Investigation of -1^st-order diffraction in conditions between thin and thick holograms

This paper explores the diffraction region between thin and thick holograms, commonly referred to as the transition region. The VOHIL model is used to assess the internal interference conditions along a specified diffraction direction. We examine the maximum phase difference between the two endpoints of the hologram for both the +1^st-order and -1^st-order diffractions through internal interference. This analysis leads to a criterion that aligns with the Klein parameter. Additionally, a new parameter, the de-phase factor, is introduced to assess the feasibility of diffraction along a chosen direction from a whole-field perspective. The variation of the de-phase factor in the -1^st-order diffraction is slower compared to other directions, except for the +1^st-order diffraction, owing to the natural existence of the -1st-order diffraction at every tiny hologram unit. The primary way to stop the -1^st-order diffraction is by adjusting the thickness if the incident angle is fixed. Thus, examining the -1^st-order diffraction is an effective way to check if a hologram is under the Bragg condition. Although rigorous simulation methods, such as rigorous coupled-wave analysis, can provide more precise results, the proposed analysis scheme, based on the VOHIL model, offers valuable physical insights into these characteristics.