Vector beams have found a myriad of applications, from laser materials processing to microscopy, and are now easily produced in the laboratory. They are usually differentiated from scalar beams by qualitative measures, for example, visual inspection of beam profiles after a rotating polarizer. Here we introduce a quantitative beam quality measure for vector beams and demonstrate it on cylindrical vector vortex beams. We show how a single measure can be defined for the vector quality, from 0 (purely scalar) to 1 (purely vector). Our measure is derived from a quantum toolkit, which we show applies to classical vector beams.
Creating high-quality vector vortex (VV) beams is possible with a myriad of techniques at low power, and while a few studies have produced such beams at high-power, none have considered the impact of amplification on the vector purity. Here we employ novel tools to study the amplification of VV beams, and in particular the purity of such modes. We outline a general toolbox for such investigations and demonstrate its use in the general case of VV beams through a birefringent gain medium. Intriguingly, we show that it is possible to enhance the purity of such beams during amplification, paving the way for high-brightness VV beams, a requirement for their use in highpower applications such as laser materials processing.
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 coastlines. With their highly polished spherical mirrors, laser resonators are almost the precise opposite of Nature, and so it came as a surprise when, in 1998, transverse intensity cross-sections of the eigenmodes of unstable canonical resonators were predicted to be fractals [Karman et al., Nature 402, 138 (1999)]. Experimental verification has so far remained elusive. Here we observe a variety of fractal shapes in transverse intensity cross-sections through the lowest-loss eigenmodes of unstable canonical laser resonators, thereby demonstrating the controlled generation of fractal light inside a laser cavity. We also advance the existing theory of fractal laser modes, first by predicting 3D self-similar fractal structure around the centre of the magnified self-conjugate plane, second by showing, quantitatively, that intensity cross-sections are most self-similar in the magnified self-conjugate plane. Our work offers a significant advance in the understanding of a fundamental symmetry of Nature as found in lasers.
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