Eigenmodes of next-generation unstable cavity lasers : kaleidoscopes, snowflakes, pentaflakes, and fractal dimension

We will report on our latest research into fractal lasers (linear systems which involve geometrically-unstable resonators with inherent magnification) [1], introducing two new classes of transverse cavity configuration. These devices are of fundamental interest as table-top generators of tunable fractal light that can be used in a wide range of applications – from optical probes (e.g., increased sensitivity in surface roughness measurements) to secure information encoding/transmission to medical imaging. Moreover, we expect them to play a pivotal role in new Nature-inspired optical architectures and devices (e.g., writing fractal structures into new materials). Attention will be paid not only to the classic kaleidoscope geometries [2], but also to recently-proposed designs which incorporate a feedback mirror whose outer boundary corresponds to increasing iterations of the von Koch snowflake [3] (a six-fold-symmetric iterated function system involving self-similar sequences of equilateral triangles – see Fig. 1) and its five-fold-symmetric counterpart, the von Koch pentaflake (constructed in a similar way to the more traditional snowflake, but using isoceles triangles). All three systems can be modelled using a two-dimensional virtual source (2D-VS) method [4], which unfolds the.unstable empty cavity into a equivalent sequence of virtual apertures of increasing size [5]. A selection of mode patterns and eigenvalue spectra will be presented, and convergence issues considered in some detail.