By Luca Dal Negro
This publication offers state of the art contributions from a few major specialists that actively paintings world wide within the swiftly becoming, hugely interdisciplinary, and interesting fields of aperiodic optics and complicated photonics. Edited via Luca Dal Negro, a well-liked researcher in those components of optical technological know-how, the e-book covers the elemental, computational, and experimental facets of deterministic aperiodic constructions, in addition to various machine and engineering functions to dense optical filters, nanoplasmonics photovoltaics and applied sciences, optical sensing, gentle assets, and nonlinear optics.
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Extra resources for Optics of Aperiodic Structures: Fundamentals and Device Applications
More complex structures displaying singular-continuous spectraa can also be conveniently generated by the symbolic substitution method . In such media, the Fourier spectra are no longer composed of individual Bragg peaks separated by well-deﬁned gaps but exhibit a structure similar to that of a Cantor set in the inﬁnite system size limit. However, one can observe a number of relatively broad peaks in ﬁnite systems, which progressively smear out as the system size increases. The chief a The support of the Fourier spectrum of singular-continuous structures can be covered by an ensemble of open intervals with an arbitrarily small total length.
Therefore, based on our previous discussion we expect that the diﬀraction pattern of a Fibonacci chain contains Bragg peaks that densely ﬁll the reciprocal space and are indexed by two Miller 19 October 7, 2013 16:9 PSP Book - 9in x 6in 01-Luca-Dal-Negro-c01 20 Aperiodic Order for Nanophotonics indices. A quantitative Fourier analysis starting from Eq. 13) where m and m are integers. 15) The ﬁnal results Eqs. , any m value can be associated with a given m). Moreover, according to Eq. 15), the brightest diﬀraction spots will appear for τ m − m ≈ 0 that implies m/m close to τ .
With pm elements), where p is a prime number and m is a positive integer. A Galois ﬁeld of order pm is usually denoted as GF( pm ). , Legendre sequences), are eﬃciently generated by a linear recursion [30, 69– 71]. Galois nanoparticle arrays can be constructed by generalizing Galois recursions in two spatial dimensions, as detailed in Refs. [30, 80]. 6g shows a calculated Galois particle array. The reciprocal Fourier space is shown in Fig. 6h, and features a broad distribution of spatial frequencies even for a relatively small array size, without the presence of a sharp Bragg peak.