Abstract

Dual optical frequency combs are an appealing solution to many optical measurement techniques due to their high spectral and temporal resolution, high scanning speed, and lack of moving parts. However, industrial and field-deployable applications of such systems are limited due to a high-cost factor and intricacy in the experimental setups, which typically require a pair of locked femtosecond lasers. Here, we demonstrate a single oscillator which produces two mode-locked output beams with a stable repetition rate difference. We achieve this via inserting two 45°-cut birefringent crystals into the laser cavity, which introduces a repetition rate difference between the two polarization states of the cavity. To mode-lock both combs simultaneously, we use a semiconductor saturable absorber mirror (SESAM). We achieve two simultaneously operating combs at 1050 nm with 175-fs duration, 3.2-nJ pulses and an average power of 440 mW in each beam. The average repetition rate is 137 MHz, and we set the repetition rate difference to 1 kHz. This laser system, which is the first SESAM mode-locked femtosecond solid-state dual-comb source based on birefringent multiplexing, paves the way for portable and high-power femtosecond dual-combs with flexible repetition rate. To demonstrate the utility of the laser for applications, we perform asynchronous optical sampling (ASOPS) on semiconductor thin-film structures with the free-running laser system, revealing temporal dynamics from femtosecond to nanosecond 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 techniques over the past four decades. Pump-probe measurements, in which a fast and periodic signal is mixed with an ultrashort optical pulse, are widely used for this purpose. By scanning the delay of a femtosecond optical pulse with respect to the periodic signal, the signal’s temporal profile can be determined. This approach, sometimes referred to as equivalent-time sampling, hinges upon two properties: the ability to achieve precise variation of the optical delay, and the use of a mixing process with a fast response time. The latter problem was addressed in early work by the use of electro-optic sampling [13], since the electro-optic effect exhibits an ultrafast response time. The other requirement, of precisely varying the optical delay, was traditionally solved by a mechanical delay line. The advent of frequency comb technology [46], and in particular dual-comb spectroscopy which uses a pair of combs with a small difference in pulse repetition rate, has enabled a revolution in optical measurement techniques. Dual-combs offer ultra-high resolution in both time and frequency, and they provide a perfectly linear scan of optical delay with no moving parts and at speeds far exceeding the capabilities of mechanical scanners. Such dual-comb laser sources have been widely pursued for optical sensing measurements [79]. These include high-resolution time-domain spectroscopy [10,11], electro-optic sampling spectroscopy [12], high-speed pump-probe measurements via asynchronous optical sampling [1315] and fast and 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 implemented successfully in many platforms, including electronically locked fiber combs [1821], solid-state Ti:sapphire lasers [22], microresonator combs [2325], and electrooptic combs via the modulation of a single laser output [2628]. However, the complexity and cost associated with a separate pair of frequency combs together with the associated locking electronics has presented a significant challenge to developing applications based on these systems. Consequently, in more recent years, several groups have developed solutions to reduce the complexity by producing mutually coherent combs from a single laser oscillator. Promising approaches include Kerr-lens mode-locked bidirectional solid-state ring lasers [29], Kerr-lens mode-locked spatially multiplexed [30] and polarization multiplexed [31] thin-disk lasers, passively mode-locked fiber lasers [3238] and mode-locked integrated external-cavity surface emitting lasers (MIXSELs) based on linear cavities and polarization multiplexing [39,40]. Free-running dual-comb laser systems were recently 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 cavity on the MIXSEL semiconductor chip, thereby allowing for mode-locking of both polarizations simultaneously. This approach yielded two mutually coherent combs at a center wavelength around 1 µm with a typical repetition rate around 2 GHz, average powers of ∼25 mW, and adjustable repetition rate differences in the kHz to MHz range. In free-running operation these lasers 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 the available average power in femtosecond operation, and requires high repetition rates typically above one gigahertz, which can be too large for some applications. In contrast, solid-state laser systems rely on longer upper state lifetime gain crystals, which facilitates the generation of higher pulse energies and lower pulse repetition rates. The high peak powers typically involved in such solid-state lasers open the path to nonlinear light-matter interactions for pump-probe spectroscopy and nonlinear optics for frequency conversion. A variety of promising laser materials 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 [4850].

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 polarization multiplexing of the modes in the oscillator by insertion of two 45°-cut birefringent crystals into the laser cavity. With this first system we realized two simultaneously fundamentally mode-locked lasers at a center frequency of 1050 nm, an average output power of 440 mW per beam at a repetition rate of 137 MHz and a pulse duration of 175 fs (sections 2 and 3). The repetition rate difference between these two combs is freely tunable up to several tens of kilohertz, yet intrinsically stable already in free-running operation. As a proof of principle application of this laser, we demonstrate asynchronous optical sampling (ASOPS) on two semiconductor thin-film structures, 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 absorption dynamics 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 a single free-running laser cavity. These laser sources will benefit a broad range of optical measurement methodologies, including rapid asynchronous sampling measurements with high temporal resolution. Moreover, the high peak power pulses produced from such oscillators enable wavelength flexibility via nonlinear frequency conversion and multi-photon spectroscopy applications.

2. Laser concept and setup

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

Here, we present a laser based on a folded end-pumped MHz cavity supporting simultaneously two cross-polarized frequency combs with sub-200 fs pulses. The schematic of the laser cavity is shown 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 two ends of the cavity to yield spatially separated spots on the SESAM and in the gain crystal.

 figure: Fig. 1.

Fig. 1. (a) Schematic of the laser cavity for simultaneous mode-locking operation of two combs 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 the output coupler (OC) and the laser beam is separated from the pump beam with a dichroic mirror (DM). (b) illustrates the splitting of the laser mode in the gain crystal and (c) the tuning of the repetition rate difference Δfrep by rotation of BF2. (d) shows the two spatially separated intracavity laser spots on the SESAM device.

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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-stabilized pump diode (DILAS Diode Laser GmbH) delivering up to 20 W by a multimode fiber (106.5 µm core diameter, NA = 0.15, M2 = 20). After collimating the output of this multimode fiber, the pump beam is split into two beams of equal power, in order to obtain two spatially separated focused 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, to the 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). This geometry helps enable the tight focusing conditions needed for efficient operation. Since the SESAM is used as the other end mirror, we use a 45° dichroic mirror (“DM” in Fig.  1) to split the 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 calcite crystals with negative GDD from Gires-Tournois-Interferometer (GTI) type mirrors (total −2200 fs2 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 enabled robust mode-locking and self-starting operation of the laser. The long upper-state lifetime of Yb:CaF2 implies that Q-switched mode-locking instabilities can occur before the laser reaches the 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 two birefringent crystals as well as the gain crystal cause the beam to diverge on the SESAM. These type of self-defocusing cavities have previously been exploited for gigahertz repetition rate solid-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 leads to a separation of the modes in the gain crystal, to allow independent pumping and avoid gain crosstalk. BF2 leads to a separation of the modes on the SESAM, to allow independent saturable absorption and avoid saturation crosstalk [56]. This separation of the two laser modes on the SESAM has proven to be critical to avoid crosstalk between the two combs and optical damage of the semiconductor thin-film structure. As shown in Fig.  1, the beams are split in the horizontal axis on the SESAM, and in the vertical axis on the gain crystal. In the rest of the cavity, the beams are well overlapped. This overlap maximizes the common path for the two polarization states in the cavity, which minimizes the difference in noise experienced by the two combs, enabling a highly stable repetition rate difference.

Each birefringent crystal introduces a delay difference between its ordinary and extraordinary waves (o- and e-waves, respectively). For 5-mm-long calcite crystal, this difference is approximately 1.6 ps per pass through the crystal [57]. Hence, two such crystals oriented the same way in the cavity would yield a round-trip delay difference of 6.4 ps, and a corresponding repetition rate difference of 120 kHz for the 137 MHz cavity. This difference is too large for high-temporal-resolution pump-probe measurements, and would lead to aliasing in dual-comb spectroscopy. Therefore, we instead mount the second crystal BF2 at 90° rotation around the optical axis compared to BF1. This enables a small difference in repetition rate of a few kilo-hertz because the role of the ordinary and extraordinary polarization is flipped between the two birefringent crystals, thereby canceling most of the optical path length difference of the two polarization 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 with respect to the c-axis, which changes the refractive index of the extraordinary wave. Since we used two different crystal lengths (4.5 mm for BF1 and 5 mm for BF2), a repetition rate difference Δfrep = 0 is reached for a significant angle of incidence on the crystal of approximately 4.8°. Note also that, while BF1 was wedged (1 degree), BF2 was not, so rotating it also avoided etalon effects on the cavity mode. For our measurements, we tuned the repetition rate difference to 1 kHz via the angle of BF2. Due to the flat end mirror (SESAM), this rotation does not couple to alignment of 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 that the upper limit was imposed by the clear aperture of BF2 and not by any physics limit of the birefringent 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) for output powers ranging from 250 mW to 440 mW for each comb [Fig.  2(a)]. The increasing intracavity power leads to pulse shortening from 275 fs (low power operation) to 175 fs (high power operation) following the expected inverse scaling to the intracavity pulse energy for soliton mode-locking [52,58]. The relatively low slope efficiency of both combs of 17% in mode-locked operation is partly due to the relatively high losses in the cavity from imperfect AR coatings of the birefringent calcite crystals and the laser crystal. The excellent output beam quality of the spatially separated combs is show in Fig.  2(b). At the nominal operation point we measure a beam quality factor for each of the two individual beams of M2 < 1.05.

 figure: Fig. 2.

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

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In Fig.  3, we show the mode-locking diagnostics of the two 1050-nm combs at the nominal operation point, which corresponds to the maximum total pump power of 7.8 W. At this operating point, the output power is 441 mW (comb 1) and 443 mW (comb 2). Given the repetition rate of 137 MHz, this corresponds to 3.2 nJ output without any external amplification. Both combs have 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) via second-harmonic generation (SHG) intensity autocorrelation. The corresponding time-bandwidth product (TBP) of the combs is 0.327 (comb 1) and 0.323 (comb 2), compared to TBP = 0.315 for ideal sech2 pulses. Both combs exhibit a transform-limited pulse duration throughout the entire mode-locking range, satisfying TBP < 1.05 × 0.315. The clean radio frequency (RF) spectrum shows that the laser is operating in fundamental mode-locking without pre and post pulses.

 figure: Fig. 3.

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

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4. Asynchronous optical sampling from free-running laser

In this section, we apply our new femtosecond dual-comb laser source for rapid asynchronous optical sampling (ASOPS) measurements on semiconductor thin-film structures, allowing for high-speed scanning of pump-probe time delays without a mechanical delay line. We measure the dynamics via a change of reflectivity for (a) a SESAM structure which is from the same wafer as the SESAM used inside the laser cavity itself and (b) a VECSEL, a more complex quantum well 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 shown in 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 comb acts as a pump, while the other comb with a slightly different comb spacing is attenuated to act as a probe. The pump-induced change of the reflectivity of the device under test is then sampled by the probe pulse similar to equivalent time sampling [13]. The probe beam amplitude is measured 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.). The back-reflected pump beam is blocked with an aperture.

 figure: Fig. 4.

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

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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 focused with an aspheric 25-mm focal length lens to 14.7 × 15.1 μm2 and 15.4 × 15.4 μm2 1/e2 beam diameters, respectively (measured on a Datray Beam'R2 – XY Scanning Slit Beam Profiler). The probe power is set to 2.8 mW whereas the pump power is adjusted in the experiments. The setup supports a pump power of up to 237 mW at the sample, and hence the sample can be pumped up to an average fluence of 1 mJ/cm2.

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

Figure  4(b) illustrates how such pump-probe scheme maps ultrafast dynamics into electronically resolvable signals. A strong pump pulse train initiates the dynamics in the target and the probe pulse samples the response at increasing delay steps at every repetition of the laser pulse. When frep >> Δfrep, the delay step size can be estimated as Δfrep / frep2 [15]. In case of 1 kHz repetition rate difference and 137 MHz repetition rate of the laser, the step size is 53 fs, smaller than the probe pulse duration. In the time scale of 1/Δfrep = 1 ms, a time window of 1/frep = 7.3 ns is sampled. While the pulses of the two combs walk through each other the ultrafast response of the target is down-sampled by the factor of frepfrep to the radio-frequency (RF) range which is easily accessible by modern electronics, yet the system is fast enough for rapid measurements not feasible 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 first use 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. The obtained trigger signal trace is schematically shown in Fig.  5(a). From the total measurement window Ttot and the number N of SFG peaks generated, we define the repetition rate difference Δfrep= N / Ttot. We compare the expected arrival time of the n-th pulse Tn = n / Δfrep versus the actual measured arrival time ${\tilde{T}}$n. The corresponding difference between these two is the time-offset δTn = Tn - ${\tilde{T}}$n shown in Fig.  5(a). During ASOPS measurement the data acquisition is triggered on the SFG signal and thus the measurement is re-timed. Such measurement re-timing suppresses 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 define the relative timing jitter quantity as ΔTn = δTn+1 - δTn, i.e. measuring the short-term changes of the arrival time difference.

 figure: Fig. 5.

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 by the total acquisition window divided by the number of measured cross-terms. (b) Timing jitter distribution extracted from the SFG cross-correlation signals in a 10 second acquisition window.

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For a 10 second acquisition window, we find that the relative timing between two consecutive trigger 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 timing uncertainty ΔTn(pp)= ΔTn Δfrep / frep for Δfrep = 947 Hz and frep = 136.5 Hz. Since this jitter is less than the pulse duration, it does not impact the measurement precision significantly. Compared to electronically locked two-oscillators [59,60], this free-running system offers the same or better timing 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 by performing measurements on AlGaAs samples with InGaAs quantum well (QW) structures. We first measure the pump-probe response of a SESAM sample of the same design as the one used to mode-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) $ \varpropto $ Vprobe(t, Fprobe, Fpump). Note that the data from the oscilloscope provides Vprobe(t, Fprobe, Fpump) measured over many SFG trigger events. We are interested in the quantity

$$\overline {{\Delta }R} ({t,\; {F_{\textrm{pump}}}} )= \frac{{{R_{\textrm{probe}}}({t,\; \; {F_{\textrm{probe}}},\; \; \; {F_{\textrm{pump}}}\; } )\; - \; {R_{\textrm{probe}}}({t,\; \; {F_{\textrm{probe}}},\; \; 0} )}}{{{R_{\textrm{probe}}}({t,\; \; \; {F_{\textrm{probe}}},0} )}}, $$
which is pump induced change of the sample reflectivity. The background probe signal level corresponding to Rprobe(t, Fprobe, 0) can vary due to any changes in the setup. Therefore, we estimate this background probe voltage, denoted Vbg, for each individual measurement time trace by averaging the signal at negative delays t such that the sample has recovered. Hence Vbg is the average of Vprobe(t, Fprobe, Fpump) for t over the range [-6.7, -0.8] ps. Given Vbg, we estimate $\overline {\mathrm{\Delta }R} = ({{V_{probe}} - {V_{bg}}} )/{V_{bg}}$.

$\overline {\mathrm{\Delta }R} $ provides pump-probe data over a timescale from 0 delay up to 1/frep as well as the pump fluence dependence. The time-zero of the delay scan is determined by the TPA signal in a bulk GaAs sample. The resulting relative reflectivity change at different pump fluences for the SESAM structure is plotted in Fig.  6(a). From the pump-probe traces one can infer rapid intra-band thermalization and slower inter-band dynamics [61,62]. For a pump average fluence 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 nonlinear effects 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, where reflectivity starts to decrease due to the TPA in the structure. By equivalence of the pump-probe measurement at pulse overlap time (i.e., at t = 0) and saturation fluence measurement [63], one can additionally extract saturation fluence information from the pump-probe setup. Thereby this single measurement setup provides a full characterization of the SESAM response.

 figure: Fig. 6.

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

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To demonstrate that the dual-comb laser can be used to perform rapid long delay range measurements, we perform a pump-probe measurement on a VECSEL chip which was used for 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 probe response is shown in Fig.  7. After the drop in reflectivity around delay t = 0 due to two photon absorption (pump induced absorption of the probe), a population inversion develops within a few picoseconds, as shown in the inset. The gain lifetime can be directly measured leading to 1.9 ns – a typical value for the upper-state lifetime of VECSEL gain structures [61]. Hence this demonstrates that the laser can be used directly for rapid long-range pump-probe measurements surpassing in terms of scanning speed any mechanical delay scan system.

 figure: Fig. 7.

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

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5. Coherent beat-note measurement

By resolving the beat notes between individual comb lines, dual-combs enable ultra-high resolution spectroscopy [8]. Achieving this high resolution requires coherence between the two combs. Therefore, in this section we present and discuss a measurement of this coherence for our laser 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 high temporal 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 to separate photodiodes, apply electronic low-pass filters, and digitize the corresponding signals. These signals, denoted s1 and s2, have the form

$${s_j}(t )= \textrm{sin}\left( {2\pi \mathop \smallint \nolimits^t ({{\nu_j}({t^{\prime}} )- \; {\nu_{\textrm{cw}}}({t^{\prime}} )} )\; dt^{\prime}} \right), $$
where νcw is the optical frequency of the cw laser, and νj denotes the line of comb j which is closest 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 of comb 2, independent of νcw. We extract this term digitally with band-pass filters, and show a typical measurement example in Fig.  8(a). The signal exhibits fluctuations within +/- 5 kHz on a 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).

 figure: Fig. 8.

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

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We note that the laser is currently assembled with generic laboratory optomechanics on an aluminum 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 already obtain stability at the few-kHz level, comparable to Δfrep. Significantly lower noise should be possible with an optimized setup. Thus, development of a setup optimized for high stability and demonstration of dual-comb spectroscopy applications will be the subject of future work.

6. Conclusions

In this paper we have presented the first diode-pumped SESAM mode-locked solid-state femtosecond dual-comb oscillator from a single cavity. The birefringent crystal multiplexing approach produces two mutually coherent combs with a tunable repetition rate difference without any active control of the cavity elements. The demonstrated laser delivers two frequency comb outputs, each with pulse duration of 175 fs and 440 mW of average power. The average laser repetition 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 the difference of the two combs and the relative timing jitter over a 1-ms timescale (the delay between subsequent pulse trigger events) was characterized to be 69.4 fs. Moreover, this first proof of principle system was not yet optimized for low-noise operation, so we anticipate even lower noise levels 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, the existing laser is already well suited to efficient nonlinear frequency conversion to spectral ranges of interest for spectroscopy such as mid-infrared, terahertz or ultraviolet. Key aspects in the power and efficiency scaling of the presented laser will be a reduction of the intracavity losses by using optimized antireflection coatings, increasing the output coupling rate, and improvements to the 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 but very fast scans or high time resolution with slower scans. The delay sweeping of the demonstrated laser covers a time window of multiple nanoseconds relevant for many practical applications. In this work we applied the laser for ASOPS measurements on SESAM and VECSEL semiconductor structures probing their nonlinear response.

This demonstrates that the presented dual-comb laser source from a single cavity is an attractive and cost-effective solution for various ASOPS and dual-comb applications such as picosecond ultrasonic imaging, time-domain terahertz spectroscopy or dual-comb spectroscopy. The rapid delay scans are well-suited for combined imaging and pump-probe measurements enabling label-free imaging in biomedical applications. When combined with nonlinear frequency conversion the presented laser platform will unpack its full potential for spectroscopic and imaging applications.

Funding

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (40B2-0_180933).

Disclosures

The authors declare no conflicts of interest.

References

1. J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Picosecond electro-optic sampling system,” Appl. Phys. Lett. 41(3), 211–212 (1982). [CrossRef]  

2. A. J. Taylor, R. S. Tucker, J. M. Wiesenfeld, C. A. Burrus, G. Eisenstein, J. R. Talman, and S. S. Pei, “Direct electro-optic sampling of a GaAs integrated circuit using a gain-switched InGaAsP injection laser,” Electron. Lett. 22(20), 1068 (1986). [CrossRef]  

3. K. J. Weingarten, M. J. W. Rodwel, and D. M. Bloom, “Picosecond optical sampling of GaAs integrated circuits,” IEEE J. Quantum Electron. 24(2), 198–220 (1988). [CrossRef]  

4. H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999). [CrossRef]  

5. A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000). [CrossRef]  

6. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288(5466), 635–639 (2000). [CrossRef]  

7. S. Schiller, “Spectrometry with frequency combs,” Opt. Lett. 27(9), 766 (2002). [CrossRef]  

8. I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414 (2016). [CrossRef]  

9. N. Picqué and T. W. Hänsch, “Frequency comb spectroscopy,” Nat. Photonics 13(3), 146–157 (2019). [CrossRef]  

10. G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm,” Nat. Photonics 12(4), 202–208 (2018). [CrossRef]  

11. A. V. Muraviev, V. O. Smolski, Z. E. Loparo, and K. L. Vodopyanov, “Massively parallel sensing of trace molecules and their isotopologues with broadband subharmonic mid-infrared frequency combs,” Nat. Photonics 12(4), 209–214 (2018). [CrossRef]  

12. I. A. Finneran, J. T. Good, D. B. Holland, P. B. Carroll, M. A. Allodi, and G. A. Blake, “Decade-Spanning High-Precision Terahertz Frequency Comb,” Phys. Rev. Lett. 114(16), 163902 (2015). [CrossRef]  

13. R. Gebs, G. Klatt, C. Janke, T. Dekorsy, and A. Bartels, “High-speed asynchronous optical sampling with sub-50fs time resolution,” Opt. Express 18(6), 5974 (2010). [CrossRef]  

14. P. A. Elzinga, R. J. Kneisler, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump/probe method for fast analysis of visible spectral signatures utilizing asynchronous optical sampling,” Appl. Opt. 26(19), 4303 (1987). [CrossRef]  

15. A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78(3), 035107 (2007). [CrossRef]  

16. M.-G. Suh and K. J. Vahala, “Soliton microcomb range measurement,” Science 359(6378), 884–887 (2018). [CrossRef]  

17. P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018). [CrossRef]  

18. A. M. Zolot, F. R. Giorgetta, E. Baumann, J. W. Nicholson, W. C. Swann, I. Coddington, and N. R. Newbury, “Direct-comb molecular spectroscopy with accurate, resolved comb teeth over 43 THz,” Opt. Lett. 37(4), 638 (2012). [CrossRef]  

19. S. Okubo, K. Iwakuni, H. Inaba, K. Hosaka, A. Onae, H. Sasada, and F.-L. Hong, “Ultra-broadband dual-comb spectroscopy across 1.0–1.9 µm,” Appl. Phys. Express 8(8), 082402 (2015). [CrossRef]  

20. Z. Chen, M. Yan, T. W. Hänsch, and N. Picqué, “A phase-stable dual-comb interferometer,” Nat. Commun. 9(1), 3035 (2018). [CrossRef]  

21. B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010). [CrossRef]  

22. K. J. Mohler, B. J. Bohn, M. Yan, G. Mélen, T. W. Hänsch, and N. Picqué, “Dual-comb coherent Raman spectroscopy with lasers of 1-GHz pulse repetition frequency,” Opt. Lett. 42(2), 318 (2017). [CrossRef]  

23. M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354(6312), 600–603 (2016). [CrossRef]  

24. A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4(3), e1701858 (2018). [CrossRef]  

25. M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018). [CrossRef]  

26. D. A. Long, A. J. Fleisher, K. O. Douglass, S. E. Maxwell, K. Bielska, J. T. Hodges, and D. F. Plusquellic, “Multiheterodyne spectroscopy with optical frequency combs generated from a continuous-wave laser,” Opt. Lett. 39(9), 2688 (2014). [CrossRef]  

27. G. Millot, S. Pitois, M. Yan, T. Hovhannisyan, A. Bendahmane, T. W. Hänsch, and N. Picqué, “Frequency-agile dual-comb spectroscopy,” Nat. Photonics 10(1), 27–30 (2016). [CrossRef]  

28. A. Shams-Ansari, M. Yu, Z. Chen, C. Reimer, M. Zhang, N. Picqué, and M. Lončar, “An integrated lithium-niobate electro-optic platform for spectrally tailored dual-comb spectroscopy,” arXiv (2020).

29. T. Ideguchi, T. Nakamura, Y. Kobayashi, and K. Goda, “Kerr-lens mode-locked bidirectional dual-comb ring laser for broadband dual-comb spectroscopy,” Optica 3(7), 748 (2016). [CrossRef]  

30. K. Fritsch, J. Brons, M. Iandulskii, K. F. Mak, Z. Chen, N. Picqué, and O. Pronin, “Dual-comb thin-disk oscillator,” arXiv:2004.10303 (2020).

31. N. Modsching, J. Drs, J. Fischer, S. Schilt, V. J. Wittwer, and T. Südmeyer, “Dual-Comb Thin-Disk Laser Oscillator Based on Polarization Splitting,” Conf. Lasers Electro-Optics, OSA Tech. Dig. (Optical Soc. Am. 2020), Pap. SF3H.2 (2020).

32. J. Fellinger, A. S. Mayer, G. Winkler, W. Grosinger, G.-W. Truong, S. Droste, C. Li, C. M. Heyl, I. Hartl, and O. H. Heckl, “Tunable dual-comb from an all-polarization-maintaining single-cavity dual-color Yb:fiber laser,” Opt. Express 27(20), 28062 (2019). [CrossRef]  

33. Y. Nakajima, Y. Hata, and K. Minoshima, “All-polarization-maintaining, polarization-multiplexed, dual-comb fiber laser with a nonlinear amplifying loop mirror,” Opt. Express 27(10), 14648 (2019). [CrossRef]  

34. S. Mehravar, R. A. Norwood, N. Peyghambarian, and K. Kieu, “Real-time dual-comb spectroscopy with a free-running bidirectionally mode-locked fiber laser,” Appl. Phys. Lett. 108(23), 231104 (2016). [CrossRef]  

35. X. Zhao, T. Li, Y. Liu, Q. Li, and Z. Zheng, “Polarization-multiplexed, dual-comb all-fiber mode-locked laser,” Photonics Res. 6(9), 853 (2018). [CrossRef]  

36. X. Zhao, G. Hu, B. Zhao, C. Li, Y. Pan, Y. Liu, T. Yasui, and Z. Zheng, “Picometer-resolution dual-comb spectroscopy with a free-running fiber laser,” Opt. Express 24(19), 21833 (2016). [CrossRef]  

37. R. Liao, Y. Song, W. Liu, H. Shi, L. Chai, and M. Hu, “Dual-comb spectroscopy with a single free-running thulium-doped fiber laser,” Opt. Express 26(8), 11046 (2018). [CrossRef]  

38. J. Olson, Y. H. Ou, A. Azarm, and K. Kieu, “Bi-Directional Mode-Locked Thulium Fiber Laser as a Single-Cavity Dual-Comb Source,” IEEE Photonics Technol. Lett. 30(20), 1772–1775 (2018). [CrossRef]  

39. S. M. Link, A. Klenner, M. Mangold, C. A. Zaugg, M. Golling, B. W. Tilma, and U. Keller, “Dual-comb modelocked laser,” Opt. Express 23(5), 5521 (2015). [CrossRef]  

40. J. Nürnberg, C. G. E. Alfieri, Z. Chen, D. Waldburger, N. Picqué, and U. Keller, “An unstabilized femtosecond semiconductor laser for dual-comb spectroscopy of acetylene,” Opt. Express 27(3), 3190 (2019). [CrossRef]  

41. R. Liao, H. Tian, W. Liu, R. Li, Y. Song, and M. Hu, “Dual-comb generation from a single laser source: principles and spectroscopic applications towards mid-IR – A Review,” J. Phys. Photonics (2020).

42. S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356(6343), 1164–1168 (2017). [CrossRef]  

43. G. Machinet, P. Sevillano, F. Guichard, R. Dubrasquet, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, F. Druon, D. Descamps, and E. Cormier, “High-brightness fiber laser-pumped 68 fs–2.3 W Kerr-lens mode-locked Yb:CaF2 oscillator,” Opt. Lett. 38(20), 4008 (2013). [CrossRef]  

44. A. Klenner, M. Golling, and U. Keller, “High peak power gigahertz Yb:CALGO laser,” Opt. Express 22(10), 11884 (2014). [CrossRef]  

45. L. M. Krüger, A. S. Mayer, Y. Okawachi, X. Ji, A. Klenner, A. R. Johnson, C. Langrock, M. M. Fejer, M. Lipson, A. L. Gaeta, V. J. Wittwer, T. Südmeyer, C. R. Phillips, and U. Keller, “Performance scaling of a 10-GHz solid-state laser enabling self-referenced CEO frequency detection without amplification,” Opt. Express 28(9), 12755 (2020). [CrossRef]  

46. P. Wasylczyk, P. Wnuk, and C. Radzewicz, “Passively modelocked, diode-pumped Yb:KYW femtosecond oscillator with 1 GHz repetition rate,” Opt. Express 17(7), 5630 (2009). [CrossRef]  

47. T. C. Schratwieser, C. G. Leburn, and D. T. Reid, “Highly efficient 1 GHz repetition-frequency femtosecond Yb3+:KY(WO4)2 laser,” Opt. Lett. 37(6), 1133 (2012). [CrossRef]  

48. F. Brunner, G. J. Spühler, J. Aus der Au, L. Krainer, F. Morier-Genoud, R. Paschotta, N. Lichtenstein, S. Weiss, C. Harder, A. A. Lagatsky, A. Abdolvand, N. V. Kuleshov, and U. Keller, “Diode-pumped femtosecond Yb:KGd(WO4)2 laser with 1.1-W average power,” Opt. Lett. 25(15), 1119 (2000). [CrossRef]  

49. S. Pekarek, C. Fiebig, M. C. Stumpf, A. E. H. Oehler, K. Paschke, G. Erbert, T. Südmeyer, and U. Keller, “Diode-pumped gigahertz femtosecond Yb:KGW laser with a peak power of 3.9 kW,” Opt. Express 18(16), 16320 (2010). [CrossRef]  

50. A. Klenner, M. Golling, and U. Keller, “A gigahertz multimode-diode-pumped Yb:KGW enables a strong frequency comb offset beat signal,” Opt. Express 21(8), 10351 (2013). [CrossRef]  

51. F. Druon, S. Ricaud, D. N. Papadopoulos, A. Pellegrina, P. Camy, J. L. Doualan, R. Moncorgé, A. Courjaud, E. Mottay, and P. Georges, “On Yb:CaF2 and Yb:SrF2: review of spectroscopic and thermal properties and their impact on femtosecond and high power laser performance,” Opt. Mater. Express 1(3), 489 (2011). [CrossRef]  

52. F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 540–556 (1996). [CrossRef]  

53. C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16(1), 46 (1999). [CrossRef]  

54. A. Klenner and U. Keller, “All-optical Q-switching limiter for high-power gigahertz modelocked diode-pumped solid-state lasers,” Opt. Express 23(7), 8532 (2015). [CrossRef]  

55. A. S. Mayer, C. R. Phillips, and U. Keller, “Watt-level 10-gigahertz solid-state laser enabled by self-defocusing nonlinearities in an aperiodically poled crystal,” Nat. Commun. 8(1), 1673 (2017). [CrossRef]  

56. S. M. Link, A. Klenner, and U. Keller, “Dual-comb modelocked lasers: semiconductor saturable absorber mirror decouples noise stabilization,” Opt. Express 24(3), 1889 (2016). [CrossRef]  

57. G. Ghosh, “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals,” Opt. Commun. 163(1-3), 95 (1999). [CrossRef]  

58. I. D. Jung, F. X. Kärtner, L. R. Brovelli, M. Kamp, and U. Keller, “Experimental verification of soliton mode locking using only a slow saturable absorber,” Opt. Lett. 20(18), 1892 (1995). [CrossRef]  

59. C. Li, N. Krauß, G. Schäfer, L. Ebner, O. Kliebisch, J. Schmidt, S. Winnerl, M. Hettich, and T. Dekorsy, “High-speed asynchronous optical sampling based on GHz Yb:KYW oscillators,” Opt. Express 25(8), 9204 (2017). [CrossRef]  

60. P. Struszewski and M. Bieler, “Asynchronous Optical Sampling for Laser-Based Vector Network Analysis on Coplanar Waveguides,” IEEE Trans. Instrum. Meas. 68(6), 2295–2302 (2019). [CrossRef]  

61. C. G. E. Alfieri, D. Waldburger, S. M. Link, E. Gini, M. Golling, G. Eisenstein, and U. Keller, “Optical efficiency and gain dynamics of modelocked semiconductor disk lasers,” Opt. Express 25(6), 6402 (2017). [CrossRef]  

62. P. Langlois, M. Joschko, E. R. Thoen, E. M. Koontz, F. X. Kärtner, E. P. Ippen, and L. A. Kolodziejski, “High fluence ultrafast dynamics of semiconductor saturable absorber mirrors,” Appl. Phys. Lett. 75(24), 3841–3843 (1999). [CrossRef]  

63. R. Fleischhaker, N. Krauß, F. Schättiger, and T. Dekorsy, “Consistent characterization of semiconductor saturable absorber mirrors with single-pulse and pump-probe spectroscopy,” Opt. Express 21(6), 6764 (2013). [CrossRef]  

64. D. Waldburger, S. M. Link, M. Mangold, C. G. E. Alfieri, E. Gini, M. Golling, B. W. Tilma, and U. Keller, “High-power 100 fs semiconductor disk lasers,” Optica 3(8), 844 (2016). [CrossRef]  

65. P. Giaccari, J.-D. Deschênes, P. Saucier, J. Genest, and P. Tremblay, “Active Fourier-transform spectroscopy combining the direct RF beating of two fiber-based mode-locked lasers with a novel referencing method,” Opt. Express 16(6), 4347 (2008). [CrossRef]  

66. J.-D. Deschênes, P. Giaccarri, and J. Genest, “Optical referencing technique with CW lasers as intermediate oscillators for continuous full delay range frequency comb interferometry,” Opt. Express 18(22), 23358 (2010). [CrossRef]  

67. T. Ideguchi, A. Poisson, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5(1), 3375 (2014). [CrossRef]  

References

  • View by:

  1. J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Picosecond electro-optic sampling system,” Appl. Phys. Lett. 41(3), 211–212 (1982).
    [Crossref]
  2. A. J. Taylor, R. S. Tucker, J. M. Wiesenfeld, C. A. Burrus, G. Eisenstein, J. R. Talman, and S. S. Pei, “Direct electro-optic sampling of a GaAs integrated circuit using a gain-switched InGaAsP injection laser,” Electron. Lett. 22(20), 1068 (1986).
    [Crossref]
  3. K. J. Weingarten, M. J. W. Rodwel, and D. M. Bloom, “Picosecond optical sampling of GaAs integrated circuits,” IEEE J. Quantum Electron. 24(2), 198–220 (1988).
    [Crossref]
  4. H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
    [Crossref]
  5. A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
    [Crossref]
  6. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288(5466), 635–639 (2000).
    [Crossref]
  7. S. Schiller, “Spectrometry with frequency combs,” Opt. Lett. 27(9), 766 (2002).
    [Crossref]
  8. I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414 (2016).
    [Crossref]
  9. N. Picqué and T. W. Hänsch, “Frequency comb spectroscopy,” Nat. Photonics 13(3), 146–157 (2019).
    [Crossref]
  10. G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm,” Nat. Photonics 12(4), 202–208 (2018).
    [Crossref]
  11. A. V. Muraviev, V. O. Smolski, Z. E. Loparo, and K. L. Vodopyanov, “Massively parallel sensing of trace molecules and their isotopologues with broadband subharmonic mid-infrared frequency combs,” Nat. Photonics 12(4), 209–214 (2018).
    [Crossref]
  12. I. A. Finneran, J. T. Good, D. B. Holland, P. B. Carroll, M. A. Allodi, and G. A. Blake, “Decade-Spanning High-Precision Terahertz Frequency Comb,” Phys. Rev. Lett. 114(16), 163902 (2015).
    [Crossref]
  13. R. Gebs, G. Klatt, C. Janke, T. Dekorsy, and A. Bartels, “High-speed asynchronous optical sampling with sub-50fs time resolution,” Opt. Express 18(6), 5974 (2010).
    [Crossref]
  14. P. A. Elzinga, R. J. Kneisler, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump/probe method for fast analysis of visible spectral signatures utilizing asynchronous optical sampling,” Appl. Opt. 26(19), 4303 (1987).
    [Crossref]
  15. A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78(3), 035107 (2007).
    [Crossref]
  16. M.-G. Suh and K. J. Vahala, “Soliton microcomb range measurement,” Science 359(6378), 884–887 (2018).
    [Crossref]
  17. P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
    [Crossref]
  18. A. M. Zolot, F. R. Giorgetta, E. Baumann, J. W. Nicholson, W. C. Swann, I. Coddington, and N. R. Newbury, “Direct-comb molecular spectroscopy with accurate, resolved comb teeth over 43 THz,” Opt. Lett. 37(4), 638 (2012).
    [Crossref]
  19. S. Okubo, K. Iwakuni, H. Inaba, K. Hosaka, A. Onae, H. Sasada, and F.-L. Hong, “Ultra-broadband dual-comb spectroscopy across 1.0–1.9 µm,” Appl. Phys. Express 8(8), 082402 (2015).
    [Crossref]
  20. Z. Chen, M. Yan, T. W. Hänsch, and N. Picqué, “A phase-stable dual-comb interferometer,” Nat. Commun. 9(1), 3035 (2018).
    [Crossref]
  21. B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010).
    [Crossref]
  22. K. J. Mohler, B. J. Bohn, M. Yan, G. Mélen, T. W. Hänsch, and N. Picqué, “Dual-comb coherent Raman spectroscopy with lasers of 1-GHz pulse repetition frequency,” Opt. Lett. 42(2), 318 (2017).
    [Crossref]
  23. M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354(6312), 600–603 (2016).
    [Crossref]
  24. A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4(3), e1701858 (2018).
    [Crossref]
  25. M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
    [Crossref]
  26. D. A. Long, A. J. Fleisher, K. O. Douglass, S. E. Maxwell, K. Bielska, J. T. Hodges, and D. F. Plusquellic, “Multiheterodyne spectroscopy with optical frequency combs generated from a continuous-wave laser,” Opt. Lett. 39(9), 2688 (2014).
    [Crossref]
  27. G. Millot, S. Pitois, M. Yan, T. Hovhannisyan, A. Bendahmane, T. W. Hänsch, and N. Picqué, “Frequency-agile dual-comb spectroscopy,” Nat. Photonics 10(1), 27–30 (2016).
    [Crossref]
  28. A. Shams-Ansari, M. Yu, Z. Chen, C. Reimer, M. Zhang, N. Picqué, and M. Lončar, “An integrated lithium-niobate electro-optic platform for spectrally tailored dual-comb spectroscopy,” arXiv (2020).
  29. T. Ideguchi, T. Nakamura, Y. Kobayashi, and K. Goda, “Kerr-lens mode-locked bidirectional dual-comb ring laser for broadband dual-comb spectroscopy,” Optica 3(7), 748 (2016).
    [Crossref]
  30. K. Fritsch, J. Brons, M. Iandulskii, K. F. Mak, Z. Chen, N. Picqué, and O. Pronin, “Dual-comb thin-disk oscillator,” arXiv:2004.10303 (2020).
  31. N. Modsching, J. Drs, J. Fischer, S. Schilt, V. J. Wittwer, and T. Südmeyer, “Dual-Comb Thin-Disk Laser Oscillator Based on Polarization Splitting,” Conf. Lasers Electro-Optics, OSA Tech. Dig. (Optical Soc. Am. 2020), Pap. SF3H.2 (2020).
  32. J. Fellinger, A. S. Mayer, G. Winkler, W. Grosinger, G.-W. Truong, S. Droste, C. Li, C. M. Heyl, I. Hartl, and O. H. Heckl, “Tunable dual-comb from an all-polarization-maintaining single-cavity dual-color Yb:fiber laser,” Opt. Express 27(20), 28062 (2019).
    [Crossref]
  33. Y. Nakajima, Y. Hata, and K. Minoshima, “All-polarization-maintaining, polarization-multiplexed, dual-comb fiber laser with a nonlinear amplifying loop mirror,” Opt. Express 27(10), 14648 (2019).
    [Crossref]
  34. S. Mehravar, R. A. Norwood, N. Peyghambarian, and K. Kieu, “Real-time dual-comb spectroscopy with a free-running bidirectionally mode-locked fiber laser,” Appl. Phys. Lett. 108(23), 231104 (2016).
    [Crossref]
  35. X. Zhao, T. Li, Y. Liu, Q. Li, and Z. Zheng, “Polarization-multiplexed, dual-comb all-fiber mode-locked laser,” Photonics Res. 6(9), 853 (2018).
    [Crossref]
  36. X. Zhao, G. Hu, B. Zhao, C. Li, Y. Pan, Y. Liu, T. Yasui, and Z. Zheng, “Picometer-resolution dual-comb spectroscopy with a free-running fiber laser,” Opt. Express 24(19), 21833 (2016).
    [Crossref]
  37. R. Liao, Y. Song, W. Liu, H. Shi, L. Chai, and M. Hu, “Dual-comb spectroscopy with a single free-running thulium-doped fiber laser,” Opt. Express 26(8), 11046 (2018).
    [Crossref]
  38. J. Olson, Y. H. Ou, A. Azarm, and K. Kieu, “Bi-Directional Mode-Locked Thulium Fiber Laser as a Single-Cavity Dual-Comb Source,” IEEE Photonics Technol. Lett. 30(20), 1772–1775 (2018).
    [Crossref]
  39. S. M. Link, A. Klenner, M. Mangold, C. A. Zaugg, M. Golling, B. W. Tilma, and U. Keller, “Dual-comb modelocked laser,” Opt. Express 23(5), 5521 (2015).
    [Crossref]
  40. J. Nürnberg, C. G. E. Alfieri, Z. Chen, D. Waldburger, N. Picqué, and U. Keller, “An unstabilized femtosecond semiconductor laser for dual-comb spectroscopy of acetylene,” Opt. Express 27(3), 3190 (2019).
    [Crossref]
  41. R. Liao, H. Tian, W. Liu, R. Li, Y. Song, and M. Hu, “Dual-comb generation from a single laser source: principles and spectroscopic applications towards mid-IR – A Review,” J. Phys. Photonics (2020).
  42. S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356(6343), 1164–1168 (2017).
    [Crossref]
  43. G. Machinet, P. Sevillano, F. Guichard, R. Dubrasquet, P. Camy, J.-L. Doualan, R. Moncorgé, P. Georges, F. Druon, D. Descamps, and E. Cormier, “High-brightness fiber laser-pumped 68 fs–2.3 W Kerr-lens mode-locked Yb:CaF2 oscillator,” Opt. Lett. 38(20), 4008 (2013).
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  44. A. Klenner, M. Golling, and U. Keller, “High peak power gigahertz Yb:CALGO laser,” Opt. Express 22(10), 11884 (2014).
    [Crossref]
  45. L. M. Krüger, A. S. Mayer, Y. Okawachi, X. Ji, A. Klenner, A. R. Johnson, C. Langrock, M. M. Fejer, M. Lipson, A. L. Gaeta, V. J. Wittwer, T. Südmeyer, C. R. Phillips, and U. Keller, “Performance scaling of a 10-GHz solid-state laser enabling self-referenced CEO frequency detection without amplification,” Opt. Express 28(9), 12755 (2020).
    [Crossref]
  46. P. Wasylczyk, P. Wnuk, and C. Radzewicz, “Passively modelocked, diode-pumped Yb:KYW femtosecond oscillator with 1 GHz repetition rate,” Opt. Express 17(7), 5630 (2009).
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  47. T. C. Schratwieser, C. G. Leburn, and D. T. Reid, “Highly efficient 1 GHz repetition-frequency femtosecond Yb3+:KY(WO4)2 laser,” Opt. Lett. 37(6), 1133 (2012).
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  48. F. Brunner, G. J. Spühler, J. Aus der Au, L. Krainer, F. Morier-Genoud, R. Paschotta, N. Lichtenstein, S. Weiss, C. Harder, A. A. Lagatsky, A. Abdolvand, N. V. Kuleshov, and U. Keller, “Diode-pumped femtosecond Yb:KGd(WO4)2 laser with 1.1-W average power,” Opt. Lett. 25(15), 1119 (2000).
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  49. S. Pekarek, C. Fiebig, M. C. Stumpf, A. E. H. Oehler, K. Paschke, G. Erbert, T. Südmeyer, and U. Keller, “Diode-pumped gigahertz femtosecond Yb:KGW laser with a peak power of 3.9 kW,” Opt. Express 18(16), 16320 (2010).
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  50. A. Klenner, M. Golling, and U. Keller, “A gigahertz multimode-diode-pumped Yb:KGW enables a strong frequency comb offset beat signal,” Opt. Express 21(8), 10351 (2013).
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  51. F. Druon, S. Ricaud, D. N. Papadopoulos, A. Pellegrina, P. Camy, J. L. Doualan, R. Moncorgé, A. Courjaud, E. Mottay, and P. Georges, “On Yb:CaF2 and Yb:SrF2: review of spectroscopic and thermal properties and their impact on femtosecond and high power laser performance,” Opt. Mater. Express 1(3), 489 (2011).
    [Crossref]
  52. F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 540–556 (1996).
    [Crossref]
  53. C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16(1), 46 (1999).
    [Crossref]
  54. A. Klenner and U. Keller, “All-optical Q-switching limiter for high-power gigahertz modelocked diode-pumped solid-state lasers,” Opt. Express 23(7), 8532 (2015).
    [Crossref]
  55. A. S. Mayer, C. R. Phillips, and U. Keller, “Watt-level 10-gigahertz solid-state laser enabled by self-defocusing nonlinearities in an aperiodically poled crystal,” Nat. Commun. 8(1), 1673 (2017).
    [Crossref]
  56. S. M. Link, A. Klenner, and U. Keller, “Dual-comb modelocked lasers: semiconductor saturable absorber mirror decouples noise stabilization,” Opt. Express 24(3), 1889 (2016).
    [Crossref]
  57. G. Ghosh, “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals,” Opt. Commun. 163(1-3), 95 (1999).
    [Crossref]
  58. I. D. Jung, F. X. Kärtner, L. R. Brovelli, M. Kamp, and U. Keller, “Experimental verification of soliton mode locking using only a slow saturable absorber,” Opt. Lett. 20(18), 1892 (1995).
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  59. C. Li, N. Krauß, G. Schäfer, L. Ebner, O. Kliebisch, J. Schmidt, S. Winnerl, M. Hettich, and T. Dekorsy, “High-speed asynchronous optical sampling based on GHz Yb:KYW oscillators,” Opt. Express 25(8), 9204 (2017).
    [Crossref]
  60. P. Struszewski and M. Bieler, “Asynchronous Optical Sampling for Laser-Based Vector Network Analysis on Coplanar Waveguides,” IEEE Trans. Instrum. Meas. 68(6), 2295–2302 (2019).
    [Crossref]
  61. C. G. E. Alfieri, D. Waldburger, S. M. Link, E. Gini, M. Golling, G. Eisenstein, and U. Keller, “Optical efficiency and gain dynamics of modelocked semiconductor disk lasers,” Opt. Express 25(6), 6402 (2017).
    [Crossref]
  62. P. Langlois, M. Joschko, E. R. Thoen, E. M. Koontz, F. X. Kärtner, E. P. Ippen, and L. A. Kolodziejski, “High fluence ultrafast dynamics of semiconductor saturable absorber mirrors,” Appl. Phys. Lett. 75(24), 3841–3843 (1999).
    [Crossref]
  63. R. Fleischhaker, N. Krauß, F. Schättiger, and T. Dekorsy, “Consistent characterization of semiconductor saturable absorber mirrors with single-pulse and pump-probe spectroscopy,” Opt. Express 21(6), 6764 (2013).
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  64. D. Waldburger, S. M. Link, M. Mangold, C. G. E. Alfieri, E. Gini, M. Golling, B. W. Tilma, and U. Keller, “High-power 100 fs semiconductor disk lasers,” Optica 3(8), 844 (2016).
    [Crossref]
  65. P. Giaccari, J.-D. Deschênes, P. Saucier, J. Genest, and P. Tremblay, “Active Fourier-transform spectroscopy combining the direct RF beating of two fiber-based mode-locked lasers with a novel referencing method,” Opt. Express 16(6), 4347 (2008).
    [Crossref]
  66. J.-D. Deschênes, P. Giaccarri, and J. Genest, “Optical referencing technique with CW lasers as intermediate oscillators for continuous full delay range frequency comb interferometry,” Opt. Express 18(22), 23358 (2010).
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  67. T. Ideguchi, A. Poisson, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5(1), 3375 (2014).
    [Crossref]

2020 (1)

2019 (5)

2018 (10)

R. Liao, Y. Song, W. Liu, H. Shi, L. Chai, and M. Hu, “Dual-comb spectroscopy with a single free-running thulium-doped fiber laser,” Opt. Express 26(8), 11046 (2018).
[Crossref]

J. Olson, Y. H. Ou, A. Azarm, and K. Kieu, “Bi-Directional Mode-Locked Thulium Fiber Laser as a Single-Cavity Dual-Comb Source,” IEEE Photonics Technol. Lett. 30(20), 1772–1775 (2018).
[Crossref]

X. Zhao, T. Li, Y. Liu, Q. Li, and Z. Zheng, “Polarization-multiplexed, dual-comb all-fiber mode-locked laser,” Photonics Res. 6(9), 853 (2018).
[Crossref]

Z. Chen, M. Yan, T. W. Hänsch, and N. Picqué, “A phase-stable dual-comb interferometer,” Nat. Commun. 9(1), 3035 (2018).
[Crossref]

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4(3), e1701858 (2018).
[Crossref]

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref]

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

A. V. Muraviev, V. O. Smolski, Z. E. Loparo, and K. L. Vodopyanov, “Massively parallel sensing of trace molecules and their isotopologues with broadband subharmonic mid-infrared frequency combs,” Nat. Photonics 12(4), 209–214 (2018).
[Crossref]

M.-G. Suh and K. J. Vahala, “Soliton microcomb range measurement,” Science 359(6378), 884–887 (2018).
[Crossref]

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
[Crossref]

2017 (5)

2016 (8)

2015 (4)

S. Okubo, K. Iwakuni, H. Inaba, K. Hosaka, A. Onae, H. Sasada, and F.-L. Hong, “Ultra-broadband dual-comb spectroscopy across 1.0–1.9 µm,” Appl. Phys. Express 8(8), 082402 (2015).
[Crossref]

I. A. Finneran, J. T. Good, D. B. Holland, P. B. Carroll, M. A. Allodi, and G. A. Blake, “Decade-Spanning High-Precision Terahertz Frequency Comb,” Phys. Rev. Lett. 114(16), 163902 (2015).
[Crossref]

S. M. Link, A. Klenner, M. Mangold, C. A. Zaugg, M. Golling, B. W. Tilma, and U. Keller, “Dual-comb modelocked laser,” Opt. Express 23(5), 5521 (2015).
[Crossref]

A. Klenner and U. Keller, “All-optical Q-switching limiter for high-power gigahertz modelocked diode-pumped solid-state lasers,” Opt. Express 23(7), 8532 (2015).
[Crossref]

2014 (3)

2013 (3)

2012 (2)

2011 (1)

2010 (4)

2009 (1)

2008 (1)

2007 (1)

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78(3), 035107 (2007).
[Crossref]

2002 (1)

2000 (3)

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288(5466), 635–639 (2000).
[Crossref]

F. Brunner, G. J. Spühler, J. Aus der Au, L. Krainer, F. Morier-Genoud, R. Paschotta, N. Lichtenstein, S. Weiss, C. Harder, A. A. Lagatsky, A. Abdolvand, N. V. Kuleshov, and U. Keller, “Diode-pumped femtosecond Yb:KGd(WO4)2 laser with 1.1-W average power,” Opt. Lett. 25(15), 1119 (2000).
[Crossref]

1999 (4)

C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16(1), 46 (1999).
[Crossref]

P. Langlois, M. Joschko, E. R. Thoen, E. M. Koontz, F. X. Kärtner, E. P. Ippen, and L. A. Kolodziejski, “High fluence ultrafast dynamics of semiconductor saturable absorber mirrors,” Appl. Phys. Lett. 75(24), 3841–3843 (1999).
[Crossref]

G. Ghosh, “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals,” Opt. Commun. 163(1-3), 95 (1999).
[Crossref]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[Crossref]

1996 (1)

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 540–556 (1996).
[Crossref]

1995 (1)

1988 (1)

K. J. Weingarten, M. J. W. Rodwel, and D. M. Bloom, “Picosecond optical sampling of GaAs integrated circuits,” IEEE J. Quantum Electron. 24(2), 198–220 (1988).
[Crossref]

1987 (1)

1986 (1)

A. J. Taylor, R. S. Tucker, J. M. Wiesenfeld, C. A. Burrus, G. Eisenstein, J. R. Talman, and S. S. Pei, “Direct electro-optic sampling of a GaAs integrated circuit using a gain-switched InGaAsP injection laser,” Electron. Lett. 22(20), 1068 (1986).
[Crossref]

1982 (1)

J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Picosecond electro-optic sampling system,” Appl. Phys. Lett. 41(3), 211–212 (1982).
[Crossref]

Abdolvand, A.

Alfieri, C. G. E.

Allodi, M. A.

I. A. Finneran, J. T. Good, D. B. Holland, P. B. Carroll, M. A. Allodi, and G. A. Blake, “Decade-Spanning High-Precision Terahertz Frequency Comb,” Phys. Rev. Lett. 114(16), 163902 (2015).
[Crossref]

Apolonski, A.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref]

Aus der Au, J.

Azarm, A.

J. Olson, Y. H. Ou, A. Azarm, and K. Kieu, “Bi-Directional Mode-Locked Thulium Fiber Laser as a Single-Cavity Dual-Comb Source,” IEEE Photonics Technol. Lett. 30(20), 1772–1775 (2018).
[Crossref]

Bartels, A.

R. Gebs, G. Klatt, C. Janke, T. Dekorsy, and A. Bartels, “High-speed asynchronous optical sampling with sub-50fs time resolution,” Opt. Express 18(6), 5974 (2010).
[Crossref]

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78(3), 035107 (2007).
[Crossref]

Baumann, E.

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

A. M. Zolot, F. R. Giorgetta, E. Baumann, J. W. Nicholson, W. C. Swann, I. Coddington, and N. R. Newbury, “Direct-comb molecular spectroscopy with accurate, resolved comb teeth over 43 THz,” Opt. Lett. 37(4), 638 (2012).
[Crossref]

Bendahmane, A.

G. Millot, S. Pitois, M. Yan, T. Hovhannisyan, A. Bendahmane, T. W. Hänsch, and N. Picqué, “Frequency-agile dual-comb spectroscopy,” Nat. Photonics 10(1), 27–30 (2016).
[Crossref]

Bernhardt, B.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010).
[Crossref]

Bieler, M.

P. Struszewski and M. Bieler, “Asynchronous Optical Sampling for Laser-Based Vector Network Analysis on Coplanar Waveguides,” IEEE Trans. Instrum. Meas. 68(6), 2295–2302 (2019).
[Crossref]

Bielska, K.

Blake, G. A.

I. A. Finneran, J. T. Good, D. B. Holland, P. B. Carroll, M. A. Allodi, and G. A. Blake, “Decade-Spanning High-Precision Terahertz Frequency Comb,” Phys. Rev. Lett. 114(16), 163902 (2015).
[Crossref]

Bloom, D. M.

K. J. Weingarten, M. J. W. Rodwel, and D. M. Bloom, “Picosecond optical sampling of GaAs integrated circuits,” IEEE J. Quantum Electron. 24(2), 198–220 (1988).
[Crossref]

Bohn, B. J.

Brons, J.

K. Fritsch, J. Brons, M. Iandulskii, K. F. Mak, Z. Chen, N. Picqué, and O. Pronin, “Dual-comb thin-disk oscillator,” arXiv:2004.10303 (2020).

Brovelli, L. R.

Brunner, F.

Burrus, C. A.

A. J. Taylor, R. S. Tucker, J. M. Wiesenfeld, C. A. Burrus, G. Eisenstein, J. R. Talman, and S. S. Pei, “Direct electro-optic sampling of a GaAs integrated circuit using a gain-switched InGaAsP injection laser,” Electron. Lett. 22(20), 1068 (1986).
[Crossref]

Camy, P.

Cardenas, J.

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4(3), e1701858 (2018).
[Crossref]

Carroll, P. B.

I. A. Finneran, J. T. Good, D. B. Holland, P. B. Carroll, M. A. Allodi, and G. A. Blake, “Decade-Spanning High-Precision Terahertz Frequency Comb,” Phys. Rev. Lett. 114(16), 163902 (2015).
[Crossref]

Cerna, R.

A. Bartels, R. Cerna, C. Kistner, A. Thoma, F. Hudert, C. Janke, and T. Dekorsy, “Ultrafast time-domain spectroscopy based on high-speed asynchronous optical sampling,” Rev. Sci. Instrum. 78(3), 035107 (2007).
[Crossref]

Chai, L.

Chen, Z.

J. Nürnberg, C. G. E. Alfieri, Z. Chen, D. Waldburger, N. Picqué, and U. Keller, “An unstabilized femtosecond semiconductor laser for dual-comb spectroscopy of acetylene,” Opt. Express 27(3), 3190 (2019).
[Crossref]

Z. Chen, M. Yan, T. W. Hänsch, and N. Picqué, “A phase-stable dual-comb interferometer,” Nat. Commun. 9(1), 3035 (2018).
[Crossref]

K. Fritsch, J. Brons, M. Iandulskii, K. F. Mak, Z. Chen, N. Picqué, and O. Pronin, “Dual-comb thin-disk oscillator,” arXiv:2004.10303 (2020).

A. Shams-Ansari, M. Yu, Z. Chen, C. Reimer, M. Zhang, N. Picqué, and M. Lončar, “An integrated lithium-niobate electro-optic platform for spectrally tailored dual-comb spectroscopy,” arXiv (2020).

Coddington, I.

Cormier, E.

Courjaud, A.

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288(5466), 635–639 (2000).
[Crossref]

Dekorsy, T.

Descamps, D.

Deschênes, J.-D.

Diddams, S. A.

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288(5466), 635–639 (2000).
[Crossref]

Doualan, J. L.

Doualan, J.-L.

Douglass, K. O.

Droste, S.

Drs, J.

N. Modsching, J. Drs, J. Fischer, S. Schilt, V. J. Wittwer, and T. Südmeyer, “Dual-Comb Thin-Disk Laser Oscillator Based on Polarization Splitting,” Conf. Lasers Electro-Optics, OSA Tech. Dig. (Optical Soc. Am. 2020), Pap. SF3H.2 (2020).

Druon, F.

Dubrasquet, R.

Dunlop, A. E.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999).
[Crossref]

Dutt, A.

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4(3), e1701858 (2018).
[Crossref]

Ebner, L.

Eisenstein, G.

C. G. E. Alfieri, D. Waldburger, S. M. Link, E. Gini, M. Golling, G. Eisenstein, and U. Keller, “Optical efficiency and gain dynamics of modelocked semiconductor disk lasers,” Opt. Express 25(6), 6402 (2017).
[Crossref]

A. J. Taylor, R. S. Tucker, J. M. Wiesenfeld, C. A. Burrus, G. Eisenstein, J. R. Talman, and S. S. Pei, “Direct electro-optic sampling of a GaAs integrated circuit using a gain-switched InGaAsP injection laser,” Electron. Lett. 22(20), 1068 (1986).
[Crossref]

Elzinga, P. A.

Erbert, G.

Fejer, M. M.

Fellinger, J.

Fiebig, C.

Finneran, I. A.

I. A. Finneran, J. T. Good, D. B. Holland, P. B. Carroll, M. A. Allodi, and G. A. Blake, “Decade-Spanning High-Precision Terahertz Frequency Comb,” Phys. Rev. Lett. 114(16), 163902 (2015).
[Crossref]

Fischer, J.

N. Modsching, J. Drs, J. Fischer, S. Schilt, V. J. Wittwer, and T. Südmeyer, “Dual-Comb Thin-Disk Laser Oscillator Based on Polarization Splitting,” Conf. Lasers Electro-Optics, OSA Tech. Dig. (Optical Soc. Am. 2020), Pap. SF3H.2 (2020).

Fleischhaker, R.

Fleisher, A. J.

Freude, W.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359(6378), 887–891 (2018).
[Crossref]

Fritsch, K.

K. Fritsch, J. Brons, M. Iandulskii, K. F. Mak, Z. Chen, N. Picqué, and O. Pronin, “Dual-comb thin-disk oscillator,” arXiv:2004.10303 (2020).

Gabel, C. W.

J. A. Valdmanis, G. Mourou, and C. W. Gabel, “Picosecond electro-optic sampling system,” Appl. Phys. Lett. 41(3), 211–212 (1982).
[Crossref]

Gaeta, A. L.

L. M. Krüger, A. S. Mayer, Y. Okawachi, X. Ji, A. Klenner, A. R. Johnson, C. Langrock, M. M. Fejer, M. Lipson, A. L. Gaeta, V. J. Wittwer, T. Südmeyer, C. R. Phillips, and U. Keller, “Performance scaling of a 10-GHz solid-state laser enabling self-referenced CEO frequency detection without amplification,” Opt. Express 28(9), 12755 (2020).
[Crossref]

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref]

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4(3), e1701858 (2018).
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Zhang, M.

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Appl. Opt. (1)

Appl. Phys. B (1)

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J. Olson, Y. H. Ou, A. Azarm, and K. Kieu, “Bi-Directional Mode-Locked Thulium Fiber Laser as a Single-Cavity Dual-Comb Source,” IEEE Photonics Technol. Lett. 30(20), 1772–1775 (2018).
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P. Struszewski and M. Bieler, “Asynchronous Optical Sampling for Laser-Based Vector Network Analysis on Coplanar Waveguides,” IEEE Trans. Instrum. Meas. 68(6), 2295–2302 (2019).
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Nat. Commun. (4)

A. S. Mayer, C. R. Phillips, and U. Keller, “Watt-level 10-gigahertz solid-state laser enabled by self-defocusing nonlinearities in an aperiodically poled crystal,” Nat. Commun. 8(1), 1673 (2017).
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T. Ideguchi, A. Poisson, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5(1), 3375 (2014).
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Z. Chen, M. Yan, T. W. Hänsch, and N. Picqué, “A phase-stable dual-comb interferometer,” Nat. Commun. 9(1), 3035 (2018).
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Nat. Photonics (5)

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N. Picqué and T. W. Hänsch, “Frequency comb spectroscopy,” Nat. Photonics 13(3), 146–157 (2019).
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Opt. Commun. (1)

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Opt. Express (19)

C. Li, N. Krauß, G. Schäfer, L. Ebner, O. Kliebisch, J. Schmidt, S. Winnerl, M. Hettich, and T. Dekorsy, “High-speed asynchronous optical sampling based on GHz Yb:KYW oscillators,” Opt. Express 25(8), 9204 (2017).
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C. G. E. Alfieri, D. Waldburger, S. M. Link, E. Gini, M. Golling, G. Eisenstein, and U. Keller, “Optical efficiency and gain dynamics of modelocked semiconductor disk lasers,” Opt. Express 25(6), 6402 (2017).
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R. Fleischhaker, N. Krauß, F. Schättiger, and T. Dekorsy, “Consistent characterization of semiconductor saturable absorber mirrors with single-pulse and pump-probe spectroscopy,” Opt. Express 21(6), 6764 (2013).
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P. Giaccari, J.-D. Deschênes, P. Saucier, J. Genest, and P. Tremblay, “Active Fourier-transform spectroscopy combining the direct RF beating of two fiber-based mode-locked lasers with a novel referencing method,” Opt. Express 16(6), 4347 (2008).
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J.-D. Deschênes, P. Giaccarri, and J. Genest, “Optical referencing technique with CW lasers as intermediate oscillators for continuous full delay range frequency comb interferometry,” Opt. Express 18(22), 23358 (2010).
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S. M. Link, A. Klenner, and U. Keller, “Dual-comb modelocked lasers: semiconductor saturable absorber mirror decouples noise stabilization,” Opt. Express 24(3), 1889 (2016).
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A. Klenner and U. Keller, “All-optical Q-switching limiter for high-power gigahertz modelocked diode-pumped solid-state lasers,” Opt. Express 23(7), 8532 (2015).
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S. Pekarek, C. Fiebig, M. C. Stumpf, A. E. H. Oehler, K. Paschke, G. Erbert, T. Südmeyer, and U. Keller, “Diode-pumped gigahertz femtosecond Yb:KGW laser with a peak power of 3.9 kW,” Opt. Express 18(16), 16320 (2010).
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A. Klenner, M. Golling, and U. Keller, “A gigahertz multimode-diode-pumped Yb:KGW enables a strong frequency comb offset beat signal,” Opt. Express 21(8), 10351 (2013).
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S. M. Link, A. Klenner, M. Mangold, C. A. Zaugg, M. Golling, B. W. Tilma, and U. Keller, “Dual-comb modelocked laser,” Opt. Express 23(5), 5521 (2015).
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J. Nürnberg, C. G. E. Alfieri, Z. Chen, D. Waldburger, N. Picqué, and U. Keller, “An unstabilized femtosecond semiconductor laser for dual-comb spectroscopy of acetylene,” Opt. Express 27(3), 3190 (2019).
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A. Klenner, M. Golling, and U. Keller, “High peak power gigahertz Yb:CALGO laser,” Opt. Express 22(10), 11884 (2014).
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L. M. Krüger, A. S. Mayer, Y. Okawachi, X. Ji, A. Klenner, A. R. Johnson, C. Langrock, M. M. Fejer, M. Lipson, A. L. Gaeta, V. J. Wittwer, T. Südmeyer, C. R. Phillips, and U. Keller, “Performance scaling of a 10-GHz solid-state laser enabling self-referenced CEO frequency detection without amplification,” Opt. Express 28(9), 12755 (2020).
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P. Wasylczyk, P. Wnuk, and C. Radzewicz, “Passively modelocked, diode-pumped Yb:KYW femtosecond oscillator with 1 GHz repetition rate,” Opt. Express 17(7), 5630 (2009).
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R. Gebs, G. Klatt, C. Janke, T. Dekorsy, and A. Bartels, “High-speed asynchronous optical sampling with sub-50fs time resolution,” Opt. Express 18(6), 5974 (2010).
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X. Zhao, G. Hu, B. Zhao, C. Li, Y. Pan, Y. Liu, T. Yasui, and Z. Zheng, “Picometer-resolution dual-comb spectroscopy with a free-running fiber laser,” Opt. Express 24(19), 21833 (2016).
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R. Liao, Y. Song, W. Liu, H. Shi, L. Chai, and M. Hu, “Dual-comb spectroscopy with a single free-running thulium-doped fiber laser,” Opt. Express 26(8), 11046 (2018).
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J. Fellinger, A. S. Mayer, G. Winkler, W. Grosinger, G.-W. Truong, S. Droste, C. Li, C. M. Heyl, I. Hartl, and O. H. Heckl, “Tunable dual-comb from an all-polarization-maintaining single-cavity dual-color Yb:fiber laser,” Opt. Express 27(20), 28062 (2019).
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Y. Nakajima, Y. Hata, and K. Minoshima, “All-polarization-maintaining, polarization-multiplexed, dual-comb fiber laser with a nonlinear amplifying loop mirror,” Opt. Express 27(10), 14648 (2019).
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Opt. Lett. (8)

K. J. Mohler, B. J. Bohn, M. Yan, G. Mélen, T. W. Hänsch, and N. Picqué, “Dual-comb coherent Raman spectroscopy with lasers of 1-GHz pulse repetition frequency,” Opt. Lett. 42(2), 318 (2017).
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D. A. Long, A. J. Fleisher, K. O. Douglass, S. E. Maxwell, K. Bielska, J. T. Hodges, and D. F. Plusquellic, “Multiheterodyne spectroscopy with optical frequency combs generated from a continuous-wave laser,” Opt. Lett. 39(9), 2688 (2014).
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A. M. Zolot, F. R. Giorgetta, E. Baumann, J. W. Nicholson, W. C. Swann, I. Coddington, and N. R. Newbury, “Direct-comb molecular spectroscopy with accurate, resolved comb teeth over 43 THz,” Opt. Lett. 37(4), 638 (2012).
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Opt. Mater. Express (1)

Optica (3)

Photonics Res. (1)

X. Zhao, T. Li, Y. Liu, Q. Li, and Z. Zheng, “Polarization-multiplexed, dual-comb all-fiber mode-locked laser,” Photonics Res. 6(9), 853 (2018).
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A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
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Sci. Adv. (1)

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Science (5)

S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356(6343), 1164–1168 (2017).
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M.-G. Suh and K. J. Vahala, “Soliton microcomb range measurement,” Science 359(6378), 884–887 (2018).
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Other (4)

A. Shams-Ansari, M. Yu, Z. Chen, C. Reimer, M. Zhang, N. Picqué, and M. Lončar, “An integrated lithium-niobate electro-optic platform for spectrally tailored dual-comb spectroscopy,” arXiv (2020).

K. Fritsch, J. Brons, M. Iandulskii, K. F. Mak, Z. Chen, N. Picqué, and O. Pronin, “Dual-comb thin-disk oscillator,” arXiv:2004.10303 (2020).

N. Modsching, J. Drs, J. Fischer, S. Schilt, V. J. Wittwer, and T. Südmeyer, “Dual-Comb Thin-Disk Laser Oscillator Based on Polarization Splitting,” Conf. Lasers Electro-Optics, OSA Tech. Dig. (Optical Soc. Am. 2020), Pap. SF3H.2 (2020).

R. Liao, H. Tian, W. Liu, R. Li, Y. Song, and M. Hu, “Dual-comb generation from a single laser source: principles and spectroscopic applications towards mid-IR – A Review,” J. Phys. Photonics (2020).

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Figures (8)

Fig. 1.
Fig. 1. (a) Schematic of the laser cavity for simultaneous mode-locking operation of two combs 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 the output coupler (OC) and the laser beam is separated from the pump beam with a dichroic mirror (DM). (b) illustrates the splitting of the laser mode in the gain crystal and (c) the tuning of the repetition rate difference Δfrep by rotation of BF2. (d) shows the two spatially separated intracavity laser spots on the SESAM device.
Fig. 2.
Fig. 2. (a) Mode-locking performance for simultaneous operation of both combs. The indicated pump power is split equally between the two laser modes. (b) The laser operates in fundamental mode with beam quality M2 < 1.05 for both beams. The beam shape is recorded at the output of the oscillator (magnified image of the output coupler) on a WinCamD-LCM-NE 1” beam profiler at the nominal operation point of the laser with 3.7 A pump current, approx. 7.8 W total pump power and 440 mW average output power from each comb.
Fig. 3.
Fig. 3. Characterization of the laser performance in simultaneous dual-comb lasing at the nominal operation point (Ppump = 7.8 W): (a), (d) optical spectrum with sech2 fit indicating soliton pulses with optical spectrum of more than 6.5 nm FWHM bandwidth at a center wavelength of approx. 1050 nm. (b), (e) Autocorrelation trace with sech2 fit. (c), (f) RF traces of the two combs with a repetition rate of 137 MHz, each for a wide frequency range and zoomed to the frep-peak with a resolution bandwidth (RBW) of 300 Hz indicating clean fundamental mode-locking.
Fig. 4.
Fig. 4. (a) Asynchronous optical sampling (ASOPS) or equivalent time sampling setup of a sample in a reflective configuration. The trigger signal for the data acquisition is obtained by sum-frequency generation (SFG) between the two combs. L1 - 100 mm focal length lens, L2 - 25 mm focal length aspheric lens. PD1 - amplified photodiode (PDA55, Thorlabs Inc.), PD2 - amplified photodiode (PDA10D2, Thorlabs Inc.). HWP - half-wave plate, PBS - polarizing beam splitter. (b) Illustration of the ASOPS measurement technique using two pulse trains with slightly different repetition rates.
Fig. 5.
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 by the total acquisition window divided by the number of measured cross-terms. (b) Timing jitter distribution extracted from the SFG cross-correlation signals in a 10 second acquisition window.
Fig. 6.
Fig. 6. Asynchronous optical sampling (ASOPS) measurement of a semiconductor saturable absorber mirror (SESAM) at different pump average fluences. At pump average fluence larger than 423 μJ/cm2, there is a dip in the signal near t = 0, which is likely caused by two-photon absorption (TPA) (inset).
Fig. 7.
Fig. 7. Vertical external cavity surface emitting laser chip (VECSEL) pump-probe measurement at 149 μJ/cm2 pump average fluence. The structure was excited via two-photon absorption (TPA) of 1050 nm light.
Fig. 8.
Fig. 8. Relative coherence of the two dual-comb outputs. (a) Representative evolution of the instantaneous frequency shift between the two combs on a 100 ms timescale. (b) Corresponding spectrum of the beat-note between the two optical lines over the 100 ms integration time with a line width < 3.1 kHz (FWHM). The center frequency of the beat-note is 28.76 MHz.

Equations (2)

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Δ R ¯ ( t , F pump ) = R probe ( t , F probe , F pump ) R probe ( t , F probe , 0 ) R probe ( t , F probe , 0 ) ,
s j ( t ) = sin ( 2 π t ( ν j ( t ) ν cw ( t ) ) d t ) ,

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