A simple and general formalism for mode coupling by a spatial, temporal or spatiotemporal perturbation in dispersive materials is developed. This formalism can be used for studying various linear and non-linear optical interactions involving a dynamic modulation of the interaction parameters such as non-reciprocal phenomena, time reversal of signals and spatiotemporal quasi phase matching.

We introduce a model of a dual-core optical waveguide with opposite signs of the group-velocity dispersion in the two cores, and a phase-velocity mismatch between them. The coupler is embedded into an active host medium, which provides for the linear coupling of a gain-loss type between the two cores. The same system can be derived, without phenomenological assumptions, by considering the three-wave propagation in a medium with the quadratic nonlinearity, provided that the depletion of the second-harmonic pump is negligible. This linear system offers an optical realization of the charge-parity symmetry, while the addition of the intracore cubic nonlinearity breaks the symmetry. By means of direct simulations and analytical approximations, it is demonstrated that the linear system generates expanding Gaussian states, while the nonlinear one gives rise to broad oscillating solitons, as well as a general family of stable stationary gap solitons.

It is shown that pairs of solitary pulses (SPs) in a linearly-coupled system with opposite group-velocity dispersions form robust breathing bound states. The system can be realized by temporal-modulation coupling of SPs with different carrier frequencies propagating in the same medium, or by coupling of SPs in a dual-core waveguide. Broad SP pairs are produced in a virtually exact form by means of the variational approximation. Strong nonlinearity tends to destroy the periodic evolution of the SP pairs.

It is shown theoretically and numerically that a simple gratings-based plasmonic structure can support a nearly-degenerate double Fano resonance which can lead to a relatively narrow spectral line shape. The double-resonance spectral location and line-shape are controllable by either adjusting the periodicity and unit-cell of the gratings or by adjusting the angle of incidence of the incoming radiation.

This study analytically analyzes the changes in the temperature profile of a homogenous and isotropic medium having the same thermal parameters as a muscular tissue, due to the heat released by a single magnetic nanoparticle (MNP) to its surroundings when subject to different magnetic field profiles. Exploring the temperature behavior of a heated MNP can be very useful predicting the temperature increment of it immediate surroundings. Therefore, selecting the most effective magnetic field profile (MFP) in order to reach the necessary temperature for cancer therapy is crucial in hyperthermia treatments. In order to find the temperature profile caused by the heated MNP immobilized inside a homogenous medium, the 3D diffusive-heat-flow equation (DHFE) was solved for three different types of boundary conditions (BCs). The change in the BC is caused by the different MF profiles (MFP), which are analyzed in this article. The analytic expressions are suitable for describing the transient temperature response of the medium for each case. The analysis showed that the maximum temperature increment surrounding the MNP can be achieved by radiating periodic magnetic pulses (PMPs) on it, making this MFP more effective than the conventional cosine profile.

It is shown theoretically and numerically that a metal-dielectric or an all-dielectric side-by-side gratings structure can support non-degenerate guided modes coupled to the same radation mode. This realizes an easy to fabricate, simple system supporting a nearly degenerate, efficiently coupled, double Fano resonance. The ensuing relatively narrow and high-visibility spectral line-shape can be useful for realizing ultra-thin optical filters.