23.4 Lasers
689
Fig. 23.75 Schematic
cycle of hole motion in a
hot-hole laser. Filled
(empty) circles represent
populated (unpopulated)
hole states. The solid lines
represent streaming motion
of heavy hole, the dashed
line represents scattering
into the light hole band.
Arrows denote radiative
intervalence-band
transitions
h ph
k
E V
hh
lh
A significant scattering process of hot carriers is interaction with optical phonons, mainly optical
phonon emission. This process has a threshold in carrier energy given by the optical phonon energy.
For sufficiently high electric fields and at low temperature, hot carriers accelerate without acoustical
phonon interaction (ballistic transport) along the crystallographic direction in which the electric field
is applied. These hot carriers reach the optical phonon energy and lose all their energy due to emission
of an optical phonon. They accelerate again, repeating this directional motion in momentum space.
This motion is called streaming motion.
For |E/B| ratios of about 1.5 kV/cmT, the heavy holes are accelerated up to energies above the optical
phonon energy (37 meV in germanium) and consequently are scattered strongly by these phonons.
Under these conditions, a few per cent of the heavy holes are scattered into the light-hole band. The
light holes remain at much lower energies and are accumulated at the bottom of the light-hole band
below the optical phonon energy as sketched in Fig. 23.75. The continuous pumping of heavy holes
into the light-hole band can lead to a population inversion. Consequently, laser radiation is emitted
from optical (radiative) intervalence-band transitions (cf. Sect. 9.9.3). The emission wavelength is in
the far-infrared around 100 µm. Typical p-Ge lasers span the frequency range 1–4 THz (300–70 µm)
[2036] and deliver 1–10 W peak output power for 1 cm
3 typical active volume.
Since the applied electric field causes considerable heating, the temperature of the laser crystal rises
quickly, within a few µs, up to 40 K. Then the laser action stops. Thus the duration of the electric-field
excitation is limited to 1–5 µs (limiting the emission power) and the repetition frequency is only a
few Hertz due to the necessary cooling. Research is underway towards high duty cycle (possibly cw)
operation by using smaller volumes and planar vertical-cavities [2037, 2038].
23.5 Semiconductor Optical Amplifiers
If the facets of a laser cavity are antireflection coated, a laser gain medium can be used as a semiconductor optical amplifier (SOA). A textbook on this subject is [2039]. Optical feedback from facets can
also be avoided using tilted facets [2040].
A tapered amplifier geometry, as shown in Fig. 23.76a, allows for laterally monomode input and a
preservation of the lateral beam quality during the propagation of the optical wave through the gain
medium. The active medium is an 8-nm compressively strained InGaAs quantum well. A typical taper
angle is 5–10
◦ . The input aperture is between 5 and 7 µm. The amplifier length is 2040 µm. More
than 20 dB optical amplification can be obtained (Fig. 23.76b). The self-oscillation is suppressed for
689
Fig. 23.75 Schematic
cycle of hole motion in a
hot-hole laser. Filled
(empty) circles represent
populated (unpopulated)
hole states. The solid lines
represent streaming motion
of heavy hole, the dashed
line represents scattering
into the light hole band.
Arrows denote radiative
intervalence-band
transitions
h ph
k
E V
hh
lh
A significant scattering process of hot carriers is interaction with optical phonons, mainly optical
phonon emission. This process has a threshold in carrier energy given by the optical phonon energy.
For sufficiently high electric fields and at low temperature, hot carriers accelerate without acoustical
phonon interaction (ballistic transport) along the crystallographic direction in which the electric field
is applied. These hot carriers reach the optical phonon energy and lose all their energy due to emission
of an optical phonon. They accelerate again, repeating this directional motion in momentum space.
This motion is called streaming motion.
For |E/B| ratios of about 1.5 kV/cmT, the heavy holes are accelerated up to energies above the optical
phonon energy (37 meV in germanium) and consequently are scattered strongly by these phonons.
Under these conditions, a few per cent of the heavy holes are scattered into the light-hole band. The
light holes remain at much lower energies and are accumulated at the bottom of the light-hole band
below the optical phonon energy as sketched in Fig. 23.75. The continuous pumping of heavy holes
into the light-hole band can lead to a population inversion. Consequently, laser radiation is emitted
from optical (radiative) intervalence-band transitions (cf. Sect. 9.9.3). The emission wavelength is in
the far-infrared around 100 µm. Typical p-Ge lasers span the frequency range 1–4 THz (300–70 µm)
[2036] and deliver 1–10 W peak output power for 1 cm
3 typical active volume.
Since the applied electric field causes considerable heating, the temperature of the laser crystal rises
quickly, within a few µs, up to 40 K. Then the laser action stops. Thus the duration of the electric-field
excitation is limited to 1–5 µs (limiting the emission power) and the repetition frequency is only a
few Hertz due to the necessary cooling. Research is underway towards high duty cycle (possibly cw)
operation by using smaller volumes and planar vertical-cavities [2037, 2038].
23.5 Semiconductor Optical Amplifiers
If the facets of a laser cavity are antireflection coated, a laser gain medium can be used as a semiconductor optical amplifier (SOA). A textbook on this subject is [2039]. Optical feedback from facets can
also be avoided using tilted facets [2040].
A tapered amplifier geometry, as shown in Fig. 23.76a, allows for laterally monomode input and a
preservation of the lateral beam quality during the propagation of the optical wave through the gain
medium. The active medium is an 8-nm compressively strained InGaAs quantum well. A typical taper
angle is 5–10
◦ . The input aperture is between 5 and 7 µm. The amplifier length is 2040 µm. More
than 20 dB optical amplification can be obtained (Fig. 23.76b). The self-oscillation is suppressed for