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We study electromagnetic field propagation through a planar three-waveguidecoupler with linear gain and loss, in a configuration that is the opticalanalog of a quantum $\mathcal{PT}$-symmetric system, and provide itsclosed-form analytic propagator. At an specific propagation length, we showthat the device provides all-optical amplitude to phase modulation with a $\pi$modulation range, if an extra binary phase is allowed in the reference signal,as well as phase to amplitude modulation, with an amplitude modulation rangethat depends linearly on the gain-to-coupling ratio of the system.

All-optical $\mathcal{PT}$-symmetric amplitude to phase modulator