In some aspects, the invention relates to methods and systems for creating apodized periodic structures, such as apodized gratings in fibers. To create the periodic structures, a photosensitive medium is exposed to a spatially-varying radiation pattern. During the exposure, the position of the radiation pattern can oscillate with the respect to the photosensitive medium, thereby changing the average local refractive index of the medium. These methods and systems may be used to create regular structures in any appropriate medium, such as doped glasses and photosensitive polymers.