I'm assuming you want an opening window as a fixed window is simple.
One option that should work fine would be to make the window from just a single piece of Lexan/polycarb, say 3/8" or 1/2" thick, with no frame. The Lexan would be stronger and stiffer than most frames - you might need, say, a window catch in each bottom corner to get a good seal on a top-hinged window, but that's not the end of the world.
A continuous plastic hinge could be used at the top which could be either just glued to the Lexan (though Plexiglas/acrylic would be better for gluing) or also attached by machine screws in tapped holes in the Lexan - this might avoid the need for a drip rail over the window, but it might be sensible to fit one anyway.
One thing you'll need is a wood frame fixed in the door skin to give you a rebate in which to fit the weather seal, though I guess the whole window could be surface-mounted on the outside of the door if that was thought to look OK.
So something like this, though I've got the hinge screw into a too-narrow section of the wood frame:
Andrew