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Abstract
Mid-infrared frequency combs are nowadays well-appreciated sources for spectroscopy and frequency metrology. Here, a comprehensive approach for characterizing a difference-frequency-generated mid-infrared frequency comb (DFG-comb) both in the time and in the frequency domain is presented. An autocorrelation scheme exploiting mid-infrared two-photon detection is used for characterizing the pulse width and to verify the optimal compression of the generated pulses reaching a pulse duration (FWHM) as low as 196 fs. A second scheme based on mid-infrared heterodyne detection employing two independent narrow-linewidth quantum cascade lasers (QCLs) is used for frequency-narrowing the modes of the DFG-comb down to 9.4 kHz on a 5-ms timescale.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
Corrections
29 January 2024: A typographical correction was made to the funding.
1. Introduction
Since more than two decades, the optical frequency comb (FC) has emerged as the leading actor of frequency metrology [1–4]. It is able to define a precision ruler in the frequency domain thanks to its equally-spaced modes characterized by a well-defined phase relation. The possibility of referencing to the primary frequency standard allows to calibrate the frequency scale in an absolute manner. Visible/near-infrared FCs can be generated by means of controlled, frequency-stabilized mode-locked femtolasers [5–7]. They are well-established resources used in many technological and precision applications [8] such as dual-comb spectroscopy [9], atomic clocks [10], quantum technologies [11,12] and optical communication [13,14]. Another spectral region that can importantly benefit from the availability of high-precision measurement techniques based on FCs is the mid infrared (MIR). This is indeed also known as the molecular fingerprint region, where the strongest absorptions related to the ro-vibrational resonances of light molecules of environmental/atmospheric interest (such as water, carbon dioxide, methane, nitrogen oxides …) lie [15–22]. In the last decades, many FCs-based spectroscopy techniques have been developed in the MIR, both in the frequency domain (such as Fourier-transform spectroscopy [23–25] and dual-comb spectroscopy [26–30]) and in the time domain [31]. Techniques such as the two-dimensional infrared spectroscopy, who makes use of ultrashort mid-infrared pulses for exploring the structure and the dynamics of molecular systems in the condensed phase on very short time scales [32], and the pump-probe transient infrared absorption spectroscopy, able to investigate the formation, the persistence and the evolution of metastable structures in phase transitions [33], requires in fact short, well-formed and repeatable MIR pulses.
The generation of mid-to-far infrared FCs is possible via two different approaches. The first one consists in down-converting near-infrared FCs via difference-frequency generation (DFG) [34–38] or using synchronously-pumped optical parametric oscillators (OPOs) [39,40]. Conceptually, a DFG-based MIR FC (DFG-comb) is obtained by mixing a visible/near-infrared FC with a pump laser in a non-linear crystal, with matching wavelength requirement to reach the MIR [41–43]. The second approach consists in generating FCs directly in the MIR. Indeed, since 2012, broadband quantum cascade lasers (QCLs) [44–47] have proven to be able to directly generate FCs (QCL-combs) [48,49]. FC generation is triggered by the third-order non-linearity characterizing their active medium [50,51]. More recently, interband cascade lasers (ICLs) [52–56] also proved to be able to generate FCs [57–59]. Both QCLs and ICLs could be successfully exploited for dual-comb spectroscopy [27,29,60] and free-space communication [61,62]. In metrological experiments, where a stable and precise frequency ruler is required, the crucial steps in the application of FCs are narrowing their emission and controlling and stabilizing their parameters, i.e. the mode spacing and the frequency offset. Moreover, in time-domain experiments, it is important to control the pulse shape and width. In this framework, several characterization techniques have been exploited. Frequency-resolved optical gating (FROG) [63], spectral phase interferometry for direct electric-field reconstruction (SPIDER) [64,65] and asynchronous upconversion sampling (ASUPS) [66] have been developed and applied to measure the pulse duration (in the time domain). Fourier-transform analysis of comb emission (FACE) [67–69] and shifted-wave interference Fourier-transform spectroscopy (SWIFTS) [70,71] have been developed and applied to measure the phase relation (in the frequency domain). Due to technological limitations, only some of these techniques can be conveniently used in the MIR.
In this work, a comprehensive approach for the characterization of a DFG-comb, operating around a wavelength of 4.4 µm, both in the time and in the frequency domain is presented. An autocorrelation scheme exploiting MIR two-photon detection is used for characterizing the pulse width and to verify the optimal compression of the generated pulses. Two-photon detection is a very convenient – yet not so widespread – approach for measuring intensity correlation [72], particularly in the MIR, where second-harmonic-generation crystals are not as readily available as in visible and near-infrared spectral regions. Moreover, a second scheme based on MIR heterodyne detection employing two independent narrow-linewidth QCLs is used for frequency-narrowing the DFG-comb and measuring the mode linewidth.
2. Methods and discussion
2.1 DFG-comb generation setup
The setup used for generating the DFG-comb is depicted in Fig. 1. An Yb-doped mode-locked fiber laser emitting pulsed light centered around 1040 nm with a repetition rate of 250 MHz (Menlo Systems mod. orange [73,74]) is used as seed. The repetition rate can be tuned and stabilized via a piezoelectric actuator and an electro-optic modulator [75]. The seed radiation is amplified and then compressed down to a pulse full width at half maximum (FWHM) of 95 fs. A polarizing beam splitter (PBS) splits the high-power femtosecond pulse into two paths, the signal arm and the pump arm. In the signal arm, the pulse is coupled into a highly-nonlinear photonic crystal fiber (PCF) generating a signal around 1350 nm wavelength. The PCF is of self-drawn type to achieve best performance. In the pump arm, a motorized linear stage is installed for optimizing the temporal overlap between the signal pulse and the pump pulse. After the optimization, the stage was kept fixed during the measurements and no active stabilization was required. The two beams are then combined by a dichroic mirror and then focused into a 3-mm-long multiperiod periodically-poled lithium niobate (PPLN) crystal for the DFG. 1.9 W of pump power and 125 mW of signal power are available for the DFG. The output of the PPLN is finally filtered by means of an optical long-pass filter (LP-filter, transmission above 2.5-µm wavelength). The generated radiation is a pulsed MIR DFG-comb working around a wavelength of 4.4 µm with the specific crystal period used for these experiments. By changing the period, the central generated wavelength can be tuned from 3 to 5 µm. The generated DFG-comb can reach up to 300 mW of average power (at 4.4 µm) and inherits the repetition rate of the seeding laser.
Fig. 1. Scheme of the setup implemented to generate the DFG-comb. An Yb-doped mode-locked fiber laser emits pulsed light centered around 1040 nm with a repetition rate of 250 MHz [73,74]. The seed laser is amplified and then compressed. A half-wave plate ($\lambda /2$) and a polarizing beam splitter (PBS) are used to split the high-power femtosecond pulse into two paths, the signal arm and the pump arm. In the signal arm, the pulse is coupled into a highly-nonlinear photonic crystal fiber (PCF) generating a signal around 1350 nm wavelength. In the pump arm, a motorized linear stage is installed for optimizing the temporal overlap between the signal pulse and the pump pulse. The two beams are then combined by a dichroic mirror and then focused into a 3-mm-long multiperiod periodically-poled lithium niobate (PPLN) crystal for the DFG process. The output of the PPLN is finally filtered by means of an optical long-pass filter (LP-filter, transmission above 2.5-µm wavelength). The generated radiation is a pulsed MIR DFG-comb working around a wavelength of 4.4 µm, determined by the phase-matching conditions imposed by the specific crystal period used for these experiments.
Fig. 2. Left: Scheme of the setup implemented to characterize the DFG-comb emission in the time domain. The DFG-comb output radiation passes through a thin variable optical attenuator (OA) and through a set of optical (wedged or anti-reflection-coated) windows W$_1$ used to alter the pulse dispersion. Then, a beam splitter (BS, $\mathrm {BS_1}$, splitting ratio 90% reflection – 10% transmission) sends it to an optical spectrum analyzer (OSA) and to a Michelson interferometer (grey dashed area). In the interferometer, a 50/50 BS ($\mathrm {BS_2}$) splits the incoming light in two arms: a fixed arm where the light is reflected via a golden mirror ($\mathrm {M_f}$) after a free-space propagation of 13 cm, and a variable arm, where the light path is varied by means of a mirror mounted on a 2.2 cm-long moving stage. The average length of the latter arm is equal to the fixed one. $\mathrm {BS_2}$ is a MIR $\textrm{CaF}_{2}$ 5-mm-thick plate BS coated on one facet (asymmetric). Its substrate is crossed three times by the fixed-arm beam and only once by the other (due to the refractive index unbalancing the refraction angle within the substrate is negligible). For compensating, a $\textrm{CaF}_{2}$ wedged window W$_2$ of the same material and thickness has been placed in front of the moving stage. The interferometer output is sent by means of another BS ($\mathrm {BS_3}$) to a detection system made of two different detectors: a fast $\textrm{HgCdTe}$ (MCT) detector ($\mathrm {D_M}$) and an InGaAs detector ($\mathrm {D_{In}}$). The detectors are reached after a free-space path in air of 3.0-m length.
Right: DFG-comb spectrum acquired with the OSA. The OSA resolution is 6 GHz. The FWHM of the spectrum is about 3 THz. The maximum is reached at 68 THz corresponding to $\lambda = {4.4}\;\mathrm{\mu}\textrm{m}$. The green dashed line evidences the effect of $\textrm{CO}_{2}$ absorption.
2.2 DFG-comb characterization setup
2.2.1 Pulse characterization and compression
For characterizing the DFG-comb emission in the time domain, an autocorrelation setup based on a Michelson interferometer was used (see Fig. 2-left). The 4.4-µm DFG-comb output beam propagates through a thin variable optical attenuator (OA) and through a set of optical windows (W$_1$ in Fig. 2-left) used to alter the pulse width. Then, a beam splitter (BS, $\mathrm {BS_1}$ in Fig. 2-left) sends it to an optical spectrum analyzer (OSA) and to a Michelson interferometer (grey dashed area). The spectrum of the DFG-comb acquired with the OSA is shown in Fig. 2-right. In the interferometer, the incoming light is split in the two arms by means of a 50/50 BS ($\mathrm {BS_2}$). In the fixed arm the light is reflected by a gold mirror after a free-space propagation of 13 cm. In the variable arm, the light path is varied by means of a mirror mounted on a 2.2-cm-long moving stage. An additional window W$_2$ has been placed in this arm with the aim of compensating the dispersion effects of the plate (asymmetric) BS ($\mathrm {BS_2}$). The average length of the latter arm is equal to the fixed one. The interferometer output is sent by means of another BS ($\mathrm {BS_3}$) to a detection system made of two different detectors: a fast $\textrm{HgCdTe}$ (MCT) detector ($\mathrm {D_M}$) and an InGaAs detector ($\mathrm {D_{In}}$). The fast MCT detector is an AC-coupled MIR photovoltaic detector (PVI-4TE-5-2x2 equipped with a MIP-10-250M-M4 preamplifier, both by Vigo System) used in the linear-response regime (one-photon absorption regime). The detector, working in the spectral region between 2 µm and 5 µm with a nominal bandwidth of 250 MHz, has been fully characterized in [76]. The InGaAs detector (FD05D from Thorlabs) is a photovoltaic detector engineered to have a linear response in the spectral region between 900 nm and 2600 nm. In our experiment it is used in the quadratic-response regime, i.e. in the two-photon absorption regime [77]. A comprehensive characterization of its two-photon detection operation can be found in Supplement 1. The adopted detection scheme allows to measure simultaneously the first-order and the second-order autocorrelations of the DFG-comb emission (see Fig. 3). The MCT detector provides the first-order autocorrelation, while the InGaAs the second-order one. The amount of group velocity dispersion (GVD) experienced by the pulses has been varied by modifying the set of optical windows (W$_1$ in Fig. 2-left). PPLN and $\textrm{CaF}_{2}$ have negative GVD while $\textrm{Ge}$ has positive GVD, therefore some Ge windows have been used for compensating the dispersion. In Fig. 3 the interferograms related to the shortest measured pulse are reported, obtained with two 5.0-mm-thick $\textrm{Ge}$ windows plus one 1.0-mm-thick $\textrm{Ge}$ window. The time scale has been calibrated by referring to the spectrum acquired with the OSA (Fig. 2-right): The carrier frequency has been assumed to be the one corresponding to the maximum of the spectrum acquired with the OSA. The first-order autocorrelation interferogram (blue curve) has been used to calculate the root mean square of the signal (RMS, yellow curve in Fig. 3), and it has been fitted to a Gaussian function (green curve), retrieving a pulse FWHM of 162 fs (the obtained FWHM must be divided by 2 since the sliding of the two replicas of the pulse created by the interferometer generates with the linear-responding detector an interferogram with a FWHM that is twice the pulse’s one [78]), which is the transform-limited pulse width in the Gaussian-shape approximation, that is always adopted in this article. From the second-order autocorrelation interferogram, the temporal intensity profile of the pulse (blue line) has been computed, obtaining a pulse FWHM of 196 fs (the autocorrelation FWHM must be divided by $\sqrt {2}$ since the sliding of the two replicas of the pulse generates with the quadratic-responding detector an interferogram with a FWHM that is $\sqrt {2}$ times the pulse’s one [78]), which is the actual pulse width. The second-order autocorrelation fit performed using the second-order autocorrelation function (yellow curve) is consistent with the interferogram (red curve). By computing the fast Fourier transform (FFT) of the interferograms, the related spectra are retrieved (see Fig. 4). From both the first-order and the second-order interferograms, a FWHM of 2.7–2.8 THz ($\Delta \nu _1$) is obtained. From the spectra it is possible to estimate the transform-limited width of the pulses according to the following equation [78]:
The obtained result is well in agreement with the value measured from the first-order interferogram. The DFG process takes place within a 3.0-mm-long PPLN crystal. The expected bandwidth of the generated radiation can be estimated from the following equation (obtained for simplicity with the sinc-shape approximation, see Supplement 1):
Fig. 3. Top: First-order autocorrelation interferogram (blue curve) acquired with the MCT detector. The RMS pulse shape is retrieved (yellow curve) and fitted to a Gaussian function (green curve). The measured FWHM is 323.3 fs.
Bottom: Second-order autocorrelation interferogram (red curve). The signal has been acquired with the InGaAs detector and normalized to the background (corresponding to the signal out of the interfering zone). The incident power has been accurately tuned with the optical attenuator (OA in Fig. 2-left) in order to optimally exploit the quadratic-response range (see Supplement 1). The ratio between the background and the maximum is smaller than the ideal value of 8. The interferogram has been fitted to the second-order autocorrelation function (yellow curve). The calculated pulse intensity profile (blue curve) is fitted to a Gaussian function (green curve), obtaining a FWHM of 277.2 fs.
In order to perform a proper optimization (minimization) of the pulse duration, different known optical windows (W$_1$ in Fig. 2-left) have been placed on the beam path. In this way, the amount of group delay dispersion (GDD) experienced by the pulses has been varied and the corresponding pulse width has been recorded (see Fig. 5). We observe that for all the acquisitions the first-order width is not affected by the dispersion (as expected), the transform-limited width is $\Delta t_{t} \simeq {163}\;\textrm{fs}$. By knowing the optical materials and the thickness of the optical windows (W$_1$) it is possible to represent the pulse width obtained from the second-order autocorrelation as a function of the GDD. The data have been fitted to the theoretical curve assuming the pulse width obtained from the first-order autocorrelation as the original width ($\Delta t_{t}$) and adding a term accounting for the third-order dispersion ($\mathrm {GDD}_3$) which cannot be compensated with the optical windows. The pulse FWHM obtained from the second-order autocorrelation is [78]:
Fig. 4. Spectra obtained from the first-order interferogram (blue curve) and from the second order one (green curve) via Fourier transform (see Fig. 3). The related Gaussian fit curves are also plotted. The two side lobes are probably Fourier transform artifacts. They are in fact not present in the spectrum acquired with the OSA represented in Fig. 2-right.
Here $\Delta t_{t}$ is the transform-limited pulse FWHM. As shown in Fig. 5, there is a good agreement between the fit function and the experimental data. The third-order dispersion term accounts for the mismatch between the first-order autocorrelation width and the minimum second-order autocorrelation width. The set of optical elements and the related values of GVD and thickness used for computing the GDD are listed in Supplement 1.
Fig. 5. Pulse width obtained from the second-order autocorrelation as a function of the GDD. The GDD has been varied by placing different optical windows on the beam path (W$_1$ in Fig. 2-left). The horizontal dashed green line indicates the transform-limited width of the pulses ($\Delta t_{t}$). The data has been fitted to the function in Eq. (3).
2.2.2 DFG-comb mode linewidth measurement and narrowing
For the DFG-comb mode linewidth measurement and narrowing, the experimental setup shown in Fig. 6 has been used. The single-tooth linewidth of the DFG-comb has been measured by heterodyning it with a narrow-linewidth single-mode QCL (locked to an external $\textrm{CaF}_{2}$ toroidal microresonator via a modulation locking scheme [82,83], ensuring a linewidth of 10 kHz on a 1-s timescale, QCL 2 in Fig. 6). The beat note between QCL 2 and the DFG-comb operating in free-running conditions is shown in Fig. 7-left. The linewidth (FWHM of the related Gaussian fit) is 84 kHz on a 5-ms timescale. In DFG-combs generated starting from a single pump FC, the offset frequency vanishes since it is automatically cancelled out in the DFG process. As a consequence, this degree of freedom does not contribute to the frequency noise, that is therefore only due to repetition-rate instabilities. In order to stabilize the DFG-comb repetition rate, two approaches are generally available. The first one consists in locking it to a stable radio-frequency local oscillator, while the second one relies on an optical stabilization where a FC mode is locked to a stable single-mode laser. By locking the DFG-comb repetition rate to the internal clock (Stanford Research Systems mod. FS725, rubidium frequency standard) no significant narrowing can be observed on the beat note as the locking bandwidth is insufficient to alter the linewidth. Therefore, we have locked it to another narrow-linewidth single-mode QCL (QCL 1 in Fig. 6, locked to an external high-finesse optical cavity via the Pound-Drever-Hall locking scheme [81], ensuring a linewidth of 9 kHz on a 5-ms timescale [84]). The beat note between QCL 2 and the DFG-comb operating in locking conditions is shown in Fig. 7-right. Supposed to equally share the residual linewidth between the two sources, a linewidth of FWHM/$\sqrt {2}$ = 9.4 kHz can be attributed to the DFG-comb tooth (assuming a Gaussian lineshape). On the other hand, the FWHM measured in free-running conditions can be fully attributed to the DFG-comb: the QCL linewidth contributes negligibly since the two linewidths add quadratically.
Fig. 6. Scheme of the setup used to measure the mode linewidth of the DFG-comb. The DGF-comb is locked to a single-mode QCL, QCL 1, locked to an external high-finesse cavity via the Pound-Drever-Hall locking scheme [81]. The DFG-comb is then beaten with a second single-mode QCL, QCL 2, locked to an external $\textrm{CaF}_{2}$ toroidal microresonator via a modulation locking scheme [82,83]. The microresonator is characterized by $Q \approx 2.2 \cdot 10^7$ and $FSR = {18.9}\;\textrm{GHz}$ at the operating wavelength. The beat-note signal is acquired via a fast detector (MCT, D$_1$) and a spectrum analyzer.
Fig. 7. Left: Beat note between the narrow-linewidth QCL (QCL 2 in Fig. 6) with the DFG-comb operating in free-running conditions.
Right: Beat note between the narrow-linewidth QCL (QCL 2) and the DFG-comb operating in locking conditions.
The sidebands 4-MHz-far from the carrier are due to the modulation locking of QCL 2 to the microresonator.
In the insets, a zoom of the related beat-note peaks with the corresponding Gaussian fits are shown.
3. Conclusion
In this work, a comprehensive characterization of a DFG-comb has been performed by using both a time-domain and a frequency-domain analysis approach. An autocorrelation scheme exploiting MIR two-photon detection has been used for characterizing the pulse width and to verify the optimal compression of the generated pulses. A pulse duration (FWHM) as low as 196 fs has been obtained. A heterodyne detection and locking scheme employing two independent narrow-linewidth QCLs has been used for frequency-narrowing the DFG-comb and measuring the mode linewidth, obtaining a value of 9.4 kHz on a 5-ms timescale. In conclusion, the characterized DFG-comb proved to be suitable to be applied both in advanced spectroscopy/frequency-metrology experiments and in time-resolved experiments such as transient absorption spectroscopy [85], providing high resolution and accuracy in a very intriguing spectral region such as the MIR.
Funding
European Union NextGenerationEU – I-PHOQS Infrastructure (IR0000016ID D2B8D520, CUP B53C22001750006); QuantERA II (101017733 - QATACOMB Project); Horizon Europe Framework Programme (101070546 - MUQUABIS Project, 87114 - Laserlab-Europe Project ); Horizon 2020 Framework Programme (820419 - Qombs Project); Italian ESFRI Roadmap (Extreme Light Infrastructure – ELI Project); Fondazione Cassa di Risparmio di Firenze (SALUS Project).
Acknowledgments
The authors gratefully thank Mauro Giuntini, Roberto Concas and Paolo Foggi for useful discussions.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are available in Ref. [86].
Supplemental document
See Supplement 1 for supporting content.
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