www.sciencemag.org/cgi/content/full/science.aam7424/DC1
Supplementary Materials for
Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser
S. M. Link,* D. J. H. C. Maas, D. Waldburger, U. Keller
*Corresponding author. Email: [email protected]
Published 11 May 2017 on Science First Release
DOI: 10.1126/science.aam7424
This PDF file includes:
Materials and Methods Figs. S1 to S3 Caption for Movie S1 References
Other Supplementary Materials for this manuscript includes the following: (available at www.sciencemag.org/cgi/content/full/science.aam7424/DC1)
Movie S1
Title: Dual-comb spectroscopy of water vapor with a free-running
semiconductor disk laser
S1 Materials and methods
S1.1 Experimental setup
The dual-comb MIXSEL benefits from the simple straight linear cavity. The linear cavity is
defined by the MIXSEL chip and an output coupler (radius of curvature 100 mm,
transmission 0.5%) as the two end mirrors (Fig. 2A). It is straightforward with this cavity design
to apply the concept of polarization duplexing by inserting a 2-mm thick, wedged birefringent
CaCO3 crystal into the cavity to split the one cavity beam into two cross-polarized and spatially
separated beams (13). Both cavity spots on the MIXSEL chip are pumped under an angle of 45°
with a commercial multimode pump diode at 808 nm, which is split with a 50:50 beam splitter
(BS). Both optical spectra are tuned with an intracavity etalon to a center wavelength of
968.3 nm to match an absorption line of water vapor. The pulse duration is 17.6 ps and 18.6 ps
and the average output power is 60 mW and 78 mW for the p- and s-polarized beam, respectively
(Fig S1). The temperature of the MIXSEL chip is kept constant with a Peltier element at 14 °C.
S1.2 Absorption calculation
The time-dependent interferograms (Fig S2) of the reference arm and the multi-pass cell arm are
recorded simultaneously with two photodetectors (PD1 and PD2) with a 5-GHz bandwidth and a
high-speed oscilloscope with a 1-GHz bandwidth. (Fig. 3A). The Fourier transformations of the
two time-dependent interferograms result in the two microwave combs (Fig. 3B) from which the
area below each peak is calculated with numeric integration. The absorption at each peak
2
position Ai is then calculated by subtracting the area of the ith peak of the reference spectrum ai,ref
from the area of the corresponding peak in the spectrum measured with the multi-pass gas cell
ai,MPC. Dividing this value by ai,ref gives the absorption:
Ai =ai,ref − ai,MPC
ai,ref (S1)
The wavelength axis can be calibrated using the optical mode spacing and Δfrep. For the absolute
wavelength position one could take a single frequency laser with known frequency or an atomic
transition. Here we directly use the absorption line of water to calibrate the absolute wavelength,
which is a commonly used method for dual-comb spectroscopy. The microwave axis (Fig. 3B)
has to be inverted compared to the wavelength axis (Fig 3 C and D) in this case. This depends on
which of the two combs between DC and the pulse repetition rates (comb1 or comb2 in Fig. 2A)
have been used for the measurement because they mirror each other. Measuring the comb at
lower microwave frequencies is preferred, since less bandwidth is required for the PDs and the
oscilloscope. The HITRAN simulation is calculate with the HITRAN database taking the
temperature, pressure, relative humidity and path length as input parameters (Fig. 3C and D).
S1.3 Full stabilization of the microwave comb
Stabilizing only a single line of the microwave comb is not sufficient to stabilize the full comb
since it depends on two parameters: the difference in repetition rate Δfrep and the difference in
carrier envelope offset (CEO) frequency ΔfCEO. Therefore two feedback loops are required. The
comb lines are a result of the beating of the optical modes of the two combined collinear OFCs.
The red line (Fig. 4b) fred is given by
fred = N2 ⋅ frep,2 + fCEO,2( )− N1 ⋅ frep,1 + fCEO,1( ) ≈ const , (S2)
3
where N1 and N2 are integers. This beat frequency is kept constant within the limits of the
feedback loop. The expression can be re-written as
fred = ΔfCEO + N2 − N1( ) ⋅ frep,1 + N2 ⋅ Δfrep ≈ const . (S3)
with Δfrep given by
Δfrep = frep,2 − frep,1 (S4)
and ΔfCEO described by
ΔfCEO = fCEO,2 − fCEO,1 . (S5)
The green line (Fig. 4b) fgreen of the comb is given by
fgreen = N2 +m( ) ⋅ frep,2 + fCEO,2( )− N1 +m( ) ⋅ frep,1 + fCEO,1( ) , (S6)
where m is an integer counting the number of lines between the red and the green line. We can
re-write fgreen and express it as a function of fred,
fgreen = ΔfCEO + N2 − N1( ) ⋅ frep,1 + N2 ⋅ Δfrep +m ⋅ Δfrep = fred +m ⋅ Δfrep ≈ const +m ⋅ Δfrep (S7)
from which we can conclude that in order to stabilize the green line, we need to stabilize both
Δfrep and one comb line, which are directly detected with PD3 and PD4 (Fig. 4A). We use PD3
and PD4 to obtain a better signal-to-noise ratio, but in principle it would also be sufficient to take
the signal from PD1 for the stabilization and therefore only use two detectors in total. Since Eq.
(S7) is true for any integer m, it is true for all microwave comb lines and therefore the full comb
is stabilized simultaneously when both feedback loops are applied.
Even though the microwave comb is fully stabilized, both optical spectra could fluctuate the
same amount in the same direction, e.g. if the two CEO frequencies are changing by the exact
4
same amount, which would not be visible in the microwave spectrum and accordingly could not
be prevented by the two feedback loops. Therefore, we characterize the absolute stability of the
modes of the optical frequency combs as well (Fig. S3) (Fig 4D).
Fig. S1 Second-harmonic autocorrelation of the two cross-polarized laser beams.
Fig. S2 Signal from optical interference of the two combined OFCs recorded with the PD in the
time domain showing time-dependent interferograms over a time span of 1 ms and 0.8 µs.
Whenever one pulse of each OFC hits the detector at the same time a strong burst peak is
recorded. The bursts are repeated every 0.25 µs, corresponding to the inverse of the difference in
pulse repetition rate Δfrep of 4 MHz.
1.0
0.8
0.6
0.4
0.2
0.050-50
delay [ps]
!p= 18.6 ps
1.0
0.8
0.6
0.4
0.2
0.0
auto
corre
latio
n [a
rb. u
.]
50-50delay [ps]
meas. sech2 fit
!p=17.6 ps
1.0
0.8
0.6
0.4
0.2
0.0
auto
corre
latio
n [a
rb. u
.]
-50 0 50delay [ps]
meas. sech2 fit
0.80.60.40.20.0time [us]
!T= 0.24 !s
8004000time [us]
60
40
20
0
-20
-40
volta
ge [m
V]
5
Fig. S3 Measurement setup for the absolute stability of the optical modes of one of the two
optical frequency combs (OFCs). A commercial highly stable single frequency laser (Toptica DL
pro) is used to generate a beat frequency with one of the modes of one OFC on the photo
detector (PD). This beat frequency is measured with a microwave spectrum analyzer (MSA) and
a frequency counter. To make sure that the measurement is not limited by the fluctuations of the
single frequency laser, its frequency is characterized with a wavelength meter. PBS polarizing
beam splitter (polarizer axis turned such that the OFCs are spatially separated), FC fiber
coupling.
Movie S1 Dual-comb spectroscopy demonstration of water vapor with the free-running dual-
comb MIXSEL in the laboratory. The laser cavity is shown during operation.
PBS
pumpdiode
MSA / frequencycounter PD
single frequency laser wavelength
meter
FCdual-combMIXSEL
6
7
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