Cavity-enhanced field-resolved spectroscopy

Letters https://doi.org/10.1038/s41566-022-01057-0 Cavity-enhanced field-resolved spectroscopy Philipp Sulzer 1,2,3,4,8 ✉, Maximilian Högner 1,2,8 ✉, Ann-Kathrin Raab1,2,5, Lukas Fürst2,6, Ernst Fill1, Daniel Gerz 1,2,7, Christina Hofer 1,2, Liudmila Voronina1,2 and Ioachim Pupeza 1,2 ✉ Femtosecond enhancement cavities1 are key to applications including high-sensitivity linear2–4 and nonlinear5,6 gas spectroscopy, as well as efficient nonlinear optical frequency conversion7–10. Yet, to date, the broadest simultaneously enhanced bandwidths amount to <20% of the central optical freque ncy8,9,11–15. Here, we present an ultrabroadband femtosecond enhancement cavity comprising gold-coated mirrors and a wedged-diamond-plate input coupler, with an average finesse of 55 for optical frequencies below 40 THz and exceeding 40 in the 120–300 THz range. Resonant enhancement of a 50-MHz-repetition-rate offset-free frequency comb spanning 22–40 THz results in a waveform-stable ultrashort circulating pulse with a spectrum supporting a Fourier limit of 1.6 cycles, enabling time-domain electric-field-resolved spectroscopy of molecular samples with temporally separated excitation and molecular response16. The contrast between the two is improved by taking advantage of destructive interference at the input coupler. At an effective interaction length with a gas of up to 81 m, this concept promises parts-per-trillion-level ultrabroadband electric-field-resolved linear and nonlinear spectroscopy of impulsively excited molecular vibrations. The spatial confinement of laser light propagating within passive free-space optical resonators enables multiple interactions of the circulating radiation with atoms, molecules or clusters located in the beam path. This underlies sensitivity enhancement2 in techniques like cavity-enhanced absorption spectroscopy3,13, cavity-ringdown spectroscopy4,11,12 noise-immune cavity-enhanced optical heterodyne molecular spectroscopy17 and cavity-enhanced Vernier spectroscopy18. The same principle enables driving (extreme) nonlinear processes, like high-harmonic generation, at multi-megahertz pulse repetition rates, generating broadband frequency combs in the vacuum/extreme ultraviolet7–10. Broadband passive enhancement in a femtosecond enhancement cavity (fsEC), however, imposes challenging requirements for the mirrors, namely, simultaneous broadband reflectivity and flat spectral phase10. Consequently, typical fsECs in the ultraviolet12, visible14,19 and infrared8,9,11,13,15,20–22 (IR) spectral regions rarely simultaneously enhance comb bandwidths broader than 10% of the central frequency, with a record value of less than 20% demonstrated in the near-IR region15. Furthermore, fsECs have so far been exclusively used in combination with time-integrating detection techniques (such as Fourier-transform infrared (FTIR) spectroscopy), requiring the detection of weak sample responses on top of—often orders of magnitude stronger—excitation intensities. This challenge to the dynamic range of linear detection11,20 becomes particularly severe with the advent of novel, (multi)-Watt-level mid-IR frequency combs23. In this Letter, we introduce ultrabroadband cavity-enhanced field-resolved spectroscopy, combining two cutting-edge photonic technologies to overcome both aforementioned shortcomings. First, employing gold-coated mirrors and reflective input coupling via a wedged24,25 diamond plate oriented close to Brewster’s angle, we realized an fsEC with a finesse exceeding 40 over multiple octaves, and demonstrated the simultaneous enhancement of an offset-free frequency comb in the 22–40 THz range. Second, the pulse-to-pulse carrier-envelope-phase (CEP)-stable electric field of this offset-free comb enables time-domain optical-waveform detection via free-space electro-optic sampling (EOS)26,27. This leverages the unparalleled dynamic range of linear detection and the excitation-power scalability afforded by EOS in the molecular fingerprint region16,28. The combination of fsEC, impulsive excitation and EOS possesses the additional advantages of temporal separation of the resonantly enhanced sample-specific molecular response from the few-cycle excitation16 and the potentially strong attenuation of the few-cycle excitation owing to destructive interference at the input coupler (IC). The working principle of an fsEC resonantly seeded by a train of CEP-stable pulses (red) is illustrated in Fig. 1a. Provided the comb lines of the driving laser overlap with the fsEC’s resonances, the seeding and circulating pulses constructively interfere inside the cavity, whereas the immediate reflection of the seeding pulses off the IC interferes destructively with a portion of the circulating field transmitted through the IC. In the case of a perfectly impedance- and mode-matched fsEC, this leads to a complete suppression of the reflected field. This changes, however, when a gas with optically active molecular vibrations is introduced in the beam path. The coherent electric field emitted as a consequence of the impulsive vibrational excitation (that is, the molecular response) consists of long-lasting oscillations (green), which, after excitation, lack a matching counterpart to destructively interfere with at the IC. Consequently, the beam reflected off the fsEC contains the enhanced molecular response and suppresses the excitation pulse. The field-resolved spectroscopy setup, which we used to elucidate these phenomena in the time domain, is sketched in Fig. 1b. A fibre-laser front end generates a frequency comb with controllable repetition rate frep and offset frequency f0 (Methods). Intrapulse difference-frequency generation (IPDFG) in a 1-mm-thick GaSe crystal inherently generates an offset-free frequency comb with an average power of approximately 0.1 W, which then seeds the fsEC. Figure 1c depicts the fsEC design. Reflective input/output coupling by means of a wedged diamond obviates the need of a partially transmissive input coupling mirror, enabling the exclusive Max-Planck-Institut für Quantenoptik, Garching, Germany. 2Ludwig-Maximilians-Universität München, Garching, Germany. 3Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada. 4Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia, Canada. 5Department of Physics, Lund University, Lund, Sweden. 6Institute of Experimental Physics, Graz University of Technology, Graz, Austria. 7Leibniz Institute of Photonic Technology—Member of the Research Alliance ‘Leibniz Health Technologies’, Jena, Germany. 8These authors contributed equally: Philipp Sulzer, Maximilian Högner. ✉e-mail: ; ; 1 Nature Photonics | www.nature.com/naturephotonics Letters Nature Photonics a Input fsEC transmission port fsEC reflection port b c Fundamental Er:fibre frequency comb f0 control Input NIR and MIR Input f–2f frep control 1.5 µm HNF + Tm:fibre amplifier 2.0 µm fs (...truncated)