EE 606: 2013-2014/II (Spring)
Home Assignment 1 Feb 10, 2014
1. A point source of light is 12 cm below the surface of a large
body of water (n = 1.33 for water). What is the radius of the
largest circle on the water surface through which the light
can emerge? (Keiser, 5ed., Prob.2.8).
2. Calculate the numerical aperture of a step-index fiber having
n1 = 1.48 and n2 = 1.46. What is the maximum entrance angle 0max
for this fiber if the outer medium is air with n = 1.00? (Keiser,
5ed., Prob.2.12).
3. A step-index multimode fiber with a numerical aperture of
0.20 supports approximately 1000 modes at an 850 nm wavelength.
a) What is the diameter of its core?
b) How many modes does the fiber support at 1320 nm?
c) How many modes does the fiber support at 1550 nm?
(Keiser, 5ed., Prob.2.18).
4. Determine the normalized frequency at 820nm for a step-index
fiber having a 25 m core radius, n1 = 1.48, and n2 = 1.46.
a) How many modes propagate in this fiber at 820nm?
b) How many modes propagate in this fiber at 1320nm?
c) How many modes propagate in this fiber at 1550nm?
(Keiser, 5ed., Prob. 2.19).
5. Find the core radius necessary for single-mode operation at
1320nm of a step-index fiber with n1 = 1.480 and n2 = 1.478. What
are the numerical aperture and maximum acceptance
angle of this fiber? (Prob. 2.21).
6. A manufacturer wishes to make a silica-core step-index fiber
with V = 75 and a numerical aperture NA = 0.30 to be used at 820
nm. If n1 = 1.458, what should the core size and
cladding index be? (Keiser, 4th
ed., Prob.2.22).
7. Draw a design curve of the fractional refractive index
difference versus the core radius a for a silica core (n1 = 1.458),
single-mode fiber to operate at 1300 nm. Suppose the fiber we
select from this curve has a 5 m core radius. Is this fiber
still single-mode at 820nm? Which modes exist in the fiber at
820nm? (Keiser, 4
th ed., Prob.2.23).
8. Commonly available single-mode fibers have beat lengths in
the range 10 cm < Lp < 2 m. What range of birefringent
refractive index differences does this correspond to for
= 1300 nm? (Keiser, 5ed., Prob.2.25).
9. Calculate the number of modes at 820nm and 1.3 m in a
graded-index fiber having a parabolic-index profile ( = 2), a 25 m
core radius, n1 = 1.48, and n2 = 1.46. How does this compare to a
step-index fiber? (Keiser, 5ed., Prob.2.27).
