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快乐十分破解秘籍:Femtosecond covariance spectroscopy
Here we establish femtosecond covariance spectroscopy as a technique that uses ultrashort stochastic light pulses to measure nonlinear material responses. By using pulses with spectrally uncorrelated fluctuations we can leverage on the noise and consider each repetition of the experiment as a measurement under different conditions. In this limit we demonstrate that nonlinear processes in the sample can be retrieved by measuring the spectral correlations in different pulses. We validate the approach by studying stimulated Raman scattering in α-quartz. This concept can be applied to reveal low-energy modes of electronic, spin, and vibrational origin and adapted to different techniques and wavelength ranges, from optical to X-ray free-electron lasers, where strong stochastic fluctuations are unavoidable.
The success of nonlinear optics relies largely on pulse-to-pulse consistency. In contrast, covariance-based techniques used in photoionization electron spectroscopy and mass spectrometry have shown that a wealth of information can be extracted from noise that is lost when averaging multiple measurements. Here, we apply covariance-based detection to nonlinear optical spectroscopy, and show that noise in a femtosecond laser is not necessarily a liability to be mitigated, but can act as a unique and powerful asset. As a proof of principle we apply this approach to the process of stimulated Raman scattering in α-quartz. Our results demonstrate how nonlinear processes in the sample can encode correlations between the spectral components of ultrashort pulses with uncorrelated stochastic fluctuations. This in turn provides richer information compared with the standard nonlinear optics techniques that are based on averages over many repetitions with well-behaved laser pulses. These proof-of-principle results suggest that covariance-based nonlinear spectroscopy will improve the applicability of fs nonlinear spectroscopy in wavelength ranges where stable, transform-limited pulses are not available, such as X-ray free-electron lasers which naturally have spectrally noisy pulses ideally suited for this approach.
?1J.O.T. and G.S. contributed equally to this work.
- ?2To whom correspondence may be addressed. Email: or .
Author contributions: D.F. conceived and led the project; J.O.T., G.S., and A. Montanaro performed the experiment; F. Glerean, F. Giusti, A. Marciniak, F.C., and D.F. contributed to performing the experiments; G.S., A. Montanaro, G.K., and F.B. developed the necessary code for data analysis and performed it; S.A. and S.M. developed the theoretical model; and J.O.T., G.S., and D.F. wrote the paper with contributions from all the other authors.
Reviewers: P.H., University of Zurich; and A.L., University of Konstanz.
The authors declare no conflict of interest.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1821048116/-/DCSupplemental.
- Copyright ? 2019 the Author(s). Published by PNAS.
This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).