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A true time delay system for optical signals includes a hollow core optical waveguide, a droplet of reflective liquid metal disposed in the hollow core, and an actuator coupled to a first end of the waveguide to move the droplet longitudinally within the hollow core. In one example, the waveguide is a hollow core photonic bandgap fiber. In one example, the actuator is a pressure actuator that introduces or removes gas into the core. Light enters the optical fiber, is transmitted through the fiber toward the reflective surface of the droplet, and is reflected back through the fiber and exits at the same end of the photonic bandgap optical fiber that it entered. The fiber optic device can provide a continuously-variable optical path length of over 3.6 meters (corresponding to a continuously-variable true-time delay of over 12 ns, or 120 periods at a 10 GHz modulation frequency), with negligible wavelength dependence across the C and L bands.