Homework #1
1. Calculate the frequency of the following optical wavelengths λ=800nm, 1300nm,
1550nm.
2. If two optical signals have a frequency separation of Δf=100GHz, what is the
wavelength separation if one of the wavelengths is λ=1550nm?
3. Assume that a digital communication system can be operated at a bit rate up to 1% of
the carrier frequency. How many audio channels at 64 kb/s can be transmitted over a
microwave carrier at f=5GHz and at λ=1.55μm?
4. A 1 hour lecture script is stored on a computer hard disk in the ASCII format.
Estimate the total number of bits assuming a delivery rate of 200 words per minute
and an average 5 letters per word. How long will it take to transmit the script at a bit
rate of 10 Gb/s?
For problems 5-7
A symmetric slab waveguide has a slab index of refraction of n2=1.5 and surrounding
refractive indices of n1=1.49.
5. What is the range of the propagation constant, β, for this waveguide?
6. What is the range of effective indices of the waveguide?
7. What is the numerical aperture of this waveguide?
Homework #2
For all problems in this homework assignment assume a wavelength of λ=1550nm.
1. A symmetric slab waveguide has a slab index of refraction of n2=1.5 and surrounding
refractive indices of n1=1.49. What is the range of waveguide thicknesses for which
this waveguide will be single mode?
2. A slab waveguide has a thickness of d=5μm, a slab index of refraction of n2=1.5 and
surrounding refractive indices of n1=1.49.
a. How many TE modes does the waveguide support?
b. How many TM modes does the waveguide support?
Figure 1
3. Figure 1 shows a ridge waveguide. n1=n3=1.5 and n2=1.6.
a. Calculate the ridge thickness t such that the second mode is cut-off at the
wavelength of λ=1 μm. (The single mode operating range is λ>1μm)
b. If d=0.8t and a=10μm, calculate the effective indices of all of the supported
modes.
4. Calculate the mode designations for the lowest 5 modes of a step index optical fiber
and calculate the normalized frequency of their cut-offs.
Homework #3
1. Problem 3.6 from the book parts b-e
2. A step index multimode fiber with a 50 μm core diameter is designed to limit the
intermodal dispersion to D=10 ns/km. What is the numerical aperture of this fiber?
Use a group index of refraction of 1.45.
3. Calculate the intermodal dispersion of the multimode optical fiber whose
specification sheet is on the web site.
n  nclad
4. A single mode fiber has an index contrast of   core
 0.0036.
ncore
a. If the cladding material is fused silica (see Table 1.1 in the book), what is the
index of refraction of the core? Use a wavelength of λ=1300nm.
b. Calculate the core radius if the fiber has a cutoff wavelength of 1.3μm.
c. Estimate the spot size (FWHM) of the fiber mode and the fraction of the mode
power inside the core when this fiber is used ay λ=1300nm. Use the
w
approximation  0.65  1.619V 3 / 2  2.879V 6 , where the electric field is
a
 2 
given by E  Eo exp   2  exp  j z  .
 w 
5. An optical communication link is constructed using a laser with a power of 8mW and
a receiver with a sensitivity of -18.5dBm. Assume that the loss associated with
coupling the laser to the optical fiber and the fiber to the receiver are respectively 1dB
and 0.5dB. The optical fiber comes in length of 10km and the loss associated with
splicing fiber section together is 0.1dB/splice. If the laser wavelength varies between
λ=1300nm and λ=1550nm what are the maximum and minimum link lengths. Use
SMF28 optical fiber.
6. Assume a propagation mode of an optical fiber has the following dispersion
relationship:

 2 
n1   12   z2  z ,

a
  
where a=30μm is the diameter of the core. Let the refractive indices of the core and
cladding be 1.50 and 1.49, respectively.
(a) Find the cutoff wavelength above which the mode cannot propagate. Express this
cutoff wavelength in terms of n1, n2, and a.
(b) Find the group velocity as a function of the wavelength at 1.30μm. Let n1g=1.55.
(c) At 1.30μm, assume the material dispersion is zero. Find the intramodal
dispersion of this propagation mode.
2
Homework 4
1. An optical communications link is constructed with SMF28 optical fiber (use
λo=1310nm) and operated with a bit rate of B=10Gbps. What is the maximum
distance using the following optical sources? (Ignore any attenuation limits.)
a. An infrared LED with a center wavelength of λ=1310nm and a linewidth of
∆λ=30nm.
b. A FP laser diode with a center wavelength of λ=1310nm and a linewidth of
∆λ=1nm.
c. A FP laser diode with a center wavelength of λ=850nm and a linewidth of
∆λ=1nm.
d. A DFB laser diode with a center wavelength of λ=1550nm and a linewidth of
∆f=20MHz.
2. A communications link is designed with SMF28 optical fiber, a receiver that has a
minimum detectable power is Pmin=-20dBm, a laser that has a power of 10mW, a
center wavelength of λ=1550nm and a linewidth of =1nm. The coupling between
the laser and fiber is 60% and between the fiber and detector is 80%. The fiber comes
in 5km sections. Each splice between fiber sections is 0.2dB and you need to design
the link with a 3dB margin of error.
a. What is the maximum link length?
b. What is the maximum bit rate at this link length?
Homework 5
1. Problem 7.3 in the book
2. Problem 7.6 in the book
3. Find a spec sheet on the web for a Fabry Perot laser diode with wavelength at
λ=1310nm.
a. What is the laser linewidth?
b. What is the laser power?
4. Find a spec sheet on the web for a DFB laser diode with wavelength at λ=1550nm.
a. What is the laser linewidth?
b. What is the laser power?
5. Find a spec sheet for dispersion compensating optical fiber (DCF). What is the length
ratio between the DCF and SMF28 for zero total dispersion?
6. If we assume that the fiber attenuation can be fixed with optical amplifiers and
dispersion can be fixed with dispersion compensating components, then the link
limitation becomes PMD. An optical link is designed to meet the OC-768 standard.
a. What is the data rate of OC-768?
b. Using the SMF28 spec sheet, what is the maximum length that this data rate
can be transmitted? (Ignore attenuation and chromatic dispersion.)