Integrated Optics - Applied Optics Fundamentals and Device Applications - page 233

the loss due to interface scattering will be at most a few tenths of a dB cm −1 .
Surface variations of less than 0.01 μm can be obtained in AlGaAs rectan-
gular waveguides produced by either chemical etching, reactive ion etch-
ing, or sputtering etching. It should be possible to limit scattering loss even
further in strip-loaded waveguides which have less sidewall scattering loss.
One technique that has been used to minimize the effect of surface rough-
ness is to either deposit a thin passivation layer on the surface or to grow a
thin GaAs or AlGaAs layer on top of the waveguide. These techniques may
be necessary anyway to protect the surface from high field strengths and
outside contamination [20]. The layers must be very thin (∼0.1 μm) for devices
that rely on the electro-optic effect because the overlap of the electric field
will be reduced as the layer thickness increases.
Propagation loss due to free-carrier absorption is not a significant problem
in AlGaAs waveguides because the carrier concentration can be adequately
reduced in the waveguiding layer. The classical expression for the attenua-
tion coefficient due to free-carrier concentration is [21]

3 2

Ne
n m

λ

0

α

fc =

(5.17)

2 2 3

4 π ( *) με σ

0

where
λ s is the vacuum wavelength of radiation being guided
e is the electronic charge
c is the speed of light in a vacuum
n is the index of refraction
ε 0 is the permittivity of free space
m * is the effective mass of the carriers
u is their mobility
N is the carrier concentration

For light in the wavelength range of 0.82-1.3 μm, traveling in an n -type doped
AlGaAs waveguide, the absorption coefficient can be approximated by

1 10 18

− − 3 − 1

(5.18)

α fc = × N (cm cm )

Since a carrier concentration of N = 10 16 cm −3 can be routinely grown in
AlGaAs layers with small aluminum concentration, one can expect α fc to be
on the order of 0.01 cm −1 or loss due to free-carrier absorption to be less than
0.1 dB cm −1 .
In curved sections of rectangular waveguides it is necessary to consider
radiation loss in addition to the three loss mechanisms discussed previ-
ously. Radiation loss is theoretically unavoidable and increases greatly as