Complexity & fractality in simple optical systems

Complexity draws on commonality of universal phenomena and brings together research in fields that are traditionally quite disparate. A key thematic in the study of complex systems is pattern emergence. Spatial pattern formation can often be categorized as either: simple (possessing a single dominant scale); or fractal (possessing proportional levels of detail across many scales). Here, we present an overview of our research on the fractal-generating properties of two distinct wave contexts: fractal eigenmodes of linear systems with inherent magnification; and spontaneous spatial fractals in nonlinear systems. Our latest research focuses on: polygonal (“kaleidoscope”) linear laser cavities; and nonlinear cavity and bulk media optical systems. Results for linear systems include the first systematic study of fully-2D transverse eigenmodes that possess significant levels of fractality. New system geometries and media types are considered for nonlinear fractal generation. We conclude with proposal and exploration of some potential applications of fractal waves