5.4 Summary
239
Table 5.1 For Problem 5.8
Coupling losses (in dB) for given axial misalignments
Core/cladding diameters (μm) 1
3
5
10
50/125
0.112
0.385 0.590 0.266
62.5/125
0.089
0.274 0.465 0.985
100/140
0.56
0.169 0.286 0.590
Table 5.2 For Problem 5.12
Parameter
Fiber 1
Fiber 2
Core index n 1
1.46
1.48
Index difference
0.010
0.015
Core radius a
50 μm
62.5 μm
Profile factor
2.00
1.80
the values α R /α E = 0.5, 0.7, and 0.9 are −6.02 dB, −3.10 dB, and −0.92 dB,
respectively.
5.10 Consider Eq. (5.36) that gives the coupling loss for two fibers with unequal
axial numerical apertures. Show that the coupling losses in decibels for the
values NA R (0)/NA E (0) = 0.5, 0.7, and 0.9 are -6.02 dB, -3.10 dB, and -
0.92 dB, respectively.
5.11 Consider Eq. (5.37) that gives the coupling loss for two fibers with different
core refractive-index profiles. If α E = 2.20, what are the coupling losses when
(a) α R = 1.80, (b) α R = 2.00? [Answers: (a) 0.44 dB; (b) 0.20 dB].
5.12 Consider two multimode graded-index fibers that have the characteristics
given in Table 5.2. If these two fibers are perfectly aligned with no gap
between them, calculate the splice losses and the coupling efficiencies for the
following cases:
Light going from fiber 1 to fiber 2.
Light going from fiber 2 to fiber 1.
[Answers: (a) L 1 → 2 (α) = 0.24 dB; (b) L 2 → 1 (a) = 1.94 dB, L 2 → 1 (NA)
= 1.89 dB].
References
1. Y. Uematsu, T. Ozeki, Y. Unno, Efficient power coupling between an MH LED and a taper-ended
multimode fiber. IEEE J. Quantum Electron. 15, 86–92 (1979)
2. H. Kuwahara, M. Sasaki, N. Tokoyo, Efficient coupling from semiconductor lasers into singlemode fibers with tapered hemispherical ends. Appl. Opt. 19, 2578–2583 (1980)
3. D. Marcuse, LED fundamentals: comparison of front and edge-emitting diodes. IEEE J.
Quantum Electron. 13, 819–827 (1977)
4. B.E.A. Saleh, M. Teich, Fundamentals of Photonics, 3 rd edn. (Wiley, 2019)
239
Table 5.1 For Problem 5.8
Coupling losses (in dB) for given axial misalignments
Core/cladding diameters (μm) 1
3
5
10
50/125
0.112
0.385 0.590 0.266
62.5/125
0.089
0.274 0.465 0.985
100/140
0.56
0.169 0.286 0.590
Table 5.2 For Problem 5.12
Parameter
Fiber 1
Fiber 2
Core index n 1
1.46
1.48
Index difference
0.010
0.015
Core radius a
50 μm
62.5 μm
Profile factor
2.00
1.80
the values α R /α E = 0.5, 0.7, and 0.9 are −6.02 dB, −3.10 dB, and −0.92 dB,
respectively.
5.10 Consider Eq. (5.36) that gives the coupling loss for two fibers with unequal
axial numerical apertures. Show that the coupling losses in decibels for the
values NA R (0)/NA E (0) = 0.5, 0.7, and 0.9 are -6.02 dB, -3.10 dB, and -
0.92 dB, respectively.
5.11 Consider Eq. (5.37) that gives the coupling loss for two fibers with different
core refractive-index profiles. If α E = 2.20, what are the coupling losses when
(a) α R = 1.80, (b) α R = 2.00? [Answers: (a) 0.44 dB; (b) 0.20 dB].
5.12 Consider two multimode graded-index fibers that have the characteristics
given in Table 5.2. If these two fibers are perfectly aligned with no gap
between them, calculate the splice losses and the coupling efficiencies for the
following cases:
Light going from fiber 1 to fiber 2.
Light going from fiber 2 to fiber 1.
[Answers: (a) L 1 → 2 (α) = 0.24 dB; (b) L 2 → 1 (a) = 1.94 dB, L 2 → 1 (NA)
= 1.89 dB].
References
1. Y. Uematsu, T. Ozeki, Y. Unno, Efficient power coupling between an MH LED and a taper-ended
multimode fiber. IEEE J. Quantum Electron. 15, 86–92 (1979)
2. H. Kuwahara, M. Sasaki, N. Tokoyo, Efficient coupling from semiconductor lasers into singlemode fibers with tapered hemispherical ends. Appl. Opt. 19, 2578–2583 (1980)
3. D. Marcuse, LED fundamentals: comparison of front and edge-emitting diodes. IEEE J.
Quantum Electron. 13, 819–827 (1977)
4. B.E.A. Saleh, M. Teich, Fundamentals of Photonics, 3 rd edn. (Wiley, 2019)