Abstract Programmable multifunctional integrated nanophotonics (PMIN) is a new paradigm that aims at designing common integrated optical hardware configurations, which by suitable programming can implement a variety of functionalities that can be elaborated for basic or more complex operations in many application fields. The interest in PMIN is driven by the surge of a considerable number of emerging applications in the fields of telecommunications, quantum information processing, sensing and neurophotonics that will be calling for flexible, reconfigurable, low-cost, compact and low-power-consuming devices, much in the same way as how field programmable gate array (FPGA) devices operate in electronics. The success of PMIN relies on the research into suitable interconnection hardware architectures that can offer a very high spatial regularity as well as the possibility of independently setting (with a very low power consumption) the interconnection state of each connecting element. Integrated waveguide meshes provide regular and periodic geometries, formed by replicating a unit cell, which can take the form of a square, hexagon or triangle, among other configurations. Each side of the cell is formed by two integrated waveguides connected by means of a Mach-Zehnder interferometer (MZI) or a tunable directional coupler that can be operated by means of an output control signal as a crossbar switch or as a variable coupler with independent power division ratio and phase shift. In this paper, we review the recent advances reported in the field of PMIN and, especially, in those based on integrated photonic waveguide meshes, both from the theoretical as well as from the experimental point of view. We pay special attention to outlining the design principles, material platforms, synthesis algorithms and practical constraints of these structures and discuss their applicability to different fields.
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