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In their most general form, wave-interface problems are inherently angular in nature. For instance, the interaction between light waves and material boundaries essentially defines the entire field of optics. The seminal works of Aceves et al. [1,2] considered scalar bright spatial solitons impinging on the planar interface between two Kerr-type media with different χ(3) susceptibilities. While these...
Uniform and regular systems can generate optical fractals. After characterizing different fractal-generating systems, emphasis is placed on the roles of boundary conditions and cavity feedback. New aspects of linear and nonlinear optical fractals are presented, along with considerations of system coherence and novel connections to some classic systems and configurations.
Reaction-diffusion systems can exhibit a Turing instability in which homogeneous states develop large-amplitude emergent patterns. These patterns are typically characterized by a single dominant length scale that corresponds to a single minimum in a modulational instability threshold curve. However, several nonlinear systems possess a hierarchy of local Turing minima. It was proposed [1] that this...
The behaviour of a scalar optical beam at the boundary between two dissimilar nonlinear media is of fundamental interest in photonics. Here, we report the first systematic generalization of our Kerr analyses to a wider class of power-law materials. Universal refraction laws will be given, and theory-simulation agreement demonstrated.
We present the first detailed account of kaleidoscope laser modes where the equivalent Fresnel number Neq and magnification M may assume arbitrary values. Properties of these linear fractal eigenmodes are explored through extensive numerical computations. Considerations are extended to demonstration and analyses of new contexts for spontaneous nonlinear optical fractals.
We present a generalized Snell's law that governs grey soliton refraction at the interface separating two defocusing Kerr media. The analysis, based on the Helmholtz theory, is valid for arbitrary angles of incidence and reveals that grey solitons undergo either external or internal refraction depending on the soliton contrast parameter.
The slowly varying envelope approximation and the ensuing Galilean boost to a local time frame are near-universal features of conventional scalar pulse models. Here, we will give an overview of our recent progress with a new approach to nonlinear pulse modelling, which is based on a Helmholtz-type formalism.
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