23.4 Lasers
669
Fig. 23.44 SEM image of
a an InP microlaser with
third-order Bragg mirrors,
b magnified view of the
front facet with three slabs,
c a 12-µm long microlaser
with five third-order
mirrors on the rear side and
three first-order mirrors on
the front side with top
contact. From [1988]; part
b reprinted with permission
from [1987], ©2001 AIP
(c)
(a)
(b)
Longitudinal Modes
The spectral positions of the laser modes for a cavity with length L is given by the condition (cf.
(19.39))
L =
m λ
2 n r (λ)
,
(23.15)
where m is a natural number and n(λ) is the dispersion of the index of refraction. The distance of
neighboring modes is given by (for large m)
=
λ
2
2 n r L
1 −
λ
n r
dn r
dλ
.
(23.16)
The dispersion dn r /dλ can sometimes be neglected.
The facets of edge-emitting lasers are typically cleaved. Cleaving bears the danger of mechanical
breakage and tends to have poor reproducibility, low yield and therefore high cost. Etched facets are
another possibility to form the cavity mirror. The etch process, typically reactive ion dry etching, must
yield sufficiently smooth surfaces to avoid scattering losses. A highly efficient distributed Bragg mirror
(cf. Sect. 19.1.4) with only a few periods can be created by using the large index contrast between the
semiconductor and air. As shown in Fig. 23.44, slabs can be etched that make a Bragg mirror with the
air gaps [1987]. In this way, very short longitudinal cavities can be made (≈ 10 µm).
23.4.5 Loss Mechanisms
While the light travels through the cavity, it is not only amplified but it also suffers losses. The internal
loss α i and the mirror loss α m contribute to the total loss α tot
α tot = α i + α m .
(23.17)
The internal loss is due to absorption in the cladding, scattering at waveguide inhomogeneities and
possibly other processes. It can be written as
α i = α 0 + α g (1 − ) ,
(23.18)
669
Fig. 23.44 SEM image of
a an InP microlaser with
third-order Bragg mirrors,
b magnified view of the
front facet with three slabs,
c a 12-µm long microlaser
with five third-order
mirrors on the rear side and
three first-order mirrors on
the front side with top
contact. From [1988]; part
b reprinted with permission
from [1987], ©2001 AIP
(c)
(a)
(b)
Longitudinal Modes
The spectral positions of the laser modes for a cavity with length L is given by the condition (cf.
(19.39))
L =
m λ
2 n r (λ)
,
(23.15)
where m is a natural number and n(λ) is the dispersion of the index of refraction. The distance of
neighboring modes is given by (for large m)
=
λ
2
2 n r L
1 −
λ
n r
dn r
dλ
.
(23.16)
The dispersion dn r /dλ can sometimes be neglected.
The facets of edge-emitting lasers are typically cleaved. Cleaving bears the danger of mechanical
breakage and tends to have poor reproducibility, low yield and therefore high cost. Etched facets are
another possibility to form the cavity mirror. The etch process, typically reactive ion dry etching, must
yield sufficiently smooth surfaces to avoid scattering losses. A highly efficient distributed Bragg mirror
(cf. Sect. 19.1.4) with only a few periods can be created by using the large index contrast between the
semiconductor and air. As shown in Fig. 23.44, slabs can be etched that make a Bragg mirror with the
air gaps [1987]. In this way, very short longitudinal cavities can be made (≈ 10 µm).
23.4.5 Loss Mechanisms
While the light travels through the cavity, it is not only amplified but it also suffers losses. The internal
loss α i and the mirror loss α m contribute to the total loss α tot
α tot = α i + α m .
(23.17)
The internal loss is due to absorption in the cladding, scattering at waveguide inhomogeneities and
possibly other processes. It can be written as
α i = α 0 + α g (1 − ) ,
(23.18)