192
4 Light Sources for Fiber Links
of external modulators are available commercially either as a separate device or as
an integral part of the laser transmitter package.
The basic limitation on the direct modulation rate of laser diodes depends on the
spontaneous and stimulated emission carrier lifetimes and on the photon lifetime. The
spontaneous carrier lifetime τ sp is a function of the semiconductor band structure and
the carrier concentration. At room temperature this lifetime is about 1 ns in GaAsbased materials for dopant concentrations on the order of 10
19 cm
−3 . The stimulated
carrier lifetime τ st depends on the optical density in the lasing cavity and is on the
order of 10 ps. The photon lifetime τ ph is the average time that the photon resides in
the lasing cavity before being lost either by absorption or by emission through the
facets. In a Fabry-Perot cavity, the photon lifetime is
1−3
τ
−1
ph =
c
n
α mat +
1
2L
ln
1
R 1 R 2
=
c
n
g th
(4.49)
For a typical value of g th = 50 cm
−1 and a refractive index in the GaAs lasing
material of n = 3.5, the photon lifetime is approximately τ ph = 2 ps. This value sets
the upper limit to the direct modulation capability of the laser diode.
A laser diode can readily be pulse modulated because the photon lifetime is much
smaller than the carrier lifetime. If the laser is completely turned off after each pulse,
the spontaneous carrier lifetime will limit the modulation rate. This is because, at the
onset of a current pulse of amplitude I p , a period of time t d given by (see Problem
4.19)
t d = τln
I p
I p + (I B − I th )
(4.50)
is needed to achieve the population inversion necessary to produce a gain that is sufficient to overcome the optical losses in the lasing cavity. In Eq. (4.50) the parameter
I B is the bias current, which is a fixed dc current applied to the laser. The parameter
τ is the average lifetime of the carriers in the combination region when the total
current I = I p + I B is close to the threshold current I th . Equation (4.50) shows that by
dc-biasing the diode at the lasing threshold current the delay time can be eliminated.
Pulse modulation is then carried out by modulating the laser only in the operating
region above the threshold current (see Fig. 4.21). In this region, the carrier lifetime
is now shortened to the stimulated emission lifetime, so that high modulation rates
are possible.
When using a directly modulated laser diode for high-speed transmission systems,
the modulation frequency can be no larger than the frequency of the relaxation oscillations of the laser field. The relaxation oscillation depends on both the spontaneous
lifetime and the photon lifetime. Theoretically, assuming a linear dependence of the
optical gain on carrier density, the relaxation oscillation occurs approximately at
4 Light Sources for Fiber Links
of external modulators are available commercially either as a separate device or as
an integral part of the laser transmitter package.
The basic limitation on the direct modulation rate of laser diodes depends on the
spontaneous and stimulated emission carrier lifetimes and on the photon lifetime. The
spontaneous carrier lifetime τ sp is a function of the semiconductor band structure and
the carrier concentration. At room temperature this lifetime is about 1 ns in GaAsbased materials for dopant concentrations on the order of 10
19 cm
−3 . The stimulated
carrier lifetime τ st depends on the optical density in the lasing cavity and is on the
order of 10 ps. The photon lifetime τ ph is the average time that the photon resides in
the lasing cavity before being lost either by absorption or by emission through the
facets. In a Fabry-Perot cavity, the photon lifetime is
1−3
τ
−1
ph =
c
n
α mat +
1
2L
ln
1
R 1 R 2
=
c
n
g th
(4.49)
For a typical value of g th = 50 cm
−1 and a refractive index in the GaAs lasing
material of n = 3.5, the photon lifetime is approximately τ ph = 2 ps. This value sets
the upper limit to the direct modulation capability of the laser diode.
A laser diode can readily be pulse modulated because the photon lifetime is much
smaller than the carrier lifetime. If the laser is completely turned off after each pulse,
the spontaneous carrier lifetime will limit the modulation rate. This is because, at the
onset of a current pulse of amplitude I p , a period of time t d given by (see Problem
4.19)
t d = τln
I p
I p + (I B − I th )
(4.50)
is needed to achieve the population inversion necessary to produce a gain that is sufficient to overcome the optical losses in the lasing cavity. In Eq. (4.50) the parameter
I B is the bias current, which is a fixed dc current applied to the laser. The parameter
τ is the average lifetime of the carriers in the combination region when the total
current I = I p + I B is close to the threshold current I th . Equation (4.50) shows that by
dc-biasing the diode at the lasing threshold current the delay time can be eliminated.
Pulse modulation is then carried out by modulating the laser only in the operating
region above the threshold current (see Fig. 4.21). In this region, the carrier lifetime
is now shortened to the stimulated emission lifetime, so that high modulation rates
are possible.
When using a directly modulated laser diode for high-speed transmission systems,
the modulation frequency can be no larger than the frequency of the relaxation oscillations of the laser field. The relaxation oscillation depends on both the spontaneous
lifetime and the photon lifetime. Theoretically, assuming a linear dependence of the
optical gain on carrier density, the relaxation oscillation occurs approximately at