Systems and methods for dual comb spectroscopy
A frequency-measurement method uses a dual frequency-comb spectrometer as an optical wavemeter to measure the frequency of a reference laser that is used to frequency-stabilize the spectrometer. The method includes measuring a walking rate of center bursts in a sequence of interferograms recorded by the spectrometer, determining a number of teeth in each of a plurality of Nyquist windows formed by the dual frequency-comb spectrometer, and determining a Nyquist number of the one Nyquist window covering the laser frequency. The reference laser frequency can then be determined from the number of teeth in each Nyquist window, the Nyquist number, and the comb spacing of either one of the two frequency combs of the dual frequency-comb spectrometer. The reference laser frequency does not need to be measured with a separate wavemeter, or calibrated with respect to a known atomic or molecular transition.
1. A method for measuring a frequency of a laser, comprising:
locking a first tooth, of a first plurality of teeth of a first frequency comb of a dual frequency-comb spectrometer, to the laser at a first offset frequency;
locking a second tooth, of a second plurality of teeth of a second frequency comb of the dual frequency-comb spectrometer, to the laser at a second offset frequency;
operating the dual frequency-comb spectrometer, with the first and second teeth locked to the laser, to generate a sequence of consecutive interferograms;
measuring a walking rate of a plurality of center bursts in the sequence of consecutive interferograms;
determining, based on the measured walking rate and a number of data points in each of the interferograms, a number of teeth in each of a plurality of Nyquist windows formed by the dual frequency-comb spectrometer;
determining a Nyquist number of one of the plurality of Nyquist windows that covers the frequency of the laser; and
determining the frequency of the laser based on (i) the number of teeth, (ii) the Nyquist number, and (iii) a comb spacing of one of the first and second frequency combs.
2. The method of claim 1 , further comprising outputting the frequency of the laser.
3. The method of claim 1 , further comprising selecting (i) the first tooth from the first plurality of teeth, (ii) the second tooth from the second plurality of teeth, (iii) the first offset frequency, and (iv) the second offset frequency so that the first and second frequency combs form the plurality of Nyquist windows.
4. The method of claim 1 , wherein said determining the Nyquist number is based on a coarse value of the frequency of the laser, the coarse value being determined to within a frequency range of each of the Nyquist windows.
5. The method of claim 1 , wherein said measuring the walking rate includes tracking a shift in a center position of the plurality of center bursts.
6. The method of claim 5 , wherein said tracking the shift includes:
fitting each center burst, of the plurality of center bursts, to an envelope function to obtain a fitted center of said each center burst; and
determining the shift from the fitted center of said each center burst.
7. The method of claim 5 , wherein a number of the consecutive interferograms equals the Nyquist number so that the center position shifts by an integer number of data points between a first interferogram of the sequence and a last interferogram of the sequence.
8. The method of claim 1 , further comprising measuring the comb spacing.
9. The method of claim 4 , further comprising measuring the coarse value of the frequency of the laser.
10. The method of claim 1 , further comprising calibrating frequency components of the dual frequency-comb spectrometer with the determined frequency of the laser.
11. The method of claim 1 , further comprising using the dual frequency-comb spectrometer to measure a gaseous sample.
12. The method of claim 1 , wherein said operating includes:
locking a first carrier-envelope-offset frequency of the first frequency comb to a frequency reference; and
locking a second carrier-envelope-offset frequency of the second frequency comb to the frequency reference.
13. The method of claim 12 , wherein:
said locking the first carrier-envelope-offset frequency includes detecting the first carrier-envelope-offset frequency with a first f-2f interferometer; and
said locking the second carrier-envelope-offset frequency includes detecting the second carrier-envelope-offset frequency with a second f-2f interferometer.