  We demonstrate that phase-difference between terahertz signals on the source
and drain of a field effect transistor (a TeraFET) induces a plasmon-assisted
dc current, which is dramatically enhanced in vicinity of plasmonic resonances.
We describe a TeraFET operation with identical amplitudes of radiation on
source and drain antennas but with a phase-shift-induced asymmetry. In this
regime, the TeraFET operates as a tunable resonant polarization-sensitive
plasmonic spectrometer operating in the sub-terahertz and terahertz range of
frequencies. We also propose an effective scheme of a phase-sensitive homodyne
detector operating in a phase-asymmetry mode, which allows for a dramatic
enhancement of the response. These regimes can be implemented in different
materials systems including silicon. The p-diamond TeraFETs could support
operation in the 200 to 600 GHz atmospheric windows.
