Analysis of characteristics concerning volume phase gratings of which refractive index distributions are continuously changeable graded types and trapezoid types

To control the spectral and angular bandwidths with high diffraction efficiency, it is important to investigate the characteristics of volume phase (VP) gratings. The relationships between the characteristics and the refractive index distributions (RIDs) inside the recording material of VP gratings are focused on. In the previous work, continuously changeable graded types were investigated. In this work, the functions expressed as continuously changeable trapezoid types of RIDs are proposed. The characteristics of trapezoid types and graded types of RIDs which change continuously from a triangular type to a rectangular type are simulated and compared using the rigorous coupled wave analysis. It becomes clear that the same bandwidths can exist for the different types of RIDs with the same refractive index modulation. They are the trapezoid types and the graded types of RIDs. Theoretically the characteristics of a certain angulated trapezoid type of RID can be considered to be the same as that of a certain rounded graded type of RID. It also becomes clear that there are some gratings whose thickness and bandwidths are the same for various trapezoid types of RIDs with the different refractive index modulation, and they are controlled. The tendency is the same as various graded types of RIDs.