Retardation calculation for achromatic and apochromatic quarter and half wave plates of gypsum based birefringent crystal

This paper presents retardation calculations for achromatic and apochromatic half and quarter wave retarders of gypsum based birefringent crystal. The calculations indicate that an achromatic wave plates can be obtained by combining gypsum crystal with KDP, ADP, MgF₂, sapphire and calcite birefringent crystals. The residual variation percentages of retardations as a function of wavelength for gypsum/KDP, gypsum/ADP, gypsum/MgF₂, gypsum/sapphire and gypsum/calcite were found to be ± 1.7%, ± 3%, ± 12.2%, ± 12.0% and ± 7.2%, respectively. To reduce the spectral variation of retardations, a third layer (apochromatic) of birefringet material is added to the aforementioned achromatic wave plates. The proposed apochromatic wave plates are gypsum/KDP/quartz, gypsum/ADP/quartz, MgF₂/ADP/gypsum, MgF₂/KDP/gypsum and gypsum/sapphire/MgF₂. The addition of a third layer has reduced spectral residual variation percentages of retardations of the aforementioned apochromatic designs to ± 0.27, ± 0.33, ± 0.3, ± 0.17 and ± 0.45, respectively.