172
4 Light Sources for Fiber Links
so that 1 + (ωτ i )
2
= 4, or ωτ i =
√
3 . Solving this expression for the frequency ω
= 2πf yields
f =
√
3
2πτ i
=
√
3
2π × 5 × 10 −9 = 55.1 MHz
(b) The 3-dB electrical bandwidth is f /
√
2 = 0.707 (55.1 MHz) = 39.0 MHz.
Sometimes, the modulation bandwidth of an LED is given in terms of the 3-dB
bandwidth of the modulated optical power P(ω); that is, it is specified at the frequency
where P(ω) = P 0 /2. In this case, the 3-dBbandwidth is determined from the ratio of
the optical power at frequency ω to the unmodulated value of the optical power P 0 .
Because the detected current is directly proportional to the optical power, this ratio
is
Ratio optical = 10 log
P(ω)
P(0)
= 10 log
I (ω)
I (0)
(4.21)
The optical 3-dB point occurs at that frequency where the ratio of the currents is
equal to 1/2. As shown in Fig. 4.15, this gives an inflated value of the modulation
bandwidth, which corresponds to an electrical power attenuation of 6 dB.
Drill Problem 4.5 A GaAlAs LED with an active region width of 1.0 μm
operates at 300°K at a current density level of J = 100 A/cm
2 . Assuming the
steady-state electron density at this current density is n = 6 × 10
16 cm
−3 , first
use Eq. (4.8) to calculate that the carrier lifetime τ is 9.6 ns. With this value
of τ, use the expression given in Example 4.8 to show that the 3-dB cutoff
frequency is 28.7 MHz.
4.3 Principles of Laser Diodes
Lasers come in many forms with dimensions ranging from the size of a grain of salt
to one that will occupy an entire room. The lasing medium can be a gas, a liquid, an
insulating crystal (solid state), or a semiconductor. For optical fiber systems the laser
sources used almost exclusively are semiconductor laser diodes. They are similar to
other lasers, such as the conventional solid-state and gas lasers, in that the emitted
radiation has spatial and temporal coherence; that is, the output radiation is highly
monochromatic and the light beam is very directional.
Despite their physical and material differences, the basic principle of operation
is the same for each type of laser. Laser action is the result of three key processes:
4 Light Sources for Fiber Links
so that 1 + (ωτ i )
2
= 4, or ωτ i =
√
3 . Solving this expression for the frequency ω
= 2πf yields
f =
√
3
2πτ i
=
√
3
2π × 5 × 10 −9 = 55.1 MHz
(b) The 3-dB electrical bandwidth is f /
√
2 = 0.707 (55.1 MHz) = 39.0 MHz.
Sometimes, the modulation bandwidth of an LED is given in terms of the 3-dB
bandwidth of the modulated optical power P(ω); that is, it is specified at the frequency
where P(ω) = P 0 /2. In this case, the 3-dBbandwidth is determined from the ratio of
the optical power at frequency ω to the unmodulated value of the optical power P 0 .
Because the detected current is directly proportional to the optical power, this ratio
is
Ratio optical = 10 log
P(ω)
P(0)
= 10 log
I (ω)
I (0)
(4.21)
The optical 3-dB point occurs at that frequency where the ratio of the currents is
equal to 1/2. As shown in Fig. 4.15, this gives an inflated value of the modulation
bandwidth, which corresponds to an electrical power attenuation of 6 dB.
Drill Problem 4.5 A GaAlAs LED with an active region width of 1.0 μm
operates at 300°K at a current density level of J = 100 A/cm
2 . Assuming the
steady-state electron density at this current density is n = 6 × 10
16 cm
−3 , first
use Eq. (4.8) to calculate that the carrier lifetime τ is 9.6 ns. With this value
of τ, use the expression given in Example 4.8 to show that the 3-dB cutoff
frequency is 28.7 MHz.
4.3 Principles of Laser Diodes
Lasers come in many forms with dimensions ranging from the size of a grain of salt
to one that will occupy an entire room. The lasing medium can be a gas, a liquid, an
insulating crystal (solid state), or a semiconductor. For optical fiber systems the laser
sources used almost exclusively are semiconductor laser diodes. They are similar to
other lasers, such as the conventional solid-state and gas lasers, in that the emitted
radiation has spatial and temporal coherence; that is, the output radiation is highly
monochromatic and the light beam is very directional.
Despite their physical and material differences, the basic principle of operation
is the same for each type of laser. Laser action is the result of three key processes: