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Abstract
We demonstrate a free-running single-cavity dual-comb optical parametric oscillator (OPO) pumped by a single-cavity dual-comb solid-state laser. The OPO ring cavity contains a single periodically-poled MgO-doped LiNbO3 (PPLN) crystal. Each idler beam has more than 245-mW average power at 3550 nm and 3579 nm center wavelengths (bandwidth 130 nm). The signal beams are simultaneously outcoupled with more than 220 mW per beam at 1499 nm and 1496 nm center wavelength. The nominal repetition rate is 80 MHz, while the repetition rate difference is tunable and set to 34 Hz. To evaluate the feasibility of using this type of source for dual-comb applications, we characterize the noise and coherence properties of the OPO signal beams. We find ultra-low relative intensity noise (RIN) below –158 dBc/Hz at offset frequencies above 1 MHz. A heterodyne beat note measurement with a continuous wave (cw) laser is performed to determine the linewidth of a radio-frequency (RF) comb line. We find a full-width half-maximum (FWHM) linewidth of around 400 Hz. Moreover, the interferometric measurement between the two signal beams reveals a surprising property: the center of the corresponding RF spectrum is always near zero frequency, even when tuning the pump repetition rate difference or the OPO cavity length. We explain this effect theoretically and discuss its implications for generating stable low-noise idler combs suitable for high-sensitivity mid-infrared dual-comb spectroscopy (DCS).
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical frequency combs (OFCs) [1–3] in the mid-IR open the door to spectroscopic measurements in the so-called molecular fingerprint region where various absorption bands of many molecules lie. Different types of light sources exist which emit in that specific wavelength region [4,5]. Among these, dual OFCs (or dual combs for short) are particularly compelling since they allow simultaneous down-conversion of all the optical comb lines to the radio-frequency (RF) domain. This allows measuring each individual line at high speed and without moving parts, thereby providing scalable acquisition speed and resolution [6,7].
Many of the dual-comb sources that have been developed operate in the short wavelength regime (< 2 µm) and are based on modelocked lasers. Typically, dual combs involve locking together a pair of separate modelocked-laser-based optical frequency combs. To reduce the complexity of such systems, solutions have recently been introduced in which both combs are generated in a single cavity. For example, our group demonstrated polarization multiplexing in a modelocked integrated external-cavity surface-emitting laser (MIXSEL) in 2015 [8] and more recently in solid-state lasers (SSLs) [9–12]. Single-cavity dual-comb laser sources are reviewed in [13]. Other work not covered in this review includes for example a different technique to polarization multiplex a dual-comb SSL and a high-power dual-comb thin-disk laser [14,15].
A lot of research efforts have targeted the development of dual-comb sources in the mid-IR, including quantum-cascade lasers [16], interband cascade lasers [17], microresonators [18], and difference-frequency generation sources based on modelocked lasers [19] or electro-optic combs [20]. In the short-wave infrared Cr2+-doped ZnS/ZnSe SSLs have also emerged as a versatile dual-comb source [21].
To access the mid-IR, a challenge with these near- and short-wave infrared laser sources is the required supercontinuum generation that is needed to cover an ultrabroad spectrum. Spectral broadening reduces the power per comb line and can introduce excess noise [22,23], which then implies longer integration times in order to achieve high sensitivity. This issue also applies to Fourier transform spectrometers based on mid- IR supercontinuum sources [24]. Accessing the mid-IR by synchronously-pumped optical parametric oscillators (OPOs) avoids this issue and offers flexible pulse parameters and a wide tuning range of the center wavelength enabled by the parametric process. Light can be generated throughout the entire phase-matching bandwidth and transparency window of materials exhibiting a ${\chi }$(2) nonlinearity [25]. It has been demonstrated that in the presence of intra-cavity dispersion a synchronously pumped OPO exhibits intensity noise comparable to its pump laser and even partly suppresses its timing jitter [26]. Thus, when pumped with low-noise SSLs [27–31], OPOs have the potential to achieve high average power, high power spectral density, low timing jitter, and shot-noise limited performance simultaneously. These features make OPOs promising candidates for dual-comb measurements when considering the trade-offs for achieving high sensitivity [32].
Yet, only highly complex systems for dual-comb OPO operation have been demonstrated. Some systems require two pump lasers and two OPO cavities [33,34]. One step towards reducing the overall system complexity has been undertaken by using a single OPO cavity, but still pumped by two individual lasers. In [35,36], the two combs are counter-propagating inside the OPO cavity and in [37,38], the two combs are co-propagating collinearly through one nonlinear crystal and are only distinguishable by the difference in the repetition rates of their respective pump lasers. In other work on multiplexing of OPO cavities, dual-wavelength operation has been shown [39–42], using either two crystals in different phase-matching configurations or techniques similar to those explored for modelocked lasers [43–45]; however, in this case all signal and idler beams share the same repetition rate, and as such they cannot be considered for dual-comb spectroscopy (DCS) or other equivalent time sampling applications.
Here, we demonstrate a free-running single-cavity dual-comb OPO pumped by a single-cavity dual-comb modelocked laser. To the best of our knowledge, this is the first time this configuration was demonstrated. The shared cavities, both in the modelocked laser and in the OPO, are especially compelling since fluctuations in cavity length seen by the two combs are strongly correlated, leading to high mutual coherence in free-running operation. The synchronously-pumped OPO is a singly-resonant ring cavity containing a single nonlinear crystal, and the two combs are counter-propagating. The two idler combs have average powers of 245 mW and 260 mW and center wavelengths of 3550 nm and 3579 nm, respectively. This represents a slightly higher average power idler generated from a mid-IR dual-comb OPO-based source compared to the results of [35]. The spectral bandwidth of more than 130 nm of each idler comb leads to a spectral overlap of about 80%. The repetition rate of the pump laser and the OPO are approximately 80 MHz, and the (tunable) repetition rate difference is set to 34 Hz. The repetition rate difference supported by the OPO is limited by a combination of the intra-cavity group delay dispersion (GDD) and the phase-matching bandwidth of the nonlinear crystal.
We perform detailed measurements of the noise and coherence properties of the dual-comb OPO. The OPO signal beams exhibit ultra-low RIN below –158 dBc/Hz at offset frequencies above 1 MHz. Moreover, by performing a heterodyne beat note measurement between the two signal combs, we observe that the center frequency of the corresponding RF spectrum remains near zero, even when changing the pump laser repetition rate frep, the repetition rate difference Δfrep, or the OPO cavity length. This behavior is in contrast to modelocked-laser-based dual combs, where the center of the RF spectrum can usually be rapidly tuned between 0 Hz and frep/2 via changes of Δfrep or the relative carrier envelope offset frequency ΔfCEO. By theoretically analyzing the tuning behavior of the comb lines with respect to pump cavity length fluctuations, we can attribute this unexpected finding to the fact that the two signal combs share the same cavity. In this context, we also find that the linewidth of the beat note between a comb line from each of the two signal combs has a full-width at half-maximum (FWHM) linewidth of only 400 Hz corresponding to a high mutual coherence of the two combs.
The proof-of-principle source demonstrated here combines the simplicity and passive stability of single-cavity dual-comb lasers with the power and wavelength flexibility of OPOs. As such and due to the relatively high average output power, this configuration represents a compelling approach for high-sensitivity free-running DCS in the near-IR or mid-IR spectral region.
The paper is structured as follows: Section 2 gives a detailed description of the experimental set-up of the OPO. In section 3, we present the performance of the OPO in terms of power, efficiency, and optical spectra. The noise and coherence properties of the signal beams of the OPO are examined in section 4 based on an intensity noise measurement, a dual-comb heterodyne measurement, and a measurement heterodyning the two combs with a cw laser. The results of the noise measurement and potential system improvements are discussed in section 5. The conclusion can be found in section 6. In the appendix we provide a detailed analysis of the tuning behaviour of an OPO comb line with cavity length fluctuations.
2. Experimental set-up
The presented dual-comb OPO is synchronously and collinearly pumped by the two output beams of a solid-state single-cavity dual-comb oscillator. This laser is based on the spatial multiplexing scheme as discussed in [12]. It uses Yb:CALGO as the gain medium, a semiconductor saturable absorber mirror (SESAM) for modelocking, and dispersion compensating mirrors for soliton formation. The two combs take a similar path in the cavity but are spatially separated on the output-coupler (OC), the gain medium and the SESAM to avoid cross-talk.
Fig. 1. Characterization of the free-running single-cavity dual-comb pump laser used in the experiment. (a) Optical spectrum at a central wavelength of 1053 nm and with a FWHM spectrum of 9.6 nm for comb 1 (blue) and 10 nm and comb 2 (red); resolution bandwidth (RBW): 0.08 nm Keysight-Agilent 70951A (diffraction grating-based spectrum analyzer). (b) Autocorrelation trace showing a FWHM pulse duration of 124 fs for comb 1 (blue) and 119 fs for comb 2 (red). (c) RF spectrum of the pump laser showing Δfrep = 34 Hz; RBW: 1 Hz.
The pump beams have an average power of 1.8 W at a center wavelength of 1053 nm, pulse durations of 124 fs (pump 1) and 119 fs (pump 2), and a FWHM optical bandwidth of 9.6 nm (pump 1) and 10.0 nm (pump 2). The corresponding diagnostics depicted in Fig. 1(a-b) show that the two pumps have almost identical characteristics. The repetition rate difference of the dual-comb pump laser is tunable and set to Δfrep = 34 Hz (Fig. 1(c)). The pump laser is free running, i.e. the repetition rate frep and the repetition rate difference Δfrep are not actively stabilized. Its repetition rate difference can be tuned up to 500 Hz without changing the laser performance.
The layout of the pumping scheme and our dual-comb OPO cavity is illustrated in Fig. 2(a). To avoid nonlinear coupling between the two OPO beams, the two pump beams, and therefore the signal beams which are resonant in the OPO ring-cavity, are counter-propagating in the nonlinear crystal. The OPO is singly-resonant for the signal beams with the fundamental mode evolution of the resonating beams being depicted in Fig. 2(b).
Fig. 2. (a) Schematic of the OPO cavity and its pumping. One of the flat mirrors is mounted on a translation stage to allow for coarse cavity length adjustment. With the UVFS wedge mounted on a translation stage the cavity length can be adjusted more precisely to optimize the synchronization between the OPO cavity and the pump repetition rate. The cavity consists of several dichroic mirrors shaded in red (details in Table 1). The output coupler (OC) has a transmission rate of 1.5% at the signal wavelength. Germanium (Ge) windows filter light < 1.9 µm. In between the laser cavity and the OPO cavity, isolators are installed on each pump path to avoid feedback into the pump laser. (b) Simulation of the evolution of the 1/e2 intensity beam radius w of the signal cavity mode, where the position of the nonlinear crystal is the start and end point of the ring cavity, and the curved optics are marked by red circles.
Table 1. Specifications of the labeled cavity mirrors from Fig. 1 and the PPLN crystal coating. Radius of curvature (ROC), reflectivity (R), fused silica (FS). For mirrors, “surface 1” in the table reflects the resonant beam of the OPO cavity.
The OPO is designed such that the two combs share all the optical elements of the cavity including the crystal, and thus any noise sources added by the OPO cavity are expected to be highly correlated. Both signal combs are p-polarized (type-0 phase-matching) to utilize the same nonlinear coefficient in the periodically-poled LiNbO3 (PPLN) crystal (d33). The crystal is 1-mm-long, 5 mol. % MgO doped, with a quasi-phase-matching (QPM) grating period of 29.98 µm (HC Photonics) and is operated at room temperature. It is anti-reflection (AR) coated on both facets (see Table 1 for details). The average power of both pump beams is 1.3 W at their respective cavity in-coupling mirrors. The power is reduced compared to the laser output due to losses in the beam routing, diagnostic pick-ups, and optical isolation. The measured pump 1/e2 beam radius at the position of the PPLN crystal is 45 µm, and the calculated mode radius for the signal cavity is 60 µm. The pump beam is intentionally smaller than the signal mode in order to ensure that almost all of the pump beam profile can be depleted by the larger and more intense signal beam inside the cavity. Experimentally, this spot size ratio was found by adjusting the focal pump spot position and size to optimize the efficiency of the OPO.
By considering the change of the center wavelength of the signal when the pump laser repetition rate is tuned, the total GDD experienced by the signal beam in the OPO cavity is estimated to be approximately –1000 fs2 (see Eq. (1) in section 3). We estimate GDD contributions of about +100 fs2 from the PPLN crystal, –20 fs2 from the Brewster plate, and +45 fs2 from the air path. The remaining GDD is likely from the coatings of the cavity mirrors.
With three beams at different center wavelengths involved, the constraints on the mirror coatings forming the OPO cavity become demanding and highly critical to its performance. The details of the mirrors M1-M6, as labeled in Fig. 2(a), are summarized in Table 1.
The idler beams are outcoupled via the dichroic mirrors M1-M3. To in-couple the pump beams, pump 1 is reflected by M1 and transmitted by M2, while pump 2 is transmitted by M6 and reflected by M3. The residual pump beams (after passing through the PPLN crystal) leave through the input path of the other pump. The signal beams are outcoupled at the mirror M4 with an output-coupling rate of 1.5% (for 1500 nm). The synchronicity of the signal cavity with the pump is obtained by scanning the OPO cavity length (total cavity length of about 3.74 m) with one flat mirror on a translation stage to an accuracy in the range of about 1 µm. The optimum cavity length, where the signal wavelength corresponds to the parametric gain peak in the PPLN crystal, is precisely adjusted by scanning the insertion of a UVFS wedge at Brewster angle into the signal beam path. For the diagnostics, the idler beams are collimated by uncoated CaF2 lenses and sent through AR-coated (1.9–6 µm) Germanium windows in order to filter out any residual pump, signal or other light generated by parasitic processes in the PPLN crystal.
3. Performance of the optical parametric oscillator
In this section, we present performance characteristics of the dual-comb OPO. All the data presented in the following is taken at the same nominal operation point. The spectra and noise measurements were taken while both combs were oscillating simultaneously. For the pump depletion and quantum efficiency measurements, the other comb had to be blocked during the measurement.
The OPO simultaneously delivers average idler powers of 245 mW (idler 1) and 260 mW (idler 2) after the Germanium windows and > 220 mW in each signal beam after the mirror M4, without correcting for any reflection losses. Figure 3 shows the signal and idler spectra. The signal beams (Fig. 3(a)) are at center wavelengths of 1499 nm and 1496 nm, with FWHM spectral bandwidth of 16.5 nm (2.2 THz) and 11.8 nm (1.6 THz). The idler beams (Fig. 3(b)) are at center wavelengths of 3550 nm and 3579 nm, with FWHM spectral bandwidth of 134 nm (3.2 THz) and 130 nm (3.0 THz). This corresponds to a spectral overlap of about 80%. Only the overlapping parts of the spectrum will contribute to a dual-comb signal.
Fig. 3. (a) Optical spectra of the signal combs; RBW: 0.08 nm Keysight-Agilent 70951A (diffraction grating based spectrum analyzer). The spectra for comb 1 (blue) and comb 2 (red) are recorded in the nominal OPO configuration used for all other measurements. The fringes arise from etalon effects in the PPLN crystal as discussed in the text. (b) Optical spectra of the idler combs; RBW: 0.12 nm Thorlabs OSA205 (Fourier transform based spectrum analyzer).
The signal and idler spectra have slightly different center wavelengths due to the different repetition rates of the two pump beams. This effect can be understood as follows. Since each signal beam must maintain synchronicity with the corresponding pump, they must have different round-trip times in the OPO cavity. Because the signal beams share exactly the same intracavity path, a different round-trip time requires a shift in center frequency, similar to the tuning characteristics of conventional synchronously-pumped OPOs. The difference in center frequency between the two signal beams can therefore be estimated via the intracavity GDD [26]:
The higher the GDD is, the less the center wavelength νc shifts to compensate for the repetition rate difference Δfrep. If frep becomes too large (here > 125 Hz), the center wavelengths of the two combs are too different to fit the phase-matching bandwidth of the PPLN crystal such that simultaneous oscillation of both combs is no longer supported.
In the spectra shown in Fig. 3, fringes are visible both in the signal and idler spectra having a periodicity of 0.5 nm and 2.5 nm, respectively. Considering the group indices of the PPLN crystal at these wavelengths, it suggests their origin is an etalon formed by the two crystal facets spaced by 1 mm. The reason for the strength of the signal fringes, higher than would be expected based on the reflectivity of the AR-coated crystal, is attributed to a resonant enhancement of the etalon effect. That is a coherent build-up of a post-pulse delayed by twice the crystal length. This effect could easily be suppressed by using a wedged or Brewster-cut crystal.
Next, we estimate the quantum efficiency of the idler generation. As the pump and idler power can only be measured outside of the cavity and not directly at the crystal, we account for transmission losses of the pump and idler beam paths to infer the efficiency of the parametric amplification process itself. The internal quantum efficiency, defined as the ratio of generated idler photons to the pump photons inside the PPLN crystal, is 78% (comb 1) and 84% (comb 2).
We define the pump depletion as:
Table 2. OPO performance and efficiency. The pump ratio indicates the number of times above oscillation threshold.
Note, that the difference in the performance of the two combs results from the fact that with Δfrep ≠ 0, as discussed above, their center wavelength will differ and thus it is not possible to tune both combs to their optimum gain configuration at the same time.
4. Noise and coherence properties of the OPO signal beams
In this section, we explore the suitability of the demonstrated single-cavity OPO architecture for DCS applications. Low RIN is beneficial for high-sensitivity DCS measurements, as quantified in [32]. SESAM-modelocked SSLs can achieve ultra-low noise performance at high (megahertz) frequencies where heterodyne DCS measurements take place [27]. Therefore, a motivating factor for our approach with OPOs is to pass this low-noise performance on to the longer-wavelength beams. To determine if the dual-comb OPO can preserve these characteristics, in the following subsections we study the relative intensity noise and coherence properties of the OPO signal beams. Although measurements of the idler would be interesting as well, for this study we focused on the signal beams since we lacked a suitable mid-IR detector able to reach a low noise floor for the idler wavelength range.
4.1. Relative intensity noise
The RIN of the OPO signal beams is characterized with baseband measurements on a signal source analyzer (SSA, Fig. 4). The SSA measures the noise on the photocurrent generated on an InGaAs photodiode. To achieve high sensitivity, we amplify the signals before the SSA as follows. We used a transimpedance amplifier to assess the low-frequency contributions below 100 kHz (in Fig. 4, the blue path). In contrast, for higher frequencies, we had to use a different approach due to the limited bandwidth of the transimpedance amplifier. We connected a bias tee to the photodetector to split the direct-current (DC) and alternating-current (AC) parts. The DC part is connected to a 50-Ω resistor and monitored with a voltmeter. The AC part is amplified with a voltage amplifier and subsequently analyzed with the SSA (in Fig. 4, the black path). The scheme using the bias tee cannot be used for low frequencies as its cut-off frequency lies at 20 kHz. The two measurements dedicated to the different frequencies are then stitched together resulting in a power spectral density (PSD) spanning from 100 Hz to 10 MHz.
Fig. 4. Baseband measurement of each OPO signal beam for the analysis of the intensity noise. Blue: the scheme for measuring noise at low frequencies. Black: the scheme for measuring noise at high frequencies. Both schemes use photodiode PD1, which is a modified Thorlabs Det10N2. TIA: transimpedance amplifier (FEMTO, DLPCA-200). BT: bias tee. VA: voltage amplifier (FEMTO, DUPVA-1-70). V: voltmeter. SSA: signal source analyzer (Keysight Technologies E5052B).
The RIN spectra of the OPO signal combs are shown in Fig. 5(a). At around –160 dBc/Hz we approach the noise floor inherent to this measurement. The noise floor was determined by blocking the optical input of the photodiode. In Fig. 5(b), we see the integrated RIN spectrum with the lower limit of the integration interval set to 100 Hz and the higher to 10 MHz. The measured RIN is lower than –158 dBc/Hz at 10 MHz, with a shot-noise limit of –166.5 dBc/Hz and –167.2 dBc/Hz. The integrated RIN is 0.02% (signal 1) and 0.025% (signal 2) when integrated from 100 Hz to 10 MHz.
Fig. 5. Intensity noise characterization of the single-cavity dual-comb OPO signal beams. (a) Baseband measurement of the RIN-PSD of each signal beam (blue and red), as well as the measurement noise floor, where the photodiode was blocked (black). (b) Integrated RIN-PSD with the integration interval from 100 Hz to 10 MHz.
4.2. Dual-comb heterodyne measurement
In this subsection, we analyze the heterodyne signal produced by mixing the two combs. The two signal beams are combined interferometrically on a beam splitter and then detected with an InGaAs photodiode. The resulting interferogram (IGM) trace exhibits peaks in time separated by 1/Δfrep that occur whenever two pulses are temporally overlapped at the beam splitter. A 1-s long trace is recorded with a fast oscilloscope, a portion of which is depicted in Fig. 6(a). The exact shape of the interferometric peaks depends on the relative phase between the two interfering combs. Figure 6(b) shows the Fourier transform of a 35-µs long time trace.
Fig. 6. (a) Exemplary IGMs (i.e. interferograms) in the time domain resulting from beating the two signal combs on a photodetector. (b) IGMs of a 35-µs long trace in the RF domain zoomed in to the MHz range.
For modelocked-laser-based dual-comb sources, including free-running dual-comb oscillators, the center of the RF spectrum can be varied between 0 Hz and frep/2 via changes of Δfrep or ΔfCEO. It is often set to approximately frep/4 to minimize the influence of aliasing in DCS [7]. However, when measuring the dual-comb interference between the two OPO signal beams, we made a surprising observation: instead of being easily tunable, the center of the RF spectrum was always fixed around zero frequency (see Fig. 6(b)). Neither changes of the OPO cavity length, nor the power of the pump diode pumping the SSL, nor mechanical perturbations, nor changes in the repetition rate difference of the SSL have shifted the position of the RF comb away from zero. This effect can be explained by considering how the optical comb line frequencies of the signal, denoted υm for a comb line index m, are affected by changes of the pump repetition rate frep. The rate of change of these frequencies, derived in the appendix, is given by:
where $2\pi \cdot {m_0} = \sum\nolimits_j {[{k_\textrm{j}}({\omega _\textrm{s}}){L_\textrm{j}}]}$ corresponds to the accumulated round-trip phase. Starting from a model case, where Δfrep = 0, such that the two signal combs are identical and hence all RF comb lines are at zero frequency. At the center of the optical spectrum, we then have m ≈ m0, and hence the tuning rate of this comb line with respect to the pump repetition rate almost vanishes. If we increase the repetition rate difference, the repetition rate of each comb will move symmetrically away from its initial value; for one comb the repetition rate increases for the other it decreases by the same amount. As a consequence, the center RF comb line for Δfrep = 0 stays the center comb line for Δfrep ≠ 0. Therefore, the RF comb remains centered near zero frequency when tuning the repetition rate or repetition rate difference of the pump. The full derivation is explained in detail in the appendix. When tuning the pump or OPO cavity length, both combs see an identical change as they share the same cavity, and hence this also does not shift the RF comb lines. Accordingly, none of the available degrees of freedom lead to a significant shift of the RF comb lines away from DC.4.3. Linewidth of the radio frequency comb lines
Because the radio frequency spectrum of the signal comb lines is so insensitive to system fluctuations, it might be expected that the RF comb lines are correspondingly stable. To evaluate this, we perform heterodyne measurements between the combs and a cw laser, similar to the approach of [46], as illustrated in Fig. 7.
Fig. 7. Beat note of the two combs with a cw lasers. cw: Toptica CTL 1550; PD2: Thorlabs DET08CFC; Lowpass filter (LPF): Mini-Circuits VLF-52 + and VLF-45+; Oscilloscope: Teledyne LeCroy WavePro 254HD.
Each comb was combined interferometrically with one cw laser at 1510 nm via beam splitters. We used two InGaAs photodiodes for heterodyne detection of the interference signals. The generated electronic beat note signals were then low-pass filtered close to the Nyquist frequency of frep/2 = 40 MHz and digitized simultaneously on a digital oscilloscope. The beat note frequencies of the cw laser with the adjacent optical comb line of each signal comb (1, 2) are given by:
As the cw laser frequency is canceled, we can apply another 200-kHz digital band-pass filter to the beat note to further isolate background noise. The measurement of those beat notes over a certain time span reveals how the dual-comb is affected by noise. The noise contribution of the third term in Eq. (6) can be neglected since the integer pre-factor (M-N) is in general much smaller than N and therefore its contribution is expected to be a lot less than the other noise contributions. In our case, this is justified as the multiplication factor |M - N| < 10 is small compared to N, which is approximately 2.48 × 106. If the linewidth of the cw laser is much narrower than the optical linewidth of the pulsed laser the latter can be directly inferred from Eq. (4) and (5).
Figure 8(a) depicts the linewidth of ydiff (t), found by taking the magnitude squared of the Fourier transform of a measurement for the OPO (green) over a time interval of 1 s and a sampling rate of 240 MHz. For comparison, we also show an equivalent measurement of the pump laser (blue). The OPO FWHM linewidth is 400 Hz, while the pump linewidth is about 2.1 kHz.
Fig. 8. (a) Linewidth of the beat note signal between a line from each signal comb. This is the magnitude squared of the Fourier transform of the measurement of ydiff (t) over a time span of 1 s. The bin size in the histogram is 100 Hz. The FWHM linewidth of the OPO (green) broadens to about 400 Hz and for the pump laser (blue) it broadens to about 2.1 kHz. (b) Frequency-noise power spectral density (FN-PSD) of fdiff (OPO in green, pump in blue) with the β-separation line (red). The grey shaded area is indicating at which frequencies the measurement is limited by the noise floor. (c) FWHM linewidth calculated according to [47], which includes contributions from FN-PSD components above the β-separation line leading to an integration interval from 1 Hz to 450 Hz for the OPO and 1 Hz to 700 Hz for the pump laser.
With the β-separation line formalism [47] applied to fdiff, we can identify the frequencies that are mainly causing the broadening. We calculate the frequency noise power-spectral density by [48–50]:
The factor of two indicates that we consider the one-sided power spectral density. Here, f is the offset frequency. In the frequency noise power-spectral density (FN-PSD), all noise contributions exceeding this geometrical line (Fig. 8(b), red):
are contributing to the linewidth broadening while the other frequencies are only affecting the wings of the spectrum. From the integrated FN-PSD in Fig. 8(c), we see that the main contributions to the linewidth broadening of the OPO (green) result from several noise peaks at a few hundred Hz. The pump linewidth (blue) has additional noise in the lower frequency range.5. Discussion of the noise and coherence properties
In this section, we discuss the implications of the noise and coherence properties for a potential application of the source for DCS in the mid-IR. Firstly, the RIN of the dual-comb OPO signal beams is as low as –158 dBc/Hz at MHz frequencies, which is attractive for high-sensitivity measurements. This helps validate the approach and shows how dual-comb OPOs can obtain noise performance comparable to modelocked solid-state lasers, which themselves achieve lower RIN than other types of modelocked lasers.
For spectroscopic measurements it is also necessary for the RF linewidth to be sufficiently narrow. The measured FWHM linewidth of 400 Hz (Fig. 8(a)) corresponds to high coherence for a free-running system using standard optical mounts on a breadboard setup. It is also significantly narrower than the pump RF linewidth (2.1 kHz), which indicates that some of the pump’s noise sources are suppressed in the OPO.
To put these measurements into perspective, we compare our OPO’s linewidth broadening to the noise performance of Er:fiber dual-comb sources which are also emitting in the signal spectral range in Table 3. We compare to Er:fiber lasers, because for free-running dual-comb OPOs no comparable results exist, besides a degenerate OPO pumped by two phase-locked lasers achieving a linewidth of 0.35 mHz over 43 s acquisition time [34]. Here, we see a difference in the coherence of the dual-comb signal by a factor of 100 between a two-cavity [51] and a single-cavity Er:fiber system [46]. Nevertheless, compared to our single-cavity OPO, the RF linewidth of the single-cavity Er:fiber dual comb over the same measurement time is still 4.0 times wider.
Table 3. FWHM linewidth broadening of the beating between two optical comb lines from Erbium:fiber (Er:fiber) dual-comb sources compared to our result of a single-cavity dual-comb OPO.
Nonetheless, to perform comb line resolved measurements without the aid of any additional continuous wave lasers to track the phase, the RF linewidth should be smaller than Δfrep when integrating the FN-PSD from high frequencies down to about Δfrep. This condition is not met in our case since Δfrep is very small (34 Hz). Although the individual RF comb lines cannot be resolved at the moment, realistic modifications to the system design could be implemented to improve the situation. As described by Eq. (1), with the use of mirrors adding more GDD to the cavity or an increase of the repetition rate, overlapping comb spectra can be obtained with higher Δfrep. For example, a repetition rate difference Δfrep = 1 kHz would be possible with GDD = –8000 fs2 and frep = 80 MHz, or with GDD = –2000 fs2 and frep = 160 MHz. For an increase of the repetition rate, the cavity design of the pump laser and the OPO needs to be modified. Yet, higher repetition rate systems for dual-comb modelocked lasers have been demonstrated a number of times [13], including results from our group [9–12]. For the multiplexing scheme in place here, an increase of the repetition rate itself already leads to a quadratic increase of the achievable repetition rate difference. Additionally, the linewidth could be reduced by upgrading the optomechanics from standard adjustable mounts on a breadboard to a more integrated optomechanical assembly. This would reduce the frequency noise contributions in the lower frequency range, and would likely damp the sharp peaks as seen in Fig. 8(b). Also, as the OPO partly inherits timing noise of the pump laser, the linewidth of the comb lines can also be reduced by upgrading the system to use a noise-optimized version of the pump laser.
For low-noise DCS measurements in the molecular fingerprint region, it is the idler beam that covers the spectrum of interest. The presented approach is sufficient to infer the idler noise performance, as well. We can determine if the OPO adds excess idler optical phase noise, since the idler phase is the difference between the pump and signal phases. Although the behavior of the idler intensity is more complicated, for small perturbations the nonlinear system can be linearized, yielding individual idler intensity fluctuations from pump and signal fluctuations. Hence, validating that the pump and signal noise are both small individually provides a strong indication that the idler is also low noise.
In the heterodyne interferometric measurement of the dual-comb signal beams we discovered that their RF spectrum remains close to the zero frequency which we attribute to the fact that they are sharing the same cavity. Having this information about the RF frequencies of the signal comb, it becomes possible to predict the RF frequencies of the idler comb while measuring the RF spectrum of the pump laser. The center frequency of the pump laser RF spectrum can be actively modified by changing Δfrep. With the idler RF spectrum being the difference of the signal and pump spectrum and the signal spectrum set to DC, the idler RF spectrum ends up being where the pump’s is, which is easily detectable and modifiable. For cases where the signal lines are to be used, the RF comb could be moved away from DC by, for example, modulating one of the signal combs with the help of an acousto-optic frequency shifter.
6. Conclusion and outlook
On the path towards a source suitable for simple yet highly sensitive DCS, we demonstrated a high-power dual-comb mid-IR singly-resonant synchronously pumped OPO which shows low-noise performance of the signal beams in free-running operation. It is the first dual-comb OPO from a single cavity being pumped by a single-cavity dual-comb pump laser. With > 245 mW in each of the two idler combs, we demonstrated a configuration with the highest power ever generated in a dual-comb OPO. In addition to the nominal laser characteristics, we systematically characterized the noise performance of the OPO signal beams. Note that the whole system, pump laser and OPO, is operated fully in free-running mode, with no stabilization of the power or repetition rates. The detected RIN at megahertz frequencies is as low as –158 dBc/Hz. In an interferometric measurement of the signal beams, we observed a novel property of our OPO system, being that the RF spectrum was pinned to around zero frequency. By considering the theoretical tuning characteristics of the OPO comb lines, this effect can be attributed to the symmetry the two combs experience in the single OPO cavity. Due to this advantageous system design where the two combs share the cavity in both the pump laser and the OPO, the beat note between a comb line from each of the two signal combs exhibits a FWHM linewidth of only 400 Hz.
Overall, our results, validating the low noise characteristics of the signal in terms of intensity and phase, show that a comb line resolved free-running system will be possible by moving to higher repetition rates. With narrower bandwidth to avoid aliasing while upgrading to a wavelength-tunable system (fan-out PPLN grating), DCS measurements across the 3-5 µm range would become possible. Similarly, with orientation patterned gallium phosphide or other advanced mid-infrared materials the same concept could be used to reach wavelengths beyond 10 µm.
Since low-noise and high-speed photodetectors are available within the signal wavelength range, one could also use those beams for DCS in the short-wave infrared, while profiting from the tunability of OPOs. This novel configuration of a dual-comb OPO, with the advantageous feature of a shared cavity both in the pump laser as well as in the OPO, already incorporates many properties for a compelling dual-comb spectroscopy source across the infrared. The remaining improvements on this path to achieve high-sensitivity comb-line-resolved measurements appear feasible to achieve in the near future.
7. Appendix
In our experiments, we discovered that the RF spectrum of the heterodyne beat signal between the two OPO signal combs stays centered around zero frequency, even when tuning the repetition rate difference of the pump or the length of the OPO cavity. To help explain this observation, in this appendix we consider how the RF comb lines change with respect to the repetition rate difference. The frequency of signal comb line m is given by:
The sensitivity of this line to the pump repetition rate ${f_{\textrm{rep}}}$ is given by:
First, we determine the rate of change of the signal center frequency ${\omega _\textrm{s}}$ with respect to frep, or equivalently with respect to the cavity length of the pump. Therefore we start from the fact that the OPO is synchronously pumped, which implies that the cavity round-trip time of the OPO signal pulses Tcav (ωs) equals the delay between subsequent pump pulses 1/frep:
The minus sign in this equation can be understood as follows. On each cavity round trip, the electric field envelope is multiplied by exp(-i${\phi}$CEO), assuming the convention exp[i(${\omega}$t-kz)]. The resulting rate of change of the phase with respect to time is hence –${\phi}$CEOfrep, which corresponds to 2πfCEO.
Next, consider how ${\phi}$CEO changes with respect to Lpump:
With Eq. (16), the derivative of fCEO with respect to frep is therefore given by:
Substituting ${\phi}$CEO into Eq. (18) and simplifying the partial derivative via the product rule yields:
The term m0 resembles a mode index. Therefore, we see that, for a comb line index m near the center of the optical spectrum, the tuning rate with respect to the pump repetition rate almost vanishes and the RF comb spectrum stays near zero frequency.
To better understand this effect, consider the limiting case where the repetition rate difference Δfrep → 0, such that the two signal combs are identical. Thus, the frequency of each RF comb line goes to zero. We can then look at the pair of comb lines closest to the center frequency of the optical spectrum and consider the influence of tuning the pump beams’ Δfrep away from 0. Assuming symmetric tuning, such that the change in frep of pump 1 is –Δfrep/2 and the change in frep of pump 2 is +Δfrep/2, we obtain:
Hence, the rate of change of the RF comb line $v_\textrm{m}^{\textrm{RF}} = \nu _m^{\textrm{comb-2}} - v_m^{\textrm{comb-1}}$ is negligible for indices m near m0, and so the RF spectrum stays near DC.
Moreover, via the change of the repetition rate the two signal combs experience an equal and opposite shift in center wavelength. Still, the effective center comb line pair stays the same since it stays mid-way between the two combs’ optical spectra. From Eq. (21) the tuning rate of this RF comb lines is nearly zero. Therefore, the corresponding RF comb line stays near 0 Hz even when tuning Δfrep. Since the “center” of the RF comb is near 0 Hz, positively and negatively detuned RF comb lines occupy the same set of frequencies, resulting in the aliasing behavior evident in Fig. 6.
Funding
Innosuisse - Schweizerische Agentur für Innovationsförderung (40B2-0_180933); Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (40B2-0_180933); European Research Council (966718).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper is available at ETH Zurich Research Collection library [52].
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