EE 230
Optical Fiber Communications
Homework 1
1. Light traveling in air strikes a glass plate at an angle θ1=33º, where θ1 is measured
between the incoming ray and the glass surface. Upon striking the glass, part of the beam
is reflected, and part is refracted. If the reflected and refracted beams make an angle of
90º with each other, what is the refractive index of the glass? What is the critical angle
for this glass?
2. Calculate the numerical aperture of a step-index fiber having indices of 1.48 and 1.46.
What is the maximum acceptance angle for this fiber if the external medium is air, with
n=1.00?
3. A step-index fiber has a 25-µm core radius, a core index of 1.48, and a cladding index
of 1.46. For each of the wavelengths 820 nm, 1320 nm, and 1550 nm, what is the
normalized frequency parameter V, the number of modes guided by the fiber, and the
percentage of the optical power flowing in the cladding?
4. Find the core radius necessary for single-mode operation at 1320 nm of a step-index
fiber with core index 1.480 and cladding index 1.478. What are the numerical aperture
and maximum acceptance angle of this fiber?
5. Calculate the number of modes at 820 nm and 1.3 µm in a graded-index fiber having
α=2, a 25-µm core radius, n1=1.48, and n2=1.46. How does this compare to a step-index
fiber?
6. Optical fiber is made by drawing a solid preform of diameter D at a speed S into an
apparatus where it emerges with diameter d and at speed s. Using conservation of mass,
derive an expression for s in terms of D,S, and d. A typical drawing speed s is 1.2 m/s for
a 125-µm diameter (d) fiber. What is the preform feed rate S in cm/min for a 9-mm
diameter (D) preform?
7. Consider an optical link consisting of a 5 km-long step-index fiber with core index
1.49 and ∆=1.0%. Find the delay difference at the fiber end between the slowest and
fastest modes. Calculate the maximum bit rate that can be transmitted over the fiber link
without significant errors. What is the bandwidth-distance product of this fiber?