11.2 Semiconductor Optical Amplifiers
445
current is applied to the device, show that the pumping rate R p = 1.25 × 10
33
(electrons/m
3 )/s. (b) Show that the zero-signal gain is g 0 = 750 m
−1 .
11.2.2 Amplifier Signal Gain
One of the most obviously important parameters of an optical amplifier is the signal
gain or amplifier gain G, which is defined as
G =
P s,out
P s,in
(11.8)
where P s,in and P s,out are the input and output powers, respectively, of the optical
signal being amplified. As noted in Chap. 4, the radiation intensity at a photon
energy hv varies exponentially with the distance traversed in a lasing cavity. Hence,
using Eq. (4.23), the single-pass gain in the active medium of the SOA is
G = exp[(g m − α mat )L] ≡ exp[g(z)L]
(11.9)
where is the optical confinement factor in the cavity, g m is the material gain
coefficient, α mat is the effective absorption coefficient of the material in the optical
path, L is the amplifier length, and g(z) is the overall gain per unit length.
Equation (11.9) shows that the gain increases with device length. However, the
internal gain is limited by gain saturation. This occurs because the carrier density
in the gain region of the amplifier depends on the optical input intensity. As the
input signal level is increased, excited carriers (electron–hole pairs) are depleted
from the active region. When there is a sufficiently large optical input power, further
increases in the input signal level no longer yield an appreciable change in the output
level because there are not enough excited carriers to provide an appropriate level of
stimulated emission. Note here that the carrier density at any point z in the amplifying
cavity depends on the signal level P s (z) at that point. In particular, near the input where
z is small, incremental portions of the device may not have reached saturation at the
same time as the sections farther down the device, where incremental portions may
be saturated because of higher values of P s (z).
An expression for the gain G as a function of the input power can be derived
by examining the gain parameter g(z) in Eq. (11.9). This parameter depends on the
carrier density and the signal wavelength. Using Eqs. (11.4) and (11.6), then at a
distance z from the input end, g(z) is given by
g(z) =
g 0
1 +
P s (z)
P amp,sat
(11.10)
445
current is applied to the device, show that the pumping rate R p = 1.25 × 10
33
(electrons/m
3 )/s. (b) Show that the zero-signal gain is g 0 = 750 m
−1 .
11.2.2 Amplifier Signal Gain
One of the most obviously important parameters of an optical amplifier is the signal
gain or amplifier gain G, which is defined as
G =
P s,out
P s,in
(11.8)
where P s,in and P s,out are the input and output powers, respectively, of the optical
signal being amplified. As noted in Chap. 4, the radiation intensity at a photon
energy hv varies exponentially with the distance traversed in a lasing cavity. Hence,
using Eq. (4.23), the single-pass gain in the active medium of the SOA is
G = exp[(g m − α mat )L] ≡ exp[g(z)L]
(11.9)
where is the optical confinement factor in the cavity, g m is the material gain
coefficient, α mat is the effective absorption coefficient of the material in the optical
path, L is the amplifier length, and g(z) is the overall gain per unit length.
Equation (11.9) shows that the gain increases with device length. However, the
internal gain is limited by gain saturation. This occurs because the carrier density
in the gain region of the amplifier depends on the optical input intensity. As the
input signal level is increased, excited carriers (electron–hole pairs) are depleted
from the active region. When there is a sufficiently large optical input power, further
increases in the input signal level no longer yield an appreciable change in the output
level because there are not enough excited carriers to provide an appropriate level of
stimulated emission. Note here that the carrier density at any point z in the amplifying
cavity depends on the signal level P s (z) at that point. In particular, near the input where
z is small, incremental portions of the device may not have reached saturation at the
same time as the sections farther down the device, where incremental portions may
be saturated because of higher values of P s (z).
An expression for the gain G as a function of the input power can be derived
by examining the gain parameter g(z) in Eq. (11.9). This parameter depends on the
carrier density and the signal wavelength. Using Eqs. (11.4) and (11.6), then at a
distance z from the input end, g(z) is given by
g(z) =
g 0
1 +
P s (z)
P amp,sat
(11.10)