Instabilities & boundary conditions:
fractal mode patterns in kaleidoscope lasers

Christian, JM; McDonald, GS; Huang, JG

Abstract

The multi-scale - or fractal - nature of transverse modes in one-dimensional (1D) unstable cavity lasers has been known since the late 1990s [1]. Early collaborations with some members of our Group demonstrated that the origin of fractality (which demands both the presence and comparable strength of multiple spatial scales) lies in a subtle interplay between small-scale diffraction effects at the mirror edges and successive round-trip magnifications [2]. Kaleidoscope lasers are fully-2D generalizations of the more familiar 1D system, where the feedback mirror has a non-trivial transverse shape, such as a regular polygon [3]. The fundamental mechanism for fractal formation is the same as for 1D cavities, but until recently these highly geometric cavity designs have received relatively little attention. We will report on recent advances in our understanding of kaleidoscope lasers, facilitated by the development of new semi-analytical techniques. Key considerations include direct calculation of mode patterns, eigenvalue spectra, and convergence phenomena (e.g., as the feedback mirror tends towards the circular limit). We have also performed what appear to be the first computations of mode fractal dimension for arbitrary cavity parameters. Some surprising results have been uncovered.
References:
[1] G. P. Karman and J. P. Woerdman, Opt. Lett. 23, 1909 (1998).
[2] G. H. C. New, M. A. Yates, J. P. Woerdman, and G. S. McDonald, Opt. Commun. 193, 261 (2001).
[3] G. S. McDonald et al., J. Opt. Soc. Am. B 17, 524 (2000); Nature 402, 138 (1999).

Citation

fractal mode patterns in kaleidoscope lasers. Poster presented at College of Science and Technology Research Showcase Day, University of Salford, Greater Manchester, UK

• Presentation Conference Type: Poster
• Conference Name: College of Science and Technology Research Showcase Day
• Conference Location: University of Salford, Greater Manchester, UK
• Start Date: Jun 20, 2012
• Deposit Date: Jul 17, 2012
• Publicly Available Date: Apr 5, 2016
• Additional Information: Event Type : Conference