__–––– Sensitivity Scaling of Dual Frequency Combs Ian Coddington, Esther Baumann, Fabrizio Giorgetta, William Swann, Nate Newbury NIST, Boulder, CO

Outline Introduction Dual-frequency comb spectroscopy Frequency- domain picture Time-domain picture Our experimental setup Deep Averaging Normalization Results for HCN rovibrational band Frequency-domain magnitude & Phase spectrum Time-domain signature Signal to noise shot noise limit dynamic range limit

Combs & Molecular Spectroscopy Comb source  Coherent, broadband  Collimated beam  High freq. accuracy & resolution (set by ref.) Phase lock Signal LO Coherent Dual-Comb Spectroscopy Comb + Cavity Enhancement  Very long effective interaction path & broadband M. J. Thorpe, et al., Science 311, 1595 (2006)., APB, 2008, 91, Gohle et al. PRL 99, (2008). Bernhardt, Nat. Photon., 4, (2009) Comb + High-resolution spectrometer  Resolve individual comb lines → resolution of comb Diddams et al. Nat. 445, 627 (2007). Gohle et al. PRL 99, (2008). Comb + FTIR  Collimated beam for long paths & low 1/f noise J. Mandon, et al., Nature Phot., 3, 99 (2009) Keilmann, et al, Opt. Lett. 29, 1542 (2004) Schiller, Opt. Lett. 27, 766 (2002) Schliesser, Opt. Eexpress, 13, 9029 (2005) Coddington, PRL, 100, (2008) Giaccari, Opt. Express, 16, 4347 (2008) Bernhardt, Nat. Photon., 4, (2009)

Dual-Comb Spectroscopy: Frequency-Domain Picture signal LO fr+ffr+f frfr Phase lock optical frequencies (~200THz) Signal LO Simple picture here assumes “perfect” phase locks i.e. linewidths <<  f r < 1/T obs ff  1-to-1 map of optical to RF  Magnitude and Phase detected RF Comb rf frequencies (MHz) Sweep bandpass x100,000 1 Hz Coddington, PRL, 100, (2008)

Dual-Comb Spectroscopy: Time-domain Picture sourcel LO Phase lock  t  t tt   t  t  Source LO Measured interferogram time Effective time In real time =  f r -1 In effective time = f r -1 Synchronous sampling shown (Sequential interferograms all in step)

Normalization -spectral broadening 2  m 1  m Signal to Noise -averaging

f r +  f ~ 100 MHz + 5 kHz E LO Phase-Locking Two Combs Together Do not need a full octave Phase lock combs to two cw lasers For high frequency accuracy, lock cw lasers to cavity Achieves sub-rad optical coherence f r ~ 100 MHz E signal 1535 nm 1560 nm Cavity stabilized Lasers

Experiment

Normalization, Processing & Reconstruction FFT Deconvolve Signal & Reference Frequency-domain data across filter BW Step filter

Frequency Domain results: Complex Absorption Profile HCN Rovibrational band of C-H overtone Magnitude & Phase Spectral span = 9 THz SNR of 4000 (peak) to 2500 (avg) at 2700 sec averaging → “Quality factor” = (# elements)(SNR) = 2×10 6 Hz 1/2 ~250  rad 2.5×10 -3 Absolute frequency accuracy ~ 10 kHz Resolution = 220 MHz → 41,000 spectral elements

∞ P  Dynamic Range Limit ENOB RIN Dividing up the spectrum -Sequentially -Parallel M (1/2)? T 1/2 [ ( RIN+D 2 / fr ) / ( N det 2 F channels ) ] 1/2  Chirping Dark Fringe RIN Monitoring Newbury, Opt. Express, 18, 7929 (2010)

Swept CW comparison P laser -> P tooth Shot Noise Limit M (1/2) T 1/2 (h -1 h ) / ( N d P ) 1/2  Detector noise Limit Dual comb the stronger technique No benefit to multiple detectors Spectral filtering is a negative Strengths Single detector (Mid IR) Background subtraction -reference channels are easy High resolution Ultra-high frequency accuracy Cavity compatibility 1/ f noise suppression Newbury, Opt. Express, 18, 7929 (2010)

Conclusion Dual-comb coherent spectroscopy can offer: High frequency resolution High frequency accuracy Phase and amplitude of frequency-domain response Low systematics Single detector Significant challenges remain Low comb tooth power limits sensitivity Improved by: Coherent averaging, multipass/cavity enhancement, detector array … Spectral coverage currently limited Spectral broadening “expensive” in photons and coherence System is complex Broader application puts strong demands on comb sources Higher powers, Greater spectral coverage, Greater robustness, Greater coherence......