144
3 Optical Signal Attenuation and Dispersion
3.10 (b) p(a) = 0.1 P 0 = P 0 e
−Ka
2 yields e
Ka
2 = 10.
This yields Ka
2
= ln 10 = 2.3.
Thus α gi = α 1 +
(α2−α1)
2.3
= 0.57α 1 + 0.43α 2
3.12
Wavelength λ
Calculated n
n from Fig. 3.9
0.2 μm
1.548
1.550
0.6 μm
1.457
1.458
1.0 μm
1.451
1.450
3.13 (a) From Eq. (3.28) for the LED σ mat /L = 3.6 ns/km
(b) For the laser diode, σ mat /L = 0.16 ns/km
References
1. D. Gloge, The optical fibre as a transmission medium. Rpts. Prog. Phys. 42, 1777–1824 (1979)
2. D.B. Keck, Fundamentals of optical waveguide fibers. IEEE Commun. Mag. 23, 17–22 (1985)
3. J.D. Musgraves, J. Hu, L. Calvez, Springer Handbook of Glass (Springer, Berlin, 2019)
4. R. Olshansky, Propagation in glass optical waveguides. Rev. Mod. Phys. 51, 341–367 (1979)
5. S.R. Nagel, in Fiber Materials and Fabrication Methods, ed. by S.E. Miller, I.P. Kaminow.
Optical Fiber Telecommunications–II (Academic, 1988)
6. K. Nagayama, M. Matsui, M. Kakui, T. Saitoh, K. Kawasaki, H. Takamizawa, Y. Ooga, I.
Tsuchiya, Y. Chigusa, Ultra low loss (0.1484 dB/km) pure silica core fiber. SEI Tech. Rev. 57,
3–6 (2003)
7. R. Maurer, Glass fibers for optical communications. Proc. IEEE 61, 452–462 (1973)
8. D.A. Pinnow, T.C. Rich, F.W. Ostermeyer, M. DiDomenico Jr., Fundamental optical attenuation
limits in the liquid and gassy state with application to fiber optical waveguide material. Appl.
Phys. Lett. 22, 527–529 (1973)
9. W.A. Gambling, H. Matsumura, C.M. Ragdale, Curvature and microbending losses in singlemode optical fibers. Opt. Quantum Electron. 11(1), 43–59 (1979)
10. T. Murao, K. Nagao, K. Saitoh, M. Koshiba, Design principle for realizing low bending losses
in all-solid photonic bandgap fibers. J. Lightw. Technol. 29(16), 2428–2435 (2011)
11. D. Gloge, Bending loss in multimode fibers with graded and ungraded core index. Appl. Opt.
11, 2506–2512 (1972)
12. J. Sakai, T. Kimura, Practical microbending loss formula for single mode optical fibers. IEEE
J. Quantum Electron. QE-15, 497–500 (1979)
13. D. Gloge, Optical fiber packaging and its influence on fiber straightness and loss. Bell Sys.
Tech. J. 54, 245–262 (1975)
14. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd edn. (Academic Press, 1991)
15. D. Gloge, E.A.J. Marcatili, D. Marcuse, S.D. Personick, in Dispersion Properties of Fibers, ed.
by S.E. Miller, A.G. Chynoweth. Optical Fiber Telecommunications (Academic Press, 1979)
16. D. Marcuse, Interdependence of waveguide and material dispersion. Appl. Opt. 18, 2930–2932
(1979)
17. D. Gloge, Weakly guiding fibers. Appl. Opt. 10, 2252–2258 (1971); Dispersion in weakly
guiding fibers. Appl. Opt. 10, 2442–2445 (1971)
18. A.E. Willner, S.M.R. Motaghian Nezam, L. Yan, Z. Pan, M.C. Hauer, Monitoring and control
of polarization-related impairments in optical fiber systems. J. Lightw. Technol. 22, 106–125
(2004)
3 Optical Signal Attenuation and Dispersion
3.10 (b) p(a) = 0.1 P 0 = P 0 e
−Ka
2 yields e
Ka
2 = 10.
This yields Ka
2
= ln 10 = 2.3.
Thus α gi = α 1 +
(α2−α1)
2.3
= 0.57α 1 + 0.43α 2
3.12
Wavelength λ
Calculated n
n from Fig. 3.9
0.2 μm
1.548
1.550
0.6 μm
1.457
1.458
1.0 μm
1.451
1.450
3.13 (a) From Eq. (3.28) for the LED σ mat /L = 3.6 ns/km
(b) For the laser diode, σ mat /L = 0.16 ns/km
References
1. D. Gloge, The optical fibre as a transmission medium. Rpts. Prog. Phys. 42, 1777–1824 (1979)
2. D.B. Keck, Fundamentals of optical waveguide fibers. IEEE Commun. Mag. 23, 17–22 (1985)
3. J.D. Musgraves, J. Hu, L. Calvez, Springer Handbook of Glass (Springer, Berlin, 2019)
4. R. Olshansky, Propagation in glass optical waveguides. Rev. Mod. Phys. 51, 341–367 (1979)
5. S.R. Nagel, in Fiber Materials and Fabrication Methods, ed. by S.E. Miller, I.P. Kaminow.
Optical Fiber Telecommunications–II (Academic, 1988)
6. K. Nagayama, M. Matsui, M. Kakui, T. Saitoh, K. Kawasaki, H. Takamizawa, Y. Ooga, I.
Tsuchiya, Y. Chigusa, Ultra low loss (0.1484 dB/km) pure silica core fiber. SEI Tech. Rev. 57,
3–6 (2003)
7. R. Maurer, Glass fibers for optical communications. Proc. IEEE 61, 452–462 (1973)
8. D.A. Pinnow, T.C. Rich, F.W. Ostermeyer, M. DiDomenico Jr., Fundamental optical attenuation
limits in the liquid and gassy state with application to fiber optical waveguide material. Appl.
Phys. Lett. 22, 527–529 (1973)
9. W.A. Gambling, H. Matsumura, C.M. Ragdale, Curvature and microbending losses in singlemode optical fibers. Opt. Quantum Electron. 11(1), 43–59 (1979)
10. T. Murao, K. Nagao, K. Saitoh, M. Koshiba, Design principle for realizing low bending losses
in all-solid photonic bandgap fibers. J. Lightw. Technol. 29(16), 2428–2435 (2011)
11. D. Gloge, Bending loss in multimode fibers with graded and ungraded core index. Appl. Opt.
11, 2506–2512 (1972)
12. J. Sakai, T. Kimura, Practical microbending loss formula for single mode optical fibers. IEEE
J. Quantum Electron. QE-15, 497–500 (1979)
13. D. Gloge, Optical fiber packaging and its influence on fiber straightness and loss. Bell Sys.
Tech. J. 54, 245–262 (1975)
14. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd edn. (Academic Press, 1991)
15. D. Gloge, E.A.J. Marcatili, D. Marcuse, S.D. Personick, in Dispersion Properties of Fibers, ed.
by S.E. Miller, A.G. Chynoweth. Optical Fiber Telecommunications (Academic Press, 1979)
16. D. Marcuse, Interdependence of waveguide and material dispersion. Appl. Opt. 18, 2930–2932
(1979)
17. D. Gloge, Weakly guiding fibers. Appl. Opt. 10, 2252–2258 (1971); Dispersion in weakly
guiding fibers. Appl. Opt. 10, 2442–2445 (1971)
18. A.E. Willner, S.M.R. Motaghian Nezam, L. Yan, Z. Pan, M.C. Hauer, Monitoring and control
of polarization-related impairments in optical fiber systems. J. Lightw. Technol. 22, 106–125
(2004)