Fig. 1. Schematics of the FDC for the conditions of (a) |Ω=1/4〉 and (b) |Ω=1/3〉; the inserts show the corresponding transverse and longitudinal frequency distributions and periodic ray trajectories. Schematics of the measurements of (c) transverse patterns and (d) spectrum. CCD, charge-coupled device; OSA, optical spectrum analyzer; Xtal, crystal.

Fig. 2. Recorded transverse patterns and spectral evolutions (see Visualization 3 and Visualization 4) versus the off-axis displacement for (a) |Ω=1/4〉 and (b) |Ω=1/3〉.

Fig. 3. Diagram of mode frequency distributions, where the dashed circles mark the positions of cooperation of transverse and longitudinal modes corresponding to states |Ω0=1/4〉, |Ω1=3/11〉, |Ω2=5/19〉, and |Ω3=7/27〉.

Fig. 4. Simulated results of intensity patterns of degenerate states of (a) |Ψ57(Ω=1/4)〉, (b) |Ψ55(Ω=3/11)〉, (c) |Ψ53(Ω=5/19)〉, and (d) |Ψ52(Ω=7/27)〉 when ϕ=π/3; the mixed states of (e) |Ω=1/4〉+0.5|Ω=3/11〉, (f) |Ω=1/4〉+0.5|Ω=3/11〉+0.5|Ω=5/19〉 when ϕ=π/3; and the mixed states of (g) |Ω=1/4〉+0.5|Ω=3/11〉, (h) |Ω=1/4〉+0.5|Ω=3/11〉+0.5|Ω=5/19〉+0.5|Ω=7/27〉 when ϕ=2π/3.