An unstabilized femtosecond semiconductor laser for dual-comb spectroscopy of acetylene

Dual-comb systems based on two optical frequency combs of slightly different line spacing emerge as powerful tools in spectroscopy and interferometry. Semiconductor lasers have a high impact in continuous-wave tunable laser spectroscopy. Here we demonstrate the first dual-comb interferometer based on a single femtosecond semiconductor laser: a dualcomb modelocked optically pumped external-cavity surface-emitting laser (MIXSEL) ideally suited for a 1 to 10 GHz comb spacing. At a center wavelength of 1.03 μm (9709 cm) we measured acetylene gas transmittance with a resolution of 2.7 GHz in 100 ms with residual errors of less than 3% using thousand comb lines without aliasing effects. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
An optical frequency comb (OFC) [1][2][3] consists of equidistant phase-coherent spectral lines, spaced by a frequency interval f rep and shifted from the origin by an offset f CEO .Such radiofrequency-referenced OFCs provide frequency rulers that enable accurate frequency, time and distance measurements [4].Dual-comb spectroscopy (DCS) [5,6] measures the time-domain interference between two OFCs of slightly different line spacing f rep,1 and f rep,2 = f rep,1 + ∆f rep on a single photo-detector within short cycling times (t min = 1/∆f rep ) and converts broadband optical spectra to the radio-frequency domain.With dual-comb spectrometers based on selfreferenced modelocked lasers, self-calibrated spectra with an instrumental line-shape that may be neglected are obtained in the near- [7] and mid-IR [8] for arbitrarily long integration times.However, such systems rely on elaborate electronics and/or digital processing to maintain or reconstruct the coherence between the two combs.To overcome complexity, several solutions explored dual-comb systems with intrinsic long coherence, such as for example with ring cavity solid state laser [9], modelocked fiber laser [10,11], electro-optical modulator [12] or micro-resonator [13].Electrically pumped semiconductor lasers such as quantum cascade lasers (QCLs) [14,15] and interband cascade lasers (ICLs) [16,17] have raised remarkable spectroscopic interest due to their direct emission in the mid-IR.Their line spacing (typically ≈10 GHz) on the other hand is usually too large for transitions of molecules in the gas phase and their span (typically <100 lines) is still rather narrow.Optically pumped semiconductor disk lasers (SDLs) [18,19] cover a spectral range from visible to mid-IR and only recently appeared as a promising technology for DCS [20].First dual-comb operation has been obtained in hybrid SDL-fiber systems [21] and with a picosecond optically pumped modelocked integrated external-cavity surface-emitting laser (MIXSEL) [22].
Here, we show dual-comb spectroscopy on acetylene using a single-source dual-comb semiconductor laser without active stabilization or external amplification.A femtosecond MIXSEL emits two pulse trains with an adjustable comb-spacing difference at a wavelength of 1.03 µm (9709 cm −1 ).We measure acetylene gas transmittance with a resolution of 2.7 GHz without aliasing effects in 100 ms with residual errors of less than 3%.Compared to other semiconductor-based dual-comb sources [14,16], the dual-comb MIXSEL [23] with its 1-5 GHz comb spacing is ideally suited for spectroscopy applications.
The MIXSEL generates a modelocked pulse train from a linear straight cavity defined by the MIXSEL chip and the output coupler (OC) as the two end mirrors.The cavity length sets the pulse repetition rate and therefore the comb spacing, i.e. for example a 3 GHz OFC requires an optical cavity length of 5 cm.The MIXSEL combines the advantages of a passively modelocked laser oscillator providing a high pulse peak power and broad bandwidth with the compactness and wavelength versatility typical of semiconductor lasers.In dual-comb operation, the initially unpolarized beam is split towards the semiconductor MIXSEL chip with intracavity birefringent crystals (BCs) (Fig. 1(a)).Two OFCs are then generated in the same straight laser resonator and intrinsically achieve high mutual coherence.In contrast to other integrated semiconductor dual-comb systems, the MIXSEL provides excellent beam quality (M 2 < 1.1) and a high degree of flexibility in frequency mode spacing [24] (1-100 GHz), which can be controlled independently from the carrier-envelope offset.Furthermore, the difference in pulse repetition rate between the cross-polarized OFCs is finely adjustable via thickness and orientation of the BCs [23].The first dual-comb MIXSEL spectroscopy proof-of-principle demonstration was based on long picosecond pulses with typically ≈0.4 nm (128 GHz) of full optical bandwidth [20], making them less attractive for spectroscopy applications.In this letter, we introduce a new generation of MIXSEL chips and demonstrate real-time DCS of acetylene with a free running femtosecond dual-comb MIXSEL emitting at 1030 nm.

Description of the laser
Extensive epitaxial and structural novelties are implemented to obtain sub-ps pulses and several nanometers of optical bandwidth in dual-comb operation.The epitaxial MIXSEL chip consists of a bottom GaAs/Al 0.98 Ga 0.02 As 0.98 P 0.02 distributed Bragg reflector (DBR) with the high reflectivity bandwidth centered at 1030 nm.A single InGaAs QW absorber follows the DBR to enable passive modelocking.A second AlAs/Al 0.15 Ga 0.85 As DBR reflects the residual pump light to prevent unwanted saturation of the saturable absorber.The strain compensated active region with 11 InGaAs QWs embedded in GaAs barriers acts as laser gain medium.Finally, a 3-pair dielectric top coating finalizes the structure and optimized the cavity roundtrip group delay dispersion.The layers are optimized to obtain a superior surface homogeneity and an efficient transversal 1D heat removal beneficial for dual-spot pumping and dual-comb operation [25].Following our pulse shortening strategies [26], we carefully engineer the chip group delay dispersion through multipair numerically-optimized dielectric top coatings.Additionally, large bandgap AlAsP strain compensation materials are developed for better carrier confinement and low two-photon absorption losses in the region of the active quantum wells (QW).Finally, we decrease the growth temperature of the absorber QW for a shorter recovery time and a sharper temporal pulse shaping.This, together with a structurally broad and flat gain profile, allows for femtosecond pulse generation.
The full structure of the dual-comb modelocked integrated external-cavity surfaceemitting laser (MIXSEL) is shown in Fig. 1(a).The laser cavity is build up from two basic elements: the MIXSEL chip and a curved output coupler with a 100-mm radius of curvature and a 0.1% output coupler.For dual-comb MIXSEL operation, the semiconductor chip is optically pumped with a single multimode pump diode (LIMO35-F100-DL808) at 808 nm whose beam is split with a 50:50 beam splitter (BS) to simultaneously pump two distinct spots on the semiconductor chip (Fig. 1(a)).
Two 0.5-mm thick wedged intracavity calcite (CaCO 3 ) birefringent crystals separate the initially unpolarized laser beam into two cross polarized pulse trains.By using two orthogonally oriented crystals, we nominally add the same optical path length to either polarization.Translating one of the wedged crystals further into the beam, allows to control the relative path lengths difference and thus the difference in repetition rate.posed but through a ach beam First, the pulse shape and duration is estimated from an intensity autocorrelation measurement (Femtochrome Research, FR-103HS).Second, the spectral characteristics of each comb are observed on an optical spectrum analyzer (OSA) (Hewlett-Packard, 70004A).Third, the laser is detected with a photodiode (PD) (NewFocus, Model: 1014) and a microwave spectrum analyzer (MSA) (Agilent E4405B) is employed to observe the repetition rates and its higher harmonics.
With the new chips, the pulse duration for the two OFCs is reduced from 18 ps [20] to sub 400 fs (Fig. 1(b)) and the usable optical bandwidth increases accordingly.The emission wavelength of the active QWs is tuned to match the position of the ro-vibrational lines in the region of the 3ν 3 band of acetylene.Due to surface inhomogeneity, the average output powers of the two modelocked beams differ slightly (28 and 24 mW) and the optical spectra are not perfectly coinciding.Nevertheless, the spectral coverage of the fs dual-comb MIXSEL spans more than 10 nm (> 2.5 THz) around 1030 nm (291 THz / 9709 cm −1 ) (Fig. 1(c)).Additionally, both OFCs are combined in the same polarization by rotating the waveplate to a π/8.They interfere on the photodetector and the MSA detects both the radiofrequency beat signal and the repetition rates (Figs.1(d)-1(f)).To sample absorption profiles with sufficient resolution and in a rapid manner, we set the MIXSEL cavity length to ≈55 mm for a mode spacing of 2.73 GHz.

Spectral aliasing
The beating of the two optical frequency combs generates down-converted microwave frequency combs symmetrically spaced around the pulse repetition rate and its harmonics.To avoid aliasing effects between these combs [27], the resolvable width of the comb ∆f rf in the radio-frequency domain must fulfill: where f rep is the fundamental pulse repetition rate considered as (f 1 + f 2 )/2, where f 1 and f 2 are the two pulse repetition rates of the dual comb system (Δf rep f rep ).The resolvable width of the comb ∆f rf in the radio-frequency domain is given by: Combining Eqs.(1) and Eq. ( 2), we obtain a condition on ∆f rep : where ∆f opt is the resolvable optical laser bandwidth.In the dual-comb MIXSEL, ∆f rep derives from the different optical path length for the two cross-polarized beams in the birefringent crystals.In the case of two orthogonally oriented wedged crystals we can write: Here represents the walk-off angle induced by the birefringence, L 0 is the common cavity optical path length, L 1 and L 2 are the respective optical thicknesses of the two crystals; ε is the additional optical path length difference introduced by wedges and/or tolerances in the crystal thickness.We consider the case of nominally identical crystal thicknesses (L 1 = L 2 ), we define tot 0 and, considering ε  L tot , we write: Combining now Eq. ( 3) with Eq. ( 5), we obtain: This describes the maximum path length difference to avoid aliasing.In the dual-comb MIXSEL, we could tune to ε ≈1 µm, which would theoretically allow large optical bandwidth without aliasing of several tens of THz.
In order exploit the broad laser spectrum without spectral filtering, we prevent aliasing effects by choosing ∆f rep with the insertion of two 0.5 mm thick wedged intracavity BCs oriented orthogonally with respect to each other as shown in Fig. 1(a).The optical path difference arises from the crystal wedges and can be finely tuned by crystal translation.In addition, the two BCs preserve a sufficient separation of the cavity spots on the MIXSEL chip.The selected ∆f rep of 51.9 kHz (Fig. 1(f)) corresponds to a cavity length difference for the cross-polarized OFCs of only ≈1 µm, which results in an aliasing-free comb largely separated from its high-frequency replica (Fig. 1(e)).The entire laser setup delivering the dual-comb signal is built in a closed box with a total volume occupancy of 23 × 32 × 11 cm 3 (Fig. 1(g)).

Fourier transform analysis
The spectroscopic signal is generated by overlapping both beams in the same polarization in a fiber coupled 50:50 beam splitter and recording their beat note with a photodiode.The time domain signal is detected on a balanced detector (Thorlabs PDB481C-AC) and recorded at a sampling rate of 2.5 GS/s on a digitizing oscilloscope (Teledyne LeCroy 6104) with 1 GHz bandwidth.The total measurement time of 100 ms is currently limited by internal memory of the oscilloscope but could easily be extended with suitable electronics.The recorded timedomain trace (Fig. 2(a)) consists of a sequence of interferograms (inset) repeating every 19 µs (1/∆f rep ).
The frequency domain spectrum is obtained with Fourier transform analysis.Parasitic intracavity reflection between the non-wedged surface of the BC and the OC produce secondary interferograms symmetrically spaced 3.3 µs from the main interferograms.These parasitic back reflections are replaced by the mean value of the interferogram.Next, the average half maximum signal-to-noise-ratio (SNR) in frequency is observed for various integration times.The SNR increases up to a value of 200 µs, the mutual coherence time of the two OFCs.For longer temporal segments, the comb lines blur out due to drifts in ∆f CEO.The time domain trace is then sliced to segments of 200 µs and a 6-fold zero filling is applied for interpolation in the frequency domain.Fast-Fourier-Transform is performed per segment without apodization and yields the complex Fourier domain signal I'(f) with a cardinal sinus instrumental response.
Measurement induced phase errors are corrected by standard means [28]: The phase of the spectrum ∠ θ is calculated at the comb line positions from real and imaginary part of the complex Fourier transform '( )  [29].Additionally, SNR could be significantly improved by an engineered prototype housing with minimized mechanical vibrations and air turbulences.

Dual-comb spectroscopy
Finally, we perform free-running dual-comb spectroscopy (DCS) by directing one OFC through a commercial multi-mode-fiber-coupled, multipass cell with a total absorption length of 80 cm containing acetylene (C 2 H 2 ) at room temperature with a nominal pressure of 987 Pa ± 10% (Fig. 3(a)).At this pressure, the absorption lines of acetylene are broadened to more than 6 GHz and can be sampled with the line spacing of 2.73 GHz.The absorption in the gas cell is governed by Beer-Lambert-Law: This formula describes the transmission of light through a gas cell of length l, where I 0 (f) is the incident light intensity and I(f) is the transmitted intensity as function of frequency (red in Fig. 3(b)).The number density n = N/V can be related to the pressure p via temperature T, volume V and the Boltzmann konstant k B using the ideal gas law: The absorption cross-section α(f) governs the frequency-dependent absorption.With the absorption cross-section being a summation of Lorentzian peaks P i (f): Herewith the absorption results in a multiplicative law as follows: The lines R (12) to R(26) of the 3ν 3 band of 12 C 2 H 2 , coincide with the last ≈0.8THz of the low-frequency tail of the MIXSEL optical spectrum (Fig. 3(b)).We calibrate our retrieved spectrum against a spectrum computed using the parameters from the HITRAN 2016 database for an a posteriori calibration of the frequency scale [30].To extract the transmittance of the sample, we use a logarithmic version of Eq. ( 12): where -ln(I 0 (f)) represents the baseline fit of the comb envelope.Data and fit are then divided by the baseline, according to Eq. ( 12), to yield the transmittance (Figs.3(c) and (d)).Without active stabilization and locking electronics, the overlay of the experimentally acquired dual-comb transmission follows line-by-line the characteristic acetylene transmission envelope as computed from the HITRAN 2016 database (Figs.3(c) and 3(d)).The residuals and the standard deviation of 0.028 attests good transmission intensity precision to our dual-comb spectrometer.etylene with a fre up.One pulse train bined with the seco spectrum recalib nvelope are match mission spectrum o ed dual-comb MI oduct of a baselin nd the HITRAN da n. d) Portion of th from the high p rum in silicon [31] for extend [32] as well as he fast and ma e intrinsic sim s.The chip us ecular fingerpr omain.To date uctor disk lase onductor disk ange [33] and f µm [34].Our ing type-II InA 8)].
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