Best advice is DO NOT MULTIPOST. Had I known you multiposted this message,
I would have ignored it in alt.pets.cats and you would have missed out on
my detailed description of one way to do it, with pictures.  Other
people with expertise in the field and a dislike of spending time replying
to a message only to find that since it was multiposted there is a
real risk of having wasted the time and effort duplicating what someone
has already posted elsewhere are likely to ignore it as well.

We have the same type of sliding glass doors in our bedroom, leading to the
outside deck along the back of the house. We choose to put in a cat door
that's mounted in a 8 inch wide by 7 foot high aluminum strip they sell in
Petsmart for around $175. Although it works fine, it is expensive, and it
does compromise the security of the home since it prevents the sliding glass
doors from closing all the way, and it is kind of flimsy. I do believe the
hole through the wall is a more elegant solution. You can always put in two
identical cat doors....One co-planer with the inside wall, and one co-planer
with the outside.....This would give you better protection against air loss,
so your heating bill wouldn't be significantly higher. We didn't do this
mainly because it is a lot of trouble, and we live in a low crime area. I
put a large eye-screw in the doorjamb, so we can chain the sliding glass
door across the 8 inch gap, and make it relatively secure.......In most
sliding glass doors, you can lay a dowel along the base, preventing the door
from being opened any further than any given length......IOW, you can cut
the dowel so the door can't be opened from the outside any further than the
width of the cat door aluminum section. We couldn't do this, because our
doors were installed backwards by the builder such that the thief on the
outside could place the dowel, preventing our escape! I would try the
aluminum device if you are in a low crime area, and the hole in the wall if
you are in a high crime area.