We construct families of fundamental, dipole, and tripole solitons in the fractional Schrödinger equation (FSE) incorporating self-focusing cubic and defocusing quintic terms modulated by factors cos 2 x and sin 2 x, respectively. While the fundamental solitons are similar to those in the model with the uniform nonlinearity, the multipole complexes exist only in the presence of the nonlinear lattice. The shapes and stability of all the solitons strongly depend on the Lévy index (LI) that determines the FSE fractionality. Stability areas are identified in the plane of LI and propagation constant by means of numerical methods, and some results are explained with the help of an analytical approximation. The stability areas are broadest for the fundamental solitons and narrowest for the tripoles.
Reflection loss on the optical component surface is detrimental to performance. Several researchers have discovered that the eyes of moths are covered with micro- and nanostructured films that reduce broadband and wide-angle light reflection. This research proposes a new type of moth-eye subwavelength structure with a waist, which is equivalent to a gradient refractive index film layer with high–low–high hyperbolic-type fill factor distribution. The diffraction order characteristics of a moth-eye subwavelength structure are first analyzed using a rigorous coupled wave analysis. The moth-eye structural parameters are optimized within the spectral range of 2–5 μm using the finite-difference time-domain method. The experimental fabrication of the moth-eye structure with a waist array upon a silicon substrate is demonstrated by using three-beam laser interferometric lithography and an inductively coupled plasma process. The experimental and simulation results show good agreement. The experimental results show that the reflectivity of the moth-eye structure with a waist is less than 1.3% when the incidence angle is less than 30°, and less than 4% when the incidence angle is less than 60°. This research can guide the development of AR broadband optical components and wide-angle applications.
Dark solitons and localized defect modes against periodic backgrounds are considered in arrays of waveguides with defocusing Kerr nonlinearity, constituting a nonlinear lattice. Bright defect modes are supported by a local increase in nonlinearity, while dark defect modes are supported by a local decrease in nonlinearity. Dark solitons exist for both types of defects, although in the case of weak nonlinearity, they feature side bright humps, making the total energy propagating through the system larger than the energy transferred by the constant background. All considered defect modes are found stable. Dark solitons are characterized by relatively narrow windows of stability. Interactions of unstable dark solitons with bright and dark modes are described.
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