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Homework 6 solution
1. P7.25: A 100/240 silica optical fiber has a core index of 1.460 and a cladding index
of 1.450. Estimate the number of propagating modes for a source wavelength (a) 850
nm, (b) 1300 nm and (c) 1550 nm.
For a 100 micrometer diameter fiber we have a = 50 x 10-6 m. Then,
2
  (50 x106 ) 
a  2
2
2
2
N  2
n

n

2
c 
  f

  (1.46)  (1.45) 

  


2
N
1.436 x109
2
.
(a) for 850 nm we have
1.436 x109
N
 1990
(850 x109 )2
Likewise, (b) N = 850 and (c) N = 598.
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2. P7.27: Suppose nf = 1.475 and nc = 1.470. Determine the numerical aperture for a
source of light incident from air. What is the maximum core diameter allowed to
support only a single propagating mode if the source wavelength is 1300 nm?
NA  sin  a 
amax 
n 2f  nc2
n0
 k01
2 n2f  nc2

1.4752  1.4702
 0.121
1
1300 x10   2.405  4.1 m,

9
2  0.121
diameter  2amax  8.2 m.
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3. P7.30: A 10. km optical link is established between a typical LED and a typical PIN
photodiode using a 1300 nm graded-index multimode fiber. Find the power margin
and the maximum frequency analog signal that can be supported by this link. Assume
2 connectors and 4 splices.
Power budget:
Source
Source-to-fiber
Connector
Fiber (1dB/km * 10km)
4 splices (.05dB each)
Connector
Fiber-to-detector
0dBm
-12dB
-0.7dB
-10dB
-0.2dB
-0.7dB
-1.5dB
-25.1dB
Power Margin=-25.1dB-(-35dBm)= 9.9dB
Frequency budget:
(from Table 7.5)
(from Table 7.5)
(from Table 7.2)
(from Table 7.5)
(from Table 7.5)
(from Table 7.5)
ENE 429 01/49
For an LED with  = 50 nm,
ns nm 

tchrom   0.003
  50nm 10km   1.5ns (see Tables 7.2, 7.3)
km 

also
ns 

tinterm   0.5
 10km   5ns (see Table 7.2)
km 

Combining,
2
2
t f  tchrom
 tinterm
 1.5ns 2  0.5ns 2  5.22ns
and using LED risetime of 10 ns from Table 7.3, and PIN diode risetime of 0.3 ns
from Table 7.4,
ts  tt2  t 2f  tr2 
10ns    5.22ns    0.3ns 
2
2
2
 11.28ns.
The rise-time budget is satisfied for t < T/2, so T > 2t, or Tmin = 22.6 ns. Since
T=1/f, we have fmax =1/Tmin=44 MHz.