Block diagram of circuit. Red arrows represent laser light, black arrows represent electronic signals. Violet symbols: detection and amplification of the optical beat note. Red symbols: heterodyning stage. Orange symbols: fast prescaling stage for large- lock. Green symbols: digital counting. Yellow symbols: D-to-A and generation of error signal. Blue symbols: PID feedback control.
Timing diagram of digital counting. Vertical blue dashed lines are guides to the eye. Counting occurs only in red shaded regions of the sample clock waveform, yielding a live time fraction of (note the broken time axis). is updated at the conclusion of a given counting window; for example, , proportional to the average counted frequency in the sample window, is output by the DAC while the binary counter is accumulating counts in the window. This latency adversely affects the stability of the servoloop at frequencies near the Nyquist frequency , and thus imposes a limit on the loop gain.
Detecting frequency fluctuations by discretely sampled counting. (a) Pictorial representation of the optical beat note frequency modulated by the noise waveform of (b). (b) Representative FM noise waveform, identifying various symbols used in the text.
Long-term locking. Time series of the optical beat note frequency , acquired over a 5 h period, for (a) the small- and (b) large- locks. For comparison, time series are also shown for the slave laser unlocked.
Optical beat note linewidth. rf spectrum analyzer traces of the optical beat note for (a) small- and (b) large- locks for the servoloops both locked and unlocked. FWHM linewidths are given for the locked data. For these measurements, the resolution bandwidth of the spectrum analyzer was 10 kHz (100 kHz) for the small-(large-) locks, respectively. The full-screen sweep time was approximately 20 ms for all traces.
Frequency stability. Absolute and relative frequency Allan deviation data are shown as red solid squares for the small- (a) and large- (b) locks, for integrations times . Points at 900 s are not true Allan deviations but rather the average deviation of 13 discrete measurements of the beat note taken at 15 min intervals over 3 h. The dashed and dashed-dot lines are fits to the measured Allan deviation points, as described in the text. Heavy black lines in both figures show the QEL relative instability discussed in Sec. V. Solid black circles are the measured relative Allan deviation of the computer-controlled reference voltage. Open black diamonds show the counting noise floor of the counting electronics as measured in a separate experiment in which the optical beat note was replaced by the output of a high-quality electronic synthesizer set to the same frequency, with the high speed divider either (a) removed, or (b) set to divide by 16. There is no contradiction in these measurements lying below the QEL line, as they were made in open loop, whereas the QEL applies only to the closed-loop stability of the locked laser beat note. Error bars are one-standard deviation statistical uncertainties.
Tuning agility. Oscilloscope traces of , proportional to , show the response of the slave laser to an abrupt step of , corresponding to jumps of 70 MHz in the (a) small- lock and (b) 416 MHz in the large- lock. The stair-case pattern visible in in (a) directly reflects the discrete sampling and counting of the beat note. The steps are not visible in (b) due to its compressed time axis.
Tuning range. The frequency of the locked optical beat note , for the (a) small- lock and (b) large- lock vs heterodyne local oscillator frequency , counted using a rf spectrum analyzer. A positive (negative) beat note corresponds to the slave laser frequency higher (lower) than the master laser. Solid red circles (solid blue squares) correspond to locking to the downshifted (upshifted) copy of the beat note from the heterodyne stage. Open symbols represent measurements made with a different value of the postheterodyne rf low-pass filter so as to lock the lowest optical beat notes for a given configuration. Curves through the data are lines of through the lowest measured beat note of each series, for the small-(large-) locks, respectively.
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