One of the important aspects of manipulating and controlling liquid transport is the design of membrane surfaces. Janus membranes with opposite wettability characteristics can be manufactured for efficient directional water transfer. In this work, two types of materials were used to fabricate membranes with an asymmetric wettability behavior: copper foam and copper mesh. One side of the membranes was treated by scanning with a femtosecond laser beam, as a result of which it was converted to a superhydrophilic state, while the untreated side remained hydrophobic. Both membranes demonstrated excellent properties of a water diode through which water droplets could easily pass from the hydrophobic side to the hydrophilic side, but not vice versa. This behavior was achieved by finding the optimal laser scanning speed. This type of Janus membrane has found applications in collecting water droplets from fog; therefore, the samples obtained were also tested in terms of harvesting micro-droplets. The Janus mesh-based structure has demonstrated a higher water collection efficiency (3.9 g/cm2 h) compared to the foam-based membrane (2.5 g/cm2 h). Since the fog-water conversion efficiency decreased over time (to 0.5 g/cm2 h in 2 weeks) due to the absorbance of organic pollutants, a coating of titanium oxide was applied to the laser-treated side of the Janus membranes. As a result, the effective function of the systems became distinctly long-lasting and was well maintained for at least 60 days. Moreover, the fabricated systems were protected from further degradation by simply placing them under sunlight for several hours. Our results prove to be useful in developing asymmetric hydrophobic-superhydrophilic membranes, which have potential applications in high-precision drop control and in harvesting water from arid environments.