A study of the brightest peaks in the diffraction pattern of Fibonacci gratings

The diffraction patterns of 1D aperiodic Fibonacci gratings (FGs) are investigated here. We derive a set of simple formulae which allow the finding of the positions and the intensities of the strongest diffraction peaks amongst the infinite ones present inside a given reciprocal space interval [ q 1 , q 2 ] , chosen according to a user-defined threshold. In this way the diffraction spectrum of FGs and of their generalizations, generalised Fibonacci gratings (GFGs), can be approximated to a good level as a set of discrete, properly indexed peaks with varying intensity, similarly to what is done for periodic structures. This approach is applied to real cases of GFGs fabricated and tested by two dedicated setups on a substrate of photorefractive Fe: LiNbO3. The experimental results are in excellent agreement with the proposed description and confirm the applicability of our approach.

[1]  Equivalence classes of Fibonacci lattices and their similarity properties , 2016, 1601.07499.

[2]  O. Zilberberg,et al.  A Thouless quantum pump with ultracold bosonic atoms in an optical superlattice , 2015, Nature Physics.

[3]  Fibonacci optical lattices for tunable quantum quasicrystals , 2015, 1504.06769.

[4]  W. K. Chang,et al.  Two-dimensional aperiodic nonlinear photonic crystal in a dual-wavelength Nd:YVO₄ laser for pulsed orange generation. , 2014, Optics express.

[5]  A. Lin,et al.  Aperiodic and randomized dielectric mirrors: alternatives to metallic back reflectors for solar cells. , 2014, Optics express.

[6]  Mark L Brongersma,et al.  Compact aperiodic metallic groove arrays for unidirectional launching of surface plasmons. , 2013, Nano letters.

[7]  O. Zilberberg,et al.  Observation of topological phase transitions in photonic quasicrystals. , 2012, Physical review letters.

[8]  Oded Zilberberg,et al.  Topological equivalence between the Fibonacci quasicrystal and the Harper model. , 2012, Physical review letters.

[9]  Zohar Ringel,et al.  Topological States and adiabatic pumping in quasicrystals. , 2011, Physical review letters.

[10]  M. Bazzan,et al.  Quantification of Iron (Fe) in Lithium Niobate by Optical Absorption , 2011 .

[11]  Luca Dal Negro,et al.  Photonic-plasmonic scattering resonances in deterministic aperiodic structures. , 2008, Nano letters.

[12]  An Hu,et al.  Dimerlike positional correlation and resonant transmission of electromagnetic waves in aperiodic dielectric multilayers , 2004 .

[13]  Ben-Yuan Gu,et al.  Nonlinear multiwavelength conversion based on an aperiodic optical superlattice in lithium niobate. , 2002, Optics letters.

[14]  John W. Cahn,et al.  Metallic Phase with Long-Range Orientational Order and No Translational Symmetry , 1984 .

[15]  Ta-you Wu,et al.  Quantum Theory of Scattering , 1962 .