Sensitivity Scaling of Dual Frequency Combs Ian Coddington

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

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 + Cavity Enhancement Ø Very long effective interaction path & broadband M. J. Thorpe, et al. , Science 311, 1595 (2006). , APB, 2008, 91, 397 -414 Gohle et al. PRL 99, 263902 (2008). Bernhardt, Nat. Photon. , 4, 55 -57 (2009) Comb source Ø Coherent, broadband Ø Collimated beam Ø High freq. accuracy & resolution (set by ref. ) Comb + High-resolution spectrometer Ø Resolve individual comb lines → resolution of comb Diddams et al. Nat. 445, 627 (2007). Gohle et al. PRL 99, 263902 (2008). Comb + FTIR ØCollimated beam for long paths & low 1/f noise J. Mandon, et al. , Nature Phot. , 3, 99 (2009) Coherent Dual-Comb Spectroscopy Signal Phaselock Keilmann, et al, Opt. Lett. 29, 1542 (2004) Schiller, Opt. Lett. 27, 766 (2002) Schliesser, Opt. Eexpress, 13, 9029 (2005) Coddington, PRL , 100, 013902 (2008) Giaccari, Opt. Express, 16, 4347 (2008) Bernhardt, Nat. Photon. , 4, 55 -57 (2009) LO

Phase lock Dual-Comb Spectroscopy: Frequency-Domain Picture Simple picture here assumes “perfect” phase locks i. e. linewidths <<Dfr < 1/Tobs signal LO Sweep bandpass Signal fr+Df LO fr x 100, 000 RF Comb optical frequencies (~200 THz) 1 Hz Df Ø 1 -to-1 map of optical to RF ØMagnitude and Phase detected Coddington, PRL , 100, 013902 (2008) rf frequencies (MHz)

Synchronous sampling shown (Sequential interferograms all in step) sourcel LO In real time =Dfr-1 In effective time = fr-1 -Dt 0 Measured interferogram Source LO Phase lock Dual-Comb Spectroscopy: Time-domain Picture Dt +Dt -Dt time Effective time 0 +Dt

Signal to Noise Normalization -averaging -spectral broadening ��� 1 mm 2 mm

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 ELO Esignal fr ~ 100 MHz Cavity stabilized Lasers fr+Df ~ 100 MHz + 5 k. Hz 1560 nm 1535 nm

Experiment

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

Frequency Domain results: Complex Absorption Profile HCN Rovibrational band of C-H overtone • • • Magnitude & Phase Spectral span = 9 THz • • Absolute frequency accuracy ~ 10 k. Hz Resolution = 220 MHz → 41, 000 spectral elements SNR of 4000 (peak) to 2500 (avg) at 2700 sec averaging → “Quality factor” = (# elements)(SNR) = 2× 106 Hz 1/2 2. 5× 10 -3 ~250 mrad

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

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

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. . .