Thanks for all of your replies but I don't think I explained our problem very well. I said we have sliding glass "pocket doors" going out to our lanai, but I probably should have described them as "stacking sliding glass doors'. The opening onto our lanai is 12 feet and we have four 3 foot sliding glass doors. If we push the left door all the way to the right, it engages the other doors, so we eventually have all four doors stacked together and the entire 12 foot space is open onto our lanai.

Since these types of doors are pretty common in TV, I thought someone would have a good idea how to provide better security against burglars or nosy alligators. Thanks for your help.

Consider this.
 

That explains a lot. All you have to do is secure the first panel. The others will not move unless the first panel moves first.

Perhaps not the most elegant appearing, but an effective solution, is installation of a hasp and staple on the first panel, which is then secured with a padlock. You have to use a very short hasp. Install it on the door jamb with very long (perhaps 3") screws into the framing that supports the door.

Be careful when drilling the screw holes in the door panel for the staple portion. You don't want to hit the glass.

The hasp does not lie flat as in the photo, below. It forms a 90 degree angle when engaging the staple.

Note that, like all door locks, it is still possible to break in (as it is for other doors in your house,) but it may be that the burglar will look for an easier target when he discovers your security on the sliding glass door.

I slide a small piece of wood on top of each slider to stop them from being lifted up.