Oh my! I always vote no curtains unless it's needed for privacy or light control. Always clean windows are needed but it looks great naked. I 'd paint the door trim white as well.

Blue water and blue wall. Lime green? Do you like textures of wicker, rattan, etc..?

Does the sun shine directly in that door? If it does I like option of cutting down on amount.

I would consider sliding panels to have a more finished look but one that is more streamlined than curtains.

I would suggest sheers only if you need a little privacy. Other than that, I would leave it without and paint the trim so it stands out.

Since it appears this door may be a high traffic area to the pool. I would suggest a more functional "blind" for the door to give you privacy. Perhaps a tight weave screen panel track system would afford you some privacy when needed but since it's a screen, would also stand up better to people touching it as they come in from the pool.

You can also get a sheer vertical blind option that would allow light in but not fully block it out as well. This would also give you the option to add a little color to this spot, maybe tie the room together as well

you guys must give all your creativity up at the office or something? sure aint doing it at home! lol

At night, I don't like to see a large window like this uncovered, especially in winter when it is a big black hole. If you are in a warm climate this may not be an issue for you.

it is when you find out the croaking frog is actually the neighborhood gator, eyeing you up for a snack. lol