# Laser optics: Fractal modes in unstable resonators

@article{Krmn1999LaserOF, title={Laser optics: Fractal modes in unstable resonators}, author={G{\'a}bor K{\'a}rm{\'a}n and G. S. McDonald and G. H. C. New and J. P. Woerdman}, journal={Nature}, year={1999}, volume={402}, pages={138-138} }

One of the simplest optical systems, consisting of two mirrors facing each other to form a resonator, turns out to have a surprising property. Stable resonators, in which the paths of the rays are confined between the two mirrors, have a well known mode structure (hermite–gaussian), but the nature of the modes that can occur in unstable reson-ant cavities (from which the rays ultimately escape) are harder to calculate, particularly for real three-dimensional situations. Here we show that these… Expand

#### Figures from this paper

#### 69 Citations

Diffractive origin of fractal resonator modes

- Physics
- 2001

The modes of unstable optical resonators possess fractal character. In this paper, the fundamental question of how and why fractals originate in one of the simplest linear optical systems is… Expand

Fractal modes of unstable lasers with polygonal and circular mirrors

- Physics
- 2001

Abstract The lowest-loss modes of unstable lasers are fractals, emerging asymptotically in the limit of high Fresnel number. The fractality depends on the shape of the feedback mirror. An explicit… Expand

Higher-order fractal laser modes

- Physics
- Conference Digest. 2000 International Quantum Electronics Conference (Cat. No.00TH8504)
- 2000

Our recent unexpected discovery that fractal pattern formation occurs in the modes of unstable optical resonators has opened up a new area in laser science. In this paper, we present recent results… Expand

Fractal laser mode structure due to iterated diffractive multiple imaging

- Physics
- 2002

A variation on iterated multiple imaging in optical resonators, a mechanism that creates fractal structure in the resonator's eigenmodes, is presented. During each round trip, side-by-side images of… Expand

Fractal light from lasers

- Physics
- Physical Review A
- 2019

Fractals, complex shapes with structure at multiple scales, have long been observed in Nature: as symmetric fractals in plants and sea shells, and as statistical fractals in clouds, mountains and… Expand

Fractal modes and multi-beam generation from hybrid microlaser resonators

- Physics, Medicine
- Nature Communications
- 2018

A hybrid optical resonator in which the spheres enable the simultaneous generation of arrays of conventional (Gaussian) and fractal laser modes is demonstrated, which is able to emit hundreds of microlaser beams and probe live motile cells. Expand

Fractal frequency spectrum in laser resonators and three-dimensional geometric topology of optical coherent waves

- Physics
- 2016

We theoretically verify that the symmetry breaking in spherical resonators can result in a fractal frequency spectrum that is full of numerous new accidental degeneracies to cluster around the… Expand

Novel optical resonators

- Physics
- 2012

Optical resonators – two mirrors facing each other, separated by a distance – are a very well studied technology. However, even such a well understood technology can sometimes present surprises. The… Expand

A Theoretical Model of Quasicrystal Resonators: A Guided Optimization Approach

- Physics
- Crystals
- 2021

Fibonacci-spaced defect resonators were analytically investigated by cavity coupling, which exhibited a series of well-defined optical modes in fractals. The analytic model can be used to predict the… Expand

Unstable resonators with polygon and von Koch-type boundary conditions : virtual source modelling of fractal eigenmodes

- Mathematics
- 2015

We will report on our latest research into modelling fractal lasers (linear systems that involve geometrically-unstable resonators with inherent magnification), and propose two new classes of cavity… Expand

#### References

SHOWING 1-6 OF 6 REFERENCES

Fractal structure of eigenmodes of unstable-cavity lasers.

- Physics, Medicine
- Optics letters
- 1998

It is shown that the eigenmodes of unstable-cavity lasers have fractal structure, in contrast with the well-known stable-c Cavity eigenModes, and the fractal dimension of the mode profiles is determined and it is related to the aperture shape. Expand

Optical Pattern Formation

- Physics
- 1999

Publisher Summary This chapter focuses on the concept of optical pattern formation. The field of optical pattern formation (OPF) studies the spatial and spatiotemporal phenomena that arise in the… Expand

Topology in chaotic scattering

- Physics
- Nature
- 1999

In chaotic scattering, an initially freely moving orbit (such as that of an atom or a star) enters a scattering region and evolves chaotically for a period of time before it escapes and returns to… Expand

Spatial grid symmetries and reduced models in the simulation of beam counterpropagation in a nonlinear medium

- Physics
- 1993

In the context of the nonlinear interaction of counterpropagating light beams, we demonstrate the unrealistic symmetries that arise in the simulation of spontaneous pattern formation when using… Expand

Fractal geometry - mathematical foundations and applications

- Mathematics, Computer Science
- 1990

Applications and examples: fractals defined by transformations examples from number theory graphs of functions examples from pure mathematics dynamical systems iteration of complex functions-Julia sets random fractals Brownian motion and Brownian surfaces multifractal measures physical applications. Expand

Experimental Observation of a Large Excess Quantum Noise Factor in the Linewidth of a Laser Oscillator Having Nonorthogonal Modes.

- Physics, Medicine
- Physical review letters
- 1996