Two-dimensional Whittaker solitons in nonlocal nonlinear media

Two-dimensional Whittaker solitons (WSs) are introduced and investigated numerically in nonlocal nonlinear media. Different classes of stable and unstable higher-order spatial optical solitons are discovered among the solutions of the generalized nonlocal nonlinear Schrödinger equation, in analogy with the linear Whittaker eigenmodes of the quantum harmonic oscillator. Specific values of the modulation depth parameter for different values of the topological charge are discussed. Our results reveal that in media with a Gaussian response function higher-order spatial WSs can exist in various families, such as two-dimensional Gaussian solitons, vortex-ring solitons, half-moon solitons, and symmetric and asymmetric single-layer and multilayer necklace solitons. The stability of WSs is addressed numerically. We establish that two-dimensional Gaussian solitons and vortex-ring solitons are stable, while other families of spatial WSs are unstable, although their stability can be improved by moving into the strongly nonlocal regime.