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Abstract
In this article, we demonstrate a dual frequency comb (DFC) based on the gain-switching of mutually injection-locked semiconductor lasers in the 2 μm wavelength region with a tunable free spectral range (FSR) between 500 MHz and 3 GHz. Through the down-conversion process enabled by DFCs, the beating spectra of the optical frequency combs were captured in a 15 MHz electrical bandwidth with high resolution and millisecond acquisition times. A first experimental demonstration of sensing CO2 with this architecture is also presented.
Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. Introduction
Optical frequency combs (OFCs) have become a widespread technology used in a variety of applications, including coherent optical communications [1,2], metrology [3], optical clocks [4], distance ranging [5] and optical sensing [6,7]. Optical sensing, particularly absorption spectroscopy, could benefit greatly from improvements to OFC technologies. OFCs offer a method for high-resolution sensing of multiple absorption peaks using a single source, offering greater selectivity than their single-mode equivalents [8]. Although optical combs enable high-resolution sensing with improved selectivity, the key factors limiting their wide implementation outside of a laboratory setting are the cost, size and complexity of the optical components required [9]. Gain-switched semiconductor laser diodes are a promising option for small scale low complexity OFC generation, with the potential for photonic integration [10–12]. Gain switching is the process of directly modulating a laser source to produce a pulsed output induced by the nonlinear response of the laser carriers [13]. In the case where pulse-to-pulse coherence is maintained, these modulated sources can be used for OFC generation [14]. Gain switching has the benefit of being low complexity and is also a tunable approach to OFC generation, where the selected modulation frequency can be varied. This allows combs with a variety of free spectral ranges (FSRs) to be generated by a single source. The majority of research on this technology has been focused on communications applications in the 1.55 $\mu$m wavelength region, but recent demonstrations have shown the potential to use these technologies in the 2 $\mu$m wavelength range [15]. This would enable applications focused on optical sensing of key gases like CO$_2$, NH$_3$ and water vapour [16–18]. For spectroscopic applications, direct detection of optical frequency combs can be time-consuming and resolution limited. A recently popularised approach used to overcome this issue is the dual-frequency comb (DFC) [19–23]. DFCs use the heterodyne beating spectrum generated by two frequency combs of slightly offset FSRs to down-convert the optical spectrum to the electrical domain. By minimising the frequency offset between the two OFCs, the amplitude information of the optical spectrum can be detected in the electrical domain with high resolution and near real-time acquisition rates [24]. This article demonstrates a tunable dual frequency comb based on mutually injection-locked gain-switched lasers operating around 2 $\mu$m. The spectral range accessed by this DFC would enable sensing of key gases CO$_2$, NH$_3$ and H$_2$O with high resolution and millisecond acquisition times. We also explore the causes of aliasing in this architecture and how they affect the functionality of the DFC. As a proof of concept, we demonstrate the detection of CO$_2$ for a range of concentrations and pressures, utilizing the proposed DFC operating at around 2 $\mu$m.
2. Experiment
Dual frequency combs take advantage of the interference pattern generated by two OFCs incident on a photodetector to down-convert large bandwidth optical spectra to the electrical domain. This way the spectral heterodyne beating tones can be detected in a fraction of the time taken to detect the full optical spectrum. Figure 1(d) shows the down-conversion process that takes place between two OFCs in a DFC configuration. Two OFCs are generated with repetition frequency $f_1$ and $f_2$, where $f_2 = f_1+\Delta f$ and $\Delta f$ is the selected difference in repetition rates. When these optical spectra are incident on a photodetector, beat tones are generated at frequencies corresponding to multiples of $\Delta f$. These beat tones contain the amplitude information of the comb line pairs that generated them, allowing for variations in the optical spectrum amplitude to be seen in the electrical spectrum. As $\Delta f$ can be selected to be very small, the optical frequency combs can be compressed into a very small electrical frequency range enabling rapid spectrum acquisition.
Fig. 1. Experimental setup for dual frequency comb generation with (a) a continuous wave primary laser injection-locking two pulsed discrete mode laser sources (b) and (c) which generate a mutually coherent dual frequency comb; (d) Shows the dual frequency comb spectrum and the down-conversion of this spectrum to the electrical domain.
Figure 1(a)-(c) shows the experimental setup used for the generation of a mutually injection-locked dual-frequency comb. In this setup, two discrete mode multiple quantum well lasers, based on a strained InGaAs on InP architecture developed by Eblana Photonics, were biased away from the laser threshold and directly modulated using an RF source [25]. The laser threshold currents were approximately 20 mA and both comb source lasers were biased at 40 mA. The modulation signal consisted of an amplified sine wave whose frequency and amplitude were varied to enable different OFC FSRs. The RF sources were synchronised through a 10 MHz reference. Polarisation controllers were used to maintain parallel polarisation between the two OFC generators. This is required to maximise the amplitude of the heterodyne beat tones generated when down-converting to the electrical domain. The two OFC generating sources were mutually injection-locked using a primary laser, as shown in Fig. 1(a). This is required to phase lock the OFCs to a common source and to prevent loss of pulse-to-pulse coherence when modulating the OFC sources below the lasing threshold. The primary laser was an EP2004 Discrete-Mode laser source, also developed by Eblana Photonics. Phase locking of OFCs is not always required in DFC applications, but is a requirement when working with low FSR OFCs, as is the case here. Injection locking OFCs in a DFC setup allows for the generation of a down-converted spectrum with very low beat tone linewidths. This prevents interference between beat tone lines when compressed into a narrow electrical frequency bandwidth [15]. The DFC optical signal was amplified using a Thulium-doped fibre amplifier (TDFA) that was tailored for long wavelength amplification [26]. An adjustable optical filter with a bandwidth of 3 nm was used to remove excess amplified spontaneous emission produced by the TDFA, protecting photodetector (EOT ET-5000) from optical saturation. The DFC was analysed in the optical domain using a Yokogawa long wavelength spectrum analyser (AQ6375B) with 6 GHz resolution. The low resolution of the OSA prevented analysis of the comb lines in the optical domain but enabled analysis of the general comb profile. The DFC was analysed in the electrical domain with an Agilent E4407b ESA and Keysight 86100D Infiniium DCA-X Wide-Bandwidth Oscilloscope.
3. Results
With DFCs it is essential to understand potential aliasing that may occur in the down-converted electrical spectrum. Aliasing occurs when there is more than one comb line pair generating a beating tone at the same frequency. In this scenario, a change in amplitude of a beating tone is not representative of a change in amplitude of one comb line of a specific wavelength. This leads to many problems when it comes to spectroscopic application. In DFCs there are two primary causes of beat tone aliasing. Firstly, aliasing can occur when the value of $\Delta f$ is too large, causing overlapping of the $\Delta f$ and $f_1-\Delta f$ beating tone spectra. This is referred to as the overlapping of the Nyquist zones. Avoiding this source of aliasing requires that $\Delta f$ satisfies Eqn. (1);
where $V_{opt}$ is the comb optical bandwidth. This is equivalent to the Nyquist sampling condition [27]. For low repetition frequency ($f_1$) OFCs, a low value of $\Delta f$ is required to satisfy the above condition. Figure 2(a) shows a DFC beating spectrum, generated by the experimental setup in Fig. 1, with 3 GHz repetition frequency and $\Delta f$ of 99 MHz. The green line outlines the $\Delta f$ beating tones and the blue line outlines the $f_1-\Delta f$ beating tones. Although the two spectra start to overlap, there is no aliasing present as the beating tones are generated at unique frequencies. Figure 2(b) shows the DFC beating spectrum generated with 3 GHz repetition frequency and $\Delta f$ of 100 MHz. In this case, clear aliasing occurs as the $\Delta f$ and $f_1-\Delta f$ beating spectra no longer occur at unique frequencies. Figure 2(c) shows single beating tones selected from the spectra in Fig. 2(a) and (b). Each plot contains an overlay of 50 sweeps with 10 kHz resolution. For the case where the beat tones are not aliased, (1) and (2), stable beating tones are detected. For the case where aliasing is present, (1+2), fluctuation in the beat tone amplitude is seen between sweeps. The power fluctuations ($\Delta P$) had a maximum value of 10 dB. Although aliasing from beat spectrum overlap is easily avoided by reducing $\Delta f$, the insight gained on the behaviour of aliased beating tones can be used for aliasing detection from the second source, injection symmetry. Figure 3(a) shows how beat tone aliasing is caused by injection symmetry. When using optical injection to establish a mutual phase correlation between two OFCs, it is not possible to inject at a frequency on the edge of the OFC spectrum as issues like side mode unlocking begin to arise [28]. Instead, injection locking is done at a frequency near the edge of the comb bandwidth, see $F_{inj}$ in Fig. 3(a). This leads to symmetries of multiples of $\Delta f$ around the injection frequency, causing aliasing of the beating tones generated by those multiples of $\Delta f$. Figure 3(b) shows the DFC beating spectrum generated with 3 GHz repetition frequency and a $\Delta f$ of 60 MHz. Looking at the beat tones (1) and (2) in Fig. (c), we can see the same power fluctuation due to the aliasing that we saw in the previous aliasing example. When looking at beat tones across the spectrum it was found that the first 5 beating tones suffered from aliasing. This method for identifying aliased beating tones was used throughout this work to accurately characterise the effective comb bandwidth, i.e. the OFC bandwidth that could be effectively used in spectroscopic applications.Fig. 2. (a) and (b) show the RF power spectra generated by a DFC with $f_1$=3 GHz and $\Delta f$=99 MHz. The dashed lines show the overlapped $\Delta f$(green) and $f_1-\Delta f$(blue) DFC beating tone spectra; (c) The comparison between DFC beating tones without aliasing, (1)/(2), and with aliasing (1+2).
Fig. 3. (a) Illustration of injection symmetry aliasing in mutually injection-locked DFC; (b) Beating spectrum for DFC with 3 GHz FSR and 60 MHz frequency offset; (c) shows the beating tones with (1) and without aliasing (2) due to injection symmetry.
In this article, the laser sources used had an operable wavelength range between 2001 nm and 2004 nm when operated in CW mode. This wavelength range enables access to absorption features for three key gases; CO$_2$, NH$_3$ and H$_2$O. Fig. 4 shows a simulated absorption spectrum for the wavelength region between 2000 nm and 2005 nm, based on data from the HITRAN database and calculated using the Tomsk SPECTRA Information System [29,30]. This is the spectral region we aim to access with our DFC. The spectrum was simulated for atmospheric conditions (20.9$\%$ O$_2$, 77.4$\%$ N$_2$ at 296 K) using mixing ratios of 400 ppmv CO$_2$, 25 ppmv NH$_3$ and relative humidity (RH) of 54$\%$ (corresponding to a mixing ratio of 15.2 ppTv). The red dots shown in Fig. 4(a) indicate where an optical frequency comb with 2 GHz FSR would intersect with the absorption spectrum. Figure 4(b) shows the integrated absorption cross-section, S, as a "stick" spectrum [30]. The length of the sticks indicates the size of S for a given wavelength position. Figure 4(a) demonstrates that the assignment of individual absorption features to different species, i.e. the selectivity of the approach, also depends on the appropriate spectral density of comb lines given by its FSR. Figure 4(c) shows a schematic comb spectrum with a FSR of 2 GHz. It can be seen that, with an FSR of 2 GHz, all features of the 15 cm$^{-1}$ wide spectrum could be detected by 180 comb lines, with each absorption feature intersected with multiple comb lines.
Fig. 4. (a) Spectrum based on data from the HITRAN database, calculated using the Tomsk SPECTRA Information System. The red dots correspond to comb line positions; (b) Stick spectrum of CO$_2$ (blue), NH$_3$ (purple) and H$_2$O (magenta), representing the integrated absorption cross-sections, S, in units of [cm$^2$/(molecule cm$^{-1}$)]. The absorption strength for CO$_2$ and H$_2$O were multiplied by factors 5 and 120, respectively, to bring them on scale; (c) Schematic of a comb spectrum with an FSR of 2 GHz.
Figure 5(a) shows the optical spectra generated by our DFC with a centre wavelength tuned between 2001 nm and 2004 nm. The OFCs were generated with a repetition frequency of 2 GHz and 2.00025 GHz respectively. The two comb source lasers were biased at 40 mA and the primary laser was biased at 70 mA, delivering -7 dBm of optical power to each comb source laser. For comb 1, the temperature was varied between 37.8$^\circ$C and 11.3$^\circ$C to achieve the desired 3 nm wavelength shift. For comb 2, the temperature was varied between 20.9$^\circ$C and 6.8 $^\circ$C. The primary laser was temperature tuned between 60.2 $^\circ$C and 33 $^\circ$C to enable injection locking of each OFC. Figure 5(b) shows the DFC beating spectra captured from the corresponding combs seen in Fig. 5(a). With a $\Delta f$ of 250 kHz, the amplitude information was compressed into a frequency bandwidth of 15 MHz. The DFC beating spectra were captured through the averaging of 10 sweeps, each taken in 5 ms, with a resolution of 30 kHz. Looking at alike comb lines for each spectrum, the SNR can be seen to occupy a range between 25 dB and 30 dB for spectra (1)-(3). However, for spectrum 4 there is an SNR reduction to 20 dB. This was caused by a loss in optical power in one of the frequency combs when operating at this wavelength. For DFC spectra (1)-(3), the peak power of comb 2 was measured to be -24 dBm. This is hidden beneath the more powerful comb 1 in Fig. 5(a). For DFC spectrum (4), at 2004 nm, the peak power of comb 2 was measured to be -30 dBm. This issue could be rectified by using a laser for comb 2 with a performance similar to that of comb 1. When the aliasing due to injection symmetry was taken into account, the DFC had functional sensing bandwidths between 74 GHz and 78 GHz. The results presented in Fig. 5 show how the DFC presented in this article could be used to target the absorption region shown in Fig. 4.
Fig. 5. (a) Optical spectra of temperature-tuned DFC with a centre frequency between 2001 nm - 2004 nm and 2 GHz FSR; (b) DFC beating spectra generated from the optical spectra labelled (1)-(4) with $\Delta f$=250 kHz.
Fig. 6. (a) and (b) show the optical spectra for DFCs with FSR between 500 MHz - 3 GHz and their associated electrical domain beating spectra respectively; (c) The optical pulse (red) and modulation signal (black) profiles for each modulation frequency.
Beyond temperature-based wavelength tunability, the gain-switched DFC architecture we propose has the advantage of offering FSR tunability. For our work, we chose to operate with FSRs between 3 GHz and 500 MHz. The upper limit of 3 GHz was imposed as it was near the laser relaxation oscillation (RO) frequency [15]. This offered the maximum pulse compression and therefore maximum OFC bandwidth. The lower limit of 500 MHz was selected due to issues with injection symmetry, as we will cover later. Figure 6(a) shows the optical spectra obtained for DFC generation with FSRs between 500 MHz and 3 GHz. It can be seen that for 2 GHz and 3 GHz, the optical bandwidth spans approximately 2 nm with a flat spectral shape. For 1 GHz and 500 MHz modulation frequencies, there is a clear reduction in spectral bandwidth caused by operating below the laser RO frequency. Looking at Fig. 6(c), a clear variation in the optical pulse profile (red) can be seen at the different modulation frequencies. When operating below the RO frequency, the initial spike in optical power is followed by a broad optical pulse, mirroring the modulation signal (black). For the low modulation frequencies, 1 GHz and 500 MHz, a broad pulse shape is produced. This results in a narrow optical bandwidth. As the modulation frequency approaches the laser RO frequency, the pulses take on a more uniform narrow profile. This allows for the generation of broad flat spectra in the optical domain. The variation in pulse formation is caused by the pulses forming from adiabatic chirp at low frequencies and dynamic chirp at frequencies near the laser RO frequency [31]. Figure 6(b) shows the DFC beat spectra generated for FSRs between 500 MHz and 3 GHz. These spectra were captured with 10 kHz resolution, 10 sweep averaging and 30 ms acquisition time per sweep. The increased resolution and sweep time were required to resolve the beating tones generated at lower FSRs. The resolution and sweep time increases lead to a 10 dB increase in SNR when compared to the previously captured results for the DFC with 2 GHz FSR. The 3 GHz and 2 GHz beating spectra demonstrate a desirable high SNR of approximately 40 dB for the majority of beating tones, with broad optical bandwidth. For this DFC setup, these could be considered optimal operating conditions. An FSR of 2 GHz would be more desirable due to the increased sensing resolution it would offer, but some applications may prefer rapid acquisition over resolution. In this case, a larger FSR reduces the number of beating tones present and therefore a lower resolution in the electrical domain needed to resolve the spectrum. This leads to lower required acquisition times. For the lower repetition frequency DFC spectra, 1 GHz and 500 MHz, there is a large variation in SNR across the comb bandwidth. The issue with low SNR tones is they quickly saturate at higher gas concentrations. This could be an issue in some applications. The high SNR (>10 dB) portions of the spectrum can enable very high-resolution sensing in a small wavelength region, even at high concentrations. One such application is sensing around 2001.1 nm, where there are absorption peaks for CO$_2$, NH$_3$ and H$_2$O in a less than 0.5 nm wide wavelength span. A high-resolution comb with a small bandwidth would be sufficient to accurately identify each gas component with high confidence in this case.
Fig. 7. Plots illustrating absorption of light from the DFC by CO$_2$ at a variety of pressures using a 64 cm absorption path length; (a) Illustrates the absorption of the DFC with 2 GHz FSR for an evacuated chamber with increasing pressure of CO$_2$, targeting absorption lines between 2003.0 nm and 2003.6 nm; (b) Compares the two absorption regions from (a); (c) Illustrates the increased spectral resolution when using a DFC with 1 GHz FSR. This measurement was executed in the spectral region of 2001.1 nm at a total pressure of 1000 mbar, i.e. 202.6 mbar of CO$_2$ and 797.4 mbar of ambient air; (d) Illustrates the absorption for the same conditions as in (c) using a DFC with 500 MHz FSR targeting the 2001.1 nm absorption line of CO$_2$.
As a proof of concept, demonstrated CO$_2$ sensing using the described DFC in a few of its potential operating configurations. These tests were conducted using a gas cell with a 64 cm path length. Free space coupling was achieved using two TC25APC-2000 triplet collimators. Figure 7(a) shows the DFC beating spectra for the 2 GHz FSR configuration centred at 2003.25 nm, passing through the gas cell containing between approximately 0 mbar and 202.6 mbar of CO$_2$. Two absorption regions can be seen in the beating spectrum. One around 1.5 MHz and another around 6.6 MHz. Due to the low-pressure conditions in the cell, the CO$_2$ absorption lines are narrow. Zooming into the absorption region in Fig. 7(b), the absorption affects up to five of the comb teeth. For the region around 6.6 MHz, strong absorption is seen for the centre line, with full beat tone saturation for 202.6 mbar of CO$_2$ in the cell. The two neighbouring tones see less of a reduction, between 1 dB and 5 dB. For CO$_2$ at 202.6 mbar, increased pressure broadening contributes to the stronger absorption in the neighbouring beat tones. The absorption region at 1.5 MHz occurs in the aliasing zone of the DFC spectrum. This can be seen by the beat tone power fluctuations. For lower pressures, the CO$_2$ detection is affected by the power fluctuations in that region. This is seen in the absorption peak at 1.3 MHz, where there is an overlap of the beating tones for the $\approx$0 mbar, 36.2 mbar and 78.3 mbar cases. In some cases, the power fluctuations can be minimized by taking many sweeps and averaging the beat tone power. For high concentrations, absorption in the aliasing zone does not pose a major problem as seen for 202.6 mbar of CO$_2$, where the beat tone power is reduced by over 10 dB. Figure 7(c) illustrates the CO$_2$ absorption feature at 2003.25 nm, as in Fig. 7(a), but with increased resolution due to the reduced FSR of 1 GHz. The chamber pressure was also increased to approximately 1 atm through the addition of ambient air. This was done to induce pressure broadening of the absorption feature. The DFC spectrum shows 7 peaks with a >10 dB reduction in power. This gives a clear high resolution outline of the absorption feature. Figure 7(d) shows the DFC spectrum at the maximum resolution of 500 MHz tuned to the CO$_2$ absorption feature around 2001.1 nm. The gas cell conditions for this test were the same as in the previous case, with 202.6 mbar of CO$_2$ buffered by ambient air to a pressure of approximately 1 atm. As mentioned earlier, this wavelength region contains absorption features of three different gases, see Fig. 4. To resolve features of different species in this region, a high-resolution DFC is required. A 500 MHz resolution outline of the CO$_2$ absorption feature is evident around 5 MHz in Fig. 7(d). With this configuration, the simultaneous detection CO$_2$, NH$_3$ and H$_2$O with high resolution using a single measurement in near real-time should be possible.
4. Conclusion
In this article, we presented a DFC architecture with tunable FSR and wavelength in a key wavelength region around 2 $\mu$m. The DFC could be temperature tuned to target wavelengths between 2000 nm and 2005 nm, allowing access to absorption features of CO$_2$, NH$_3$ and H$_2$O. The tunable FSR enabled the generation of DFCs with sensing resolutions between 500 MHz and 3 GHz. These resolutions are sufficient for detailed molecular absorption mapping of the wavelength region in question, with each absorption line being intersected with multiple comb lines. The short acquisition times for DFCs were also demonstrated, with a total integrated sweep time of 50 ms returning beating spectra with SNR approaching 30 dB. In the case of the 2004 nm DFC, this was found to be 20 dB. A clear experimental demonstration of the architecture’s ability to detect CO$_2$ was also carried out. This was done at multiple DFC wavelengths and FSRs, showing how the tunable nature of the DFC can meet the requirements of a variety of sensing applications.
Funding
Higher Education Authority (North-South Research Program HIGH-GREEN); Science Foundation Ireland (21/FFP-A/8973); Irish Research Council (GOPIG/2017/385); Science Foundation Ireland (IPIC(12/RC/2276-P2)); Irish Research eLibrary.
Acknowledgments
Authors would like to acknowledge; Science Foundation Ireland Q1 (21/FFP-A/8973); Irish Research Council (GOPIG/2017/385); Science Foundation Ireland (IPIC(12/RC/2276-P2); and HIGHGREEN North-South Research Programme, a collaborative scheme arising from the Government’s Shared Island initiative delivered by the Higher Education Authority (HEA) on behalf of the Department of Further and Higher Education, Research Innovation and Science (DFHERIS), in Ireland.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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