In this section we present calculations, performed using the method
of Section 8.4, for a practical
substrate choice
of sodium fluoride (the lowest refractive index common mineral, with
at a wavelength of 852nm), and investigate how this
changes the atom waveguide properties from those presented above.
We increased
to 1.7 (dense flint glass, e.g. BaSF type)
in order to provide
sufficient index difference from the substrate.
Fixing the width at
, we found that a height
gave the largest
of
, and allowed both modes to be
sufficiently far from cut-off (greater than half the power being carried inside
the guide for both modes).
The result is a goodness factor
which is approximately half that of the
case, with a
corresponding halving of the achievable product of depth and
coherence time according to (8.11), and doubling of the
heating rate at a given
and
according to
(8.13).
The shorter decay lengths of 56nm and 68nm (compared to 93nm and 137nm
for
) cause the typical trapping distance
to be
reduced by a factor of roughly 1.8.
We found that in order to reproduce the depth of K
and
m of the upper trap of Figure 8.3
(with
unchanged) we needed
mW, giving
ms.
The large power increase over the 1mW required for
is explained by the fact that this
is now towards the upper
limit practically achievable rather than the lower.
(If
is instead scaled in proportion to the new decay lengths,
the required increase in
is only a factor 1.7).
In this example, we find the transverse oscillation frequencies have
increased to
kHz and
kHz, compared to the original
kHz and
kHz.
The increase in
is explained entirely by the shorter decay lengths,
and the increase in
(by a factor of over 3) is attributed to tighter
optical mode shapes.
It is clear that this latter effect outweighs the decrease in
,
implying that the inclusion of the substrate has
actually increased
by 50%.
In summary, the
effects of including a realistic substrate limit the maximum trapping
distance that can be achieved (because of the reduction in decay lengths),
lower the goodness factor, increase the heating rate and the
required optical power, but also
increase the oscillation frequencies.
For our substrate choice, each of these changes was approximately
a factor of 2, and we believe that they do not alter the basic practicality
of implementing our proposed waveguide.
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