A new and improved undulator design is provided that enables a variable period length for the production of synchrotron radiation from both medium-energy and high energy storage rings. The variable period length is achieved using a staggered array of pole pieces made up of high permeability material, permanent magnet material, or an electromagnetic structure. The pole pieces are separated by a variable width space. The sum of the variable width space and the pole width would therefore define the period of the undulator. Features and advantages of the invention include broad photon energy tunability, constant power operation and constant brilliance operation.