4.3 Principles of Laser Diodes
179
For an uncoated cleaved facet the reflectivity is only about 30%. To reduce the
loss in the cavity and to make the optical feedback stronger, the facets typically are
coated with a dielectric material. This can produce a reflectivity of about 99 percent
for the rear facet and 90% for the front facet through which the lasing light emerges.
At the lasing threshold, a steady-state oscillation takes place, and the magnitude
and phase of the returned wave must be equal to those of the original wave. This
gives the conditions
I(2L) = I(0)
(4.26)
for the amplitude and
e
− j2β L
= 1
(4.27)
for the phase. Equation (4.27) gives information concerning the resonant frequencies of the Fabry-Perot cavity. This is discussed further in Sect. 4.3.2. From Eq. (4.26)
one can determine which modes have sufficient gain for sustained oscillation, and
one can find the amplitudes of these modes. The condition to just reach the lasing
threshold is the point at which the optical gain is equal to the total loss α t in the
cavity. From Eq. (4.26), this condition is
g th = α t = α mat +
1
2L
ln
1
R 1 R 2
= α mat + α end
(4.28)
where α end is the end mirror loss in the lasing cavity. Thus, for lasing to occur it
is necessary to have the gain g ≥ g th . This means that the pumping source that
maintains the population inversion must be sufficiently strong to support or exceed
all the energy-consuming mechanisms within the lasing cavity.
The mode that satisfies Eq. (4.28) reaches threshold first. Theoretically, at the onset
of this condition, all additional energy introduced into the laser should augment the
growth of this particular mode. In practice, various phenomena lead to the excitation
of more than one mode. Studies on the conditions needed for longitudinal singlemode operation show that important factors are thin active regions and a high degree
of temperature stability.
Example 4.11 Assume for GaAs that R 1 = R 2 = R = 0.32 for uncoated facets (i.e.,
32 percent of the radiation is reflected at a facet) and α mat ≈ 10 cm
−1 . What is the
gain threshold for a 500-μm long laser diode (Note: L = 500 × 10
-4 cm
-1 )?
Solution From Eq. (4.28)
g th = α mat +
1
2L
ln
1
R 2
= 10 +
1
2
500 × 10 −4
ln
1
(0.32) 2
= 33 cm
−1
179
For an uncoated cleaved facet the reflectivity is only about 30%. To reduce the
loss in the cavity and to make the optical feedback stronger, the facets typically are
coated with a dielectric material. This can produce a reflectivity of about 99 percent
for the rear facet and 90% for the front facet through which the lasing light emerges.
At the lasing threshold, a steady-state oscillation takes place, and the magnitude
and phase of the returned wave must be equal to those of the original wave. This
gives the conditions
I(2L) = I(0)
(4.26)
for the amplitude and
e
− j2β L
= 1
(4.27)
for the phase. Equation (4.27) gives information concerning the resonant frequencies of the Fabry-Perot cavity. This is discussed further in Sect. 4.3.2. From Eq. (4.26)
one can determine which modes have sufficient gain for sustained oscillation, and
one can find the amplitudes of these modes. The condition to just reach the lasing
threshold is the point at which the optical gain is equal to the total loss α t in the
cavity. From Eq. (4.26), this condition is
g th = α t = α mat +
1
2L
ln
1
R 1 R 2
= α mat + α end
(4.28)
where α end is the end mirror loss in the lasing cavity. Thus, for lasing to occur it
is necessary to have the gain g ≥ g th . This means that the pumping source that
maintains the population inversion must be sufficiently strong to support or exceed
all the energy-consuming mechanisms within the lasing cavity.
The mode that satisfies Eq. (4.28) reaches threshold first. Theoretically, at the onset
of this condition, all additional energy introduced into the laser should augment the
growth of this particular mode. In practice, various phenomena lead to the excitation
of more than one mode. Studies on the conditions needed for longitudinal singlemode operation show that important factors are thin active regions and a high degree
of temperature stability.
Example 4.11 Assume for GaAs that R 1 = R 2 = R = 0.32 for uncoated facets (i.e.,
32 percent of the radiation is reflected at a facet) and α mat ≈ 10 cm
−1 . What is the
gain threshold for a 500-μm long laser diode (Note: L = 500 × 10
-4 cm
-1 )?
Solution From Eq. (4.28)
g th = α mat +
1
2L
ln
1
R 2
= 10 +
1
2
500 × 10 −4
ln
1
(0.32) 2
= 33 cm
−1