Narrow stop band optical filter using one-dimensional regular Fibonacci/Rudin Shapiro photonic quasicrystals

Effects of deterministic disorder at deeply subwavelength scales in multilayered dielectric metamaterials

“…and wavevector k e ≡ (k x , k ze ) = k √ ε e sin θ i , k √ ε e cos θ i , with k = ω/c = 2π/λ denoting the vacuum wavenumber (and c and λ the corresponding wave velocity and wavelength, respectively). Previous studies on GRS-type multilayered dielectric structures [34][35][36][37][38][39] have focused on the diffractive (photonic-crystal) regime characterized by moderately thick layers, showing interesting light-transport properties in terms of bandgap, filtering and field-enhancement. Here, we focus instead on the insofar unexplored deeply subwavelength regime, characterized by d a,b λ, in which the optical properties of such metamaterials are typically well described by simple EMT models based on Maxwell-Garnett-type mixing formulas [7].…”

“…Moreover, we focus on the deeply subwavelength parameter regime 0.01λ < d < 0.05λ, and on incidence directions assumed parameters, this angular-incidence range guarantees that the field is evanescent in the "a"-type layers and propagating in the "b"-type ones. The regime characterized by smaller angles of incidence (0 < θ i < 30 o ), in which the field is propagating in both layers, has been extensively investigated in previous studies on photonic crystals [34][35][36][37][38][39], and is not of interest here. Overall, the assumed parameter regime is rather unusual, as the phase-accumulation mechanism is essentially dominated by the discrete jumps (Fresnel-type reflection/transmission) at the layer interfaces rather than the delay acquired via propagation through the (deeply subwavelength) layers.…”

“…Accordingly, alternative terms such as "flat-spectrum aperiodic order" or "pseudo-randomness" are also utilized in the topical literature to define this type of geometries. So far, in electromagnetics and optical engineering, GRS sequences have been explored in connection with antenna arrays [27], spread-spectrum communications and encryption [28], diffuse scattering [29,30], nanoplasmonic arrays [31][32][33], and photonic crystals [34][35][36][37][38][39].…”

Non‐Bragg Bands in Acoustic Quasi‐Periodic Fibonacci Waveguides

“…Interface states, Zak phase, and bandgaps in Fibonacci quasi‐crystals are gradually becoming topics of general interest . For instance, Baboux et al measured and discussed the topological invariants of edge states in polaritonic Fibonacci quasi‐crystals, whereas Trabelsi et al numerically investigated the multichannel filter characteristics of Fibonacci structures in 1D photonic quasi‐crystals …”

“…[5] For instance, Baboux et al measured and discussed the topological invariants of edge states in polaritonic Fibonacci quasi-crystals, [6] whereas Trabelsi et al numerically investigated the multichannel filter characteristics of Fibonacci structures in 1D photonic quasi-crystals. [7] It is well known that the Fibonacci sequence has many interesting features in mathematics and natural phenomena. On the geometric configurations, the Fibonacci structure is between the periodic and aperiodic structures, which results in its significant common features such as the fractal spectrum and selfsimilar behavior.…”