  One of the fundamental limitations in photonics is the lack of a
bidirectional transducer that can convert optical information into electronic
signals or vice versa. In acoustics or at microwave frequencies, wave signals
can be simultaneously measured and modulated by a single transducer. In optics,
however, optical fields are generally measured via reference-based
interferometry or holography using silicone-based image sensors, whereas they
are modulated using spatial light modulators. Here, we propose a scheme for an
optical bidirectional transducer using a spatial light modulator. By exploiting
the principle of time-reversal symmetry of light scattering, two-dimensional
reference-free measurement and modulation of optical fields are realized. We
experimentally demonstrate the optical bidirectional transducer for optical
information consisting of 128 x 128 spatial modes at visible and short-wave
infrared wavelengths.
