Theoretical beam splitting characteristics of double-layer rectangular phase gratings (DLRPGs) are reported. Computer simulation shows that these DLRPGs not only can be used as common beam splitters with higher than 89% di raction e ciencies and 95% energy distribution uniformities but also exhibit novel splitting properties; one DLRPG can generate a series of beam numbers with 70% di raction e ciencies by changing in real time the incident angles of a reading beam. This means that a single beam splitter can operate as several common beam splitters. IntroductionBeam splitters have wide applications in optical ®elds such as data storage, optical ®bre communication, complex optical interconnection and integrated optics. They can be used as wavelength division multiplexers, couplers, ®lters, beam combiners, etc. Several approaches have been proposed for fabricating the beam splitters, such as Dammann gratings [1±3] and complex holograms [4]. More recently, strati®ed volume holographic gratings (SVHGs) have also been used to make the beam splitters [5, 6], which exhibit high di raction e ciencies, a simple optical recording system, etc., but the grating pro®les have a sinusoidal modulation which is di cult to control and fabricate in experiments.In addition, to date, all beam splitters have a common property, namely each splitter can fan out only a ®xed beam numbers. To gain other output beam numbers, one has to use other splitters. For example, if we require two, three and four output beams respectively, then three splitters are needed (as shown in ®gure 1 (a)).Rectangular pro®le gratings are easy to design and fabricate by computer and, additionally, Pascual et al. [7] have con®rmed that the copying technique with partial coherent light, when used to fabricate optical elements, can attain an exact reproduction of the original modulation pro®le. This makes fabrication of rectangular SVGHs feasible. In this paper, we shall theoretically demonstrate that the rectangular phase SVHGs not only can act as common beam splitters (®gure 1 (a))