Fig. 1. Ray-wave multimode resonators. (a) Transverse mode intensity from ray-wave cavity satisfying the SU(2) Lie group condition of coupled harmonic oscillation^[14]; (b) experimental setup of a ray-wave cavity^[15]

Fig. 2. Degenerate cavity lasers. (a) Basic structure of degenerate cavity lasers^[18]; (b) multiple transverse mode oscillations in a degenerate cavity without inserting a far-field aperture^[4]; (c) single transverse mode oscillation in a degenerate cavity after inserting a far-field aperture^[4]; (d) relationship between output energy and the number of modes, where the red solid line represents the result of the degenerate cavity and the blue dashed line represents the result of the stable hemispherical cavity^[21]

Fig. 3. Principles and properties of random lasers. (a) Schematic of the structure of conventional lasers^[22]; (b) random lasing generation principle^[22]; (c) schematic of localized random laser^[22]; (d) schematic of diffusive random laser^[22]; (e) emission spectrum of localized random laser^[4]; (f) emission spectrum of diffusive random laser^[4]

Fig. 4. WGM microcavity lasers and wave-chaotic microcavity lasers. (a) A ray trajectory (left) and the intensity distribution (right) in a WGM microcavity^[4]; (b) a ray trajectory in a D-shaped wave-chaotic microcavity^[4]; (c)‒(d) simulated intensity distribution in a D-shaped wave-chaotic microcavity and a stadium-shaped wave-chaotic microcavity from Ref.[65]

Fig. 5. Structure and control of a photonic network laser. (a) Far-field images of a photonic network laser (left panel: far-field fluorescence image; right panel: far-field lasing image)^[72]; (b) pump threshold power of the photonic network lasers decreases as the network connectivity (D) increases^[72]; (c) shaping the spatial mode distribution of the pump light through a digital micromirror device^[73]; (d) under different spatial mode pumping conditions, the frequency mode of photonic lasers can be flexibly tuned from single-frequency emission (top and middle subfigures) to dual-frequency emission (bottom subfigure)^[73]

Fig. 6. Applications of low-coherence lasers in speckle-free imaging. (a) Speckle-free imaging of degenerate cavity laser with small pinhole (high coherence) and large pinhole (low coherence)^[21]; (b) application of suppressing meta-holographic artifacts by degenerate cavity laser^[80], the speckle gradually disappears as the spatial coherence is lowered (increasing the number of spatial modes NE); (c) speckle pattern and full-field imaging at the end of a multimode fiber by emission from the FP laser and D cavity laser, where C denotes speckle contrast^[6]; (d) speckle pattern and full-field imaging of O-shaped (left) and D-shaped (right) VCSELs^[88]; (e) full-field imaging of broadband laser, narrowband laser, amplified spontaneous emission and random laser sources after passing through a scattering medium^[26]

Fig. 7. Applications of VCSELs-based degenerate cavity laser in multimodality imaging^[79]. (a) Schematic of the VCSELs-based degenerate cavity laser, the coherence of the output laser can be controlled by varying the size of aperture; (b) Xenopus embryonic heart and its beating cycle; (c) Xenopus embryonic heart under highly coherent illumination; (d)‒(f) speckle-free imaging of Xenopus embryonic heart beating at diastole (d), diastole (e), end-systole (f) phases under lowly coherent illumination; (g)‒(i) speckle patterns of Xenopus embryonic heart beating at diastole (g), diastole (h), end-systole (i) phases under highly coherent illumination

Fig. 8. Ultrafast solution of iterative problems based on degenerate cavity lasers (DCL). (a) Real-time wavefront shaping based on a DCL^[105]; (b) imaging through scattering media based on a DCL^[106]; (c) rapid phase retrieval based on a DCL^[108]

Fig. 9. Simulation and mapping of physical systems based on DCLs. (a) Simulation of a spin system^[110]; (b) simulation of anionic-parity-time symmetry^[113]; (c) simulation of a synchronization system^[114]

Fig. 10. Coherent perfect absorbers based on anti-lasers. (a) Random perfect absorber based on random laser setup^[117]; (b) arbitrary transverse-mode perfect absorber based on the design of a degenerate cavity laser^[118]; (c) transverse-mode output intensity distributions when the self-imaging condition of a degenerate cavity perfect absorber is (right) and is not (left) satisfied^[118]

Fig. 11. Random number generation based on a multi-mode semiconductor laser^[122]. (a) Schematic diagram of the broad-area multi-mode semiconductor laser; (b) spatiotemporal distribution of the emission of the multi-mode semiconductor laser

Fig. 12. Other new applications of multimode lasers. (a) An ambient pH sensor based on a random multimode laser^[125]; (b) spatiotemporal distribution of high-power and high-stability laser output achieved with a chaotic microcavity multimode laser^[126]; (c) vortex laser array output with defects self-healing capabilities realized with a multimode degenerate cavity^[9]; (d) schematic of parallel random LiDAR with spatial multiplexing of a multimode degenerate cavity^[128]