Two-dimensional solitons in Laguerre-Gaussian potentials

We obtain two-dimensional self-trapped optical waves that are solutions of the nonlinear Schrodinger equation with the support of Laguerre-Gaussian and harmonic potentials. In this model we show that, contrary to the common scenario where the two-dimensional soliton solutions can only be obtained by numerical methods, it is possible to obtain a corresponding closed-form expression for the soliton solutions and angular momentum and also for the conservation laws, such as the norm and the Hamiltonian. Remarkably, we find that these nonlinear modes can also be stabilized provided they remain below a threshold norm value. The completely local nonlinear medium analyzed here resembles, up to a certain point, a strongly non-local medium, thus allowing us to make some connections between linear and nonlinear systems. We corroborate the theoretical predictions by using numerical spectral techniques.