A class of four-parameter solvable profiles of the electromagnetic admittance
has recently been discovered by applying the newly developed Property & Field
Darboux Transformation method (PROFIDT). These profiles are highly flexible. In
addition, the related electromagnetic-field solutions are exact, in closed-form
and involve only elementary functions. In this paper, we focus on those who are
S-shaped and we provide all the tools needed for easy implementation. These
analytical bricks can be used for high-level modeling of lightwave propagation
in photonic devices presenting a piecewise-sigmoidal refractive-index profile
such as, for example, antireflection layers, rugate filters, chirped filters
and photonic crystals. For small amplitude of the index modulation, these
elementary profiles are very close to a cosine profile. They can therefore be
considered as valuable surrogates for computing the scattering properties of
components like Bragg filters and reflectors as well. In this paper we present
an application for antireflection layers and another for 1D quasicrystals (QC).
The proposed S-shaped profiles can be easily manipulated for exploring the
optical properties of smooth QC, a class of photonic devices that adds to the
classical binary-level QC.Comment: 14 pages, 18 fi
