Integrated Optics - Applied Optics Fundamentals and Device Applications - page 234

the radius of curvature of the bend is decreased. The radiation loss depends
exponentially on bend radius as given by the expression [22]

⎛ ⎞

− 2 β − β

z 0 − 1

L C = exp R dB cm

(5.19)

⎜ ⎟

1

q β

⎝ ⎠

0

where
C 1 is a constant that depends on the dimensions of the waveguide and on
the shape of the optical mode
R is the radius of curvature of the bend
β z is the propagation constant of the optical mode in the waveguide
β 0 is the propagation constant of unguided light in the confining medium
surrounding the waveguide
q is the extinction coefficient of the optical mode in the confining medium

The key parameters in this expression are β z , β 0 , and R . In order to compen-
sate for decreasing R it is necessary to increase B z and/or to decrease B 0 ,
that is, to increase the index of refraction difference between the waveguide
and confining medium. Calculations done by Goell [23] for the case of rect-
angular dielectric waveguides of approximately 1.0 μm width indicate that
an index change of only 1% is sufficient to reduce radiation loss to less than
0.1 dB cm −1 for a bend radius of 1 mm. In summary, theoretical calculations
and data published in the literature show that with AlGaAs waveguides,
losses due to free-carrier absorption, surface scattering, and radiation loss
can be kept within reasonable limits, while interband absorption loss rep-
resents the largest challenge. Other material systems may present loss prob-
lems of a greater magnitude than the AlGaAs system.

5.5.4 Material Growth: MOCVD versus MBE

Waveguide structures and devices are grown by a number of fabrication tech-
niques, including the metal organic chemical vapor deposition (MOCVD)
and molecular beam epitaxy (MBE) approaches. Both of these technologies
have demonstrated excellent device results [24]. It is important to gather data
and make comparisons between MOCVD and MBE for a particular device
application in making a choice between the two growth techniques. In the
following section some of the differences, advantages, and disadvantages of
the two systems will be discussed.
MOCVD presently has the lead in total output of the number of wafers that
can be grown. The MOCVD technique is relatively well proven for the man-
ufacture of a variety of AlGaAs system lasers and laser arrays [25]. MOCVD
growth rates are four to five times faster than MBE growth rates; however,
MBE manufacturers are developing sophisticated machines with multiple
growth chambers capable of growing several wafers simultaneously. Since