Application of multiple-length-scale methods to the study of optical fiber transmission
- C. R. Menyuk
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It is natural to apply multiple-length-scale methods to the study of optical-fiber transmission because the key length scales span 13 orders of magnitude and cluster in three main groups. At the lowest scale, corresponding to micrometers, the full set of Maxwell's equations should be used. At the intermediate scale, corresponding to the range from one centimeter to tens of meters, the coupled nonlinear Schrödinger equation should be used. Finally, at the longest length scale, corresponding to the range from tens to thousands of kilometers, the Manakov-PMD equation should be used, and, when polarization mode dispersion can be neglected and the fiber gain and loss can be averaged out, one arrives at the scalar nonlinear Schrödinger equation. As an illustrative example of multiple-scale-length techniques, the nonlinear Schrödinger equation will be derived, carefully taking into account the actual length scales that are important in optical-fiber transmission.
- N. Bloembergen, Nonlinear Optics. Reading (MA): Benjamin (1965) 229 pp.
- Y. R. Shen, The Principles of Nonlinear Optics. New York: Wiley (1984) 563 pp.
- G. P. Agrawal, Nonlinear Fiber Optics. San Diego: Academic (1995) 592 pp.
- A. Hasegawa and Y. Kodama, Solitons in Optical Communications. Oxford: Clarendon (1995) 320 pp.
- A. Hasegawa and F. D. Tappert, Transmission of stationary nonlinear pulses optical pulses in dispersive dielectric fibers. I. Anomalous dispersion. Appl. Phys. Lett. 23 (1973) 142–144.
- C. R. Menyuk, Pulse propagation in an elliptically birefringent Kerr medium. IEEE J. Quantum Electron. 25 (1989) 2674–2682.
- C. R. Menyuk, Impairments due to nonlinearity and birefringence in optical fiber transmission systems. In: A. E. Willner and C. R. Menyuk (eds), System Technologies. Washington: Optical Society of America TOPS Vol. 12 (1997) 523 pp.
- S. B. Alexander, The WDM Revolution. In: A. E. Willner and C. R. Menyuk (eds), System Technologies. Washington: Optical Society of America TOPS Vol. 12 (1997) 523 pp.
- Examples of currently available commercial software packages are BroadNeD and OPALS by Virtual Photonics F.C.
- H. Poincaré, Les méthodes nouvelles de la mécanique céleste, tome I. Paris: Gauthier-Villars (1892) 385 pp.
- A large number of such problems can be found cited by H. Minorsky, Nonlinear Oscillations. Princeton (NJ): Van Nostrand (1962) 714 pp.; A. Nayfeh, Perturbation Methods. New York: Wiley (1973) 425 pp.
- Y. Kodama, Optical solitons in a monomode fiber. J. Stat. Phys. 39 (1985) 597–614.
- P. Appell, Henri Poincaré. Paris: Plon-Nourrit (1925) 121 pp.
- J. Gowar, Optical Communication Systems. New York: Prentice Hall (1993) 696 pp.
- C. R. Menyuk, D. Wang and A. N. Pilipetskii, Repolarization of polarization-scrambled signals due to polarization dependent loss. IEEE Photon. Technol. Lett. 9 (1997) 1247–1249.
- A. R. Chraplyvy, Limitations on lightwave communications imposed by optical-fiber nonlinearities. J. Lightwave Technol. 8 (1990) 1548–1557.
- R. W. Hellwarth, Third-order optical susceptibilities of liquids and solids. Prog. Quant. Electron. 5 (1977) 1–68.
- C. R. Menyuk, M. N. Islam and J. P. Gordon, Raman effect in birefringent optical fibers. Opt. Lett. 16 (1991) 566–568.
- R. H. Stolen, J. P. Gordon, W. J. Tomlinson and H. A. Haus, Raman response function of silica core fibers. J. Opt. Soc. Am. B 6 (1989) 1159–1166.
- P. K. A. Wai and C. R. Menyuk, Polarization decorrelation in optical fibers with randomly varying birefringence. Opt. Lett. 19 (1994) 1517–1519.
- P. K. A. Wai and C. R. Menyuk, Anisotropic diffusion of the state of polarization in optical fibers with randomly varying birefringence. Opt. Lett. 20 (1995) 2490–2492.
- C. R. Menyuk and P. K. A. Wai, Polarization evolution and dispersion in fibers with spatially varying birefringence. J. Opt. Soc. Am. B 11 (1994) 1288–1296.
- P. K. A. Wai and C. R. Menyuk, Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence. J. Lightwave Technol. 14 (1996) 148–157.
- C. D. Poole and J. Nagel, Polarization effects in lightwave systems. In: I. P. Kaminow and T. L. Koch (eds), Optical Fiber Telecommunications, Vol. IIIA. San Diego: Academic (1997) 608 pp.
- C. D. Poole, Statistical treatment of polarization dispersion in single-mode fiber. Opt. Lett. 13 (1988) 687–689.
- D. Marcuse, C. R. Menyuk and P. K. A. Wai, Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence. J. Lightwave Technol. 15 (1997) 1735–1746.
- L. F. Mollenauer, S. G. Evangelides, Jr. and H. A. Haus, Long-distance soliton propagation using lumped amplifiers and dispersion shifted fiber. J. Lightwave Technol. 9 (1991) 194–197.
- K. J. Blow and N. J. Doran, Average soliton dynamics and the operation of soliton systems with lumped amplifiers. IEEE Photon. Technol. Lett. 3 (1991) 369–371.
- J. C. Bronski and J. N. Kutz, Modulational stability of plane waves in nonreturn-to-zero communications systems with dispersion management. Opt. Lett. 21 (1996) 937–939.
- S. K. Turitsyn, Theory of average pulse propagation in high-bit-rate optical transmission systems with strong dispersion management. JETP Lett. 65 (1997) 845–851, (Pisma Zh. Eksp. Tear. Fiz. 65 (1997) 812–817).
- Y. Kodama, S. Kumar and A. Manuta, Chirped nonlinear pulse propagation in a dispersion-compensated system. Opt. Lett. 22 (1997) 1689–1691.
- Application of multiple-length-scale methods to the study of optical fiber transmission
Journal of Engineering Mathematics
Volume 36, Issue 1-2 , pp 113-136
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- optical fibers
- multiple length scales
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- C. R. Menyuk (1)
- Author Affiliations
- 1. Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, Baltimore, MD, 21250, U.S.A