Draft:Parallel Stacked Mirror Model
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Comment: Inline citations needed. Also, please provide some way to access the sources. CabinetCavers----DEPOSIT OPINION, [valued customer] 12:56, 5 February 2026 (UTC)
The Parallel Stacked Mirror (PSM) model is a semi-analytical method used in optics to describe diffraction in volume phase gratings and reflection holograms. The approach interprets a dielectric grating as an infinite sequence of infinitesimally thin layers, each producing a small Fresnel reflection. The cumulative interference of these reflections synthesizes the diffracted waves. In the limit of vanishing layer thickness, the method leads to coupled first-order differential equations for the forward (reference) and backward (signal) fields.
The model provides an alternative formulation to coupled-wave theories such as the treatment introduced by Kogelnik for thick holographic gratings. At Bragg resonance, the PSM equations reduce to the same diffraction efficiency expressions as conventional coupled-wave theory, including the characteristic hyperbolic tangent dependence of diffraction efficiency on grating thickness and index modulation. The PSM interpretation differs conceptually in that it derives energy transfer between waves directly from local Fresnel reflections rather than from an assumed modal coupling ansatz.
The method can be extended to treat slanted gratings by rotation of coordinates and to spatially multiplexed gratings containing several superposed grating vectors. In this generalised form (sometimes referred to as the N-PSM model), a single incident wave couples simultaneously to multiple diffracted orders. At Bragg resonance the resulting equations are equivalent to N-coupled-wave theory, while remaining computationally simpler than rigorous coupled-wave analysis (RCWA) of Maxwell’s equations. For weak to moderate index modulations typical of holographic recording materials, the predictions of the model have been reported to agree closely with rigorous numerical methods.
The PSM framework has been applied to the analysis of reflection volume gratings, multiplexed holograms, and polychromatic (multi-wavelength) holographic elements.
References
[edit]- H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell System Technical Journal, 1969.
- L. Solymar, “Two-dimensional N-coupled wave theory for volume holograms,” Optics Communications, 1977.
- D. Brotherton-Ratcliffe, “A treatment of the general volume holographic grating as an array of parallel stacked mirrors,” Journal of Modern Optics, 2012.
- D. Brotherton-Ratcliffe, “Analytical treatment of the polychromatic spatially multiplexed volume holographic grating,” Applied Optics, 2012.
- M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar grating diffraction,” Journal of the Optical Society of America, 1981.