6.2. SEMICONDUCTOR OPTICAL AMPLIFIERS 233
whereR 1 andR 2 are the facet reflectivities,νmrepresents the cavity-resonance frequen-
cies [see Eq. (3.3.5)], and∆νLis the longitudinal-mode spacing, also known as the free
spectral range of the FP cavity. The single-pass amplification factorGcorresponds to
that of a TW amplifier and is given by Eq. (6.1.7) when gain saturation is negligible.
Indeed,GFPreduces toGwhenR 1 =R 2 =0.
As evident from Eq. (6.2.1),GFP(ν)peaks wheneverνcoincides with one of the
cavity-resonance frequencies and drops sharply in between them. The amplifier band-
width is thus determined by the sharpness of the cavity resonance. One can calculate
the amplifier bandwidth from the detuningν−νmfor whichGFPdrops by 3 dB from
its peak value. The result is given by
∆νA=
2 ∆νL
πsin−^1(
1 −G
√
R 1 R 2
( 4 G
√
R 1 R 2 )^1 /^2
)
. (6.2.2)
To achieve a large amplification factor,G
√
R 1 R 2 should be quite close to 1. As seen
from Eq. (6.2.2), the amplifier bandwidth is then a small fraction of the free spectral
range of the FP cavity (typically,∆νL∼100 GHz and∆νA<10 GHz). Such a small
bandwidth makes FP amplifiers unsuitable for most lightwave system applications.
TW-type SOAs can be made if the reflection feedback from the end facets is sup-
pressed. A simple way to reduce the reflectivity is to coat the facets with anantire-
flection coating. However, it turns out that the reflectivity must be extremely small
(<0.1%) for the SOA to act as a TW amplifier. Furthermore, the minimum reflectivity
depends on the amplifier gain itself. One can estimate the tolerable value of the facet
reflectivity by considering the maximum and minimum values ofGFPfrom Eq. (6.2.1)
near a cavity resonance. It is easy to verify that their ratio is given by
∆G=
GmaxFP
GminFP=
(
1 +G
√
R 1 R 2
1 −G
√
R 1 R 2
) 2
. (6.2.3)
If∆Gexceeds 3 dB, the amplifier bandwidth is set by the cavity resonances rather
than by the gain spectrum. To keep∆G<2, the facet reflectivities should satisfy the
condition
G
√
R 1 R 2 < 0. 17. (6.2.4)
It is customary to characterize the SOA as a TW amplifier when Eq. (6.2.4) is satisfied.
A SOA designed to provide a 30-dB amplification factor (G=1000) should have facet
reflectivities such that
√
R 1 R 2 < 1. 7 × 10 −^4.
Considerable effort is required to produce antireflection coatings with reflectivities
less than 0.1%. Even then, it is difficult to obtain low facet reflectivities in a predictable
and regular manner. For this reason, alternative techniques have been developed to
reduce the reflection feedback in SOAs. In one method, the active-region stripe is tilted
from the facet normal, as shown in Fig. 6.4(a). Such a structure is referred to as the
angled-facetortilted-stripestructure [9]. The reflected beam at the facet is physically
separated from the forward beam because of the angled facet. Some feedback can still
occur, as the optical mode spreads beyond the active region in all semiconductor laser
devices. In practice, the combination of an antireflection coating and the tilted stripe
can produce reflectivities below 10−^3 (as small as 10−^4 with design optimization). In