avalanche photodiodes," IEEE Photon. Technology. Letters, vol. 14, no. 4,pp. 522-524, Apr. 2002.
[51] -, Optical Signal-to-Noise Ratio and the Q-Factor in Fiber-Optic Communication Systems, Application Note, MAXIM High Frequency/Fiber Communications Group, http://pdfserv.maximic. com/arpdf/AppNotes/4hfan902.pdf, 2002.
[52] H. J. R. Dutton, Understanding Optical Communications, IBM Corporation, 1998.
[53] A. Cappy, F. Danneville, G. Dambrine, and B. Tamen, "Noise analysis in devices under nonlinear operation," Solid-State Electronics, vol. 43, no. 1, pp. 21-26, Jan. 1999.
[54] A. H. Tehranchi, N. Granpayeh, and E. Mortazy, "Modulation instability in optical fibers in the presence of higher order effects," in Proc Australasian Conference on Optics, Lasers, & Spectroscopy, ACOLS 2003, p. 79, Melbourne, Australia, Dec. 2003.
[55] A. H. Tehranchi, N. Granpayeh, and E. Mortazy, "The effects of noise amplification and soliton generation in anomalous dispersion regime of optical fibers," in Proc. SPIE, Fluctuations and Noise inPhotonics and Quantum Optics II, vol. 5468, pp. 85-92, Spain, May 2004.
[56] E. Mortazy and M. K. Moravvej-Farshi, "A New model for optical communication systems," Journal Optical Fiber Technology, vol. 11, no. 1, pp. 69-80, Jan. 2005.
[1] ابراهيم مرتاضي، وحيد احمدي و محمد كاظم مروج فرشي، "مدل سازي مداري واندازه گيري نويز در ليزرهاي نيمه هادي، " مجله علمي-پژوهشي دانشگاه تبريز، شماره 31،صص83-77،تابستان 1382.
[2] وحيد احمدي، ابراهيم مرتاضي، محمدكاظم مروج فرشي، و عباس ظريفكار، "اندازه گيري و آناليز نويز شدت و فاز در ليزرهاي مخابراتي چند مد،" مجله.علمی پژوهشی امیرکبیر، شماره 53،صص258-249،زمستان 1381.
[3] ابراهيم مرتاضي، انداز هگيري و تحليل مشخص ههاي نويز ليزرهاي مخابراتي، پايان نامه كارشناسي ارشد، دانشگاه تربيت مدرس، تابستان 1380.
[4] عباس ظريفكار، مد لسازي و شبي هسازي نويز د ر ليزرها ي نيمه هادي، رساله . دكتري، گروه الكترونيك، دانشگاه تربيت مدرس، تابستان 1380.
[5] E. Mortazy, V. Ahmadi, and M. K. Moravvej-Farshi, "An Integrated equivalent circuit model for relative intensity noise and frequency noise spectrum of a multimode semiconductor laser," IEEE, J.Quantum Electron, vol. 38, no. 10, pp. 1366-1371, Oct. 2002.
[6] E. Mortazy, V. Ahmadi, and M. K. Moravvej-Farshi, "Circuit modeling and measurement of noise for a semiconductor laser diode," in Proc 10th Iranian Conf. on Electrical Engineering,ICEE2002, vol. 1, pp. 568-575,Tabriz, Iran, May 2002.
[7] E. Mortazy, V. Ahmadi, M. K. Moravvej-Farshi, and A. Zarifkar, "Mode partition, mode hopping and phase noise in a two-mode semiconductor laser," in Proc Int. Conf. on Advanced Optoelectronics and Lasers, CAOL’2003, IEEE/LEOS proceedings, vol. 1, pp. 245-247, Alushta, Ukraine, Sep. 2003.
8] E. Mortazy, F. Shahshahani, V. Ahmadi, A. H. Tehranchi and M. K. Moravvej-Farshi, "The Effect of spatial hole burning on relative intensity noise in DFB laser diodes," in Proc Australasian Conference on Optics, Lasers, & Spectroscopy, ACOLS 2003,p. 159, Melbourne, Australia, Dec. 2003.
[9] E. Mortazy, F. Shahshahani, V. Ahmadi, A. H. Tehranchi, and M. K. Moravvej-Farshi, "The effect of grating structure on relative intensity noise in DFB laser diode," in Proc. SPIE, Fluctuations and Noise in Photonics and Quantum Optics II, vol. 5468, pp. 154-164, Spain, May 2004.
[10] V. Ahmadi, F. Shahshahani, and E. Mortazy, "Analysis of RIN in DFB semiconductor laser diodes using three rate equations model," in Proc Int. Symposium on Telecommunications, IST2003, pp. 215-218, Isfahan, Iran, Aug. 2003.
[11] A. Zarifkar, A. Falahatpisheh, M. K. Moravvej-Farshi, and E. Mortazy, "Semiconductor laser noise analysis including spatial variations in the lateral direction," in Proc Int. Conf. on Advanced Optoelectronics and Lasers, CAOL’2003, IEEE/LEOS proceedings, vol. 1, pp. 242-244, Alushta, Ukraine, Sep. 2003. [12] Y. Yamamoto, "AM and FM quantum noise in semiconductor lasers-Part I: theoretical analysis," IEEE J. Quantum Electron., vol. 19, no. 1, pp. 34-46, Jan. 1983.
[13] Y. C. Tseng and J. C. S. Woo, "Phase noise characteristics associated with low-frequency noise in submicron SOI MOSFET feedback oscillator for RF IC’s," IEEE Electron Device Letters,vol. 20, no. 1, pp. 54-56, Jan. 1999.
[14] F. Shahshahani, V. Ahmadi, and K. Mirabbaszadeh, "Concave tapered grating of DFB laser at high power operation for reduced spatial hole-burning effect," Elsevier J. of Materials Science and Engineering B., vol. 96, no. 1, pp. 1-7, Oct. 2002.
[15] C. H. Henry and R. F. Kazarinov, "Quantum noise in photonics," Reviews of Modern Physics, vol. 68, no. 3, pp.801-853, Jul. 1996.
[16] C. Harder, J. Katz, S. Margalit, J. Shacham, and A. Yariv, "Noise equivalent circuit of a semiconductor laser diode," IEEE J. Quantum Electron., vol. 18, no. 3, pp. 333-337, Mar. 1982.
[17] T. T. Bich-Ha and J. Mollier, "Noise equivalent circuit of a two mode semiconductor laser with the contribution of both the linear and the nonlinear gain," IEEE J. Selected Topics in Quantum Electronics, vol. 3, no. 2, pp. 304-308, Apr. 1997.
[18] T. K. Yee, "Analysis of the intensity noise of nearly single longitudinal- mode semiconductor lasers," IEEE J. Quantum Electron., vol. 22, no. 2, pp. 275-285, Feb. 1986.
[19] W. Strefer, A. Hardy, D. R. Scifres, and R. D. Burnham, "Analysis of diode laser properties-Part II," IEEE J. Quantum Electron., vol. 19, no. 6, pp. 991-1001, Jun. 1983.
[20] Y. Z. Shan and B. X. Du, "A theoretical analysis on transmission characteristics of semiconductor lasers," IEEE J. Quantum Electron., vol. 18, no. 4, pp. 601-609, Apr. 1982.
[21] M. Ohtsu and Y. Teramachi, "Analyses of mode partition and mode hopping in semiconductor lasers," IEEE J. Quantum Electron., vol. 25, no. 1, pp. 31-38, Jan. 1989.
[22] M. P. van Exter, M. B. Willemsen, and J. P. Woerdman, "Effect of mode-partition noise on intensity squeezing in a two-mode laser," J. Opt. B: Quantum Semiclass, Opt., vol. 1, no. 6, pp. 637-645,Dec. 1999.
[23] K. Ogawa, "Analysis of mode partition noise in laser transmission systems," IEEE J. Quantum Electron., vol. 18, no. 5, pp. 849-855, May 1982.
[24] T. B. Anderson and B. R. Clarke, "Modeling Mode Partition Noise in Nearly Single-Mode Intensity Modulated lasers," IEEE J. Quantum Electron., vol. 29, no. 1, pp. 3-13, Jan. 1993 .
[25] M. R. Alalusi and R. B. Darling, "Effects of nonlinear gain on mode hopping in semiconductor laser diodes," IEEE J. Quantum Electron.,vol. 31, no. 7, pp. 1181-1192, Jul. 1995.
[26] M. F. S. Ferreira, J. R. F. Rocha, and J. L. Pinto, "Analysis of the frequency noise of tunable multi section DBR lasers," IEEE J. Quantum Electron., vol. 28, no. 4, pp. 833-841, Apr. 1992.
[27] K. P. Ho, "Spectral density of cross-phase modulation induced phase noise," Optics Communications, vol. 169, no. 1-6, pp. 63-68, Oct. 1999.
[28] K. Kikuchi, "Effect of 1/f type noise on semiconductor laser line width residual in high-power limit," IEEE J. Quantum Electron., vol. 25, no. 4, pp. 684-688, Apr. 1989.
[29] Y. Yamamoto, T. Mukai, and S. Saito, "Quantum phase noise and line width of a semiconductor laser," Electronic Letters, vol. 17, no. 9, pp. 327-329, May 1981.
[30] G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed., New York: Van Nostrand Reinhold, 1993.
[31] E. Desurvire, Erbium-Doped Fiber Amplifier, John Wily & Sons Ltd., 1994.
[32] W. Johnstone, B. Culshaw, D. Walsh, D. Moodie, and I. Mauchline, "Student laboratory experiments on erbium doped fiber amplifiers and lasers," SPIE Proceeding in Optics and Photonics, vol. 3831, pp. 259-267, Cancun, Mexico, Jul. 1999.
[33] P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers, Academic Press, 1999.
[34] S. Shimada, Optical Amplifiers and Their Applications, John Wily & Sons Ltd., 1994.
[35] J. H. Franz and V. K. Jain, Optical Communications, Alpha Science International Ltd., 2000.
[36] C. Y. J. Chu and H. Ghafori-Shiraz, "Equivalent circuit theory of spontaneous emission power in semiconductor laser optical amplifiers," J. Lightwave Technology, vol. 12, no. 5, pp. 760-767,May 1994.
[37] H. Ghafori-Shiraz, Fundamentals of Laser Diode Amplifiers, John Wily & Sons Ltd., 1996.
[38] S. M. K. Thiyagarajan and A. F. J. Levi, "Noise in voltage-biased scaled semiconductor laser diodes," Solid-State Electronics, vol. 43, no. 1, pp. 33-39, Jan. 1999.
[39] K. Sato and H. Toba, "Reduction of mode partion noise by using semiconductor optical amplifier," IEEE J. Selected Topics in Quantum Electronics, vol. 7, no. 2, pp. 328-333, Mar./Apr. 2001.
[40] A. A. M. Saleh, "Nonlinear models of traveling-wave optical amplifier," Electronics Letters, vol. 24, no. 14, pp. 835-837, Jul. 1988.
[41] L. Thylen, M. Gustavsson, T. K. Gustafson, I. Kim, and A. Karlsson, "Calculation of photon and current fluctuations in traveling-wave semiconductor laser amplifier," IEEE J. Quantum Electronics, vol. 27, no. 6, pp. 1251-1258, Jun. 1991.
[42] D. Marcuse, "Computer model of an injection laser amplifier," IEEE J. Quantum Electron., vol. 19, no. 1, pp. 63-73, Jan. 1983.
[43] G. Morthier and B. Moeyersoon, "Intensity noise and linewidth of laser diodes with integrated semiconductor optical amplifier," IEEE Photonics Technology Letters, vol. 14, no. 12, pp. 1644-1646, Dec. 2002.
[44] E. S. Bjorlin and J. E. Bowers, "Noise figure of vertical-cavity semiconductor optical amplifiers," IEEE Journal Quantum Electronics, vol. 38, no. 1, pp. 61-66, Jan. 2002.
[45] W. Rideout, E. Eichen, J. Schlafer, J. Lacourse, and E. Meland, "Relative intensity noise in semiconductor optical amplifiers," IEEE Photonics Technology Letters, vol. 1, no. 12 , pp. 438-440,Dec. 1989.
[46] M. A. Summerfield and R. S. Tucker, "Noise figure and conversion efficiency of four-wave mixing in semiconductor optical amplifiers," Electronics Letters, vol. 31, no. 14, pp. 1159-1160, Jul. 1995.
[47] _, Fast Semiconductor Detectors, www.medphys.ucl.ac.uk/research/ borg/homepages/davek/phd/chapter3.pdf, 2002.
[48] A. Yariv, Optical Electronics in Modern Communications, Oxford University Press Inc., 1993.
[49] R. C. Woods, "Noise effects in avalanche photodiodes," IEEE Trans. on Education, vol. 43, no. 3, pp. 321-323, Aug. 2000.
[50] B. K. Ng, J. P. R. David, R. C. Tozer, M. Hopkinson, G. Hill, and G. J. Rees, "Excess noise characteristics of Al0.8Ga0.2As avalanche photodiodes," IEEE Photon. Technology. Letters, vol. 14, no. 4,pp. 522-524, Apr. 2002.
[51] -, Optical Signal-to-Noise Ratio and the Q-Factor in Fiber-Optic Communication Systems, Application Note, MAXIM High Frequency/Fiber Communications Group, http://pdfserv.maximic. com/arpdf/AppNotes/4hfan902.pdf, 2002.
[52] H. J. R. Dutton, Understanding Optical Communications, IBM Corporation, 1998.
[53] A. Cappy, F. Danneville, G. Dambrine, and B. Tamen, "Noise analysis in devices under nonlinear operation," Solid-State Electronics, vol. 43, no. 1, pp. 21-26, Jan. 1999.
[54] A. H. Tehranchi, N. Granpayeh, and E. Mortazy, "Modulation instability in optical fibers in the presence of higher order effects," in Proc Australasian Conference on Optics, Lasers, & Spectroscopy, ACOLS 2003, p. 79, Melbourne, Australia, Dec. 2003.
[55] A. H. Tehranchi, N. Granpayeh, and E. Mortazy, "The effects of noise amplification and soliton generation in anomalous dispersion regime of optical fibers," in Proc. SPIE, Fluctuations and Noise inPhotonics and Quantum Optics II, vol. 5468, pp. 85-92, Spain, May 2004.
[56] E. Mortazy and M. K. Moravvej-Farshi, "A New model for optical communication systems," Journal Optical Fiber Technology, vol. 11, no. 1, pp. 69-80, Jan. 2005.