Fig. 1. Vortex phenomenon in nature. (a) Spiral galaxy; (b) Hurricane

Fig. 2. Dislocations in crystals^[1]

Fig. 3. Generation of optical vortex via the cross-phase^[18-20]. (a) Distribution of cross-phase; (b) Generation of high-order optical vortex via the low-order cross-phase; (c) Shaping and singularity manipulation of high-order optical vortex via the high-order cross-phase; (d) Generation of Hermite-Gaussian-like optical vortex via the low-order cross-phase; (e) Experimental setup for generation of optical vortex via the cross-phase

Fig. 4. (a) Setup of quadruple topological charges of optical vortex based on SPP^[23]; (b) Setup of cascaded and double-pass SPPs^[22]; (c) Experimental intensity distributions of optical vortex via the setup of cascaded and double-pass SPPs^[22]; (d) Fiber SPP made by Fiber Photonics Co

Fig. 5. (a) Superposition of multiple optical vortices^[26]; (b) Pixel-level polarization modulation via the pure phase SLM^[29]

Fig. 6. Adjustable vortex laser and optical vortex detector^[33]. (a) Structure of Q-board; (b) Adjustable

Fig. 7. (a) Small scatterer in the spiral phase^[39]; (b) Frequency shift between the illumination and the detection light^[40]; (c) Observed power spectrum under the illumination of white light^[41]

Fig. 8. (a) Free space detection; (b) Detection results of symmetrical objects^[45]

Fig. 9. (a) Tiny scatter model^[47]; (b) Detection principle with small lateral displacement^[47]

Fig. 10. Manipulation and the gyroscopic effect of vortices in BEC^[52]. (a) Gyroscopic effect of vortices in gasiform BEC; (b) BEC gyroscope model based on matter wave in the system of cold atom; (c) Manipulation on the excitation-polaritons by optical vortex carrying orbital angular momentum; (d) Spontaneous interference of excitation-polaritons due to the phase imprinting of the superimposed optical vortices

Fig. 11. Bose-Einstein Condensates of Exciton Polariton in the semiconductor flat microcavity^[54]. (a) Semiconductor flat microcavity formed with distributed Bragg mirrors where the semiconductor quantum wells enmeshed in the microcavity; (b) Side view of the semiconductor flat microcavity; (c) Location distribution of refractive index and field intensity in the microcavity corresponding to Fig.11(b)

Fig. 12. Dynamic characteristic of excitation-polariton BEC in semiconductor microcavities^[58]. (a) Evolution of superposition of excitation-polariton vortices driven by pump beam; (b) Rotary dynamic characteristic of superposition of excitation-polariton vortices

Fig. 13. System of exciton polariton condensates on the rotational state^[59]. (a) System of volute superposition state of exciton polariton condensates on the rotational state; (b) Relationship between the instantaneous angular rate of the superposition state of exciton polariton vortices and the rotate speed of the system (the rotation angle at the rotation rate of and ) 旋转状态下的激子极化激元凝聚体系^[59]。(a)旋转状态下的激子极化激元涡旋叠加态体系；(b)激子极化激元涡旋叠加态瞬时转动角速率与体系转速的关系(限定时间内转速为 和 情况下涡旋叠加态转过的角度对比)