Appendix A
System of Units
The international system of units (known as the SI, short forSyst`eme International)is
used in this book. The three fundamental units in the SI are meter (m), second (s), and
kilogram (kg). A prefix can be added to each of them to change its magnitude by a
multiple of 10. Mass units are rarely required in this book. Most common measures
of distance used are km (10^3 m) and Mm (10^6 m). On the other hand, common time
measures are ns (10−^9 s), ps (10−^12 s), and fs (10−^15 s). Other common units in this
book are Watt (W) for optical power and W/m^2 for optical intensity. They can be related
to the fundamental units through energy because optical power represents the rate of
energy flow (1 W = 1 J/s). The energy can be expressed in several other ways using
E=hν=kBT=mc^2 , wherehis the Planck constant,kBis the Boltzmann constant, and
cis the speed of light. The frequencyνis expressed in hertz (1 Hz = 1 s−^1 ). Of course,
because of the large frequencies associated with the optical waves, most frequencies in
this book are expressed in GHz or THz.
In the design of optical communication systems the optical power can vary over
several orders of magnitude as the signal travels from the transmitter to the receiver.
Such large variations are handled most conveniently using decibel units, abbreviated
dB, commonly used by engineers in many different fields. Any ratioRcan be converted
into decibels by using the general definition
R(in dB)=10 log 10 R. (A.1)The logarithmic nature of the decibel allows a large ratio to be expressed as a much
smaller number. For example, 10^9 and 10−^9 correspond to 90 dB and−90 dB, respec-
tively. SinceR=1 corresponds to 0 dB, ratios smaller than 1 are negative in the decibel
system. Furthermore, negative ratios cannot be written using decibel units.
The most common use of the decibel scale occurs for power ratios. For instance,
the signal-to-noise ratio (SNR) of an optical or electrical signal is given by
SNR=10 log 10 (PS/PN), (A.2)wherePSandPNare the signal and noise powers, respectively. The fiber loss can also
be expressed in decibel units by noting that the loss corresponds to a decrease in the