existence of defect or disorder will inevitably result in the destruction of intrinsic photonic bandgaps, thus impairing the practical performance of desired design for wave propagation. [2] By contrary, recent developments in micro-and nanophotonics have demonstrated that disorder structure with spatially inhomogeneous material, including random or chaotic structures, could be well utilized as an another degree of freedom to yield various new optical phenomena. [3][4][5] Particularly, a variety of nonconventional optical functionalities have been proposed in diverse areas of optical applications, ranging from optical Anderson localization in deep subwavelength photonic structures, [6] broadband momentum transformation and spatiotemporal instability suppression in a chaotic optical microcavity, [7,8] and optical transition in the disordered plasmonic system [9,10] to perfect focusing in disordered media. [11,12] Consisting of arrays of artificial nanostructures (or meta-atoms), metasurface can arbitrarily manipulate the amplitude, phase, and polarization of the incident light field at subwavelength scale [13][14][15] and therefore has been widely applied to planar imaging, [16][17][18][19] meta-holograms, [20][21][22] quantum optics, [23][24][25][26] and complex beam generators. [27][28][29][30][31] Most recently, disorder engineering has been introduced into metasurface by randomly manipulating the spatially inhomogeneous phase retardation of meta-atoms, Recently, disordered metasurfaces have attracted considerable interest due to their potential applications in imaging, holography, and wavefront shaping. However, how to emerge long-range ordered phase distribution in disordered metasurfaces remains an outstanding problem. Here, a general framework is proposed to generate a spatially homogeneous in-plane phase distribution from a disordered metasurface, by engineering disorder parameters together with topology optimization. As a proof-of-concept demonstration, an all-dielectric disordered supercell metasurface with relatively homogeneous in-plane phase fluctuation is designed by disorder parameter engineering, manifesting as polarization conversion-dependent random scattering or unidirectional transmission. Then, a topology optimization approach is utilized to overcome the lattice coupling effect and to further improve the homogeneity of complex electric field fluctuation. In comparison with the initial supercell metasurface, both the phase fluctuation range and the relative efficiency of the topologyoptimized freeform metasurface are significantly improved, leading to a long-range ordered electric field distribution. Moreover, three experimental realizations are performed, all of which agree well with the theoretical results. This methodology may inspire more exotic optical phenomena and find more promising applications in disordered metasurfaces and disordered optics.
