The presence of spatial inhomogeneity in a nonlinear medium results in the breaking of the translational invariance of the underlying propagation equation. As a result traveling wave soliton solutions do not exist in general for such systems, while stationary solitons are located in fixed positions with respect to the inhomogeneous spatial structure. In simple photonic structures with monochromatic modulation of the linear refractive index, soliton position and stability do not depend on the characteristics of the soliton such as power, width and propagation constant. In this work, we show that for more complex photonic structures where either one of the refractive indices (linear or nonlinear) is modulated by more than one wavenumbers, or both of them are modulated, soliton position and stability depends strongly on its characteristics. The latter results in additional functionality related to soliton discrimination in such structures. The respective power (or width / propagation constant) dependent bifurcations are studied in terms of a Melnikov-type theory. The latter is used for the determination of the specific positions, with respect to the spatial structure, where solitons can be located. A wide variety of cases are studied, including solitons in periodic and quasiperiodic lattices where both the linear and the nonlinear refractive index are spatially modulated. The investigation of a wide variety of inhomogeneities provides physical insight for the design of a spatial structure and the control of the position and stability of a localized wave.

A generic photonic coupler with active and lossy parts, gain saturation, and asymmetric characteristics is examined. Saturable activity is shown to be able to enhance the overall stability of the steady states, prevent evolution to undesirable unbounded modes, and allow for bistable operation in specific regions of the parametric space. Both stability and bistability are studied in the phase space of the system, where the basins of attraction of each state are identified, providing an accurate description of the dependence of the electric fields on the initial conditions. Continuous families of exceptional points are detected via suitable regulation of the coupling and asymmetry features of the configuration. In this way, a complete description of the nonlinear dynamics landscape is provided, which should be crucial for multiple application-driven designs incorporating such a ubiquitous optical component.

A novel method for obtaining analytical solitary wave solutions of the nonlinear Kronig-Penney model in periodic photonic structures with self-defocusing nonlinearity is applied for providing generic families of solutions corresponding to the gaps of the linear band structure. Characteristic cases are shown to be quite robust under propagation.

A phase space method is employed for the construction of analytical solitary wave solutions of the nonlinear Kronig-Penney model in a photonic structure. This class of solutions is obtained under quite generic conditions, while the method is applicable to a large variety of systems. The location of the solutions on the spectral band gap structure as well as on the low dimensional space of system’s conserved quantities is studied, and robust solitary wave propagation is shown.

The density fluctuations and blobs present in the edge region of magnetic fusion devices can scatter radio frequency (RF) waves through refraction, reflection, diffraction, and coupling to other plasma waves. This, in turn, affects the spectrum of the RF waves and the electromagnetic power that reaches the core of the plasma. The usual geometric optics analysis of RF scattering by density blobs accounts for only refractive effects. It is valid when the amplitude of the fluctuations is small, of the order of 10%, compared to the background density. In experiments, density fluctuations with much larger amplitudes are routinely observed, so that a more general treatment of the scattering process is needed. In this paper, a full-wave model for the scattering of RF waves by a blob is developed. The full-wave approach extends the range of validity well beyond that of geometric optics; however, it is theoretically and computationally much more challenging. The theoretical procedure, although similar to that followed for the Mie solution of Maxwell's equations, is generalized to plasmas in a magnetic field. Besides diffraction and reflection, the model includes coupling to a different plasma wave than the one imposed by the external antenna structure. In the model, it is assumed that the RF waves interact with a spherical blob. The plasma inside and around the blob is cold, homogeneous, and imbedded in a uniform magnetic field. After formulating the complete analytical theory, the effect of the blob on short wavelength electron cyclotron waves and longer wavelength lower hybrid waves is studied numerically.

We consider the asymmetric active coupler (AAC) consisting of two coupled dissimilar waveguides with gain and loss. We show that under generic conditions, not restricted by parity-time symmetry, there exist finite-power, constant-intensity nonlinear supermodes (NS), resulting from the balance between gain, loss, nonlinearity, coupling and dissimilarity. The system is shown to possess non-reciprocal dynamics enabling directed power transport functionality.