Attach a curved drapery rod directly above the arched doorway. Specially designed to accommodate arched doorways and windows, these curved drapery rods are prone to allowing curtains to slide down on the rod. You can overcome this problem by tightly securing the curtains to the rods.
Install an adjustable spring-pressure rod across the width of the arch. Hang tab curtains along the rod or sheer pocket curtains on it. There will be a few inches of space above the rod, so if you would prefer to cut down on the light that shows through, hang a valance above it.
Attach a traditional rod just above and beyond the doorway. You'll will only be able to see the architectural detail of the arch when the drapes are pulled back, but you will be provided with privacy when the curtains are down.
Install tie back hooks approximately 48 inches from the floor on either side of the arch. This gives you the option of tying the drapes back when you don't want privacy and dropping them during times you prefer privacy.