Cavity equations for a laser with an externally injected signal

We extend the cavity equations of motion for lasers with arbitrary output coupling [ Appl. Phys. Lett.36, 412 ( 1980)] to include an externally injected signal. The external signal is initially introduced into the cavity through the output coupler and enters the formulation through the boundary condition on the cavity electric field. A transformation is performed so that the injected signal is eliminated from the boundary condition and replaced by a driving-polarization term in the equations of motion for the cavity field that develops as a result of laser gain. We illustrate the use of this new formulation by applying it to an injection-seeded, gain-switched, standing-wave pulsed oscillator. The intracavity intensities as functions of axial position and time are compared for single-frequency and multiple-frequency operation.