Here are some design notes when it comes to modern pergola designs. The most common pergola design is to have decorative and somewhat rounded ends on the beam. The easiest way of creating a more modern pergola is to do away with the decorative ends.
Belgravia House in London by Todhunter Earle. Even though this is a rooftop garden, the design show would be excellent for any long, narrow yard. Great way to break up the space by making different "zones"!
Teak Fence and Backyard Garden Deck - City Beautiful Carpentry: A modern design using reclaimed teak from china. By using reclaimed wood, this client ensured that no trees were felled to create his ultimate backyard meditation garden.