Fractal laser sources: new analyses, results and contexts

Christian, JM; McDonald, GS; Heyes, AS; Huang, JG

Abstract

A series of significant new extensions concerning fractal light generation are reported. Firstly, we summarise techniques and results from the first full analysis of the linear modes of ‘fractal lasers’ [1] – unstable-cavity geometries with arbitrary Fresnel number Neq and arbitrary round-trip magnification M. Secondly, simulations and analyses for new contexts of laser-driven ‘nonlinear fractal generators’ [2] – where analogous nonlinear processes spontaneously generate fractals – are presented. Finally, we outline why such fractal laser sources may play a pivotal role in future Nature-inspired devices and
system architectures.

Our discovery of fractal laser modes from unstable-cavity lasers [1] uncovered a general class of linear systems (with repeated magnification) that possess fractal eigenmodes. However, numerical or analytical analyses was limited to modes of either: very limited fractality, laser cavities with Neq ≈ O(1); or unlimited fractality, when Neq >> O(1). General properties of fractal modes from these two extremes are, perhaps unsurprisingly, different. Building on Fresnel diffraction theory developments [3], we report
fractal mode characteristics in the important intermediate regime – corresponding to real-world systems with significant and exploitable fractality (see Figure 1).

<FIGURE 1>

Figure 1. Lowest-loss eigenmode patterns for ‘kaleidoscope fractals lasers’ with Neq = 30 and M = 1.5.

We further proposed fractal light generation through entirely-nonlinear mechanisms [2]. The context examined was a single configuration with a particular nonlinearity.
Generalisation of this work to new contexts - with profoundly different nonlinearities and experimental configurations, such as ring cavities and cavity-less contexts – will be summarised. The huge spatial bandwidths associated with fractal sources have potential exploitation within novel technological contexts. We conclude with a brief account of such potential new technologies.

References
[1] Karman G P, McDonald G S, New G H C and Woerdman JP, Nature 402, 138 (1999).
[2] Huang J G and McDonald G S, Phys. Rev. Lett. 94, 174101 (2005).
[3] Huang J G, Christian J M and McDonald G S, J. Opt. Soc. Am. A 23, 2768 (2006).

Citation

Christian, J., McDonald, G., Heyes, A., & Huang, J. (2010, August). Fractal laser sources: new analyses, results and contexts. Presented at National Photonics Conference, Photon 10, Southampton, UK

• Presentation Conference Type: Other
• Conference Name: National Photonics Conference, Photon 10
• Conference Location: Southampton, UK
• Start Date: Aug 23, 2010
• End Date: Aug 26, 2010
• Publication Date: Aug 23, 2010
• Deposit Date: Oct 13, 2011
• Publicly Available Date: Apr 5, 2016
• Publisher URL: http://photon10.iopconfs.org/
• Additional Information: Event Type : Conference