10.8 Summary
431
Problems
10.1 A DWDM optical transmission system is designed to have 100-GHz channel
spacings. How many wavelength channels can be utilized in the 1536-to1556-nm spectral band?
10.2 Assume that a 32-channel DWDM system has uniform channel spacings of
ν = 100 GHz and let the frequency ν n correspond to the wavelength λ n .
Using this correspondence, let the wavelength λ 1 = 1550 nm. Calculate the
wavelength spacing between the first two channels (between channels 1 and
2) and between the last two channels (between channels 31 and 32). From
the result, what can be concluded about using an equal wavelength spacing
definition in this wavelength band instead of the standard equal frequency
channel spacing specification?
10.3 Assume that for a given tap coupler the throughput and coupled powers are
230 μW and 5 μW, respectively, for an input power of 250 μW.
(a) What is the coupling ratio?
(b) What are the insertion losses?
(c) Find the excess loss of the coupler.
10.4 A product sheet for a 2 × 2 single-mode biconical tapered coupler with a 40/60
splitting ratio states that the insertion losses are 2.7 dB for the 60-percent
channel and 4.7 dB for the 40-percent channel.
(a) If the input power P 0 = 200 μW, find the output levels P 1 and P 2 .
(b) Find the excess loss of the coupler.
(c) From the calculated values of P 1 and P 2 , verify that the splitting ratio is
40/60.
10.5 Consider the coupling ratios as a function of pull lengths shown in Fig. 10.34
for a fused biconical tapered coupler. The performances are given for 1310nm and 1540-nm operation. Discuss the behavior of the coupler for each
wavelength if its pull length is stopped at the following points: A, B, C, D,
E, and each F.
10.6 Suppose an engineer has two 2 × 2 waveguide couplers (couplers A and B)
that have identical channel geometries and spacings, and are formed on the
same substrate material. If the index of refraction of coupler A is larger than
that of coupler B, which device has a larger coupling coefficient κ? What
does this imply about the device lengths needed in each case to form a 3-dB
coupler?
10.7 Consider an optical fiber transmission star coupler that has seven inputs and
seven outputs. Suppose the coupler is constructed by arranging the seven
fibers in a circular pattern (a ring of six with one in the center). This fiber
bundle then is put against the end a glass rod that serves as the mixing element.
Let the rod diameter be 300 μm.
431
Problems
10.1 A DWDM optical transmission system is designed to have 100-GHz channel
spacings. How many wavelength channels can be utilized in the 1536-to1556-nm spectral band?
10.2 Assume that a 32-channel DWDM system has uniform channel spacings of
ν = 100 GHz and let the frequency ν n correspond to the wavelength λ n .
Using this correspondence, let the wavelength λ 1 = 1550 nm. Calculate the
wavelength spacing between the first two channels (between channels 1 and
2) and between the last two channels (between channels 31 and 32). From
the result, what can be concluded about using an equal wavelength spacing
definition in this wavelength band instead of the standard equal frequency
channel spacing specification?
10.3 Assume that for a given tap coupler the throughput and coupled powers are
230 μW and 5 μW, respectively, for an input power of 250 μW.
(a) What is the coupling ratio?
(b) What are the insertion losses?
(c) Find the excess loss of the coupler.
10.4 A product sheet for a 2 × 2 single-mode biconical tapered coupler with a 40/60
splitting ratio states that the insertion losses are 2.7 dB for the 60-percent
channel and 4.7 dB for the 40-percent channel.
(a) If the input power P 0 = 200 μW, find the output levels P 1 and P 2 .
(b) Find the excess loss of the coupler.
(c) From the calculated values of P 1 and P 2 , verify that the splitting ratio is
40/60.
10.5 Consider the coupling ratios as a function of pull lengths shown in Fig. 10.34
for a fused biconical tapered coupler. The performances are given for 1310nm and 1540-nm operation. Discuss the behavior of the coupler for each
wavelength if its pull length is stopped at the following points: A, B, C, D,
E, and each F.
10.6 Suppose an engineer has two 2 × 2 waveguide couplers (couplers A and B)
that have identical channel geometries and spacings, and are formed on the
same substrate material. If the index of refraction of coupler A is larger than
that of coupler B, which device has a larger coupling coefficient κ? What
does this imply about the device lengths needed in each case to form a 3-dB
coupler?
10.7 Consider an optical fiber transmission star coupler that has seven inputs and
seven outputs. Suppose the coupler is constructed by arranging the seven
fibers in a circular pattern (a ring of six with one in the center). This fiber
bundle then is put against the end a glass rod that serves as the mixing element.
Let the rod diameter be 300 μm.