Fig. 1. (a) Experimental setup for transforming a globally incoherent field at plane A into a custom-designed partially coherent beam at plane B using a linear optical transformation system T. (b) Generation of the globally incoherent field at plane A: D is a dynamic diffuser to reduce spatial coherence of the incident focused laser beam, L1 is a collimating lens, L2 and L3 form an afocal imaging system of magnification m′=1/5, G is a Gaussian filter, and the metasurface is placed at plane A. The beam radii at planes D, G, and A are wD, wG, and wA, and the coherence radii at G and B are σG and σB.

Fig. 2. Properties of RAP beams of order m=0 with λ=633  nm, w0=300  μm, and q=1/30. (a) Cross sections of the DOC and (b) far-field (at z=10zR) spectral densities when C0=−1, ρs→0 (black), ρs=1 (red), ρs=2 (green), and ρs=4 (blue).

Fig. 3. (a) Operating geometry and design parameters of the Bragg carrier grating. θ is the first Bragg angle of incidence from air to the substrate of refractive index ns and θ′ from the substrate to the grating layer with refractive index n. h is the groove depth, c is the ridge width, and d is the period. (b) Efficiency η−1 of order l=−1 as a function of the fill factor in TE polarization. (c) Efficiency η−1 as a function of angle of incidence for different fill factors.

Fig. 4. SEM images of a fabricated grating. (a) Side view. (b) Top view.

Fig. 5. Measured absolute value of the spatial DOC μ(Δx,z0) (blue) and the spectral density S(x,z0) (orange) at plane A.

Fig. 6. Spatially varying transmission efficiency η−1 of the designed metasurface for the RAP beams of order (a) m=3 and (b) m=0.

Fig. 7. Measured and simulated complex degrees of source-plane spatial coherence of the RAP beam with m=3 (top row) and m=0 (bottom row). (a)–(d) Absolute values and (e)–(h) phases of μ(Δx,Δy). Here, (a), (b), (e), and (f) are the measured results, while (c), (d), (g), and (h) are the simulated results.

Fig. 8. Illustration of propagation characteristics of RAP-beam with m=3. The measured intensity profiles at four different propagation distances are in the top row, and the simulation is in the bottom row.

Fig. 9. Same as Fig. 8 but for the beam with m=0. The parameters used for the calculations were w0=210  μm, R=1/7.5, and q=1/30.