Page 109 - Fiber Optic Communications Fund

90 Fiber Optic Communications

2.3 A step-index multi-mode fiber has to be designed to support bit rates up to 10 Mb/s. The link length is
1.5 km. Calculate the upper limit on the relative index difference, Δ. Assume the core refractive index
is approximately equal to the cladding refractive index.
(Ans: Δ ≤ 0.02.)
∘
2.4 In a step-index multi-mode fiber, the critical angle for the core–cladding interface is 85 . The core
refractive index is 1.46 and the core diameter is 100 μm. Find (a) the V-number and (b) the approximate
number of guided modes M at the wavelength 1.3 μm.
(Ans: V = 25.79, M = 332.)

2.5 The maximum achievable bit rate–distance product in a step-index multi-mode fiber is 16 Mb/s⋅km.
The core refractive index n (≈ cladding index n ) = 1.45. Calculate (a) the numerical aperture and (b)
1 2
the critical angle for the core–cladding interface.
(Ans: (a) 0.2795; (b) 1.3768 rad.)

2.6 A step-index multi-mode fiber has an acceptable angle of 0.2077 rad and the critical angle for the
core–cladding interface is 1.4266 rad. Calculate the speed of light in the fiber core. It may be assumed
that ray-optics theory is valid.

8
(Ans: 2.076 × 10 m/s.)
2.7 A single-mode fiber has to be designed to operate at 1.55 μm with a cutoff wavelength less than 1.5 μm.
The core and cladding refractive indices are 1.45 and 1.445, respectively. Calculate the maximum
allowable core radius.

(Ans: 4.77 μm.)
2.8 The power launched into a fiber is 5 mW and the power at the fiber output is 0.3 mW. Calculate the
fiber loss in dBm units.
(Ans: 12.22 dBm.)

2.9 A 40-km single-mode fiber has a dispersion parameter D = 10 ps/nm⋅km. An optical signal of band-
width 10 GHz is launched into the fiber. Find the delay between the highest- and lowest-frequency
components. The carrier wavelength = 1.55 μm.
(Ans: 32.033 ps.)
2.10 A single-mode fiber has a zero-dispersion wavelength at 1550 nm. The dispersion slope =
2
0.06 ps/nm /km. Find the absolute dispersion |D| at 1600 nm. Assume that the dispersion varies
linearly with wavelength.
(Ans: 3 ps/nm/km.)
2.11 A Gaussian pulse is transmitted in a long single-mode fiber with dispersion coefficient =
2
2
−10 ps /km. The input and output pulse widths (FWHM) are 8 ps and 32 ps, respectively. Calculate
the fiber length.
(Ans: 8.9 km.)