Page 80 - Fiber Optic Communications Fund

Optical Fiber Transmission 61

Thus, we see that the power is proportional to the absolute square of the field envelope s(t, z). Throughout
this book, unless otherwise specified, we set K = 1 so that the absolute square of the electric field envelope
is equal to the power.
Often it is convenient to use the logarithmic unit for power. The optical power in dBm units is expressed as
[ ]
power (mW)
power (dBm) = 10 log 10 . (2.124)
1mW
In Eq. (2.124), 1 mW is chosen as a reference power and the letter “m” in dBm is a reminder of the 1 mW
reference. For example, 1 mW of transmitter power corresponds to 0 dBm. If the transmitter power is increased
to 2 mW, a factor of 2 in linear scale corresponds to 3 dB, and, therefore, in this case, the transmitter power is
3 dBm. Note that the optical power expressed in dBm units is not really a unit of power such as mW, but the
ratio of the power in mW and 1 mW expressed in dB units. Typically, the loss and gain in a fiber-optic system
are expressed in dB units. The advantage of using dBm units is that multiplications and divisions involving
power and loss factors can be replaced by additions and subtractions as illustrated in Examples 2.8 and 2.9.
Inverting Eq. (2.124), we find

power (mW) = 10 power (dBm)∕10 mW. (2.125)

Example 2.4

The power transmitted in a fiber-optic system is 0.012 W. (a) Convert this into dBm units. (b) The received
power is −5 dBm. Convert this into mW units.

Solution:
(a) From Eq. (2.124), the transmitted power in dBm units is
[ 12 mW ]
P (dBm)= 10 log = 10.79 dBm. (2.126)
tr 10
1mW
(b) The received power is
P (dBm)=−5 dBm. (2.127)
rec
Using Eq. (2.125), we find
P (mW)= 10 −5∕10 mW = 0.3162 mW. (2.128)
rec

Example 2.5 Rectangular Pulse
The laser shown in Fig. 2.26 operates at 375 THz. It is turned on for 50 ps and then turned off. Sketch the field
2
envelope at the screen if the medium is (a) free space, (b) fiber with = 0, (c) fiber with =−21 ps /km.
2
2
Ignore fiber loss.
Solution:
Under steady-state conditions, the electric field intensity of a CW laser (ignoring the transverse field distri-
bution) may be written as
F(t, 0)= f(t)= A exp [−i2f t], (2.129)
0