Fig. 1. Phase reconstruction via metasurface-integrated quantum analog operation. (a) Schematic of non-local mode selection by metasurface-integrated quantum analog operation. F^1, F^2, F^3, and F^4 are the differential operators. The green area has been designed to construct differential operators, and the blue area can be extended to construct other operators. (b) Three modes of metasurface-integrated quantum analog operation system and corresponding differential output results through non-local mode selection. (c) Theoretical phase gradient in x-direction. (d) Theoretical phase gradient in y-direction. (e) Theoretical two-dimensional (2D) phase gradient. (f) Theoretical phase distribution calculated by the 2D phase gradient.

Fig. 2. Experimental setup. Setup schematic: HWP, half-wave plate; QWP, quarter-wave plate; PBS, polarization beam splitter; M, mirror; QC, quartz crystal; L, Lens; BBOs, β-BaB₂O₄ crystals; LPF, long-pass filter; FC, fiber coupler; BS, beam splitter; SMF, single mode fiber; SPCM, single photon counting module; ICCD, intensified charge coupled device. Inset, the experimental results of the polarization interference curves.

Fig. 3. Experimental results of analog operation. (a–c) Experimental results of quantum analog operation in three modes, respectively. (d) Experimental results of classical analog operation in third mode. (e) Schematic of the detailed local optical axes of the four regions being designed on the metasurface. (f) The SNR in experimental imaging results of classical and quantum analog operation, respectively, under different pump powers.

Fig. 4. Process of quantitative phase reconstruction by Fourier integration. (a, b) Experimental measurement results of phase gradient in the x- and y-directions, respectively. (c) Experimental measurement results of 2D phase gradient. (d, e) Results of phase gradient reconstruction in the x- and y-directions, respectively, which is obtained by taking the derivative of the reconstructed normalized phase distribution. in the x- and y-directions, respectively. (f) Results of 2D phase gradient reconstruction. (g) Variation curve of the residual with coefficient K, which shows the process of solving the optimization problem. (h) Schematic diagram of minimum residuals. (i) Normalized results of phase reconstruction. (j) Quantitative results of phase reconstruction. (k) Results of the reconstructed depth corresponding to the white dotted lines.

Fig. 5. Quantitative phase reconstruction results. (a, b, e, f) The measured phase gradient results of phase objects- "01" and "Tai Chi", respectively. (c, g) Quantitative phase reconstruction results of "01" and "Tai Chi", respectively. (d, h) Results of the reconstructed phase value corresponding to the white dotted lines of "01" and "Tai Chi", respectively.