Fig. 4

Nonlinearity-induced dynamical rotation of \(p\)-orbital corner states. a1, b1 Excitation of the top corner of a nontrivial BKL with a dipole-like beam initially tilted at (a1) \(\theta =-3{0}^{\circ }\) and (b1) \(\theta =3{0}^{\circ }\) with respect to the \(y\)-axis. a2–a4 Experimental output of the orbital corner state under an initial excitation corresponding to (a1), showing a clockwise rotation under the action of a self-focusing nonlinearity (with a bias field of 175 kV/m). b2–b4 Opposite rotation observed under the same nonlinearity when the initial excitation corresponds to (b1). The grey triangle in each panel outlines the BKL boundaries. Note that no rotation occurs when the dipole is initially oriented along the \(y\)-axis. c Orbital band structure calculated from the discrete NLSE at a dimensionless distance \(Z=50,\) for a probe beam incident at \(\theta =3{0}^{\circ }\) and propagating under both linear (\(\gamma =0\)) and nonlinear (\(\gamma =0.6\)) regimes. A tilted dipole-like beam excites two orthogonal orbital corner modes which are nearly degenerate in the linear regime (\({\Delta \beta }_{L}\approx 0\)). Here, the nonlinearity lifts the degeneracy and increases the difference \({\Delta \beta }_{NL}\) between the nonlinear eigenvalues, in turn leading to a rotation of the orbital state. Insets illustrate the orientation of a probe beam at \(Z=25\) in the two regimes