Critical field patterns in optical Fibonacci multilayers

Optical coatings with 13, 34, 55, and 89 quarter-wave layers of high- and low-index dielectric materials arranged in Fibonacci sequences F6, F8, F9, and F10, respectively, were deposited with use of a reactive low-voltage ion plating process. The calculated average transmission (Tave) for ϕ = (1/2 ± 1/4)π follows a power law Tave ≈ Nm−δ, where Nm is the number of optical quarter-wave layers in a Fibonacci sequence Fm. The critical exponent δ for these multilayers is compared with a renormalization calculation of the exponent governing the total energy width for an electronic system of Fibonacci layers. Spectral-transmittance measurements of the experimental Fibonacci multilayers show some deviation from the calculated spectral transmittance, which is due primarily to absorption in the short-wavelength range, but these measurements do still indicate that the observed optical field patterns are critical.