COL cover story: Asymmetric Mathieu beams
At: 2019/1/7 15:09:25 by admin

Optical lattices are structures oflight generated by interfering optical laser beams, that resemble a crystallattice. This interference creates a standing wave pattern that can be usefulfor the study and applications of light-matter interactions. A technique togenerate such structures is using nondiffracting beams, i.e. beams whoseintensity shape remains invariant under propagation, allowing a key feature incontrolling light and optical manipulation of matter. However, obtainingnondiffracting beams can constitute a challenging problem because thesebeams must satisfy several restrictive mathematical conditions. In fact, animportant and still open question is to determine what kind of transverse shapesimposed on a laser beam can be invariant propagated.


To date, there are several techniquesfocused on symmetry relations, numerical relaxation procedures or even in geneticalgorithms to obtain novel and complex quasi-nondiffracting patterns. However, truly invariant and useful patternsare even by far more difficult to obtain, being the mathematical efforts togenerate these nondiffracting beams formidable.


Researchers from Tecnologico deMonterrey at Mexico have been able to generate a novel kind of nondiffractingstructure, the asymmetric Mathieu beam and they have corroborated experimentallytheir theoretical prediction by generating and propagating these beams,demonstrating their invariant behavior. These novel nondiffracting beams havethree control parameters: the degree of ellipticity, the degree of asymmetryand the location of the respective symmetry breaking. Moreover, these beams canbe implemented in an experimental setup by an easy modification to the standardand more well-known nondiffracting Mathieu beams. The generation of asymmetricMathieu beams can be interesting for studying and developing new technologies in manipulation of Bose-Einsteincondensates, applications of optical lattices for quantumcomputing, trapping of in-vivo and colloidalparticles, and for soliton routing, just to name afew. This work has been published in Chinese Optics Letters, Vol. 16, Issue 12,2018  (Arturo Barcelo-Chong, et al..AsymmetricMathieu beams).


Associate professor Servando Lopez-Aguayo,leader of the research project, believes that these results could shed light onnovel techniques to generate even more complex invariant structures. As a holygrail, the Mexican researchers are looking to create truly and useful nondiffractingbeams on demand, being also interested in diffraction management to achieve differentkind of propagation dynamics.


Further work will be focused onapplications of these nondiffracting modes, for example, in nonlinear opticsfor self-trapped beams in routing and steering and in the generation of dynamicoptical asymmetric lattices.

Graphic Discription:Examples of asymmetricMathieu-Gauss beams. Different rows correspond to different degrees of asymmetry(low asymmetry to high asymmetry, from up to down, respectively). Differentcolumns correspond to different ellipticities (low ellipticity to highellipticity, from left to right, respectively).

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