Continuous Vernier filtering of an optical frequency comb for broadband cavity-enhanced molecular spectroscopy

https://doi.org/10.1016/j.jqsrt.2016.09.021Get rights and content

Highlights

  • A recently introduced Cavity-Enhanced Direct-Frequency-Comb Spectroscopy technique is discussed in detail.

  • It relies on the continuous-Vernier-filtering regime, defined in this paper.

  • Spectra with high sensitivity covering 2000cm1 at 2 GHz resolution are obtained.

  • A complete formalism is presented to adjust spectra at atmospheric conditions.

Abstract

We have recently introduced the Vernier-based Direct Frequency Comb Cavity-Enhanced Spectroscopy technique which allows us to record broadband spectra at high sensitivity and GHz resolution (Rutkowski and Morville, 2014) [1]. We discuss here the effect of Vernier filtering on the observed lineshapes in the 3ν+δ band of water vapor and the entire A-band of oxygen around 800 nm in ambient air. We derive expressions for the absorption profiles resulting from the continuous Vernier filtering method, testing them on spectra covering more than 2000 cm−1 around 12,500 cm−1. With 31,300 independent spectral elements acquired at the second time scale, an absorption baseline noise of 2×108cm1 is obtained, providing a figure of merit of 1.1×10−10 cm−1/Hz per spectral element with a cavity finesse of 3000 and a cavity round-trip length around 3.3 m.

Introduction

Optical frequency combs (OFC), generated by femtosecond mode-locked lasers, are recognized to be very powerful devices for spectroscopy. They offer large optical bandwidth (Δν) discretized at the comb teeth frequencies. They are defined by the repetition rate of the femtosecond oscillator frep and by a carrier-envelope offset frequency fceo translating the entire comb of a constant value comprised between 0 and frep, each comb tooth frequency being indexed by an integer n and defined as νnlas=n·frep+fceo. Several approaches [2], [3], [4], [5], [6], [7], [8] have been designed to combine OFCs with the extended path lengths associated with high finesse cavities to attain high sensitivity in molecular absorption spectra. Some resolve the comb mode structure (with 1 GHz mode locked laser) [2], [3], some are fast (around or below the ms timescale of acquisition) [4], [5], some are particularly sensitive (baseline noise around 10−4) [6], but none truly exploit the full bandwidth of the OFCs, restricting the accessible spectral range to roughly a few hundred wavenumbers, around ten percent of the entire range of a typical Titanium:Sapphire (Ti:Sa) mode-locked laser.

Recently, we have developed the Vernier continuous filtering technique, combining an OFC with a high finesse cavity to achieve the measurement of the full OFC spectrum with high sensitivity, GHz resolution and sub-second acquisition time [1]. The Vernier filtering deliberately mismatches in a controlled fashion the laser repetition rate and the cavity free spectral range FSRc (as are the two scales of a Vernier caliper). The spectral cavity output then exhibits a new comb whose mode-spacing is sufficiently large to be dispersed with a low resolution optical grating. This Vernier filtering scheme was adopted as a strategy to calibrate telescope spectra, creating the so-called astro-comb [9], [10]. Gohle et al. [2] first applied this approach to laboratory molecular spectroscopy, resolving the 1 GHz mode structure of a Ti:Sa mode-locked laser over 4 THz (130 cm−1) in 10 ms, but at the price of a poor sensitivity (absorption baseline noise of a few 106cm1 with an effective optical path-length around 300 m). In 2014, the same philosophy was extended to a 250 MHz Erbium doped fiber mode-locked laser [8] without the comb mode resolution (a resolution of 1.1 GHz was obtained). A spectral coverage of 160cm1 and a sensitivity of 8×108cm1 (with an effective optical path-length of 11 km) was demonstrated on a time scale of 1 s. Still, only a small part of the OFC was exploited and sensitivity performances were again limited by the strong frequency-to-amplitude noise conversion resulting from the unstabilized cavity with respect to the stabilized OFC. In this work, we present our approach [1] characterized by the degree of mismatch between FSRc and frep. In astro-comb or previous works in molecular spectroscopy, the mismatch is large enough to filter out the comb teeth adjacent to the tooth transmitted by the cavity. Each tooth of the new comb created at the cavity output thus corresponds to a single tooth of the original optical comb. The cavity length is slightly swept to extract spectroscopic information from the sample placed inside it, allowing to transmit the comb teeth successively through the cavity. The cavity transmission is thus modulated by the matching condition. Conversely, our scheme involves sufficiently small mismatches to simultaneously (partially) transmit several adjacent teeth. The matching condition is always fulfilled and the cavity length sweep induces a continuous transmission. This approach is conceptually similar to the so-called ‘precision sweep of frep with cavity filtration’ discussed by Thorpe et al. in [11] where frep is swept instead of the cavity length. In this paper, they provide a temporal cavity transmission revealing absorption lines of C2H2 without quantitative determination of the frequency and absorption scales. Here we show that, with an appropriate cavity locking scheme, this continuous Vernier filtering enables to probe the entire range of a free-running 100 MHz repetition rate Ti:Sa mode-locked laser, at GHz resolution and with a high sensitivity. With this approach implemented with an open-air cavity, an absorption baseline noise of 2×108cm1 is demonstrated with an effective optical path-length of 1.5 km and a spectral coverage larger than 2000cm1 with 31,300 independent spectral elements acquired in 1 s. We derive a full analytical model to describe the cavity transmission in presence of intracavity absorbing species for this continuous Vernier filtering regime. We show that both the real and imaginary part of the resonant molecular response need to be taken into account to explain the marked effect of the sign of the comb-cavity mismatch on the measured line profiles. Using the full model and a non-linear fitting algorithm, we present the results of the 3ν+δ water vapor band adjustment in ambient air over more than 100cm1 including more than 350 lines. We also assess the sensitivity capabilities of this approach from spectra of the first hot band of the b1Σg+X3Σg doubly forbidden band of oxygen in ambient air.

Section snippets

Identification of the perfect match

The Vernier approach relies on a controlled mismatch between FSRc and frep from the reference position corresponding to the perfect match (PM). In the frequency domain, the PM occurs when both the scale and the origin of the OFC are tuned to match those of the cavity grid. In our system, FSRc (controlled by the cavity length), and fceo are tuned to match frep and the cavity offset frequency f0 respectively. A large fraction of the OFC modes are transmitted simultaneously through the cavity. It

Experimental setup

The setup is described in Fig. 6. The OFC is provided by a 90 MHz mode-locked Ti:Sapphire laser with a FWHM bandwidth of 30 THz centered at λ=785 nm delivering an average output power of around 0.5 W. The beam is mode-matched to the open-air optical cavity formed by four broadband dielectric mirrors in a bow-tie arrangement, lowering high-order modes excitation below the percent level. Input and output couplers have a nominal transmission of 0.1% and dominate cavity losses, resulting in a cavity

Results and performances

Molecular spectroscopic information, such as width, position and strength of atmospheric transitions, can be deduced from the normalized cavity transmission using the formalism developed in Section 2.5. Especially, Eqs. (18), (19) show that the measured signal is not a simple convolution of the absorption line with the Vernier order profile, and specifically that the sign of the length mismatch affects the result. To check the model validity, two averaged cavity transmissions were recorded with

Conclusions and outlook

We have presented a detailed description of our recently-introduced Vernier scheme to perform Cavity-Enhanced Direct Frequency Comb Spectroscopy. We have developed a formalism to explain the behavior of the Vernier filtering of a frequency comb with a mismatched cavity. This formalism applies equally to positive and negative mismatches, and corrects raw spectra for the instrumental response with a precision of 100 MHz on the frequency scale. Cavity dispersion, which is one of the major bandwidth

Acknowledgements

Financial support by the Fédération André Marie Ampère of the Lyon University is gratefully acknowledged. We are also very grateful to the referees, whose remarks have helped us to improve our manuscript considerably.

References (17)

  • L.S. Rothman et al.

    The HITRAN2012 molecular spectroscopic database

    J Quant Spectrosc Radiat Transf

    (2013)
  • L. Rutkowski et al.

    Broadband cavity-enhanced molecular spectra from Vernier filtering of a complete frequency comb

    Opt Lett

    (2014)
  • C. Gohle et al.

    Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra

    Phys Rev Lett

    (2007)
  • L. Nugent-Glandorf et al.

    Mid-infrared virtually imaged phased array spectrometer for rapid and broadband trace gas detection

    Opt Lett

    (2012)
  • B. Bernhardt et al.

    Cavity-enhanced dual-comb spectroscopy

    Nat Photon

    (2009)
  • R. Grilli et al.

    Cavity-enhanced multiplexed comb spectroscopy down to the photon shot noise

    Phys Rev A: At Mol Opt Phys

    (2012)
  • A. Foltynowicz et al.

    Cavity-enhanced optical frequency comb spectroscopy in the mid-infrared application to trace detection of hydrogen peroxide

    Appl Phys B: Lasers Opt

    (2013)
  • A. Khodabakhsh et al.

    Noise-immune cavity-enhanced optical frequency comb spectroscopy: a sensitive technique for high-resolution broadband molecular detection

    Appl Phys B: Lasers Opt

    (2015)
There are more references available in the full text version of this article.

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