While solar sails have been designed before (NASA's had a solar sail program back in the 1970s), materials available until the last decade or so were much too heavy to design a practical solar sailing vehicle. Besides being lightweight, the material must be highly reflective and able to tolerate extreme temperatures. The giant sails being tested by NASA today are made of very lightweight, reflective material that is upwards of 100 times thinner than an average sheet of stationery. This "aluminized, temperature-resistant material" is called CP-1. Another organization that is developing solar sail technology, the Planetary Society (a private, non-profit group based in Pasadena, California), supports the Cosmos 1, which boasts solar sails that are made of aluminum-reinforced Mylar and are approximately one fourth the thickness of a one-ply plastic trash bag.
The reflective nature of the sails is key. As photons (light particles) bounce off the reflective material, they gently push the sail along by transferring momentum to the sail. Because there are so many photons from sunlight, and because they are constantly hitting the sail, there is a constant pressure (force per unit area) exerted on the sail that produces a constant acceleration of the spacecraft. Although the force on a solar-sail spacecraft is less than a conventional chemical rocket, such as the space shuttle, the solar-sail spacecraft constantly accelerates over time and achieves a greater velocity.
You might be wondering what happens when the spacecraft finds itself far from sunlight. An onboard laser could take over providing the necessary propulsion to the sails.
Solar power - check. Solar sails - check. But how do we get the sails and their spacecraft into space? Let's take a look.