Page 406 - Tunable Lasers Handbook

366 Paul Zorabedian

between an ambient with index of refraction no and a substrate of index n5, a single
dielectric layer of index

and thickness
t=- h
4% .

will reduce the reflectance to zero at a wavelength h (in air). Because of the finite
lateral extent of the guided optical wave in the laser diode, the optimum coating
design cannot be derived analytically as for plane waves. These formulas are use-
ful only as a guide, with no replaced by unity (refractive index of air) and nx
replaced by rz,n, the modal refractive index of the active-region waveguide. The
modal index depends on the vertical and lateral structure of the laser diode and is
between the bulk reactive indices of the materials used in the active layer and
cladding layers. The design of single-layer antireflection coatings was studied by
Saitoh and coworkers [25]. They found that nopt > n,,, and that topt > h/4nopt where
IZ opt and tOpt are, respectively, the optimum film index and thickness values. They
also showed that the tolerances for achieving a low reflectance with single-layer
coatings are quite small. To achieve a facet reflectance of 10-4 requires film
index and thickness tolerances of f 0.02 and f 2 nm, respectively. However, with
careful process control or real-time in situ monitoring of the facet emission dur-
ing coating [26-281, facet reflectances on the order of 10" can be obtained
reproducibly with single-layer coatings.

2.10.2.2 Multilayer Coating Design
Multilayer dielectric coatings are used to broaden the low-reflectance band-
width and relax the thickness tolerances of the individual layers. Double-layer coat-
ings are applied in a high-low index sequence with the higher index layer in contact
with the substrate. A maximally broad double-layer coating is obtained with
nl = (z)

24
,

h
t2 = __
4n2 '