Concentration Dependence of Line Shapes in the Band of Acetylene Matthew Cich, Damien Forthomme, Greg Hall, Chris McRaven, Trevor Sears, Sylvestre Twagirayezu

ωrωr ω0ω0 Frequency comb-referenced measurements ω rep and ω o are fixed to the GPS atomic clock standard. Optical frequencies good to better than ω opt = n ω rep + ω 0 2 Lock external laser frequency to comb component ωrωr ω laser = n ω rep + ω 0 + ω laser-off ω0ω0 Use the comb as a frequency ruler by phase locking a spectroscopic laser to a single comb line. We are currently limited to optical wavelengths between 1 and 2 microns.

Line shape measurements 3 Signal-to-noise ratios are 5x10 4 or higher. Low-pressure, Doppler-broadened line, with fit to Gaussian, no variable parameters, no instrumental contribution. At higher pressures collisions interrupt the phase during absorption. The observed line shape then includes information on the dynamics of collision processes. Profiles are more complicated. Expect T 1/2 change in broadening.

Remote Sensing Applications 4 Spectroscopic line intensities and shapes allow us to learn about physical and chemical conditions at inaccessible locations. The atmospheric sensing community, and others, rely on the HITRAN ( spectroscopic database, which is a synthesis of published spectroscopic data of molecules relevant to (mostly) atmospheric chemistry.

Dual Beam Spectrometer 5 Fractional baseline noise reduced to ~5x10 -5 by careful balancing of the power on the signal and reference detectors.

Single Line (P(11) e ) 6 Peak absorption of ~40% Line shape functions? Use quadratic speed- dependent Voigt (QSDV)

Isolated Lines? Measure the line shape as a function of concentration, pressure and temperature. Weak hot band lines blend with the main line in ways that are difficult to quantify- particularly if their positions and intensities are not well known. 7 Schematic background spectrum Subtract QSDV line profile for P(11) with closest hot band lines.

Quantify the Effects Model assuming main plus two weak lines nearby, what are the effects on the modeled spectrum? Middle trace: fit top line using QSDV profile with two additional lines as in HITRAN. Lower trace: effect of 50% change in one hot band intensity and shift. The shape of the residual is typical. Data, central part of a trace 296K, 5.464T, 5.15%

Variation with Temperature Hot band line closest to P(11) has the largest variation and effect

Effects on Line Shape Parameters δ 2 accounts for asymmetry (speed dependence of pressure shift). At higher temperatures, its value is skewed by poor treatment of hot band lines. Contrast to narrowing ( γ 2 ) that shows regular T- dependence.

C 2 H 2 hot band sub-Doppler measurements Most important are the v 4 and v 5 hot bands. HITRAN errors are ±0.001 cm -1 at best. Example of R(12) f hot band line: (17) GHz. Fractional uncertainty 8x Observed/ GHz 18 mTorr pressure With 2-Lorentzian fit. Higher resolution steps across line profile

C 2 H 2 4 hot bands HITRAN has J-dependent errors. We measure some small perturbations that reflect level crossings of dark states 12

Summary Line profiles measured at signal to noise ratios of up to 10 5 for multiple concentrations. Challenging data for line shape models. Weak (~10 -3 ) hot band lines affect line profiles at the level of up to 1% and to do better than 1% for analytical measurements the background lines must be accurately known. Frequency measured many lines in v 4 and v 5 hot bands. Their positions will be added to the C 2 H 2 data base at some point. Spectroscopic parameters can be refined. Weak perturbations give information on level crossings of dark states. At the current level of precision, the effects of a component of a mixture can be modelled by its mole fraction for all line shape models considered.

Greg Hall, Damien Forthomme, Sylvestre Twagirayezu Acknowledgements Chris McRaven (now at Menlo Systems) Gary Lopez (Brown), Matt Cich (just graduated) Arlan Mantz. US Department of Energy, Chemical Physics Program!

Aside: Noise at Line Center? Off line, fractional noise is ~5x10 -5, on line center it’s approximately 10x worse? This is with ~40% attenuation. Suggests the response part of the detection system is not linear. Record A(signal), B(reference) and take: Algebraically cancels if system is linear. Probably an issue with the relative gains in the two lock-in amplifiers. Problem in that this could also affect the line shape measurement (at 5x10 -4 level). Typically, δ is ~0.01, amplitude noise on the laser.

Cavity-enhanced absorption Sub-Doppler measurements in a cavity. Laser locked to cavity; cavity referenced to comb; wavelength modulation detection. 1550nm LASER Beat Detection GPS-referenced Frequency Comb Wavemeter Fiber Amplifier PDH λ/4 Etalon PZT Detector and Lock-in amplifier EOM Lock to sideband PC Absorption cell is FPE. Finesse ~600 Current feedback PZT feed forward 16 Locking and processing electronics EOM

C 2 H 2 5 hot bands HITRAN has regular J-dependent errors. Upper level is regular. 17

Cavity-enhanced absorption Sub-Doppler measurements in a cavity. Laser locked to cavity; cavity referenced to comb; wavelength modulation detection. 1550nm LASER Beat Detection GPS-referenced Frequency Comb Wavemeter EOM Fiber Amplifier PDH λ/4 Etalon PZT LP 300 Hz Phase Detector Lockbox Detector Lock-in Amplifier PC Signal Transmission EOM 188+/-1 MHz 800 Hz 192 MHz Lockbox Lock to sideband φ φ Absorption cell is FPE Current feedback PZT feed forward 18

Other Regions 19 Clearly not isolated, and even if the overlapping lines do not actually perturb the main line, they cause baseline shifts and apparent line position errors if not accounted for correctly.