
312 OPTICS FOR ENGINEERS
contributions are never perfectly matched in phase. In this particular example, an incremental
time delay
t
f
=
dt
df
f ,
with
dt
df
=−(1/3) × 10
−18
s/Hz, as might result from a modest amount of dispersive glass
in the path, is introduced. As can be seen in the gure, the amplitude is lower and the pulse
width is longer.
In Figure 10.1E and F, the laser is not mode-locked and the phase of each mode is chosen
randomly. The sum in Equation 10.17 becomes
E =
12
m=−12
E
m
=
12
m=−12
e
i
{
2π
[
f
center
+m×FSR
]
t+φ
m
}
. (10.18)
This situation is the normal one in multimode lasers, unless special efforts are made to lock
the modes. The resulting irradiance