We numerically demonstrate the existence of parabolic and rectangular self-similar propagations of optical beams in saturable media. Rectangular self-similar evolution is achieved by imposing an external optical potential (lattice) that acts as a pulse shaping mechanism and it is shown that a rectangular shaped profile can be obtained by providing a delicate balance between the nonlinearity and saturation of the medium.
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Bakırtaş et al. (2023) studied this question.
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