Mid-infrared cross-comb spectroscopy

Abstract

Dual-comb spectroscopy has been proven beneficial in molecular characterization but remains challenging in the mid-infrared region due to difficulties in sources and efficient photodetection. Here we introduce cross-comb spectroscopy, in which a mid-infrared comb is upconverted via sum-frequency generation with a near-infrared comb of a shifted repetition rate and then interfered with a spectral extension of the near-infrared comb. We measure CO₂ absorption around 4.25 µm with a 1-µm photodetector, exhibiting a 233-cm^-1 instantaneous bandwidth, 28000 comb lines, a single-shot signal-to-noise ratio of 167 and a figure of merit of 2.4 × 10⁶ Hz^1/2. We show that cross-comb spectroscopy can have superior signal-to-noise ratio, sensitivity, dynamic range, and detection efficiency compared to other dual-comb-based methods and mitigate the limits of the excitation background and detector saturation. This approach offers an adaptable and powerful spectroscopic method outside the well-developed near-IR region and opens new avenues to high-performance frequency-comb-based sensing with wavelength flexibility.

Fig. 1. Cross-comb spectroscopy.

a Schematic of the setup. ν_L and ν_T, center optical frequencies of the NIR local FC and MIR target FCs. f_ceo and f_rep, carrier–envelope offset frequency and repetition rate of a FC. f_r,L and f_r,T, repetition rate of the local FC and the target FC. δ, difference between f_r,L and f_r,T. PD, photodetector. b–d Principle of the tooth mapping in frequency domain. An example target tooth, together with its corresponding SFG teeth and RF teeth, is denoted by a dashed line to demonstrate the one-to-one mapping. n (m): index of the example tooth of the target FC (local FC). b Optical spectra. c Zoomed-in view of the grey-shadowed area in (b). df_n denotes the distance of the SFG teeth (dashed lines) generated by the n_th target tooth from their respective closest readout tooth. d Heterodyne beat notes in the RF domain, obtained by square-law detection of the interference between the SFG FC and readout FC with a single NIR detector. Band B (C) is the result of the beating between SFG teeth with their nearest (second nearest) readout tooth, while band A (D) is the result of the beating between two SFG teeth from the same SFG group (two adjacent SFG groups). The arrows denote the optical tooth pairs in (c) that contribute to the dashed RF tooth. e CCS in time domain. In addition to the typical CCS interferogram (solid blue curve), a typical DCS interferogram (dashed red curve) is plotted for comparison. Note that this illustration describes the case where the target, local and readout FCs are all short pulses, which is not necessary for general CCS. While the DCS interferogram baseline is delay-independent since the envelopes of two pulses are delay-independent, the envelope of the SFG signal in CCS is delay-dependent, which gives a delay-dependent baseline and makes the interferogram “vertically asymmetric”. This time-domain delay-dependent baseline in CCS interferogram corresponds to band A and D in frequency domain, which can be canceled out via balanced detection. More details can be found in Supplementary Sections 1.2, 2, 3 and 5. FID, free induction decay.

Fig. 2. Comparison of detection efficiency, bandwidth, SNR and DR between short-pulse CCS and other dual-comb-based techniques.

a–c Power gain function G(ω) for quantification of detection efficiency and bandwidth for three upconversion methods: short-pulse CCS (a), C.W. upconversion DCS (b), and EOS (c). The spectral amplitude of the target (E_T (ω)) and spectral intensities of the local (${∣E_L\left(\omega \right)∣}^2$) and readout (${∣E_R\left(\omega \right)∣}^2$) FCs are denoted by curves in red, green, and purple, respectively. The instrument response function H(ω) is the convolution of $E_L^{*}\left(-\omega \right)$ and E_R (ω), and its spectral intensity ($G\left(\omega \right)={∣H\left(\omega \right)∣}^2$) is denoted by the black curve for each method. a Short-pulse CCS. h₀, w₀ and S_L(R) denote the height (PSD), width (bandwidth), and area (total average power) of the local (readout) spectrum, respectively. Δω_T, ω_T,min, ω_T, ω_T,max denote the bandwidth and minimum, center, and maximum optical frequency of the target spectrum to be detected, respectively. w_G, h_G and S_G denote the width, maxima, and total area of (under) G(ω), respectively. b C.W. upconversion DCS. c EOS. The grey-dashed area of G_EOS (ω) denotes the part not effectively used in detection since it does not overlap with the target spectrum. d–e Comparison between DCS (red curves) and CCS (blue curves) interferograms at FID. d SNR comparison. Here we assume enough optical power for both techniques to saturate the detector for highest SNR. In DCS, the weak FID must be accompanied by the strong background from the excitation pulse center, which only contributes to noise here. Contrarily, CCS is free from such a background and can get an interference pattern of higher visibility with smaller noise. i_signal, the range of the beating signal. i_bg, the background current; i_sat, the saturation level of the detector. e DR comparison. Here we assume enough optical power for both techniques to detect an identical level of weak absorption. In DCS, a large part of the detector DR is occupied by the background. The higher the sensitivity (lower detection limit) reached, the larger the background, and the smaller the remaining DR. However, in principle, CCS does not have such problem and can make use of a larger part of the detector DR.

Fig. 3. Experimental results of CCS of CO₂.

a Five consecutive interferograms with a 1-ms temporal spacing, corresponding to δ = 1 kHz. The “without sample” result (blue) is measured when the optical path is purged with nitrogen (N₂), and the “with sample” measurement (red) is taken when the path is not purged and atmospheric CO₂ is present. All measurements are carried out at room temperature and atmospheric pressure without extra control. b The central 14 µs of one example interferogram. Blowups depicting additional details of the center-burst and FID are shown in panel (c) and (d), respectively. The lower temporal axes denote the lab time while the upper ones denote the effective time, which are related by the equation $t_{Lab}/t_{Effective}=f_{rL}/\delta$. e Spectra of band B of the RF FC, obtained by Fourier transforms of 498 consecutive unapodized interferograms, for measurements both with and without CO₂, are shown in red (I_s (f)) and blue (I_r (f)), respectively. The inset is a zoomed-in view to show resolved comb lines, which are separated by δ = 1000 Hz in the RF domain corresponding to f_r,L = 250,250,820 Hz in the optical domain. f Measured molecular absorbance spectrum (light blue curve), A(f), defined by $A\left(f\right)=-\ln \left[I_r\left(f\right)/I_s\left(f\right)\right]$. The result is obtained from 498 interferograms (for both “with” and “without sample”) each apodized with a 100-µs window. The black curve (inverted) denotes the theoretical model, which is derived by fitting the absorption lines from the HITRAN database (red lines) with a Lorentzian lineshape to the experimental result. The upper axes in both (e) and (f) denote the optical frequency in wavenumber.

Fig. 4. Comparison of principles and features of different dual-comb-based techniques for MIR spectroscopy.

a–d Simplified schematics of different techniques. a General dual-comb spectroscopy with an asymmetric (dispersive) configuration. The second MIR FC, which does not pass through the sample, is often referred to as the “local FC” or “slave FC” in other works. However, in the context of this work, it is named the “MIR readout FC” since it samples the MIR target FC linearly, by which a linear cross-correlation signal is generated to give the spectral information of the target FC. b C.W. upconversion DCS. The MIR target FC is generated by the DFG between the NIR C.W. laser and the “master NIR comb”, which is not shown in this simplified schematic. This method can be considered as a special case of CCS, in which the “local FC” contains only one “comb tooth”. Note that using an SFG or DFG process for the nonlinear upconversion of the MIR target FC does not make a fundamental difference. c Dual-comb EOS. It can also be considered as a special case of CCS, in which the local FC is so broadband that it also serves as the readout FC. The lower-frequency part of the local FC can be regarded as an effective “local FC”, while the higher-frequency part can be regarded as an effective “readout FC”, in the context of CCS. d General cross-comb spectroscopy. e Table comparing features of different techniques. (i) In principle, CCS does not require short pulses as the NIR local FC. However, the (short) local pulses enhance the upconversion efficiency and enable temporal gating. (ii) If the electric field of the readout FC (and local FC if applicable) is (are) known, all four techniques can fully reconstruct the electric field of the target pulse. However, this extra information is not necessary for the purpose of general absorption spectroscopy.

Fig. 5. Envisaged on-chip implementation of CCS.

Two NIR comb sources of different repetition rates, which are also possible to integrate, are used to pump a single nanophotonic chip. One of the NIR combs is used to pump an on-chip sub-harmonic OPO for the MIR target FC generation, which may then interact with the sample in a long waveguide. The other NIR comb is split into two parts, which are used to function as the local FC via SFG and generate the readout FC via supercontinuum generation in separate poled regions. The outputs are interfered on chip and measured with a NIR balanced detector, which may also be brought on chip.