Fig. 1: Frequency metrology across microwave, optical, and free-electron domains.
From: Unifying frequency metrology across microwave, optical, and free-electron domains
a Frequency range of electromagnetic waves and free-electron matter waves. b Frequency locking scheme across microwave, optical, and free-electron domains. Microwave and optical domains are connected by a fully stabilized optical frequency comb with the carrier-envelope-offset frequency fceo and the repetition rate frep being stabilized. A continuous-wave (CW) laser is offset locked to one comb tooth via a local oscillator (LO) at frequency fLO. The CW laser then coherently modulates the phase of an electron beam, generating sidebands in the electron spectrum that are regularly spaced by the photon energy hfopt. c Experimental setup. A CW laser pumps a Si3N4 photonic chip-based microresonator in a transmission electron microscope (TEM) to modulate the electron phase and broaden the electron spectrum measured in a post-column electron spectrometer. A wavelength meter performs coarse measurement of the laser frequency. The transmitted CW laser is mixed with a stabilized optical frequency comb (OFC) to generate microwave beatnotes that are measured with an electronic spectrum analyzer (ESA). An optical spectrum analyzer (OSA) monitors the laser and the OFC. An optical phase-locked loop (OPLL) offset-locks the laser to one comb tooth. The beatnote and a 10 MHz microwave local oscillator (LO) are mixed at a 12-bit double-balanced digital phase detector (DPD) that accounts for large phase slips induced by frequency fluctuations. The DPD output, or error signal, is fed to a servo controller to adjust the laser frequency. Blue paths represent fiber connections, and black lines stand for electronic connections. EDFA erbium-doped fiber amplifier, FPC fiber polarization controller, PD photodetector, OSC oscilloscope, OBPF optical bandpass filter.
