Fig. 4: Focusing, defocusing, and diffraction-free propagation of the nonlinear edge states.

a Self-focusing of the edge state at \(n_2 \, > \, 0\) (Δ1 = 140 MHz) with increase of temperature. Scale bar: 200 μm. b Self-defocusing of the edge state at \(n_2 \, < \, 0\) (Δ1 = 125 MHz) with increase of the temperature. c Formation of diffraction-free edge states under the action of focusing nonlinearity \(n_2 \, > \, 0\) (Δ1 = 135 MHz) weaker than in panel a, when the pattern keeps the same functional form for different temperatures. The probe power is \(400\,\upmu {\mathrm{W}}\). b, c share the same scale bar as (a).