femtosecond dual-comb yb:caf2 laser from a single free ......research article vol. 28, no. 20/28...

Research Article Vol. 28, No. 20 / 28 September 2020 / Optics Express 30275

Femtosecond dual-comb Yb:CaF2 laser from asingle free-running polarization-multiplexedcavity for optical sampling applications

BENJAMIN WILLENBERG,1,2,* JUSTINAS PUPEIKIS,1,2LÉONARD M. KRÜGER,1 FLORIAN KOCH,1CHRISTOPHER R. PHILLIPS,1 AND URSULA KELLER11Department of Physics, Institute of Quantum Electronics, ETH Zurich, Switzerland2Equal contributors*[email protected]

Abstract: Dual optical frequency combs are an appealing solution to many optical measurementtechniques due to their high spectral and temporal resolution, high scanning speed, and lack ofmoving parts. However, industrial and field-deployable applications of such systems are limiteddue to a high-cost factor and intricacy in the experimental setups, which typically require a pairof locked femtosecond lasers. Here, we demonstrate a single oscillator which produces twomode-locked output beams with a stable repetition rate difference. We achieve this via insertingtwo 45°-cut birefringent crystals into the laser cavity, which introduces a repetition rate differencebetween the two polarization states of the cavity. To mode-lock both combs simultaneously,we use a semiconductor saturable absorber mirror (SESAM). We achieve two simultaneouslyoperating combs at 1050 nm with 175-fs duration, 3.2-nJ pulses and an average power of 440 mWin each beam. The average repetition rate is 137 MHz, and we set the repetition rate differenceto 1 kHz. This laser system, which is the first SESAM mode-locked femtosecond solid-statedual-comb source based on birefringent multiplexing, paves the way for portable and high-powerfemtosecond dual-combs with flexible repetition rate. To demonstrate the utility of the laser forapplications, we perform asynchronous optical sampling (ASOPS) on semiconductor thin-filmstructures with the free-running laser system, revealing temporal dynamics from femtosecond tonanosecond time scales.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Ultrashort pulsed lasers have enabled the continuous advancement of ultrafast sampling techniquesover the past four decades. Pump-probe measurements, in which a fast and periodic signal ismixed with an ultrashort optical pulse, are widely used for this purpose. By scanning the delayof a femtosecond optical pulse with respect to the periodic signal, the signal’s temporal profilecan be determined. This approach, sometimes referred to as equivalent-time sampling, hingesupon two properties: the ability to achieve precise variation of the optical delay, and the use of amixing process with a fast response time. The latter problem was addressed in early work by theuse of electro-optic sampling [1–3], since the electro-optic effect exhibits an ultrafast responsetime. The other requirement, of precisely varying the optical delay, was traditionally solvedby a mechanical delay line. The advent of frequency comb technology [4–6], and in particulardual-comb spectroscopy which uses a pair of combs with a small difference in pulse repetitionrate, has enabled a revolution in optical measurement techniques. Dual-combs offer ultra-highresolution in both time and frequency, and they provide a perfectly linear scan of optical delaywith no moving parts and at speeds far exceeding the capabilities of mechanical scanners. Suchdual-comb laser sources have been widely pursued for optical sensing measurements [7–9]. Theseinclude high-resolution time-domain spectroscopy [10,11], electro-optic sampling spectroscopy

#403072 https://doi.org/10.1364/OE.403072Journal © 2020 Received 20 Jul 2020; revised 4 Sep 2020; accepted 14 Sep 2020; published 25 Sep 2020

https://orcid.org/0000-0002-6822-951Xhttps://orcid.org/0000-0003-4236-7030https://orcid.org/0000-0001-5307-153Xhttps://orcid.org/0000-0002-1689-8041https://doi.org/10.1364/OA_License_v1


[12], high-speed pump-probe measurements via asynchronous optical sampling [13–15] and fastand precise optical ranging [16,17].Traditionally, dual-comb systems have been based on a pair of individually stabilized optical

frequency combs from two different mode-locked lasers. This approach has been implementedsuccessfully in many platforms, including electronically locked fiber combs [18–21], solid-stateTi:sapphire lasers [22], microresonator combs [23–25], and electrooptic combs via the modulationof a single laser output [26–28]. However, the complexity and cost associated with a separate pairof frequency combs together with the associated locking electronics has presented a significantchallenge to developing applications based on these systems. Consequently, in more recent years,several groups have developed solutions to reduce the complexity by producing mutually coherentcombs from a single laser oscillator. Promising approaches include Kerr-lens mode-lockedbidirectional solid-state ring lasers [29], Kerr-lens mode-locked spatially multiplexed [30] andpolarization multiplexed [31] thin-disk lasers, passively mode-locked fiber lasers [32–38] andmode-locked integrated external-cavity surface emitting lasers (MIXSELs) based on linearcavities and polarization multiplexing [39,40]. Free-running dual-comb laser systems wererecently reviewed in [41].In our previously demonstrated MIXSEL approach, we introduced a 45°-cut birefringent

crystal into a straight laser cavity to spatially separate the two polarization states of the cavityon the MIXSEL semiconductor chip, thereby allowing for mode-locking of both polarizationssimultaneously. This approach yielded two mutually coherent combs at a center wavelengtharound 1 µm with a typical repetition rate around 2 GHz, average powers of ∼25 mW, andadjustable repetition rate differences in the kHz to MHz range. In free-running operation theselasers have successfully been used for gas-phase spectroscopy of water vapor and acetylene[40,42]. However, the short upper state lifetime of the semiconductor gain chip limits theavailable average power in femtosecond operation, and requires high repetition rates typicallyabove one gigahertz, which can be too large for some applications. In contrast, solid-state lasersystems rely on longer upper state lifetime gain crystals, which facilitates the generation ofhigher pulse energies and lower pulse repetition rates. The high peak powers typically involvedin such solid-state lasers open the path to nonlinear light-matter interactions for pump-probespectroscopy and nonlinear optics for frequency conversion. A variety of promising lasermaterials for femtosecond end-pumped solid-state lasers have been explored in recent years,including Yb:CaF2 [43], Yb:CALGO [44,45], Yb:KYW [46,47], Yb:KGW [48–50].In this paper, we demonstrate the first SESAM mode-locked diode-pumped solid-state

femtosecond laser in dual-comb operation from a single cavity. We achieve this via polarizationmultiplexing of the modes in the oscillator by insertion of two 45°-cut birefringent crystals intothe laser cavity. With this first system we realized two simultaneously fundamentally mode-lockedlasers at a center frequency of 1050 nm, an average output power of 440 mW per beam at arepetition rate of 137 MHz and a pulse duration of 175 fs (sections 2 and 3). The repetitionrate difference between these two combs is freely tunable up to several tens of kilohertz, yetintrinsically stable already in free-running operation. As a proof of principle application of thislaser, we demonstrate asynchronous optical sampling (ASOPS) on two semiconductor thin-filmstructures, a SESAM and a Vertical-External-Cavity Surface-Emitting Laser (VECSEL) device(section 4). The free-running laser system allows us to rapidly resolve the nonlinear absorptiondynamics of the SESAM on the tens of picosecond timescale and the two-photon absorption(TPA) initiated gain dynamics of the VECSEL structure on the several nanosecond timescale,both with sub-200 fs resolution.Our approach is promising for robust, cost-effective and flexible dual-comb high peak

power lasers since dual-comb operation can be obtained with high stability directly from asingle free-running laser cavity. These laser sources will benefit a broad range of opticalmeasurement methodologies, including rapid asynchronous sampling measurements with high


temporal resolution. Moreover, the high peak power pulses produced from such oscillatorsenable wavelength flexibility via nonlinear frequency conversion and multi-photon spectroscopyapplications.

2. Laser concept and setup

The presented laser is based on a bulk Yb:CaF2 gain crystal. The gain medium exhibits a broadand smooth emission spectrum, good thermal properties, and isotropic crystal structure withnegligible birefringence [51]. This isotropic structure is highly important for the polarization-based multiplexing approach since similar gain properties in both polarization states of the cavityare desired. Yb:CaF2 is available in good crystal quality with relatively high doping concentrationand can therefore be pumped efficiently and cost-effectively by spatially-multimode high-powerlaser diodes emitting at 980 nm. With this material, multi-watt level operation with sub-100 fspulses directly from the oscillator with optical-to-optical efficiencies exceeding 30% have beendemonstrated [43].

Here, we present a laser based on a folded end-pumped MHz cavity supporting simultaneouslytwo cross-polarized frequency combs with sub-200 fs pulses. The schematic of the laser cavity isshown in Fig. 1. The two polarization states in the cavity are split with two birefringent CaCO3(calcite) crystals which are cut at 45° with respect to the crystal c-axis and inserted at the twoends of the cavity to yield spatially separated spots on the SESAM and in the gain crystal.

Fig. 1. (a) Schematic of the laser cavity for simultaneous mode-locking operation of twocombs via polarization multiplexing with two birefringent calcite crystals (BF1 and BF2)in the Yb:CaF2 gain crystal (G) and on the SESAM. The laser is end-pumped through theoutput coupler (OC) and the laser beam is separated from the pump beam with a dichroicmirror (DM). (b) illustrates the splitting of the laser mode in the gain crystal and (c) thetuning of the repetition rate difference ∆frep by rotation of BF2. (d) shows the two spatiallyseparated intracavity laser spots on the SESAM device.

The two laser modes have 1/e2 radii of 65 µm in the Yb:CaF2 gain crystal (“G” in Fig. 1),which has a length of 3 mm and 5% at. doping. We use a single 980-nm wavelength-stabilizedpump diode (DILAS Diode Laser GmbH) delivering up to 20 W by a multimode fiber (106.5 µmcore diameter, NA= 0.15, M2 = 20). After collimating the output of this multimode fiber, thepump beam is split into two beams of equal power, in order to obtain two spatially separatedfocused spots in the Yb:CaF2 crystal, i.e. one for each laser polarization. To obtain these beams,we first split the pump into two beams with a plate beam splitter, and then recombine them using


a D-shaped mirror to create two parallel rays. These rays are then imaged, with a scale factor, tothe gain crystal (not shown in Fig. 1). The laser is pumped through the flat output coupler (2.8%transmission for the laser wavelength, high transmission for 980 nm pump; “OC” in Fig. 1). Thisgeometry helps enable the tight focusing conditions needed for efficient operation. Since theSESAM is used as the other end mirror, we use a 45° dichroic mirror (“DM” in Fig. 1) to splitthe laser output from the pump input.We achieve fundamental soliton mode-locking [52] in the negative dispersion regime by

compensating the positive group delay dispersion (GDD) introduced by the gain and calcitecrystals with negative GDD from Gires-Tournois-Interferometer (GTI) type mirrors (total −2200fs2 per cavity round-trip). A single quantum well semiconductor saturable absorber mirror(SESAM) with a modulation depth of 0.9% and a saturation fluence of 16 µJ/cm2 enabledrobust mode-locking and self-starting operation of the laser. The long upper-state lifetime ofYb:CaF2 implies that Q-switched mode-locking instabilities can occur before the laser reachesthe continuous-wave mode-locked state [53], leading to high intensities inside the laser cavity.Therefore, in order to clamp the intensity below the damage threshold of the optical components,especially the SESAM, we chose a cavity design where the induced self-focusing in the twobirefringent crystals as well as the gain crystal cause the beam to diverge on the SESAM. Thesetype of self-defocusing cavities have previously been exploited for gigahertz repetition ratesolid-state lasers [54,55].

A broadband anti-reflection (AR) coated birefringent crystal is placed at each end of the cavity(BF1 and BF2 in Fig. 1), to spatially separate the two modes at the active elements. BF1 leadsto a separation of the modes in the gain crystal, to allow independent pumping and avoid gaincrosstalk. BF2 leads to a separation of the modes on the SESAM, to allow independent saturableabsorption and avoid saturation crosstalk [56]. This separation of the two laser modes on theSESAM has proven to be critical to avoid crosstalk between the two combs and optical damage ofthe semiconductor thin-film structure. As shown in Fig. 1, the beams are split in the horizontalaxis on the SESAM, and in the vertical axis on the gain crystal. In the rest of the cavity, the beamsare well overlapped. This overlap maximizes the common path for the two polarization states inthe cavity, which minimizes the difference in noise experienced by the two combs, enabling ahighly stable repetition rate difference.Each birefringent crystal introduces a delay difference between its ordinary and extraordi-

nary waves (o- and e-waves, respectively). For 5-mm-long calcite crystal, this difference isapproximately 1.6 ps per pass through the crystal [57]. Hence, two such crystals oriented thesame way in the cavity would yield a round-trip delay difference of 6.4 ps, and a correspondingrepetition rate difference of 120 kHz for the 137 MHz cavity. This difference is too large forhigh-temporal-resolution pump-probe measurements, and would lead to aliasing in dual-combspectroscopy. Therefore, we instead mount the second crystal BF2 at 90° rotation around theoptical axis compared to BF1. This enables a small difference in repetition rate of a few kilo-hertzbecause the role of the ordinary and extraordinary polarization is flipped between the twobirefringent crystals, thereby canceling most of the optical path length difference of the twopolarization states [40].For fine tuning of the repetition rate difference, we rotate the birefringent crystal next to the

SESAM (BF2) in the horizontal plane. This rotation changes the angle θ of propagation withrespect to the c-axis, which changes the refractive index of the extraordinary wave. Since weused two different crystal lengths (4.5 mm for BF1 and 5 mm for BF2), a repetition rate difference∆f rep = 0 is reached for a significant angle of incidence on the crystal of approximately 4.8°. Notealso that, while BF1 was wedged (1 degree), BF2 was not, so rotating it also avoided etalon effectson the cavity mode. For our measurements, we tuned the repetition rate difference to 1 kHz viathe angle of BF2. Due to the flat end mirror (SESAM), this rotation does not couple to alignmentof the cavity, and hence it is straightforward to tune the repetition rate difference continuously in


the range of 40 Hz to 3.35 kHz without any performance changes to the laser output. Note thatthe upper limit was imposed by the clear aperture of BF2 and not by any physics limit of thebirefringent multiplexing technique.

3. Laser mode-locking characteristics

We denote the two combs as comb 1 (p-polarized output) and comb 2 (s-polarized output).We find simultaneous self-starting mode-locking of both combs (i.e. dual-comb operation) foroutput powers ranging from 250 mW to 440 mW for each comb [Fig. 2(a)]. The increasingintracavity power leads to pulse shortening from 275 fs (low power operation) to 175 fs (highpower operation) following the expected inverse scaling to the intracavity pulse energy for solitonmode-locking [52,58]. The relatively low slope efficiency of both combs of 17% in mode-lockedoperation is partly due to the relatively high losses in the cavity from imperfect AR coatings ofthe birefringent calcite crystals and the laser crystal. The excellent output beam quality of thespatially separated combs is show in Fig. 2(b). At the nominal operation point we measure abeam quality factor for each of the two individual beams of M2 < 1.05.

Fig. 2. (a) Mode-locking performance for simultaneous operation of both combs. Theindicated pump power is split equally between the two laser modes. (b) The laser operatesin fundamental mode with beam quality M2 < 1.05 for both beams. The beam shapeis recorded at the output of the oscillator (magnified image of the output coupler) on aWinCamD-LCM-NE 1” beam profiler at the nominal operation point of the laser with 3.7 Apump current, approx. 7.8 W total pump power and 440mW average output power fromeach comb.

In Fig. 3, we show the mode-locking diagnostics of the two 1050-nm combs at the nominaloperation point, which corresponds to the maximum total pump power of 7.8 W. At this operatingpoint, the output power is 441 mW (comb 1) and 443 mW (comb 2). Given the repetition rateof 137 MHz, this corresponds to 3.2 nJ output without any external amplification. Both combshave a clean sech2-shaped spectrum with full-width at half maximum (FWHM) 6.8 nm (comb 1)and 6.9 nm (comb 2). We measure pulse durations of 177 fs (comb 1) and 172 fs (comb 2) viasecond-harmonic generation (SHG) intensity autocorrelation. The corresponding time-bandwidthproduct (TBP) of the combs is 0.327 (comb 1) and 0.323 (comb 2), compared to TBP= 0.315 forideal sech2 pulses. Both combs exhibit a transform-limited pulse duration throughout the entiremode-locking range, satisfying TBP < 1.05× 0.315. The clean radio frequency (RF) spectrumshows that the laser is operating in fundamental mode-locking without pre and post pulses.


Fig. 3. Characterization of the laser performance in simultaneous dual-comb lasing at thenominal operation point (Ppump = 7.8 W): (a), (d) optical spectrum with sech2 fit indicatingsoliton pulses with optical spectrum of more than 6.5 nm FWHM bandwidth at a centerwavelength of approx. 1050 nm. (b), (e) Autocorrelation trace with sech2 fit. (c), (f) RFtraces of the two combs with a repetition rate of 137MHz, each for a wide frequency rangeand zoomed to the frep-peak with a resolution bandwidth (RBW) of 300Hz indicating cleanfundamental mode-locking.

4. Asynchronous optical sampling from free-running laser

In this section, we apply our new femtosecond dual-comb laser source for rapid asynchronousoptical sampling (ASOPS) measurements on semiconductor thin-film structures, allowing forhigh-speed scanning of pump-probe time delays without a mechanical delay line. We measurethe dynamics via a change of reflectivity for (a) a SESAM structure which is from the same waferas the SESAM used inside the laser cavity itself and (b) a VECSEL, a more complex quantumwell gain structure for optically pumped semiconductor lasers.

4.1. ASOPS principle

For the proof of principle experiments we have implemented a reflective ASOPS setup as shownin Fig. 4(a), directly using the free-running oscillator output without any feedback on the laser.We employ a non-collinear pump-probe configuration with identical polarizations. One combacts as a pump, while the other comb with a slightly different comb spacing is attenuated to actas a probe. The pump-induced change of the reflectivity of the device under test is then sampledby the probe pulse similar to equivalent time sampling [1–3]. The probe beam amplitude ismeasured using photodiode PD2 as shown in the figure. After analog 50 MHz low-pass filtering,the signal is digitized and recorded on an oscilloscope (WavePro 254HD, LeCroy Corp.). Theback-reflected pump beam is blocked with an aperture.The pump and probe beam average power is adjusted with a half-wave plate (HWP) and

polarizing beam splitter (PBS) pair for each separately. The pump and probe beams are focusedwith an aspheric 25-mm focal length lens to 14.7× 15.1 µm2 and 15.4× 15.4 µm2 1/e2 beamdiameters, respectively (measured on a Datray Beam’R2 – XY Scanning Slit Beam Profiler). Theprobe power is set to 2.8 mW whereas the pump power is adjusted in the experiments. The setupsupports a pump power of up to 237 mW at the sample, and hence the sample can be pumped upto an average fluence of 1 mJ/cm2.


Fig. 4. (a) Asynchronous optical sampling (ASOPS) or equivalent time sampling setup of asample in a reflective configuration. The trigger signal for the data acquisition is obtainedby sum-frequency generation (SFG) between the two combs. L1 - 100mm focal lengthlens, L2 - 25mm focal length aspheric lens. PD1 - amplified photodiode (PDA55, ThorlabsInc.), PD2 - amplified photodiode (PDA10D2, Thorlabs Inc.). HWP - half-wave plate, PBS -polarizing beam splitter. (b) Illustration of the ASOPS measurement technique using twopulse trains with slightly different repetition rates.

Data acquisition on the oscilloscope is triggered by a sum-frequency generation (SFG) signalbetween the two combs. The signal is generated when pulses from the two pulse trains overlapin a 5-mm-long β-BaB2O4 (BBO) SFG crystal oriented for type-I phase-matching. The SFGsignal is recorded with photodiode PD1 which directly triggers the data acquisition. The repeatedtrigger enables signal averaging directly on the oscilloscope. Triggered data acquisition helps tore-time the pulse overlap thus removes the influence of any slow timing drifts.

Figure 4(b) illustrates how such pump-probe schememaps ultrafast dynamics into electronicallyresolvable signals. A strong pump pulse train initiates the dynamics in the target and the probepulse samples the response at increasing delay steps at every repetition of the laser pulse. Whenf rep >> ∆frep, the delay step size can be estimated as ∆f rep / f rep2 [15]. In case of 1 kHz repetitionrate difference and 137 MHz repetition rate of the laser, the step size is 53 fs, smaller than theprobe pulse duration. In the time scale of 1/∆f rep = 1 ms, a time window of 1/f rep = 7.3 ns issampled. While the pulses of the two combs walk through each other the ultrafast response ofthe target is down-sampled by the factor of f rep/∆f rep to the radio-frequency (RF) range which iseasily accessible by modern electronics, yet the system is fast enough for rapid measurements notfeasible by mechanical delay scans.

4.2. Dual-comb trigger fluctuations

To verify that the demonstrated dual-comb laser can be used for ASOPS measurements we firstuse the trigger setup as shown in Fig. 4(a) to perform timing jitter characterization. In this setup,we measure a peak in the SFG signal when pulses from the two combs overlap in time. Theobtained trigger signal trace is schematically shown in Fig. 5(a). From the total measurementwindow T tot and the number N of SFG peaks generated, we define the repetition rate difference∆f rep= N / T tot. We compare the expected arrival time of the n-th pulse Tn = n / ∆f rep versusthe actual measured arrival time T̃n. The corresponding difference between these two is thetime-offset δTn = Tn - T̃n shown in Fig. 5(a). During ASOPS measurement the data acquisition istriggered on the SFG signal and thus the measurement is re-timed. Such measurement re-timingsuppresses long-term drifts on the repetition rate difference between the two frequency combs.Thus, to quantify how much the re-timed signal drifts during the measurement window we definethe relative timing jitter quantity as ∆Tn = δTn+1 - δTn, i.e. measuring the short-term changes ofthe arrival time difference.


Fig. 5. (a) Illustration of the timing jitter between the two pulse trains measured by sum-frequency generation (SFG). Solid vertical lines indicate the average arrival time defined bythe total acquisition window divided by the number of measured cross-terms. (b) Timingjitter distribution extracted from the SFG cross-correlation signals in a 10 second acquisitionwindow.

For a 10 second acquisition window, we find that the relative timing between two consecutivetrigger signals (SFG signal n and SFG signal n+1) fluctuates around 10 ns root-mean-square(RMS) as shown in Fig. 4(b). This translates into 69.4 fs of pump-probe measurement timinguncertainty ∆Tn(pp)= ∆Tn ∆f rep / f rep for ∆f rep = 947 Hz and f rep = 136.5 Hz. Since this jitter isless than the pulse duration, it does not impact the measurement precision significantly. Comparedto electronically locked two-oscillators [59,60], this free-running system offers the same or bettertiming precision without any stabilization electronics.

4.3. ASOPS of SESAM and VECSEL

We demonstrate the applicability of the free-running dual-comb oscillator for ASOPS byperforming measurements on AlGaAs samples with InGaAs quantum well (QW) structures. Wefirst measure the pump-probe response of a SESAM sample of the same design as the one used tomode-lock the dual-comb laser. We measure it at a series of values of the average pump fluence,up to 1 mJ/cm2. The experimental data corresponds to a probe voltage Vprobe(t, Fprobe, Fpump)which is a function of pump-probe optical delay t, pump fluence Fpump and probe fluence Fprobe.We assume this signal is proportional to reflectivity, i.e. Rprobe(t, Fprobe, Fpump)∝ Vprobe(t, Fprobe,Fpump). Note that the data from the oscilloscope provides Vprobe(t, Fprobe, Fpump) measured overmany SFG trigger events. We are interested in the quantity

∆R(t, Fpump) =Rprobe(t, Fprobe, Fpump ) − Rprobe(t, Fprobe, 0)

Rprobe(t, Fprobe, 0), (1)

which is pump induced change of the sample reflectivity. The background probe signal levelcorresponding to Rprobe(t, Fprobe, 0) can vary due to any changes in the setup. Therefore, weestimate this background probe voltage, denoted Vbg, for each individual measurement time traceby averaging the signal at negative delays t such that the sample has recovered. Hence Vbg is theaverage of Vprobe(t, Fprobe, Fpump) for t over the range [-6.7, -0.8] ps. Given Vbg, we estimate∆R = (Vprobe − Vbg)/Vbg.

∆R provides pump-probe data over a timescale from 0 delay up to 1/f rep as well as thepump fluence dependence. The time-zero of the delay scan is determined by the TPA signalin a bulk GaAs sample. The resulting relative reflectivity change at different pump fluencesfor the SESAM structure is plotted in Fig. 6(a). From the pump-probe traces one can inferrapid intra-band thermalization and slower inter-band dynamics [61,62]. For a pump averagefluence of 34 µJ/cm2 we extract 0.7 ps and 7.1 ps for the fast and slow recovery time constants,respectively. Furthermore, from the traces one can see that at fluences larger than 423 µJ/cm2,which corresponds to the average fluence used in our dual-comb laser cavity, additional nonlineareffects in the SESAM such as TPA start to alter the response (see Fig. 6 inset). This time-resolved


measurement helps to identify that the SESAM is operated at onset of the rollover regime, wherereflectivity starts to decrease due to the TPA in the structure. By equivalence of the pump-probemeasurement at pulse overlap time (i.e., at t= 0) and saturation fluence measurement [63], onecan additionally extract saturation fluence information from the pump-probe setup. Thereby thissingle measurement setup provides a full characterization of the SESAM response.

Fig. 6. Asynchronous optical sampling (ASOPS) measurement of a semiconductor saturableabsorber mirror (SESAM) at different pump average fluences. At pump average fluencelarger than 423 µJ/cm2, there is a dip in the signal near t= 0, which is likely caused bytwo-photon absorption (TPA) (inset).

To demonstrate that the dual-comb laser can be used to perform rapid long delay rangemeasurements, we perform a pump-probe measurement on a VECSEL chip which was usedfor sub-100 fs semiconductor laser demonstration [64]. We do not use a separate pump laser;instead, the structure is excited by TPA of the tightly focused pump pulses. The measured proberesponse is shown in Fig. 7. After the drop in reflectivity around delay t= 0 due to two photonabsorption (pump induced absorption of the probe), a population inversion develops within afew picoseconds, as shown in the inset. The gain lifetime can be directly measured leading to1.9 ns – a typical value for the upper-state lifetime of VECSEL gain structures [61]. Hence thisdemonstrates that the laser can be used directly for rapid long-range pump-probe measurementssurpassing in terms of scanning speed any mechanical delay scan system.


Fig. 7. Vertical external cavity surface emitting laser chip (VECSEL) pump-probe measure-ment at 149 µJ/cm2 pump average fluence. The structure was excited via two-photonabsorption (TPA) of 1050 nm light.

5. Coherent beat-note measurement

By resolving the beat notes between individual comb lines, dual-combs enable ultra-highresolution spectroscopy [8]. Achieving this high resolution requires coherence between the twocombs. Therefore, in this section we present and discuss a measurement of this coherence for ourlaser by measuring the frequency difference between a pair of comb lines (one from each comb).In order to isolate a particular pair of comb lines and determine their relative phase with hightemporal resolution, we perform heterodyne beat-note measurements with a continuous-wave(cw) single-frequency local oscillator. This measurement is analogous to the one presented in[65,66]. Such measurements can also enable dual-comb spectroscopy with free-running combs[67].The cw laser (Toptica DLC CTL 1050) output at 1050 nm is split into two parts, and each

is interferometrically combined with one of the combs. We direct these combined beams toseparate photodiodes, apply electronic low-pass filters, and digitize the corresponding signals.These signals, denoted s1 and s2, have the form

sj(t) = sin(2π ∫ t(νj(t′) − νcw(t′)) dt′

), (2)

where νcw is the optical frequency of the cw laser, and νj denotes the line of comb j which isclosest to νcw. We allow these frequencies to vary with time, since all the lasers are free-running.

The product s1 · s2 of the two signals includes a term which has the difference frequency, (ν2 –νcw) – (ν1 – νcw)= ν2 – ν1, i.e. the frequency difference between a line of comb 1 and a line ofcomb 2, independent of νcw. We extract this term digitally with band-pass filters, and show atypical measurement example in Fig. 8(a). The signal exhibits fluctuations within +/- 5 kHz ona 100 ms time scale with an RMS below 1.4 kHz. This corresponds to a linewidth of 3.1 kHz(FWHM of the smoothed beat-note spectrum) as shown in Fig. 8(b).

We note that the laser is currently assembled with generic laboratory optomechanics on analuminum breadboard, and surrounded by a simple box with a hole for the output beams. Hence,even with no special care for laser stability in terms of mechanical or other noise sources, we


Fig. 8. Relative coherence of the two dual-comb outputs. (a) Representative evolutionof the instantaneous frequency shift between the two combs on a 100ms timescale. (b)Corresponding spectrum of the beat-note between the two optical lines over the 100msintegration time with a line width < 3.1 kHz (FWHM). The center frequency of the beat-noteis 28.76MHz.

already obtain stability at the few-kHz level, comparable to ∆frep. Significantly lower noiseshould be possible with an optimized setup. Thus, development of a setup optimized for highstability and demonstration of dual-comb spectroscopy applications will be the subject of futurework.

6. Conclusions

In this paper we have presented the first diode-pumped SESAM mode-locked solid-statefemtosecond dual-comb oscillator from a single cavity. The birefringent crystal multiplexingapproach produces two mutually coherent combs with a tunable repetition rate difference withoutany active control of the cavity elements. The demonstrated laser delivers two frequency comboutputs, each with pulse duration of 175 fs and 440 mW of average power. The average laserrepetition rate was 137 MHz and the repetition rate difference was set to 1 kHz. The polarization-based multiplexing of the two modes in the laser cavity leads to intrinsically low-noise in thedifference of the two combs and the relative timing jitter over a 1-ms timescale (the delay betweensubsequent pulse trigger events) was characterized to be 69.4 fs. Moreover, this first proof ofprinciple system was not yet optimized for low-noise operation, so we anticipate even lower noiselevels in the future.The Ytterbium-doped CaF2 gain medium represents an excellent platform for power and

bandwidth scalability beyond the parameters we already demonstrated here. Nonetheless, theexisting laser is already well suited to efficient nonlinear frequency conversion to spectral rangesof interest for spectroscopy such as mid-infrared, terahertz or ultraviolet. Key aspects in thepower and efficiency scaling of the presented laser will be a reduction of the intracavity losses byusing optimized antireflection coatings, increasing the output coupling rate, and improvements tothe mode matching between the laser modes and the pump focusing.

The wide tunability of the repetition rate difference between the two combs allows for coarse butvery fast scans or high time resolution with slower scans. The delay sweeping of the demonstratedlaser covers a time window of multiple nanoseconds relevant for many practical applications. Inthis work we applied the laser for ASOPS measurements on SESAM and VECSEL semiconductorstructures probing their nonlinear response.

This demonstrates that the presented dual-comb laser source from a single cavity is an attractiveand cost-effective solution for various ASOPS and dual-comb applications such as picosecondultrasonic imaging, time-domain terahertz spectroscopy or dual-comb spectroscopy. The rapiddelay scans are well-suited for combined imaging and pump-probe measurements enabling


label-free imaging in biomedical applications. When combined with nonlinear frequencyconversion the presented laser platform will unpack its full potential for spectroscopic andimaging applications.

Funding

SchweizerischerNationalfonds zur Förderung derWissenschaftlichenForschung (40B2-0_180933).

Disclosures

The authors declare no conflicts of interest.

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