Transfer-matrix analysis of Fibonacci quasi-periodic dielectric multilayers for broadband optical back-reflection

Abstract

Thin-film optics and radiative-transfer applications, including rear reflectors for energy converters, depend heavily on optical coating design and broadband light control in layered dielectric materials. Using a 2-µm crystalline-silicon absorber, this study shows a methodical transfer-matrix analysis of quasi-periodic Fibonacci TiO₂/SiO₂ multilayers as broadband back reflectors. Sellmeier parameterizations characterize material dispersion, while an analytical fit to tabulated optical data captures silicon absorption. At similar layer counts, Fibonacci stacks from generation orders 4–10 (5–89 layers) are compared against random multilayers and periodic quarter-wave distributed Bragg reflectors (DBRs). Under AM1.5 G illumination, performance is assessed using a photon-flux-weighted reflectance metric together with the matching short-circuit current density J_sc from a planar two-pass absorption model. Quarter-wave thicknesses are d_A=57.6 nm and d_B=102.9 nm at a 600 nm design wavelength. For 34 layers, the Gen-8 Fibonacci structure yields J_sc=22.50 mA cm^-2, representing a 17.4% increase over a no-reflector baseline and 92.3% of the ideal planar upper bound. While Fibonacci stacks have better broadband reflectance than DBRs (71.8% vs 60.2%), DBRs generate greater J_sc (24.04 mA cm^-2) because of their spectral alignment with strong silicon absorption, therefore emphasizing a spectral-selectivity trade-off. Optimizing design wavelength helps to close this difference; the Fibonacci structure achieves J_sc=23.70 mA cm^-2 at λ₀=475 nm. Field-intensity profiles show clear light-trapping processes, and tolerance testing demonstrates resilience. Reported findings apply to TE polarisation.