Fig. 1. q-HShPs based on vortex waves with different topological charges (m=0,±1) as excitation sources of hyperbolic materials without off-diagonal permittivity tensor elements at 718cm−1. (a)–(c) The simulated magnetic fields of different topological charges. (d)–(f) The corresponding intensities (|H|) of different topological charges. (g)–(i) The corresponding FFT (Re[Hz]) of different topological charges.

Fig. 2. Analytical results of q-HShPs based on the vortex with different topological charges (m=±1,±2,±3,±4) as excitation sources of hyperbolic materials without off-diagonal permittivity tensors at 718cm−1. (a)–(d) The analytical magnetic fields of positive topological charges. (e)–(h) The analytical magnetic fields of negative topological charges.

Fig. 3. Explanation of asymmetric q-HShPs in hyperbolic materials. (a) and (d) are the imaginary components of θ′ for εuu=−3+0.3i, εvv=1+0.3i and εuu=3+0.3i, εvv=1+0.3i, respectively. (b) and (e) The corresponding magnetic fields of vortex waves (m=1) as excitation sources at 718cm−1. (c) and (f) The corresponding intensities of vortex waves (m=1) as excitation sources at 718cm−1.

Fig. 4. The critical symmetry transition between the left-skewed and right-skewed q-HShPs induced by the vortex waves at 718cm−1. (a) The symmetry transition for different topological charges and different scaling factors. (b)–(f) The corresponding symmetric magnetic fields (away from the source) for different topological charges (m=0,±1,±2) and different scaling factors (f=0,±0.5,±1) at 718cm−1, respectively.

Fig. 5. More distinct asymmetric q-HShPs for decreasing and increasing scaling factors f induced by the vortex waves (m=1) at 718cm−1. (a)–(c) The magnetic fields of different scaling factors (f=+1.5,±0.5). (d)–(f) The corresponding intensities (|H|) of different scaling factors (f=+1.5,±0.5).