NOISE-IMMUNE CAVITY-ENHANCED OPTICAL FREQUENCY COMB SPECTROSCOPY

We present noise-immune cavity-enhanced optical frequency comb spectroscopy (NICE-OFCS), a recently developed technique for sensitive, broadband, and high resolution spectroscopyfootnote{A. Khodabakhsh, C. Abd Alrahman, and A. Foltynowicz, Opt. Lett. 39, 5034-5037 (2014).}. In NICE-OFCS an optical frequency comb (OFC) is locked to a high finesse cavity and phase-modulated at a frequency precisely equal to (a multiple of) the cavity free spectral range. Since each comb line and sideband is transmitted through a separate cavity mode in exactly the same way, any residual frequency noise on the OFC relative to the cavity affects each component in an identical manner. The transmitted intensity contains a beat signal at the modulation frequency that is immune to frequency-to-amplitude noise conversion by the cavity, in a way similar to continuous wave noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS)footnote{J. Ye, L. S. Ma, and J. L. Hall, J. Opt. Soc. Am. B 15, 6-15 (1998).}. The light transmitted through the cavity is detected with a fast-scanning Fourier-transform spectrometer (FTS) and the NICE-OFCS signal is obtained by fast Fourier transform of the synchronously demodulated interferogram. Our NICE-OFCS system is based on an Er:fiber femtosecond laser locked to a cavity with a finesse of $sim$9000 and a fast-scanning FTS equipped with a high-bandwidth commercial detector. We measured NICE-OFCS signals from the 3nub{1}+nub{3} overtone band of chem{CO_2} around 1.57 $mu$m and achieved absorption sensitivity 6.4$times$10$^{-11}$cm$^{-1}$Hz$^{-1/2}$ per spectral element, corresponding to a minimum detectable chem{CO_2} concentration of 25 ppb after 330 s integration timefootnote{A. Khodabakhsh, A. C. Johansson, and A. Foltynowicz, Appl. Phys. B (2015) doi:10.1007/s00340-015-6010-7.}. We will describe the principles of the technique and its technical implementation, and discuss the spectral lineshapes of the NICE-OFCS signals

OPTICAL FREQUENCY COMB FOURIER TRANSFORM SPECTROSCOPY WITH RESOLUTION EXCEEDING THE LIMIT SET BY THE OPTICAL PATH DIFFERENCE

Fourier transform spectrometers (FTS) based on optical frequency combs (OFC) allow detection of broadband molecular spectra with high signal-to-noise ratios within acquisition times orders of magnitude shorter than traditional FTIRs based on thermal sourcesfootnote{Mandon, J., G. Guelachvili, and N. Picque, textit{Nat. Phot.}, 2009. textbf{3}(2): p. 99-102.}. Due to the pulsed nature of OFCs the interferogram consists of a series of bursts rather than a single burst at zero optical path difference (OPD). The comb mode structure can be resolved by acquiring multiple bursts, in both mechanical FTS systemsfootnote{Zeitouny, M., et al., textit{Ann. Phys.}, 2013. textbf{525}(6): p. 437-442.} and dual-comb spectroscopyfootnote{Zolot, A.M., et al., textit{Opt. Lett.}, 2012. textbf{37}(4): p. 638-640.}. However, in all existing demonstrations the resolution was ultimately limited either by the maximum available OPD between the interferometer arms or by the total acquisition time enabled by the storage memory. We present a method that provides spectral resolution exceeding the limit set by the maximum OPD using an interferogram containing only a single burst. The method allows measurements of absorption lines narrower than the OPD-limited resolution without any influence of the instrumental lineshape function. We demonstrate this by measuring undistorted CO$_{2}$ and CO absorption lines with linewidth narrower than the OPD-limited resolution using OFC-based mechanical FTS in the near- and mid-infrared wavelength ranges. The near-infrared system is based on an Er:fiber femtosecond laser locked to a high finesse cavity, while the mid-infrared system is based on a Tm:fiber-laser-pumped optical parametric oscillator coupled to a multi-pass cell. We show that the method allows acquisition of high-resolution molecular spectra with interferometer length orders of magnitude shorter than traditional FTIR

Sensitive and broadband measurement of dispersion in a cavity using a Fourier transform spectrometer with kHz resolution

Optical cavities provide high sensitivity to dispersion since their resonance frequencies depend on the index of refraction. We present a direct, broadband, and accurate measurement of the modes of a high finesse cavity using an optical frequency comb and a mechanical Fourier transform spectrometer with a kHz-level resolution. We characterize 16000 cavity modes spanning 16 THz of bandwidth in terms of center frequency, linewidth, and amplitude. We retrieve the group delay dispersion of the cavity mirror coatings and pure N${_2}$ with 0.1 fs${^2}$ precision and 1 fs${^2}$ accuracy, as well as the refractivity of the 3{\nu}1+{\nu}3 absorption band of CO${_2}$ with 5 x 10${^{-12}}$ precision. This opens up for broadband refractive index metrology and calibration-free spectroscopy of entire molecular bands

Sub-Doppler optical-optical double-resonance spectroscopy using a cavity-enhanced frequency comb probe

Accurate parameters of molecular hot-band transitions, i.e., those starting from vibrationally excited levels, are needed to accurately model high-temperature spectra in astrophysics and combustion, yet laboratory spectra measured at high temperatures are often unresolved and difficult to assign. Optical-optical double-resonance (OODR) spectroscopy allows the measurement and assignment of individual hot-band transitions from selectively pumped energy levels without the need to heat the sample. However, previous demonstrations lacked either sufficient resolution, spectral coverage, absorption sensitivity, or frequency accuracy. Here we demonstrate OODR spectroscopy using a cavity-enhanced frequency comb probe that combines all these advantages. We detect and assign sub-Doppler transitions in the 3${\nu}$${_3}$${\leftarrow}$${\nu}$${_3}$ spectral range of methane with frequency accuracy and sensitivity more than an order of magnitude better than before. This technique will provide high-accuracy data about excited states of a wide range of molecules that is urgently needed for theoretical modeling of high-temperature data and cannot be obtained using other methods

Vernier coupling of a femtosecond frequency comb with an optical cavity for broadband molecular spectroscopy

Les lasers femtosecondes à modes bloqués révèlent une structure spectrale de peigne de fréquence, couvrant plusieurs dizaines de THz. Mon travail de thèse s'est concentré sur l'étude et la mise en place d'un dispositif optique couplant le peigne laser dans une cavité optique. Le peigne et les résonances de cavités y sont délibérément désaccordés à la manière d'un Vernier, faisant apparaitre dans la transmission spectrale de la cavité un Moiré de fréquence dont la périodicité est inversement proportionnelle à ce désaccord. La première partie présente un formalisme permettant une compréhension fine de ce couplage et identifiant deux régimes en filtrages dits de «haute» résolution, où la structure de peigne est entièrement résolue, et de «basse» résolution où la résolution est donnée par le désaccord. La seconde partie décrit la réalisation expérimentale de ce couplage, détaillant la stratégie d'asservissement employée afin de stabiliser les résonances de la cavité (F=3000) par rapport au peigne laser au kHz. Enfin, ce couplage est appliqué à la spectroscopie moléculaire. Les spectres mesurés de l'air ambiant, dans des temps d'acquisition d'une seconde, exploitent l'intégralité du spectre du laser, soit 40THz (750 850nm), avec une résolution de 2GHz. La sensibilité en absorption atteint 10−9 /cm après moyenne. Cette haute sensibilité résulte d'une immunité aux bruits de conversion fréquence-Amplitude du couplage Vernier «basse» résolution et permet l'obtention d'un rapport signal sur bruit supérieur à 104. Ces performances conduisent à établir une figure de mérite de 4 × 10−11 cm−1/ √ Hz, plaçant ce résultat au troisième rang de l'état de l'art internationalFemtosecond mode-Locked lasers are generators of optical frequency ‘combs’, whose distinct frequencies cover many tens or hundreds of THz. My PhD work has focused on the study and construction of a particular coupling scheme in an optical cavity, named Vernier coupling. Here, the laser comb and the cavity resonances are deliberately mismatched, as a Vernier rule. This creates Moiré pattern in the cavity spectral transmission, with a periodicity related to the inverse of the mismatch. The first part details the theory behind the coupling of laser and optical cavity modes. Two regimes are identified, called “high” resolution Vernier filtering, when the laser comb structure is probed mode by mode, and “low” resolution filtering where the linewidth of one Vernier order is given by the mismatch. The second part describes the experimental realization of this coupling scheme. It details the locking strategy used to control the resonance position of the cavity (F=3000) in regards of the laser comb (kHz scale). Finally, I present spectra recorded with this setup, focusing on molecular spectroscopy. The spectra of ambient air are recorded in acquisition times around 1 s, that cover the full bandwidth of the femtosecond laser ( 40 THz, 750-850 nm), at 2 GHz resolution. The sensitivity of the absorption measurement reaches 10−9 /cm, with averaging. This high sensitivity comes from an immunity to the frequency-To-Amplitude noise conversion of the “low” resolution Vernier coupling, leading to a signal to noise ratio better than 104. These performances give the spectrometer figure of merit of 4×10−11 cm−1/√ Hz, currently taking third place in rank international state of the art rankin