Fig. 1. Focusing beyond diffraction-limit via wavefront shaping^[12]. (a) Focusing system with conventional lens; (b) focusing system with random scattering media; (c) focal spot of conventional lens; (d) focal spot beyond diffraction-limit via wavefront shaping

Fig. 2. Non-invasive focusing via two-photon fluorescence signal^[50]. (a) Experimental setup; (b) speckle pattern acquired by CCD before optimization; (c) focal spot acquired by CCD after optimization

Fig. 3. Measuring setup and principle of acousto-optic transmission matrix^[54]

Fig. 4. Polarization recovery by broadband wavefront shaping^[16]. (a) Polarization distribution of speckle before optimization; (b) polarization distribution of focal spot after optimization

Fig. 5. Polarization manipulation via vector transmission matrix^[59]. (a) Experimental setup; (b) results of polarization manipulation

Fig. 6. Control of pulse time-domain characteristics via heterodyne signals^[61]. (a) Experimental setup; (b) optimized results

Fig. 7. Pulse compression by optimizing two-photon fluorescence signals^[62]. (a) Experimental setup; (b) pulse width before optimization; (c) pulse width after optimization

Fig. 8. Control of pulse time-domain characteristics via multispectral transmission matrix^[65]. (a) Experimental setup; (b)-(e) pulse shape modulation by using multispectral transmission matrix

Fig. 9. Schematic of directional transmission of optical energy via transmission eigenchannels^[67]

Fig. 10. Principle of point-spread-function engineering based on transmission matrix^[14]

Fig. 11. Direct computational imaging of detected output speckle via transmission matrix method^[9]. (a) Experimental setup for transmission matrix measurement; (b) original image; (c) restored image

Fig. 12. Measurement setup and principle of fluorescence-based transmission matrix^[48]

Fig. 13. Non-invasive imaging via two-photon fluorescence signals^[50]. (a) Microscope image of the tissue using memory effect; (b) transmission microscope image of the same object without scattering medium

Fig. 14. Principle of non-line-of-sight imaging using the object as a guidestar^[78]

Fig. 15. Endoscopic imaging system based on a single multimode optical fiber^[79]. (a) Experimental setup; (b)(c) imagings of different neural tissues in mice

Fig. 16. Schematic of holography using scattering^[84]. (a)(b) Fourier holography using conventional lens; (c)(d) holography using wavefront shaping combined with scattering effect

Fig. 17. Comparison of conventional multi-plane projection and three-dimensional scattering-assisted dynamic holography^[85]. (a) Conventional multi-plane projection; (b) three-dimensional scattering-assisted dynamic holography

Fig. 18. OAM communication scheme based on transmission matrix method^[92]. (a) Experimental setup; (b) demonstration of OAM beam complex amplitude recovery; (c) comparison of experimentally measured OAM spectrum with theoretical OAM spectrum

Fig. 19. Experimental setup for conversion between different angular momentums^[15]. (a) OAM-OAM; (b) OAM-SAM; (c) SAM-SAM; (d) SAM-OAM

Fig. 20. Second harmonic focusing via feedback-based wavefront shaping method^[102]. (a) Schematic of principle; (b) speckle pattern of second harmonic light before optimization; (c) spot focusing pattern of second harmonic light after optimization

Fig. 21. Manipulation of nonlinear processes in multimode fibers via feedback-based wavefront shaping method^[19]. (a) Experimental setup; (b) comparison of optimized and unoptimized intensity of four-wave mixing signal

Fig. 22. Nonlinear scattering signal manipulation via scattering matrix method^[104]. (a) Scattering matrix measurement setup and principle; (b) dynamic scanning results of sum-frequency signals

Fig. 23. Focusing photon pairs in the target two-photon output state^[106]. (a) Experimental setup; (b) different photonic states focused at different spatial locations; (c) two-photon state coincidence counting rate

Fig. 24. Scattering compensation of entangled photon pairs by optimizing the pump wavefront^[110]. (a) Experimental setup; (b) experimental results

Fig. 25. Near-infrared speckle wavemeter based on nonlinear frequency conversion^[113]. (a) Experimental setup; (b) confusion matrix for wavelength detection

Fig. 26. Spectrometer based on on-chip randomized structure^[116]. (a) Structure of the spectrometer obtained by scanning electron microscope; (b) spectral resolution of the spectrometer

Fig. 27. Computational steps for realizing the discrete Fourier transform via transmission matrix method^[121]