Pattern formation in nonlinear optics

Pattern formation is a fascinating process and a great source of scientific research. One of the fathers of this scientific discipline was Sir D'Arcy Thompson, a Scottish biologist and mathematician who wrote an original and influential book dealing with structure forming in living organisms ("On growth and Form", 1917). My interest for pattern formation was initially oriented towards physical systems like liquids and optical devices but I have now an increased interest for the study of biological systems. In the figure below, you can see the results of experiments with lasers where you see that the optical plane waves destabilize and fall into five different kinds of new patterns. The bifurcation parameter (Δ x) is related to the spatial displacement in the feedback loop of a nonlinear interferometer. Details of the experimental setup may be found in this reference (Phys. Rev. A, 54, 3472, 1996).

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