Morphology-Dependent Resonances in Two Concentric Spheres with Variable Refractive Index in the Outer Layer: Analytic Solutions

In many applications constant or piecewise constant refractive index profiles are used to study the scattering of plane electromagnetic waves by a spherical object. When the structured media has variable refractive indices, this is more of a challenge. In this paper, we investigate the morphology dependent resonances for the scattering of electromagnetic waves from two concentric spheres when the outer shell has a variable refractive index. The resonance analysis is applied to the general solutions of the radial Debye potential for both transverse magnetic and transverse electric modes. Finally, the analytic conditions to determine the resonance locations for this system are derived in the closed form of both modes. Our numerical results are provided with discussion.

Mathematical Fundamentals of a Diagnostic Method by Long Nonlinear Waves for the Structured Media

We have proven that the long wave with finite amplitude responds to the structure of the medium. The heterogeneity in a medium structure always introduces additional nonlinearity in comparison with the homogeneous medium. At the same time, a question appears on the inverse problem, namely, is there sufficient information in the wave field to reconstruct the structure of the medium? It turns out that the knowledge on the evolution of nonlinear waves enables us to form the theoretical fundamentals of the diagnostic method to define the characteristics of a heterogeneous medium using the long waves of finite amplitudes (inverse problem). The mass contents of the particular components can be denoted with specified accuracy by this diagnostic method.

High resolution spectral metrology leveraging topologically enhanced optical activity in fibers

Optical rotation, a form of optical activity, is a phenomenon employed in various metrological applications and industries including chemical, food, and pharmaceutical. In naturally-occurring, as well as structured media, the integrated effect is, however, typically small. Here, we demonstrate that, by exploiting the inherent and stable spin-orbit interaction of orbital angular momentum fiber modes, giant, scalable optical activity can be obtained, and that we can use this effect to realize a new type of wavemeter by exploiting its optical rotary dispersion. The device we construct provides for an instantaneous wavelength-measurement technique with high resolving power R = 3.4 × 106 (i.e., resolution < 0.3 pm at 1-μm wavelengths) and can also detect spectral bandwidths of known lineshapes with high sensitivity.

Photonic flat-band lattices and unconventional light localization

Flat-band systems have attracted considerable interest in different branches of physics in the past decades, providing a flexible platform for studying fundamental phenomena associated with completely dispersionless bands within the whole Brillouin zone. Engineered flat-band structures have now been realized in a variety of systems, in particular, in the field of photonics. Flat-band localization, as an important phenomenon in solid-state physics, is fundamentally interesting in the exploration of exotic ground-state properties of many-body systems. However, direct observation of some flat-band phenomena is highly nontrivial in conventional condensed-matter systems because of intrinsic limitations. In this article, we briefly review recent developments on flat-band localization and the associated phenomena in various photonic lattices, including compact localized states, unconventional line states, and noncontractible loop states. We show that the photonic lattices offer a convenient platform for probing the underlying physics of flat-band systems, which may provide inspiration for exploring the fundamentals and applications of flat-band physics in other structured media from metamaterials to nanophotonic materials.