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The effects of the coating thickness on the physical performance of a Fabry-erot interferometer (FP) are investigated. The FP is modeled as three media separated by two thin films and not merely by two interfaces. We show that the transmitted intensity obeys an Airy function, but not the reflected intensity because of the appearance of a complex factor… (More)
We determine the range of thicknesses and refractive indices for which omnidirectional reflection from quasiperiodic dielectric multilayers occurs. By resorting to the notion of area under the transmittance curve, we assess in a systematic way the performance of the different Fibonacci multilayers.
We reelaborate on the basic properties of lossless multilayers. We show that the transfer matrices for these multilayers have essentially the same algebraic properties as the Lorentz group SO(2, 1) in a (2 + 1)-dimensional space-time as well as the group SL(2, R) underlying the structure of the ABCD law in geometrical optics. By resorting to the Iwasawa… (More)
We suggest a geometrical framework in which to discuss periodic layered structures in the unit disk. Bandgaps appear when the point representing the system approaches the unit circle. We show that the trace of the matrix describing the basic period allows for a classification in three families of orbits with quite different properties. The laws of… (More)
We elaborate on the consequences of the factorization of the transfer matrix of any lossless multilayer in terms of three basic matrices of simple interpretation. By considering the bilinear transformation that this transfer matrix induces in the complex plane, we introduce the concept of multilayer transfer function and study its properties in the unit… (More)
We use the concept of turns to provide a geometrical representation of the action of any lossless multilayer, which can be considered to be analogous in the unit disk to sliding vectors in Euclidean geometry. This construction clearly shows the peculiar effects arising in the composition of multilayers. A simple optical experiment revealing the appearance… (More)
We suggest a geometrical framework to discuss the action of slabs of negatively refracting materials. We show that these slabs generate the same orbits as normal materials, but traced out in opposite directions. This property allows us to confirm that the action of any lossless multilayer can be optically cancelled by putting it together with the multilayer… (More)
We determine the optimal thicknesses for which omnidirectional reflection from generalized Fibonacci quasicrystals occurs. By capitalizing on the idea of wavelength- and angle-averaged reflectance, we assess in a consistent way the performance of the different systems. Our results indicate that some of these aperiodic arrangements can largely over-perform… (More)
The Fabry-Perot interferometer is modeled as three media separated by two thin films of finite thickness. We propose a compromise between the peak transmittance and fringe finesse when the coatings are absorbing.