We propose an intensity modulator based on injection locking of a resonant cavity with gain that has a linear transfer function, multigigahertz bandwidth, possible optical gain, and very low V(pi). The arcsine phase response of the injection-locked resonant cavity placed in one arm of a Mach-Zehnder interferometer is the key to the true linear performance of this modulator. The first (to our knowledge) demonstration of this modulator with 5 GHz bandwidth, V(pi) of approximately 2.6 mV, and 95 dB spur-free dynamic range is reported here.