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We report new rogue wave patterns in the nonlinear Schrödinger equation. These patterns include heart-shaped structures, fan-shaped sectors, and many others, that are formed by individual Peregrine waves. They appear when multiple internal parameters in the rogue wave solutions get large. Analytically, we show that these new patterns are described asymptotically by root structures of Adler–Moser polynomials through a dilation. Since Adler–Moser polynomials are generalizations of the Yablonskii–Vorob’ev polynomial hierarchy and contain free complex parameters, these new rogue patterns associated with Adler–Moser polynomials are much more diverse than previous rogue patterns associated with the Yablonskii–Vorob’ev polynomial hierarchy. We also compare analytical predictions of these patterns to true solutions and demonstrate good agreement between them. 

We experimentally demonstrate that a probe beam at one wavelength, although exhibiting a weak nonlinear response on its own, can be modulated and controlled by a pump beam at another wavelength in plasmonic nanosuspensions, leading to ring-shaped pattern generation. In particular, we show that the probe and pump wavelengths can be interchanged, but the hollow beam patterns appear only in the probe beam, thanks to the gold nanosuspensions that exhibit a strong nonlinear response to pump beam illumination at the plasmonic resonant frequencies. Colloidal suspensions consisting of either gold nanospheres or gold nanorods are employed as nonlinear media, which give rise to refractive index changes and cross-phase modulation between the two beams. We perform a series of experiments to examine the dynamics of hollow beam generation at a fixed probe power as the pump power is varied and find that nonlinear beam shaping has a different power threshold in different nanosuspensions. Our results will enhance the understanding of nonlinear light–matter interactions in plasmonic nanosuspensions, which may be useful for applications in controlling light by light and in optical limiting.