Fig. 1. CGCS images with positive Gaussian curvature. (a) Smooth and (b) rough. (c) Light beam transmits on the rough CGCS. (d) Local rough surface.

Fig. 2. Beam is transmitting in a Gaussian correlated random potential. (a) and (b) are the plane waves propagating on a flat surface and a CGCS, respectively, and the white line is the evolution of the ScI with light transmission. (c) and (d) are the Gaussian light propagating on flat surfaces and CGCSs, respectively. (e) Change of the ScI of the plane waves on the CGCS with different curvatures. (f) The position of the first branching point of plane wave varies with the curvature of the curved surface and the magnitude of the random potential field V0.

Fig. 3. (a) Evolution of the Gaussian beams in random fields on the CGCS. (b) Change of the maximum intensity of light with respect to transmission. (c) Evolution of the transverse light intensity distribution.

Fig. 4. (a) Evolution of the entropy of the optical branched flow when it transmits on a curved surface. (P1)–(P4) Light intensity probability distribution. For the different correlation lengths, the branched flow entropy of the beam varies with the transmission on (b) the flat surface and (c) the CGCS.

Fig. 5. (a) Evolution of the coherence degree of the branched flow with transmission on a flat surface. (b) and (c) are the relationship between the attenuation factor b and the random potential field parameters V0 and lc, respectively. (d) Theoretical evolution of branching flow entropy under different curvatures. (e) Evolution of the coherence degree of the branched flow on curved surfaces with different curvatures. (f) Change of the position of its first peak in the curve of (e) with different curvature. (g) Theoretical evolution of the probability distribution of the light intensity with different ρ on a flat surface.