Page 214 - Introduction to Information Optics

Exercises 1 99

photons are incident on the receiver during a single 1 bit ? (assume equal
one and zeros).
3.3 A bare silica fiber has n l = 1.46, n 2 — 1.0, and radius a = 25 /mi. Under
the maximum angle of incidence,
(a) Calculate the number of reflections that would take place in travers-
ing a kilometer length of the fiber.
(b) Assuming a loss of only 0.01% of power at each reflection at the
core-cladding interface, calculate the corresponding loss in dB/km.
=
3.4 Consider a single mode optical fiber with n 1 = 15 and w 2 1-485 at
wavelength A — 0.82 /mi. If the core radius is 50 /mi, how many modes
can propagate? Repeat if the wavelength is changed to 1.2 /mi (Hint;
Students can use the approximation formula for large V number.)
3.5 Consider a step index fiber with n l = 1.45, A = 0.003, and a = 3 /mi.
(a) For X = 0.9 /mi, calculate the value of V. Is this single mode fiber?
Explain why or why not.
(b) For A = 1.55 /mi, recalculate the effective refractive index, n, for this
fiber. (Hint: A simple computer program made from MathCAD,
MatLAB, C++ may be used.)
3.6 A single mode fiber has n t = 1.465, n 2 = 1.45, operating at A = 1.55 f.im.
Draw the transversal mode field dispersion for (a) radius a = 2.3 /mi and
(b) a— 1.3 /mi.
3.7 In a fiber-optic communication system, the light source is an LED
operating at A = 0.85 /mi with a spectral width of 30 nm. Calculate the
material dispersion AT in 1 km due to material dispersion and the
maximum bit rate for this fiber.
3.8 Repeat Prob. 3.7 if the light source becomes a laser with a spectral width
of 1 nm.
3.9 Consider a step index silica fiber operating at 1550 nm. If we know that
n 2 — 1.45, A = 0.00905, a = 2.15 /<m, and the light source spectral band-
width Ax, = 1 nm, calculate the waveguide dispersion for this single mode
fiber 1 km long. (Hint: The approximation formula

0.08 + 0.549 x (2.834 - V) 2
dV

can be used.)
3.10 Describe the principles of the light-emitting diode and the diode laser.
3.11 Sketch the output light spectrum of the LED, conventional diode laser,
and DFB diode laser.
3.12 A GaAs laser diode has 1.5 nm gain linewidth and a cavity length of 0.5
mm. Sketch the output spectrum, including the emitted wavelengths and
the number of longitudinal modes. Assume that n = 3.35, A = 0.9 /*m.