Spectroscopic Measurement of High-Frequency Electric Fields in a Plasma by Observation of Two-Quantum Transitions and Spectral Line Shifts

We have observed normally forbidden two-quantum transitions in the optical spectrum of a helium plasma. We induced these transitions by applying a microwave field to a separately generated steady-state helium discharge. Measurements of the relative intensity and wave-length of the optical photons emitted in the two-quantum transition $5{}_{}{}^1{}_{}{}^{}F_{}^0{}_{}{}^{}\to 2{}_{}{}^1{}_{}{}^{}P_{}^0{}_{}{}^{}$ in He I determined both the frequency and the strength of the microwave field in the plasma. The field strength was also measured by observation of the Stark shift of a spectral line and by measurement of the microwave power input and the $Q$ of the microwave cavity. All measurements of the field strength are in satisfactory agreement and indicate an rms microwave field strength in the plasma of about 215 V/cm. The spectroscopic measurement of the frequency of the microwave field is within 3% of the actual value, and the measured polarization of the radiation agrees with theory.