We show that non-paraxial nonlinear optics can be described in terms of a generalized quantum mechanics that is nowadays studied in the field of quantum gravity. The key point is the so-called generalized uncertainty principle (GUP) that describes particle localization on a scale comparable with the Planck length. The GUP has one-to-one correspondence to the resolution limit of non-paraxial propagation. When including nonlinearity, in one spatial dimension, it turns out that self-focusing forces the electromagnetic field to reach the profile of the so-called “maximally localized states” that are studied in the GUP literature. These findings address the possibility of realizing simulation of quantum gravity models in optics, with applications in microscopy, and following a recent experimental demonstrations of highly non-paraxial solitons.
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