Planar, buried, ion-exchanged glass waveguides: Diffusion characteristics

A detailed theoretical and experimental study of Ag+-Na+ exchange in soda-lime silicate glasses in a molten bath containing a mixture of NaNO
3
and Ag+ is presented. With no applied field, concentration profiles
C(x, t)
(and therefore, the index profiles for low concentrations) are given by complementary error function. The estimated value for the self-diffusion coefficient
D
of Ag+ is 0.133 μm
²
/min for low concentrations and it monotonically increases with the surface concentration C
0
until it saturates at about 0.3 μm
²
/min for
C_{0} \geq 10^{-3}
MF. However, square root dependence of diffusion depth with time seems to be independent of the C
0
. Presence of an external field
E
causes the effective depth of diffusion to increase. In fact, for large
E
fields, the profile can accurately be described by
C/C_{0} = \frac{1}{2} erfc(x' - r)
where
r = \mu Et/\sqrt{2Dt}
where μ is the ionic mobility of Ag
⁺
in glass. We define a new diffusion depth
W
as the distance from the surface to the
1/e
concentration point, and for large fields,
W
varies linearly with
E
and
t
. Experimental results yielded a value of 15.55 μm
²
/
V
min forμ. As before, square root dependence of
W
with
t
and the linear variation of
W
versus C
0
for
C_{0} \leq 10^{-3}
MF, with
W
saturating for
C_{0} > 10^{-3}
MF, were observed in the case of field assisted diffusion. A two-step process, where a surface waveguide formed in the first step with either
E
equal to zero or some finite value, is modified by performing a second diffusion in pure sodium nitrate to produce a buried, symmetrical fiber-like profile. This process is also studied in detail.