Page 155 - Fiber Optic Communications Fund

136 Fiber Optic Communications

Exercises
3.1 Explain the three processes by which a ligh twave interacts with an atom.

3.2 The operating wavelength of an optical source is 400 nm. Calculate the ratio of spontaneous to stim-
ulated emission rate under thermal equilibrium. Assume T = 293 K. Is the optical source coherent?
Provide an explanation.
33
(Ans: 4.12 × 10 .No.)
3.3 In an atomic system, the spontaneous lifetime associated with 2 → 1 transition is 3 ns and the Einstein
2
21
3
coefficient B is 6 × 10 m ∕J ⋅ s . Calculate the energy difference between the levels 1 and 2. Assume
8
that the speed of light is 1.5 × 10 m∕s.
(Ans: 2.73 × 10 −19 J.)
3.4 In an atomic system under thermal equilibrium conditions, the population density of the ground level
26
is 2 × 10 m −3 and the energy difference between the levels is 1.5 eV. Calculate the population density
∘
of the excited level. Assume that the temperature is 30 C.
−3
(Ans: 22 m .)
3.5 Under thermal equilibrium conditions, the ratio of spontaneous emission rate to stimulated emission
26
−3
17
rate is 2.33 × 10 , the population density of the ground state is 1.5 × 10 m , and the temperature
is 300 K. Calculate (a) the energy difference between the levels and (b) the population density of the
excited level.
8
−3
(Ans: (a) 1.65 × 10 −19 J; (b) 6.47 × 10 m .)
3.6 An electron has a momentum of 4.16 × 10 −26 kg ⋅ m∕s. Calculate (a) the De Brogile wavelength and
(b) the wavenumber.
−8
−1
8
(Ans: (a) 1.59 × 10 m; (b) 3.94 × 10 m .)
−1
3.7 A Fabry–Perot laser diode has a cavity length of 250 μm, the internal loss coefficient is 45 cm , and
the photon lifetime is 1.18 ps. Calculate the mirror reflectivity. Assume that the reflectivities are equal
7
and the velocity of light in the active region is 9.09 × 10 m/s.
(Ans: R = R = 0.299.)
2
1
3.8 If one end of the laser cavity of Exercise 3.7 is coated with a dielectric reflector so that its reflectivity
is 0.95, calculate the photon lifetime. Other parameters are the same as in Exercise 3.7.
(Ans: 1.56 ps.)
3.9 Show that the peak wavelength of the light emitted is related to the band-gap energy by
1.24
(μm)= .
E (eV)
g
Here, (μm) indicates that the wavelength is in units of μm.