Abstract

Time-frequency (TF) analysis is a powerful tool for exploring ultrafast dynamics in atoms and molecules. While some TF methods have demonstrated their usefulness and potential in several quantum systems, a systematic comparison among them is still lacking. To this end, we compare a series of classical and contemporary TF methods by taking hydrogen atom in a strong laser field as a benchmark. In addition, several TF methods such as Cohen class distribution other than the Wigner-Ville distribution, reassignment methods, and the empirical mode decomposition method are first introduced to exploration of ultrafast dynamics. Among these TF methods, the synchrosqueezing transform successfully illustrates the physical mechanisms in the multiphoton ionization regime and in the tunneling ionization regime. Furthermore, an empirical procedure to analyze an unknown complicated quantum system is provided, suggesting the versatility of TF analysis as a new viable venue for exploring quantum dynamics.

© 2015 Optical Society of America

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References

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  1. T. Fuji, T. Saito, and T. Kobayashi, “Dynamical observation of Duschinsky rotation by sub-5-fs real-time spectroscopy,” Chem. Phys. Lett. 11(2), 99–116 (2011).
  2. T. Kobayashi and A. Yabushita, “Transition-state spectroscopy using ultrashort laser pulses,” Chem Rec. 11(2), 99–116 (2011).
    [Crossref] [PubMed]
  3. M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wave packet,” Phys. Rev. A 54(1), R37 (1996).
    [Crossref] [PubMed]
  4. L. Wang, W. Liu, and C. Fang, “Elucidating low-frequency vibrational dynamics in calcite and water with time-resolved third-harmonic generation spectroscopy,” Phys. Chem. Chem. Phys. 17(26), 17034 (2015).
    [Crossref] [PubMed]
  5. A. Volpato and E. Collini, “Time-frequency methods for coherent spectroscopy,” Opt. Express 23(15), 20040–20050 (2015).
    [Crossref] [PubMed]
  6. J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: Efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys 139(22), 224103 (2013).
    [Crossref] [PubMed]
  7. Y. Deng, Q. Sun, F. Liu, C. Wang, and Q. Xing, “Terahertz time-resolved spectroscopy with wavelet-transform,” in International Congress on Image and Signal Processing (IEEE, 2010), pp. 3462–3464.
    [Crossref]
  8. C. Y. Wong, R. M. Alvey, D. B. Turner, K. E. Wilk, D. A. Bryant, P. M. G. Curmi, R. J. Silbey, and G. D. Scholes, “Electronic coherence lineshapes reveal hidden excitonic correlations in photosynthetic light harvesting,” Nat. Chem. 4(5), 396–404 (2012).
    [Crossref] [PubMed]
  9. S. D. McClure, D. B. Turner, P. C. Arpin, T. Mirkovic, and G. D. Scholes, “Coherent oscillations in the PC577 cryptophyte antenna occur in the excited electronic state,” J. Phys. Chem. 118(5), 1296–1308 (2014).
    [Crossref]
  10. D. B. Turner, R. Dinshaw, K.-K. Lee, M. S. Belsley, K. E. Wilk, P. M. G. Curmic, and G. D. Scholes, “Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis,” Phys. Chem. Chem. Phys. 14, 4857–4874 (2012).
    [Crossref] [PubMed]
  11. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
    [Crossref]
  12. C. C. Chirila, I. Dreissigacker, E. V. van der Zwan, and M. Lein, “Emission times in high-order harmonic generation,” Phys. Rev. A 81(3), 033412 (2010).
    [Crossref]
  13. C. Figueira de Morisson Faria, M. Dorr, W. Becker, and W. Sandner, “Time-frequency analysis of two-color high-harmonic generation,” Phys. Rev. A 60(2), 1377–1384 (1999).
    [Crossref]
  14. P. Antoine, B. Piraux, D. B. Milosevic, and M. Gajda, “Generation of ultrashort pulses of harmonics,” Phys. Rev. A 54(3), R1761–R1764 (1996).
    [Crossref] [PubMed]
  15. X. M. Tong and Shih I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61(2), 021802(R) (2000).
    [Crossref]
  16. X. Chu, S. I. Chu, and C. Laughlin, “Spectral and temporal structures of high-order harmonic generation of Na in intense mid-ir laser fields,” Phys. Rev. A 64(1), 013406 (2001).
    [Crossref]
  17. J. Chen, S. I. Chu, and J. Liu, “Time-frequency analysis of molecular high-harmonic generation spectrum by means of wavelet transform and Wigner distribution techniques,” J. Phys. B: At. Mol. Opt. Phys. 39(22), 4747–4758 (2006).
    [Crossref]
  18. F. Risoud, J. Caillat, A. Maquet, R. Taieb, and C. Leveque, “Quantitative extraction of the emission times of high-order harmonics via the determination of instantaneous frequencies,” Phys. Rev. A 88(4), 043415 (2013).
    [Crossref]
  19. P.-C. Li, Y.-L. Sheu, C. Laughlin, and S.-I Chu, “Role of laser-driven electron-multirescattering in resonance-enhanced below-threshold harmonic generation in He atoms,” Phys. Rev. A 90(4), 041401(R) (2014).
    [Crossref]
  20. P.-C. Li, Y.-L. Sheu, C. Laughlin, and S.-I Chu, “Dynamical origin of near- and below-threshold harmonic generation of Cs in an intense mid-infrared laser field,” Nat. Comm. 6, 7178 (2015).
    [Crossref]
  21. S. Phillips, R. J. Gledhill, J. W. Essex, and C. M. Edge, “Application of the Hilbert-Huang transform to the analysis of molecular dynamics simulations,” J. Phys. Chem. A 107(24), 4869–4876 (2003).
    [Crossref]
  22. M. Orini, R. Bailon, L. T. Mainardi, P. Laguna, and P. Flandrin, “Characterization of dynamic interactions between cardiovascular signals by time-frequency coherence,” IEEE Trans. Biomed. Eng 59(3), 663–673 (2012).
    [Crossref]
  23. Y. F. Suprunenko, P. T. Clemson, and A. Stefanovska, “Chronotaxic systems: a new class of self-sustained nonautonomous oscillators,” Phys. Rev. Lett. 111(2), 024101 (2013).
    [Crossref] [PubMed]
  24. M. Niethammer, L. J. Jacobs, J. Qu, and J. Jarzynski, “Time-frequency representations of Lamb waves,” J. Acoust. Soc. Am. 109(5 Pt 1), 1841–1847 (2001).
    [Crossref] [PubMed]
  25. P. Wang, J. Gao, and Z. Wang, “Time-frequency analysis of seismic data using synchrosqueezing transform,” IEEE Geosci. Remote Sens. Lett. 11(12), 2042–2044 (2014).
    [Crossref]
  26. A. Ludwig, J. Maurer, B. M. Mayer, C. R. Phillips, L. Gallmann, and U. Keller, “Breakdown of the dipole approximation in strong-field ionization,” Phys. Rev. Lett. 113(24), 243001 (2014).
    [Crossref] [PubMed]
  27. C. Yao and S. I. Chu, “Generalized pseudospectral methods with mappings for bound and resonance state problems,” Chem. Phys. Lett. 204(3–4), 381–388 (1993).
    [Crossref]
  28. X. M. Tong and S. I. Chu, “Theoretical study of multiple high-order harmonic generation by intense ultrashort pulsed laser fields: a new generalized pseudospectral time-dependent method,” Chem. Phys. 217(2–3), 119–130 (1997).
    [Crossref]
  29. Z. Chang, Fundamentals of attosecond optics (CRC, 2011).
    [Crossref]
  30. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
    [Crossref] [PubMed]
  31. P. Flandrin, Time-frequency/time-scale analysis, wavelet analysis and its applications (Academic, 1999).
  32. I. Daubechies, Ten lectures on wavelets (Society for Industrial and Applied Mathematics, 1992).
    [Crossref]
  33. J. C. O’Neill and P. Flandrin, “Virtues and vices of quartic timefrequency distributions,” IEEE Trans. Signal Process. 48(9), 2641–2650 (2000).
    [Crossref]
  34. B. Boashash and B. Ristich, “Polynomial Wigner-Ville distributions and time-varying higher-order spectra,” in Time-Frequency and Time-Scale Analysis, in Proceedings of IEEE-SP Int. Symp. (1992), pp. 31–34.
  35. P. Flandrin, F. Auger, and E. Chassande-Mottin, Time-frequency signal processing (CRC, 2003).
  36. F. Auger and P. Flandrin, “Improving the readability of time-frequency and time-scale representations by the reassignment method,” IEEE Trans. Signal Process.,  43(5), 1068–1089 (1995).
    [Crossref]
  37. F. Auger, P. Flandrin, Y. T. Lin, S. McLaughlin, S. Meignen, T. Oberlin, and H. T. Wu, “Time-frequency reassignment and synchrosqueezing,” IEEE Signal Processing Mag. 30(6), 32–41 (2013).
    [Crossref]
  38. I. Daubechies, J. Lu, and H. T. Wu, “Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool,” Appl. Comput. Harmon. Anal. 30(1), 243–261 (2011).
    [Crossref]
  39. H. T. Wu, Adaptive analysis of complex data sets Doctoral dissertation (Princeton University, 2011).
  40. Y.-C. Chen, M. Y. Cheng, and H. T. Wu, “Nonparametric and adaptive modeling of dynamic periodicity and trend with heteroscedastic and dependent errors,” J. R. Stat. Soc. B 76(3), 651–682 (2014).
    [Crossref]
  41. T. Oberlin, S. Meignen, and V. Perrier, “Second-order synchrosqueezing transform or invertible reassignment? towards ideal time-frequency representations,” IEEE Trans. Signal Process. 63(5), 1335–1344 (2015).
    [Crossref]
  42. L. Cohen, Time-frequency analysis, signal processing series (Prentice-Hall, 1995).
  43. D. Gabor, “Theory of communication,” Proc. IEE,  93, 429–457 (1946).
  44. N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time Series analysis,” Proc. R. Soc. A 454(1971), 903–995 (1998).
    [Crossref]
  45. G. Rilling and P. Flandrin, “One or two frequencies? the empirical mode decomposition answers,” IEEE Trans. Signal Process. 56(1), 85–95 (2008).
    [Crossref]
  46. S. H. Lin, Advances in multi-photon processes and spectroscopy (World Scientific Publishing, 2010), Vol. 19.
  47. K. Mishima, K. Nagaya, M. Hayashi, and S. H. Lin, “Towards the realization of the quantum chemistry approach to tunneling photoionization processes in strong laser fields,” J. Chem. Phys. 122(2), 024104 (2005).
    [Crossref] [PubMed]
  48. H. Mineo, K. Nagaya, M. Hayashi, and S. H. Lin, “Theoretical studies of high-harmonic generation based on the KeldyshFaisalReiss theory,” J. Phys. B: At. Mol. Opt. Phys. 40(12), 2435–2451 (2007).
    [Crossref]
  49. Y. Nomura, Y. Fujimura, and H. Kono, “Theory of quantum beats in timeresolved multiphoton ionization of molecules,” J. Chem. Phys. 88(3), 1501–1510 (1988).
    [Crossref]
  50. M. Gavrila, Atoms in intense laser fields (Academic, 1992).
  51. P. Gibbon, Short pulse laser interactions with matter (Imperial College, 2005).
  52. E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in a Keldysh-scaled system,” Nature Photon. 4(6), 352–356 (2010).
    [Crossref]
  53. J. H. Shirley, “Solution of the Schrodinger equation with a hamiltonian periodic in time,” Phys. Rev. B 138(4B), B979–B987 (1965).
    [Crossref]
  54. L. Y. Hsu, D. Xie, and H. Rabitz, “Light-driven electron transport through a molecular junction based on cross-conjugated systems,” J. Chem. Phys. 141(12), 124703 (2014).
    [Crossref] [PubMed]
  55. L. Y. Hsu and H. Rabitz, “Coherent light-driven electron transport through polycyclic aromatic hydrocarbon: laser frequency, field intensity, and polarization angle dependence,” Phys. Chem. Chem. Phys. 17(32), 20617–20629 (2015).
    [Crossref] [PubMed]
  56. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
    [Crossref] [PubMed]
  57. K. C. Kulander, K. J. Schafer, and J. L. Krause, in Proceedings of the Workshop on Super-Intense Laser Atom Physics (SILAP) III. (Plenum, 1993).

2015 (5)

P.-C. Li, Y.-L. Sheu, C. Laughlin, and S.-I Chu, “Dynamical origin of near- and below-threshold harmonic generation of Cs in an intense mid-infrared laser field,” Nat. Comm. 6, 7178 (2015).
[Crossref]

T. Oberlin, S. Meignen, and V. Perrier, “Second-order synchrosqueezing transform or invertible reassignment? towards ideal time-frequency representations,” IEEE Trans. Signal Process. 63(5), 1335–1344 (2015).
[Crossref]

L. Y. Hsu and H. Rabitz, “Coherent light-driven electron transport through polycyclic aromatic hydrocarbon: laser frequency, field intensity, and polarization angle dependence,” Phys. Chem. Chem. Phys. 17(32), 20617–20629 (2015).
[Crossref] [PubMed]

L. Wang, W. Liu, and C. Fang, “Elucidating low-frequency vibrational dynamics in calcite and water with time-resolved third-harmonic generation spectroscopy,” Phys. Chem. Chem. Phys. 17(26), 17034 (2015).
[Crossref] [PubMed]

A. Volpato and E. Collini, “Time-frequency methods for coherent spectroscopy,” Opt. Express 23(15), 20040–20050 (2015).
[Crossref] [PubMed]

2014 (6)

L. Y. Hsu, D. Xie, and H. Rabitz, “Light-driven electron transport through a molecular junction based on cross-conjugated systems,” J. Chem. Phys. 141(12), 124703 (2014).
[Crossref] [PubMed]

Y.-C. Chen, M. Y. Cheng, and H. T. Wu, “Nonparametric and adaptive modeling of dynamic periodicity and trend with heteroscedastic and dependent errors,” J. R. Stat. Soc. B 76(3), 651–682 (2014).
[Crossref]

P. Wang, J. Gao, and Z. Wang, “Time-frequency analysis of seismic data using synchrosqueezing transform,” IEEE Geosci. Remote Sens. Lett. 11(12), 2042–2044 (2014).
[Crossref]

A. Ludwig, J. Maurer, B. M. Mayer, C. R. Phillips, L. Gallmann, and U. Keller, “Breakdown of the dipole approximation in strong-field ionization,” Phys. Rev. Lett. 113(24), 243001 (2014).
[Crossref] [PubMed]

P.-C. Li, Y.-L. Sheu, C. Laughlin, and S.-I Chu, “Role of laser-driven electron-multirescattering in resonance-enhanced below-threshold harmonic generation in He atoms,” Phys. Rev. A 90(4), 041401(R) (2014).
[Crossref]

S. D. McClure, D. B. Turner, P. C. Arpin, T. Mirkovic, and G. D. Scholes, “Coherent oscillations in the PC577 cryptophyte antenna occur in the excited electronic state,” J. Phys. Chem. 118(5), 1296–1308 (2014).
[Crossref]

2013 (4)

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: Efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys 139(22), 224103 (2013).
[Crossref] [PubMed]

Y. F. Suprunenko, P. T. Clemson, and A. Stefanovska, “Chronotaxic systems: a new class of self-sustained nonautonomous oscillators,” Phys. Rev. Lett. 111(2), 024101 (2013).
[Crossref] [PubMed]

F. Risoud, J. Caillat, A. Maquet, R. Taieb, and C. Leveque, “Quantitative extraction of the emission times of high-order harmonics via the determination of instantaneous frequencies,” Phys. Rev. A 88(4), 043415 (2013).
[Crossref]

F. Auger, P. Flandrin, Y. T. Lin, S. McLaughlin, S. Meignen, T. Oberlin, and H. T. Wu, “Time-frequency reassignment and synchrosqueezing,” IEEE Signal Processing Mag. 30(6), 32–41 (2013).
[Crossref]

2012 (3)

M. Orini, R. Bailon, L. T. Mainardi, P. Laguna, and P. Flandrin, “Characterization of dynamic interactions between cardiovascular signals by time-frequency coherence,” IEEE Trans. Biomed. Eng 59(3), 663–673 (2012).
[Crossref]

C. Y. Wong, R. M. Alvey, D. B. Turner, K. E. Wilk, D. A. Bryant, P. M. G. Curmi, R. J. Silbey, and G. D. Scholes, “Electronic coherence lineshapes reveal hidden excitonic correlations in photosynthetic light harvesting,” Nat. Chem. 4(5), 396–404 (2012).
[Crossref] [PubMed]

D. B. Turner, R. Dinshaw, K.-K. Lee, M. S. Belsley, K. E. Wilk, P. M. G. Curmic, and G. D. Scholes, “Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis,” Phys. Chem. Chem. Phys. 14, 4857–4874 (2012).
[Crossref] [PubMed]

2011 (3)

I. Daubechies, J. Lu, and H. T. Wu, “Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool,” Appl. Comput. Harmon. Anal. 30(1), 243–261 (2011).
[Crossref]

T. Fuji, T. Saito, and T. Kobayashi, “Dynamical observation of Duschinsky rotation by sub-5-fs real-time spectroscopy,” Chem. Phys. Lett. 11(2), 99–116 (2011).

T. Kobayashi and A. Yabushita, “Transition-state spectroscopy using ultrashort laser pulses,” Chem Rec. 11(2), 99–116 (2011).
[Crossref] [PubMed]

2010 (2)

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in a Keldysh-scaled system,” Nature Photon. 4(6), 352–356 (2010).
[Crossref]

C. C. Chirila, I. Dreissigacker, E. V. van der Zwan, and M. Lein, “Emission times in high-order harmonic generation,” Phys. Rev. A 81(3), 033412 (2010).
[Crossref]

2009 (1)

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
[Crossref]

2008 (1)

G. Rilling and P. Flandrin, “One or two frequencies? the empirical mode decomposition answers,” IEEE Trans. Signal Process. 56(1), 85–95 (2008).
[Crossref]

2007 (1)

H. Mineo, K. Nagaya, M. Hayashi, and S. H. Lin, “Theoretical studies of high-harmonic generation based on the KeldyshFaisalReiss theory,” J. Phys. B: At. Mol. Opt. Phys. 40(12), 2435–2451 (2007).
[Crossref]

2006 (1)

J. Chen, S. I. Chu, and J. Liu, “Time-frequency analysis of molecular high-harmonic generation spectrum by means of wavelet transform and Wigner distribution techniques,” J. Phys. B: At. Mol. Opt. Phys. 39(22), 4747–4758 (2006).
[Crossref]

2005 (1)

K. Mishima, K. Nagaya, M. Hayashi, and S. H. Lin, “Towards the realization of the quantum chemistry approach to tunneling photoionization processes in strong laser fields,” J. Chem. Phys. 122(2), 024104 (2005).
[Crossref] [PubMed]

2003 (1)

S. Phillips, R. J. Gledhill, J. W. Essex, and C. M. Edge, “Application of the Hilbert-Huang transform to the analysis of molecular dynamics simulations,” J. Phys. Chem. A 107(24), 4869–4876 (2003).
[Crossref]

2001 (2)

M. Niethammer, L. J. Jacobs, J. Qu, and J. Jarzynski, “Time-frequency representations of Lamb waves,” J. Acoust. Soc. Am. 109(5 Pt 1), 1841–1847 (2001).
[Crossref] [PubMed]

X. Chu, S. I. Chu, and C. Laughlin, “Spectral and temporal structures of high-order harmonic generation of Na in intense mid-ir laser fields,” Phys. Rev. A 64(1), 013406 (2001).
[Crossref]

2000 (2)

X. M. Tong and Shih I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61(2), 021802(R) (2000).
[Crossref]

J. C. O’Neill and P. Flandrin, “Virtues and vices of quartic timefrequency distributions,” IEEE Trans. Signal Process. 48(9), 2641–2650 (2000).
[Crossref]

1999 (1)

C. Figueira de Morisson Faria, M. Dorr, W. Becker, and W. Sandner, “Time-frequency analysis of two-color high-harmonic generation,” Phys. Rev. A 60(2), 1377–1384 (1999).
[Crossref]

1998 (1)

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time Series analysis,” Proc. R. Soc. A 454(1971), 903–995 (1998).
[Crossref]

1997 (1)

X. M. Tong and S. I. Chu, “Theoretical study of multiple high-order harmonic generation by intense ultrashort pulsed laser fields: a new generalized pseudospectral time-dependent method,” Chem. Phys. 217(2–3), 119–130 (1997).
[Crossref]

1996 (2)

P. Antoine, B. Piraux, D. B. Milosevic, and M. Gajda, “Generation of ultrashort pulses of harmonics,” Phys. Rev. A 54(3), R1761–R1764 (1996).
[Crossref] [PubMed]

M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wave packet,” Phys. Rev. A 54(1), R37 (1996).
[Crossref] [PubMed]

1995 (1)

F. Auger and P. Flandrin, “Improving the readability of time-frequency and time-scale representations by the reassignment method,” IEEE Trans. Signal Process.,  43(5), 1068–1089 (1995).
[Crossref]

1994 (1)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref] [PubMed]

1993 (2)

C. Yao and S. I. Chu, “Generalized pseudospectral methods with mappings for bound and resonance state problems,” Chem. Phys. Lett. 204(3–4), 381–388 (1993).
[Crossref]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref] [PubMed]

1988 (1)

Y. Nomura, Y. Fujimura, and H. Kono, “Theory of quantum beats in timeresolved multiphoton ionization of molecules,” J. Chem. Phys. 88(3), 1501–1510 (1988).
[Crossref]

1965 (1)

J. H. Shirley, “Solution of the Schrodinger equation with a hamiltonian periodic in time,” Phys. Rev. B 138(4B), B979–B987 (1965).
[Crossref]

1946 (1)

D. Gabor, “Theory of communication,” Proc. IEE,  93, 429–457 (1946).

Agostini, P.

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in a Keldysh-scaled system,” Nature Photon. 4(6), 352–356 (2010).
[Crossref]

Almeida, J.

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: Efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys 139(22), 224103 (2013).
[Crossref] [PubMed]

Alvey, R. M.

C. Y. Wong, R. M. Alvey, D. B. Turner, K. E. Wilk, D. A. Bryant, P. M. G. Curmi, R. J. Silbey, and G. D. Scholes, “Electronic coherence lineshapes reveal hidden excitonic correlations in photosynthetic light harvesting,” Nat. Chem. 4(5), 396–404 (2012).
[Crossref] [PubMed]

Antoine, P.

P. Antoine, B. Piraux, D. B. Milosevic, and M. Gajda, “Generation of ultrashort pulses of harmonics,” Phys. Rev. A 54(3), R1761–R1764 (1996).
[Crossref] [PubMed]

Arpin, P. C.

S. D. McClure, D. B. Turner, P. C. Arpin, T. Mirkovic, and G. D. Scholes, “Coherent oscillations in the PC577 cryptophyte antenna occur in the excited electronic state,” J. Phys. Chem. 118(5), 1296–1308 (2014).
[Crossref]

Auger, F.

F. Auger, P. Flandrin, Y. T. Lin, S. McLaughlin, S. Meignen, T. Oberlin, and H. T. Wu, “Time-frequency reassignment and synchrosqueezing,” IEEE Signal Processing Mag. 30(6), 32–41 (2013).
[Crossref]

F. Auger and P. Flandrin, “Improving the readability of time-frequency and time-scale representations by the reassignment method,” IEEE Trans. Signal Process.,  43(5), 1068–1089 (1995).
[Crossref]

P. Flandrin, F. Auger, and E. Chassande-Mottin, Time-frequency signal processing (CRC, 2003).

Bailon, R.

M. Orini, R. Bailon, L. T. Mainardi, P. Laguna, and P. Flandrin, “Characterization of dynamic interactions between cardiovascular signals by time-frequency coherence,” IEEE Trans. Biomed. Eng 59(3), 663–673 (2012).
[Crossref]

Balcou, P.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref] [PubMed]

Becker, W.

C. Figueira de Morisson Faria, M. Dorr, W. Becker, and W. Sandner, “Time-frequency analysis of two-color high-harmonic generation,” Phys. Rev. A 60(2), 1377–1384 (1999).
[Crossref]

Belsley, M. S.

D. B. Turner, R. Dinshaw, K.-K. Lee, M. S. Belsley, K. E. Wilk, P. M. G. Curmic, and G. D. Scholes, “Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis,” Phys. Chem. Chem. Phys. 14, 4857–4874 (2012).
[Crossref] [PubMed]

Boashash, B.

B. Boashash and B. Ristich, “Polynomial Wigner-Ville distributions and time-varying higher-order spectra,” in Time-Frequency and Time-Scale Analysis, in Proceedings of IEEE-SP Int. Symp. (1992), pp. 31–34.

Bryant, D. A.

C. Y. Wong, R. M. Alvey, D. B. Turner, K. E. Wilk, D. A. Bryant, P. M. G. Curmi, R. J. Silbey, and G. D. Scholes, “Electronic coherence lineshapes reveal hidden excitonic correlations in photosynthetic light harvesting,” Nat. Chem. 4(5), 396–404 (2012).
[Crossref] [PubMed]

Caillat, J.

F. Risoud, J. Caillat, A. Maquet, R. Taieb, and C. Leveque, “Quantitative extraction of the emission times of high-order harmonics via the determination of instantaneous frequencies,” Phys. Rev. A 88(4), 043415 (2013).
[Crossref]

Castro, E.

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: Efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys 139(22), 224103 (2013).
[Crossref] [PubMed]

Catoire, F.

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in a Keldysh-scaled system,” Nature Photon. 4(6), 352–356 (2010).
[Crossref]

Chang, Z.

Z. Chang, Fundamentals of attosecond optics (CRC, 2011).
[Crossref]

Chassande-Mottin, E.

P. Flandrin, F. Auger, and E. Chassande-Mottin, Time-frequency signal processing (CRC, 2003).

Chen, J.

J. Chen, S. I. Chu, and J. Liu, “Time-frequency analysis of molecular high-harmonic generation spectrum by means of wavelet transform and Wigner distribution techniques,” J. Phys. B: At. Mol. Opt. Phys. 39(22), 4747–4758 (2006).
[Crossref]

Chen, Y.-C.

Y.-C. Chen, M. Y. Cheng, and H. T. Wu, “Nonparametric and adaptive modeling of dynamic periodicity and trend with heteroscedastic and dependent errors,” J. R. Stat. Soc. B 76(3), 651–682 (2014).
[Crossref]

Cheng, M. Y.

Y.-C. Chen, M. Y. Cheng, and H. T. Wu, “Nonparametric and adaptive modeling of dynamic periodicity and trend with heteroscedastic and dependent errors,” J. R. Stat. Soc. B 76(3), 651–682 (2014).
[Crossref]

Chin, A. W.

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: Efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys 139(22), 224103 (2013).
[Crossref] [PubMed]

Chirila, C. C.

C. C. Chirila, I. Dreissigacker, E. V. van der Zwan, and M. Lein, “Emission times in high-order harmonic generation,” Phys. Rev. A 81(3), 033412 (2010).
[Crossref]

Chu, S. I.

J. Chen, S. I. Chu, and J. Liu, “Time-frequency analysis of molecular high-harmonic generation spectrum by means of wavelet transform and Wigner distribution techniques,” J. Phys. B: At. Mol. Opt. Phys. 39(22), 4747–4758 (2006).
[Crossref]

X. Chu, S. I. Chu, and C. Laughlin, “Spectral and temporal structures of high-order harmonic generation of Na in intense mid-ir laser fields,” Phys. Rev. A 64(1), 013406 (2001).
[Crossref]

X. M. Tong and S. I. Chu, “Theoretical study of multiple high-order harmonic generation by intense ultrashort pulsed laser fields: a new generalized pseudospectral time-dependent method,” Chem. Phys. 217(2–3), 119–130 (1997).
[Crossref]

C. Yao and S. I. Chu, “Generalized pseudospectral methods with mappings for bound and resonance state problems,” Chem. Phys. Lett. 204(3–4), 381–388 (1993).
[Crossref]

Chu, S.-I

P.-C. Li, Y.-L. Sheu, C. Laughlin, and S.-I Chu, “Dynamical origin of near- and below-threshold harmonic generation of Cs in an intense mid-infrared laser field,” Nat. Comm. 6, 7178 (2015).
[Crossref]

P.-C. Li, Y.-L. Sheu, C. Laughlin, and S.-I Chu, “Role of laser-driven electron-multirescattering in resonance-enhanced below-threshold harmonic generation in He atoms,” Phys. Rev. A 90(4), 041401(R) (2014).
[Crossref]

Chu, Shih I.

X. M. Tong and Shih I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61(2), 021802(R) (2000).
[Crossref]

Chu, X.

X. Chu, S. I. Chu, and C. Laughlin, “Spectral and temporal structures of high-order harmonic generation of Na in intense mid-ir laser fields,” Phys. Rev. A 64(1), 013406 (2001).
[Crossref]

Clemson, P. T.

Y. F. Suprunenko, P. T. Clemson, and A. Stefanovska, “Chronotaxic systems: a new class of self-sustained nonautonomous oscillators,” Phys. Rev. Lett. 111(2), 024101 (2013).
[Crossref] [PubMed]

Cohen, L.

L. Cohen, Time-frequency analysis, signal processing series (Prentice-Hall, 1995).

Collini, E.

Corkum, P. B.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref] [PubMed]

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref] [PubMed]

Curmi, P. M. G.

C. Y. Wong, R. M. Alvey, D. B. Turner, K. E. Wilk, D. A. Bryant, P. M. G. Curmi, R. J. Silbey, and G. D. Scholes, “Electronic coherence lineshapes reveal hidden excitonic correlations in photosynthetic light harvesting,” Nat. Chem. 4(5), 396–404 (2012).
[Crossref] [PubMed]

Curmic, P. M. G.

D. B. Turner, R. Dinshaw, K.-K. Lee, M. S. Belsley, K. E. Wilk, P. M. G. Curmic, and G. D. Scholes, “Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis,” Phys. Chem. Chem. Phys. 14, 4857–4874 (2012).
[Crossref] [PubMed]

Daubechies, I.

I. Daubechies, J. Lu, and H. T. Wu, “Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool,” Appl. Comput. Harmon. Anal. 30(1), 243–261 (2011).
[Crossref]

I. Daubechies, Ten lectures on wavelets (Society for Industrial and Applied Mathematics, 1992).
[Crossref]

Deng, Y.

Y. Deng, Q. Sun, F. Liu, C. Wang, and Q. Xing, “Terahertz time-resolved spectroscopy with wavelet-transform,” in International Congress on Image and Signal Processing (IEEE, 2010), pp. 3462–3464.
[Crossref]

DiMauro, L. F.

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in a Keldysh-scaled system,” Nature Photon. 4(6), 352–356 (2010).
[Crossref]

Dinshaw, R.

D. B. Turner, R. Dinshaw, K.-K. Lee, M. S. Belsley, K. E. Wilk, P. M. G. Curmic, and G. D. Scholes, “Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis,” Phys. Chem. Chem. Phys. 14, 4857–4874 (2012).
[Crossref] [PubMed]

Dorr, M.

C. Figueira de Morisson Faria, M. Dorr, W. Becker, and W. Sandner, “Time-frequency analysis of two-color high-harmonic generation,” Phys. Rev. A 60(2), 1377–1384 (1999).
[Crossref]

Dreissigacker, I.

C. C. Chirila, I. Dreissigacker, E. V. van der Zwan, and M. Lein, “Emission times in high-order harmonic generation,” Phys. Rev. A 81(3), 033412 (2010).
[Crossref]

Edge, C. M.

S. Phillips, R. J. Gledhill, J. W. Essex, and C. M. Edge, “Application of the Hilbert-Huang transform to the analysis of molecular dynamics simulations,” J. Phys. Chem. A 107(24), 4869–4876 (2003).
[Crossref]

Essex, J. W.

S. Phillips, R. J. Gledhill, J. W. Essex, and C. M. Edge, “Application of the Hilbert-Huang transform to the analysis of molecular dynamics simulations,” J. Phys. Chem. A 107(24), 4869–4876 (2003).
[Crossref]

Fang, C.

L. Wang, W. Liu, and C. Fang, “Elucidating low-frequency vibrational dynamics in calcite and water with time-resolved third-harmonic generation spectroscopy,” Phys. Chem. Chem. Phys. 17(26), 17034 (2015).
[Crossref] [PubMed]

Figueira de Morisson Faria, C.

C. Figueira de Morisson Faria, M. Dorr, W. Becker, and W. Sandner, “Time-frequency analysis of two-color high-harmonic generation,” Phys. Rev. A 60(2), 1377–1384 (1999).
[Crossref]

Flandrin, P.

F. Auger, P. Flandrin, Y. T. Lin, S. McLaughlin, S. Meignen, T. Oberlin, and H. T. Wu, “Time-frequency reassignment and synchrosqueezing,” IEEE Signal Processing Mag. 30(6), 32–41 (2013).
[Crossref]

M. Orini, R. Bailon, L. T. Mainardi, P. Laguna, and P. Flandrin, “Characterization of dynamic interactions between cardiovascular signals by time-frequency coherence,” IEEE Trans. Biomed. Eng 59(3), 663–673 (2012).
[Crossref]

G. Rilling and P. Flandrin, “One or two frequencies? the empirical mode decomposition answers,” IEEE Trans. Signal Process. 56(1), 85–95 (2008).
[Crossref]

J. C. O’Neill and P. Flandrin, “Virtues and vices of quartic timefrequency distributions,” IEEE Trans. Signal Process. 48(9), 2641–2650 (2000).
[Crossref]

F. Auger and P. Flandrin, “Improving the readability of time-frequency and time-scale representations by the reassignment method,” IEEE Trans. Signal Process.,  43(5), 1068–1089 (1995).
[Crossref]

P. Flandrin, F. Auger, and E. Chassande-Mottin, Time-frequency signal processing (CRC, 2003).

P. Flandrin, Time-frequency/time-scale analysis, wavelet analysis and its applications (Academic, 1999).

Fuji, T.

T. Fuji, T. Saito, and T. Kobayashi, “Dynamical observation of Duschinsky rotation by sub-5-fs real-time spectroscopy,” Chem. Phys. Lett. 11(2), 99–116 (2011).

Fujimura, Y.

Y. Nomura, Y. Fujimura, and H. Kono, “Theory of quantum beats in timeresolved multiphoton ionization of molecules,” J. Chem. Phys. 88(3), 1501–1510 (1988).
[Crossref]

Gabor, D.

D. Gabor, “Theory of communication,” Proc. IEE,  93, 429–457 (1946).

Gajda, M.

P. Antoine, B. Piraux, D. B. Milosevic, and M. Gajda, “Generation of ultrashort pulses of harmonics,” Phys. Rev. A 54(3), R1761–R1764 (1996).
[Crossref] [PubMed]

Gallmann, L.

A. Ludwig, J. Maurer, B. M. Mayer, C. R. Phillips, L. Gallmann, and U. Keller, “Breakdown of the dipole approximation in strong-field ionization,” Phys. Rev. Lett. 113(24), 243001 (2014).
[Crossref] [PubMed]

Gao, J.

P. Wang, J. Gao, and Z. Wang, “Time-frequency analysis of seismic data using synchrosqueezing transform,” IEEE Geosci. Remote Sens. Lett. 11(12), 2042–2044 (2014).
[Crossref]

Gavrila, M.

M. Gavrila, Atoms in intense laser fields (Academic, 1992).

Gibbon, P.

P. Gibbon, Short pulse laser interactions with matter (Imperial College, 2005).

Gledhill, R. J.

S. Phillips, R. J. Gledhill, J. W. Essex, and C. M. Edge, “Application of the Hilbert-Huang transform to the analysis of molecular dynamics simulations,” J. Phys. Chem. A 107(24), 4869–4876 (2003).
[Crossref]

Hayashi, M.

H. Mineo, K. Nagaya, M. Hayashi, and S. H. Lin, “Theoretical studies of high-harmonic generation based on the KeldyshFaisalReiss theory,” J. Phys. B: At. Mol. Opt. Phys. 40(12), 2435–2451 (2007).
[Crossref]

K. Mishima, K. Nagaya, M. Hayashi, and S. H. Lin, “Towards the realization of the quantum chemistry approach to tunneling photoionization processes in strong laser fields,” J. Chem. Phys. 122(2), 024104 (2005).
[Crossref] [PubMed]

Hsu, L. Y.

L. Y. Hsu and H. Rabitz, “Coherent light-driven electron transport through polycyclic aromatic hydrocarbon: laser frequency, field intensity, and polarization angle dependence,” Phys. Chem. Chem. Phys. 17(32), 20617–20629 (2015).
[Crossref] [PubMed]

L. Y. Hsu, D. Xie, and H. Rabitz, “Light-driven electron transport through a molecular junction based on cross-conjugated systems,” J. Chem. Phys. 141(12), 124703 (2014).
[Crossref] [PubMed]

Huang, N. E.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time Series analysis,” Proc. R. Soc. A 454(1971), 903–995 (1998).
[Crossref]

Huelga, S. F.

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: Efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys 139(22), 224103 (2013).
[Crossref] [PubMed]

Ivanov, M.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
[Crossref]

Ivanov, M. Y.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref] [PubMed]

Jacobs, L. J.

M. Niethammer, L. J. Jacobs, J. Qu, and J. Jarzynski, “Time-frequency representations of Lamb waves,” J. Acoust. Soc. Am. 109(5 Pt 1), 1841–1847 (2001).
[Crossref] [PubMed]

Jarzynski, J.

M. Niethammer, L. J. Jacobs, J. Qu, and J. Jarzynski, “Time-frequency representations of Lamb waves,” J. Acoust. Soc. Am. 109(5 Pt 1), 1841–1847 (2001).
[Crossref] [PubMed]

Keller, U.

A. Ludwig, J. Maurer, B. M. Mayer, C. R. Phillips, L. Gallmann, and U. Keller, “Breakdown of the dipole approximation in strong-field ionization,” Phys. Rev. Lett. 113(24), 243001 (2014).
[Crossref] [PubMed]

Kobayashi, T.

T. Fuji, T. Saito, and T. Kobayashi, “Dynamical observation of Duschinsky rotation by sub-5-fs real-time spectroscopy,” Chem. Phys. Lett. 11(2), 99–116 (2011).

T. Kobayashi and A. Yabushita, “Transition-state spectroscopy using ultrashort laser pulses,” Chem Rec. 11(2), 99–116 (2011).
[Crossref] [PubMed]

Kono, H.

Y. Nomura, Y. Fujimura, and H. Kono, “Theory of quantum beats in timeresolved multiphoton ionization of molecules,” J. Chem. Phys. 88(3), 1501–1510 (1988).
[Crossref]

Krause, J. L.

K. C. Kulander, K. J. Schafer, and J. L. Krause, in Proceedings of the Workshop on Super-Intense Laser Atom Physics (SILAP) III. (Plenum, 1993).

Krausz, F.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
[Crossref]

Krushelnick, K.

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in a Keldysh-scaled system,” Nature Photon. 4(6), 352–356 (2010).
[Crossref]

Kulander, K. C.

K. C. Kulander, K. J. Schafer, and J. L. Krause, in Proceedings of the Workshop on Super-Intense Laser Atom Physics (SILAP) III. (Plenum, 1993).

L’Huillier, A.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref] [PubMed]

Laguna, P.

M. Orini, R. Bailon, L. T. Mainardi, P. Laguna, and P. Flandrin, “Characterization of dynamic interactions between cardiovascular signals by time-frequency coherence,” IEEE Trans. Biomed. Eng 59(3), 663–673 (2012).
[Crossref]

Laughlin, C.

P.-C. Li, Y.-L. Sheu, C. Laughlin, and S.-I Chu, “Dynamical origin of near- and below-threshold harmonic generation of Cs in an intense mid-infrared laser field,” Nat. Comm. 6, 7178 (2015).
[Crossref]

P.-C. Li, Y.-L. Sheu, C. Laughlin, and S.-I Chu, “Role of laser-driven electron-multirescattering in resonance-enhanced below-threshold harmonic generation in He atoms,” Phys. Rev. A 90(4), 041401(R) (2014).
[Crossref]

X. Chu, S. I. Chu, and C. Laughlin, “Spectral and temporal structures of high-order harmonic generation of Na in intense mid-ir laser fields,” Phys. Rev. A 64(1), 013406 (2001).
[Crossref]

Lee, K.-K.

D. B. Turner, R. Dinshaw, K.-K. Lee, M. S. Belsley, K. E. Wilk, P. M. G. Curmic, and G. D. Scholes, “Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis,” Phys. Chem. Chem. Phys. 14, 4857–4874 (2012).
[Crossref] [PubMed]

Lein, M.

C. C. Chirila, I. Dreissigacker, E. V. van der Zwan, and M. Lein, “Emission times in high-order harmonic generation,” Phys. Rev. A 81(3), 033412 (2010).
[Crossref]

Leveque, C.

F. Risoud, J. Caillat, A. Maquet, R. Taieb, and C. Leveque, “Quantitative extraction of the emission times of high-order harmonics via the determination of instantaneous frequencies,” Phys. Rev. A 88(4), 043415 (2013).
[Crossref]

Lewenstein, M.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref] [PubMed]

Li, P.-C.

P.-C. Li, Y.-L. Sheu, C. Laughlin, and S.-I Chu, “Dynamical origin of near- and below-threshold harmonic generation of Cs in an intense mid-infrared laser field,” Nat. Comm. 6, 7178 (2015).
[Crossref]

P.-C. Li, Y.-L. Sheu, C. Laughlin, and S.-I Chu, “Role of laser-driven electron-multirescattering in resonance-enhanced below-threshold harmonic generation in He atoms,” Phys. Rev. A 90(4), 041401(R) (2014).
[Crossref]

Lin, S. H.

H. Mineo, K. Nagaya, M. Hayashi, and S. H. Lin, “Theoretical studies of high-harmonic generation based on the KeldyshFaisalReiss theory,” J. Phys. B: At. Mol. Opt. Phys. 40(12), 2435–2451 (2007).
[Crossref]

K. Mishima, K. Nagaya, M. Hayashi, and S. H. Lin, “Towards the realization of the quantum chemistry approach to tunneling photoionization processes in strong laser fields,” J. Chem. Phys. 122(2), 024104 (2005).
[Crossref] [PubMed]

S. H. Lin, Advances in multi-photon processes and spectroscopy (World Scientific Publishing, 2010), Vol. 19.

Lin, Y. T.

F. Auger, P. Flandrin, Y. T. Lin, S. McLaughlin, S. Meignen, T. Oberlin, and H. T. Wu, “Time-frequency reassignment and synchrosqueezing,” IEEE Signal Processing Mag. 30(6), 32–41 (2013).
[Crossref]

Liu, F.

Y. Deng, Q. Sun, F. Liu, C. Wang, and Q. Xing, “Terahertz time-resolved spectroscopy with wavelet-transform,” in International Congress on Image and Signal Processing (IEEE, 2010), pp. 3462–3464.
[Crossref]

Liu, H. H.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time Series analysis,” Proc. R. Soc. A 454(1971), 903–995 (1998).
[Crossref]

Liu, J.

J. Chen, S. I. Chu, and J. Liu, “Time-frequency analysis of molecular high-harmonic generation spectrum by means of wavelet transform and Wigner distribution techniques,” J. Phys. B: At. Mol. Opt. Phys. 39(22), 4747–4758 (2006).
[Crossref]

Liu, W.

L. Wang, W. Liu, and C. Fang, “Elucidating low-frequency vibrational dynamics in calcite and water with time-resolved third-harmonic generation spectroscopy,” Phys. Chem. Chem. Phys. 17(26), 17034 (2015).
[Crossref] [PubMed]

Long, S. R.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time Series analysis,” Proc. R. Soc. A 454(1971), 903–995 (1998).
[Crossref]

Lu, J.

I. Daubechies, J. Lu, and H. T. Wu, “Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool,” Appl. Comput. Harmon. Anal. 30(1), 243–261 (2011).
[Crossref]

Ludwig, A.

A. Ludwig, J. Maurer, B. M. Mayer, C. R. Phillips, L. Gallmann, and U. Keller, “Breakdown of the dipole approximation in strong-field ionization,” Phys. Rev. Lett. 113(24), 243001 (2014).
[Crossref] [PubMed]

Mainardi, L. T.

M. Orini, R. Bailon, L. T. Mainardi, P. Laguna, and P. Flandrin, “Characterization of dynamic interactions between cardiovascular signals by time-frequency coherence,” IEEE Trans. Biomed. Eng 59(3), 663–673 (2012).
[Crossref]

Maquet, A.

F. Risoud, J. Caillat, A. Maquet, R. Taieb, and C. Leveque, “Quantitative extraction of the emission times of high-order harmonics via the determination of instantaneous frequencies,” Phys. Rev. A 88(4), 043415 (2013).
[Crossref]

March, A. M.

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in a Keldysh-scaled system,” Nature Photon. 4(6), 352–356 (2010).
[Crossref]

Maurer, J.

A. Ludwig, J. Maurer, B. M. Mayer, C. R. Phillips, L. Gallmann, and U. Keller, “Breakdown of the dipole approximation in strong-field ionization,” Phys. Rev. Lett. 113(24), 243001 (2014).
[Crossref] [PubMed]

Mayer, B. M.

A. Ludwig, J. Maurer, B. M. Mayer, C. R. Phillips, L. Gallmann, and U. Keller, “Breakdown of the dipole approximation in strong-field ionization,” Phys. Rev. Lett. 113(24), 243001 (2014).
[Crossref] [PubMed]

McClure, S. D.

S. D. McClure, D. B. Turner, P. C. Arpin, T. Mirkovic, and G. D. Scholes, “Coherent oscillations in the PC577 cryptophyte antenna occur in the excited electronic state,” J. Phys. Chem. 118(5), 1296–1308 (2014).
[Crossref]

McLaughlin, S.

F. Auger, P. Flandrin, Y. T. Lin, S. McLaughlin, S. Meignen, T. Oberlin, and H. T. Wu, “Time-frequency reassignment and synchrosqueezing,” IEEE Signal Processing Mag. 30(6), 32–41 (2013).
[Crossref]

Meignen, S.

T. Oberlin, S. Meignen, and V. Perrier, “Second-order synchrosqueezing transform or invertible reassignment? towards ideal time-frequency representations,” IEEE Trans. Signal Process. 63(5), 1335–1344 (2015).
[Crossref]

F. Auger, P. Flandrin, Y. T. Lin, S. McLaughlin, S. Meignen, T. Oberlin, and H. T. Wu, “Time-frequency reassignment and synchrosqueezing,” IEEE Signal Processing Mag. 30(6), 32–41 (2013).
[Crossref]

Milosevic, D. B.

P. Antoine, B. Piraux, D. B. Milosevic, and M. Gajda, “Generation of ultrashort pulses of harmonics,” Phys. Rev. A 54(3), R1761–R1764 (1996).
[Crossref] [PubMed]

Mineo, H.

H. Mineo, K. Nagaya, M. Hayashi, and S. H. Lin, “Theoretical studies of high-harmonic generation based on the KeldyshFaisalReiss theory,” J. Phys. B: At. Mol. Opt. Phys. 40(12), 2435–2451 (2007).
[Crossref]

Mirkovic, T.

S. D. McClure, D. B. Turner, P. C. Arpin, T. Mirkovic, and G. D. Scholes, “Coherent oscillations in the PC577 cryptophyte antenna occur in the excited electronic state,” J. Phys. Chem. 118(5), 1296–1308 (2014).
[Crossref]

Mishima, K.

K. Mishima, K. Nagaya, M. Hayashi, and S. H. Lin, “Towards the realization of the quantum chemistry approach to tunneling photoionization processes in strong laser fields,” J. Chem. Phys. 122(2), 024104 (2005).
[Crossref] [PubMed]

Nagaya, K.

H. Mineo, K. Nagaya, M. Hayashi, and S. H. Lin, “Theoretical studies of high-harmonic generation based on the KeldyshFaisalReiss theory,” J. Phys. B: At. Mol. Opt. Phys. 40(12), 2435–2451 (2007).
[Crossref]

K. Mishima, K. Nagaya, M. Hayashi, and S. H. Lin, “Towards the realization of the quantum chemistry approach to tunneling photoionization processes in strong laser fields,” J. Chem. Phys. 122(2), 024104 (2005).
[Crossref] [PubMed]

Niethammer, M.

M. Niethammer, L. J. Jacobs, J. Qu, and J. Jarzynski, “Time-frequency representations of Lamb waves,” J. Acoust. Soc. Am. 109(5 Pt 1), 1841–1847 (2001).
[Crossref] [PubMed]

Nomura, Y.

Y. Nomura, Y. Fujimura, and H. Kono, “Theory of quantum beats in timeresolved multiphoton ionization of molecules,” J. Chem. Phys. 88(3), 1501–1510 (1988).
[Crossref]

O’Neill, J. C.

J. C. O’Neill and P. Flandrin, “Virtues and vices of quartic timefrequency distributions,” IEEE Trans. Signal Process. 48(9), 2641–2650 (2000).
[Crossref]

Oberlin, T.

T. Oberlin, S. Meignen, and V. Perrier, “Second-order synchrosqueezing transform or invertible reassignment? towards ideal time-frequency representations,” IEEE Trans. Signal Process. 63(5), 1335–1344 (2015).
[Crossref]

F. Auger, P. Flandrin, Y. T. Lin, S. McLaughlin, S. Meignen, T. Oberlin, and H. T. Wu, “Time-frequency reassignment and synchrosqueezing,” IEEE Signal Processing Mag. 30(6), 32–41 (2013).
[Crossref]

Orini, M.

M. Orini, R. Bailon, L. T. Mainardi, P. Laguna, and P. Flandrin, “Characterization of dynamic interactions between cardiovascular signals by time-frequency coherence,” IEEE Trans. Biomed. Eng 59(3), 663–673 (2012).
[Crossref]

Perrier, V.

T. Oberlin, S. Meignen, and V. Perrier, “Second-order synchrosqueezing transform or invertible reassignment? towards ideal time-frequency representations,” IEEE Trans. Signal Process. 63(5), 1335–1344 (2015).
[Crossref]

Phillips, C. R.

A. Ludwig, J. Maurer, B. M. Mayer, C. R. Phillips, L. Gallmann, and U. Keller, “Breakdown of the dipole approximation in strong-field ionization,” Phys. Rev. Lett. 113(24), 243001 (2014).
[Crossref] [PubMed]

Phillips, S.

S. Phillips, R. J. Gledhill, J. W. Essex, and C. M. Edge, “Application of the Hilbert-Huang transform to the analysis of molecular dynamics simulations,” J. Phys. Chem. A 107(24), 4869–4876 (2003).
[Crossref]

Piraux, B.

P. Antoine, B. Piraux, D. B. Milosevic, and M. Gajda, “Generation of ultrashort pulses of harmonics,” Phys. Rev. A 54(3), R1761–R1764 (1996).
[Crossref] [PubMed]

Plenio, M. B.

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: Efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys 139(22), 224103 (2013).
[Crossref] [PubMed]

Power, E. P.

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in a Keldysh-scaled system,” Nature Photon. 4(6), 352–356 (2010).
[Crossref]

Prior, J.

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: Efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys 139(22), 224103 (2013).
[Crossref] [PubMed]

Qu, J.

M. Niethammer, L. J. Jacobs, J. Qu, and J. Jarzynski, “Time-frequency representations of Lamb waves,” J. Acoust. Soc. Am. 109(5 Pt 1), 1841–1847 (2001).
[Crossref] [PubMed]

Rabitz, H.

L. Y. Hsu and H. Rabitz, “Coherent light-driven electron transport through polycyclic aromatic hydrocarbon: laser frequency, field intensity, and polarization angle dependence,” Phys. Chem. Chem. Phys. 17(32), 20617–20629 (2015).
[Crossref] [PubMed]

L. Y. Hsu, D. Xie, and H. Rabitz, “Light-driven electron transport through a molecular junction based on cross-conjugated systems,” J. Chem. Phys. 141(12), 124703 (2014).
[Crossref] [PubMed]

Rilling, G.

G. Rilling and P. Flandrin, “One or two frequencies? the empirical mode decomposition answers,” IEEE Trans. Signal Process. 56(1), 85–95 (2008).
[Crossref]

Risoud, F.

F. Risoud, J. Caillat, A. Maquet, R. Taieb, and C. Leveque, “Quantitative extraction of the emission times of high-order harmonics via the determination of instantaneous frequencies,” Phys. Rev. A 88(4), 043415 (2013).
[Crossref]

Ristich, B.

B. Boashash and B. Ristich, “Polynomial Wigner-Ville distributions and time-varying higher-order spectra,” in Time-Frequency and Time-Scale Analysis, in Proceedings of IEEE-SP Int. Symp. (1992), pp. 31–34.

Saito, T.

T. Fuji, T. Saito, and T. Kobayashi, “Dynamical observation of Duschinsky rotation by sub-5-fs real-time spectroscopy,” Chem. Phys. Lett. 11(2), 99–116 (2011).

Sandner, W.

C. Figueira de Morisson Faria, M. Dorr, W. Becker, and W. Sandner, “Time-frequency analysis of two-color high-harmonic generation,” Phys. Rev. A 60(2), 1377–1384 (1999).
[Crossref]

Schafer, K. J.

K. C. Kulander, K. J. Schafer, and J. L. Krause, in Proceedings of the Workshop on Super-Intense Laser Atom Physics (SILAP) III. (Plenum, 1993).

Scholes, G. D.

S. D. McClure, D. B. Turner, P. C. Arpin, T. Mirkovic, and G. D. Scholes, “Coherent oscillations in the PC577 cryptophyte antenna occur in the excited electronic state,” J. Phys. Chem. 118(5), 1296–1308 (2014).
[Crossref]

C. Y. Wong, R. M. Alvey, D. B. Turner, K. E. Wilk, D. A. Bryant, P. M. G. Curmi, R. J. Silbey, and G. D. Scholes, “Electronic coherence lineshapes reveal hidden excitonic correlations in photosynthetic light harvesting,” Nat. Chem. 4(5), 396–404 (2012).
[Crossref] [PubMed]

D. B. Turner, R. Dinshaw, K.-K. Lee, M. S. Belsley, K. E. Wilk, P. M. G. Curmic, and G. D. Scholes, “Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis,” Phys. Chem. Chem. Phys. 14, 4857–4874 (2012).
[Crossref] [PubMed]

Shen, Z.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time Series analysis,” Proc. R. Soc. A 454(1971), 903–995 (1998).
[Crossref]

Sheu, Y.-L.

P.-C. Li, Y.-L. Sheu, C. Laughlin, and S.-I Chu, “Dynamical origin of near- and below-threshold harmonic generation of Cs in an intense mid-infrared laser field,” Nat. Comm. 6, 7178 (2015).
[Crossref]

P.-C. Li, Y.-L. Sheu, C. Laughlin, and S.-I Chu, “Role of laser-driven electron-multirescattering in resonance-enhanced below-threshold harmonic generation in He atoms,” Phys. Rev. A 90(4), 041401(R) (2014).
[Crossref]

Shih, H. H.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time Series analysis,” Proc. R. Soc. A 454(1971), 903–995 (1998).
[Crossref]

Shirley, J. H.

J. H. Shirley, “Solution of the Schrodinger equation with a hamiltonian periodic in time,” Phys. Rev. B 138(4B), B979–B987 (1965).
[Crossref]

Silbey, R. J.

C. Y. Wong, R. M. Alvey, D. B. Turner, K. E. Wilk, D. A. Bryant, P. M. G. Curmi, R. J. Silbey, and G. D. Scholes, “Electronic coherence lineshapes reveal hidden excitonic correlations in photosynthetic light harvesting,” Nat. Chem. 4(5), 396–404 (2012).
[Crossref] [PubMed]

Sistrunk, E.

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in a Keldysh-scaled system,” Nature Photon. 4(6), 352–356 (2010).
[Crossref]

Stefanovska, A.

Y. F. Suprunenko, P. T. Clemson, and A. Stefanovska, “Chronotaxic systems: a new class of self-sustained nonautonomous oscillators,” Phys. Rev. Lett. 111(2), 024101 (2013).
[Crossref] [PubMed]

Stolow, A.

M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wave packet,” Phys. Rev. A 54(1), R37 (1996).
[Crossref] [PubMed]

Sun, Q.

Y. Deng, Q. Sun, F. Liu, C. Wang, and Q. Xing, “Terahertz time-resolved spectroscopy with wavelet-transform,” in International Congress on Image and Signal Processing (IEEE, 2010), pp. 3462–3464.
[Crossref]

Suprunenko, Y. F.

Y. F. Suprunenko, P. T. Clemson, and A. Stefanovska, “Chronotaxic systems: a new class of self-sustained nonautonomous oscillators,” Phys. Rev. Lett. 111(2), 024101 (2013).
[Crossref] [PubMed]

Taieb, R.

F. Risoud, J. Caillat, A. Maquet, R. Taieb, and C. Leveque, “Quantitative extraction of the emission times of high-order harmonics via the determination of instantaneous frequencies,” Phys. Rev. A 88(4), 043415 (2013).
[Crossref]

Tong, X. M.

X. M. Tong and Shih I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61(2), 021802(R) (2000).
[Crossref]

X. M. Tong and S. I. Chu, “Theoretical study of multiple high-order harmonic generation by intense ultrashort pulsed laser fields: a new generalized pseudospectral time-dependent method,” Chem. Phys. 217(2–3), 119–130 (1997).
[Crossref]

Tung, C. C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time Series analysis,” Proc. R. Soc. A 454(1971), 903–995 (1998).
[Crossref]

Turner, D. B.

S. D. McClure, D. B. Turner, P. C. Arpin, T. Mirkovic, and G. D. Scholes, “Coherent oscillations in the PC577 cryptophyte antenna occur in the excited electronic state,” J. Phys. Chem. 118(5), 1296–1308 (2014).
[Crossref]

C. Y. Wong, R. M. Alvey, D. B. Turner, K. E. Wilk, D. A. Bryant, P. M. G. Curmi, R. J. Silbey, and G. D. Scholes, “Electronic coherence lineshapes reveal hidden excitonic correlations in photosynthetic light harvesting,” Nat. Chem. 4(5), 396–404 (2012).
[Crossref] [PubMed]

D. B. Turner, R. Dinshaw, K.-K. Lee, M. S. Belsley, K. E. Wilk, P. M. G. Curmic, and G. D. Scholes, “Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis,” Phys. Chem. Chem. Phys. 14, 4857–4874 (2012).
[Crossref] [PubMed]

van der Zwan, E. V.

C. C. Chirila, I. Dreissigacker, E. V. van der Zwan, and M. Lein, “Emission times in high-order harmonic generation,” Phys. Rev. A 81(3), 033412 (2010).
[Crossref]

Villeneuve, D. M.

M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wave packet,” Phys. Rev. A 54(1), R37 (1996).
[Crossref] [PubMed]

Volpato, A.

Vrakking, M. J. J.

M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wave packet,” Phys. Rev. A 54(1), R37 (1996).
[Crossref] [PubMed]

Wang, C.

Y. Deng, Q. Sun, F. Liu, C. Wang, and Q. Xing, “Terahertz time-resolved spectroscopy with wavelet-transform,” in International Congress on Image and Signal Processing (IEEE, 2010), pp. 3462–3464.
[Crossref]

Wang, L.

L. Wang, W. Liu, and C. Fang, “Elucidating low-frequency vibrational dynamics in calcite and water with time-resolved third-harmonic generation spectroscopy,” Phys. Chem. Chem. Phys. 17(26), 17034 (2015).
[Crossref] [PubMed]

Wang, P.

P. Wang, J. Gao, and Z. Wang, “Time-frequency analysis of seismic data using synchrosqueezing transform,” IEEE Geosci. Remote Sens. Lett. 11(12), 2042–2044 (2014).
[Crossref]

Wang, Z.

P. Wang, J. Gao, and Z. Wang, “Time-frequency analysis of seismic data using synchrosqueezing transform,” IEEE Geosci. Remote Sens. Lett. 11(12), 2042–2044 (2014).
[Crossref]

Wilk, K. E.

C. Y. Wong, R. M. Alvey, D. B. Turner, K. E. Wilk, D. A. Bryant, P. M. G. Curmi, R. J. Silbey, and G. D. Scholes, “Electronic coherence lineshapes reveal hidden excitonic correlations in photosynthetic light harvesting,” Nat. Chem. 4(5), 396–404 (2012).
[Crossref] [PubMed]

D. B. Turner, R. Dinshaw, K.-K. Lee, M. S. Belsley, K. E. Wilk, P. M. G. Curmic, and G. D. Scholes, “Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis,” Phys. Chem. Chem. Phys. 14, 4857–4874 (2012).
[Crossref] [PubMed]

Wong, C. Y.

C. Y. Wong, R. M. Alvey, D. B. Turner, K. E. Wilk, D. A. Bryant, P. M. G. Curmi, R. J. Silbey, and G. D. Scholes, “Electronic coherence lineshapes reveal hidden excitonic correlations in photosynthetic light harvesting,” Nat. Chem. 4(5), 396–404 (2012).
[Crossref] [PubMed]

Wu, H. T.

Y.-C. Chen, M. Y. Cheng, and H. T. Wu, “Nonparametric and adaptive modeling of dynamic periodicity and trend with heteroscedastic and dependent errors,” J. R. Stat. Soc. B 76(3), 651–682 (2014).
[Crossref]

F. Auger, P. Flandrin, Y. T. Lin, S. McLaughlin, S. Meignen, T. Oberlin, and H. T. Wu, “Time-frequency reassignment and synchrosqueezing,” IEEE Signal Processing Mag. 30(6), 32–41 (2013).
[Crossref]

I. Daubechies, J. Lu, and H. T. Wu, “Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool,” Appl. Comput. Harmon. Anal. 30(1), 243–261 (2011).
[Crossref]

H. T. Wu, Adaptive analysis of complex data sets Doctoral dissertation (Princeton University, 2011).

Wu, M. C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time Series analysis,” Proc. R. Soc. A 454(1971), 903–995 (1998).
[Crossref]

Xie, D.

L. Y. Hsu, D. Xie, and H. Rabitz, “Light-driven electron transport through a molecular junction based on cross-conjugated systems,” J. Chem. Phys. 141(12), 124703 (2014).
[Crossref] [PubMed]

Xing, Q.

Y. Deng, Q. Sun, F. Liu, C. Wang, and Q. Xing, “Terahertz time-resolved spectroscopy with wavelet-transform,” in International Congress on Image and Signal Processing (IEEE, 2010), pp. 3462–3464.
[Crossref]

Yabushita, A.

T. Kobayashi and A. Yabushita, “Transition-state spectroscopy using ultrashort laser pulses,” Chem Rec. 11(2), 99–116 (2011).
[Crossref] [PubMed]

Yao, C.

C. Yao and S. I. Chu, “Generalized pseudospectral methods with mappings for bound and resonance state problems,” Chem. Phys. Lett. 204(3–4), 381–388 (1993).
[Crossref]

Yen, N. C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time Series analysis,” Proc. R. Soc. A 454(1971), 903–995 (1998).
[Crossref]

Zheng, Q.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time Series analysis,” Proc. R. Soc. A 454(1971), 903–995 (1998).
[Crossref]

Appl. Comput. Harmon. Anal. (1)

I. Daubechies, J. Lu, and H. T. Wu, “Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool,” Appl. Comput. Harmon. Anal. 30(1), 243–261 (2011).
[Crossref]

Chem Rec. (1)

T. Kobayashi and A. Yabushita, “Transition-state spectroscopy using ultrashort laser pulses,” Chem Rec. 11(2), 99–116 (2011).
[Crossref] [PubMed]

Chem. Phys. (1)

X. M. Tong and S. I. Chu, “Theoretical study of multiple high-order harmonic generation by intense ultrashort pulsed laser fields: a new generalized pseudospectral time-dependent method,” Chem. Phys. 217(2–3), 119–130 (1997).
[Crossref]

Chem. Phys. Lett. (2)

C. Yao and S. I. Chu, “Generalized pseudospectral methods with mappings for bound and resonance state problems,” Chem. Phys. Lett. 204(3–4), 381–388 (1993).
[Crossref]

T. Fuji, T. Saito, and T. Kobayashi, “Dynamical observation of Duschinsky rotation by sub-5-fs real-time spectroscopy,” Chem. Phys. Lett. 11(2), 99–116 (2011).

IEEE Geosci. Remote Sens. Lett. (1)

P. Wang, J. Gao, and Z. Wang, “Time-frequency analysis of seismic data using synchrosqueezing transform,” IEEE Geosci. Remote Sens. Lett. 11(12), 2042–2044 (2014).
[Crossref]

IEEE Signal Processing Mag. (1)

F. Auger, P. Flandrin, Y. T. Lin, S. McLaughlin, S. Meignen, T. Oberlin, and H. T. Wu, “Time-frequency reassignment and synchrosqueezing,” IEEE Signal Processing Mag. 30(6), 32–41 (2013).
[Crossref]

IEEE Trans. Biomed. Eng (1)

M. Orini, R. Bailon, L. T. Mainardi, P. Laguna, and P. Flandrin, “Characterization of dynamic interactions between cardiovascular signals by time-frequency coherence,” IEEE Trans. Biomed. Eng 59(3), 663–673 (2012).
[Crossref]

IEEE Trans. Signal Process. (4)

F. Auger and P. Flandrin, “Improving the readability of time-frequency and time-scale representations by the reassignment method,” IEEE Trans. Signal Process.,  43(5), 1068–1089 (1995).
[Crossref]

J. C. O’Neill and P. Flandrin, “Virtues and vices of quartic timefrequency distributions,” IEEE Trans. Signal Process. 48(9), 2641–2650 (2000).
[Crossref]

T. Oberlin, S. Meignen, and V. Perrier, “Second-order synchrosqueezing transform or invertible reassignment? towards ideal time-frequency representations,” IEEE Trans. Signal Process. 63(5), 1335–1344 (2015).
[Crossref]

G. Rilling and P. Flandrin, “One or two frequencies? the empirical mode decomposition answers,” IEEE Trans. Signal Process. 56(1), 85–95 (2008).
[Crossref]

J. Acoust. Soc. Am. (1)

M. Niethammer, L. J. Jacobs, J. Qu, and J. Jarzynski, “Time-frequency representations of Lamb waves,” J. Acoust. Soc. Am. 109(5 Pt 1), 1841–1847 (2001).
[Crossref] [PubMed]

J. Chem. Phys (1)

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: Efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys 139(22), 224103 (2013).
[Crossref] [PubMed]

J. Chem. Phys. (3)

K. Mishima, K. Nagaya, M. Hayashi, and S. H. Lin, “Towards the realization of the quantum chemistry approach to tunneling photoionization processes in strong laser fields,” J. Chem. Phys. 122(2), 024104 (2005).
[Crossref] [PubMed]

Y. Nomura, Y. Fujimura, and H. Kono, “Theory of quantum beats in timeresolved multiphoton ionization of molecules,” J. Chem. Phys. 88(3), 1501–1510 (1988).
[Crossref]

L. Y. Hsu, D. Xie, and H. Rabitz, “Light-driven electron transport through a molecular junction based on cross-conjugated systems,” J. Chem. Phys. 141(12), 124703 (2014).
[Crossref] [PubMed]

J. Phys. B: At. Mol. Opt. Phys. (2)

H. Mineo, K. Nagaya, M. Hayashi, and S. H. Lin, “Theoretical studies of high-harmonic generation based on the KeldyshFaisalReiss theory,” J. Phys. B: At. Mol. Opt. Phys. 40(12), 2435–2451 (2007).
[Crossref]

J. Chen, S. I. Chu, and J. Liu, “Time-frequency analysis of molecular high-harmonic generation spectrum by means of wavelet transform and Wigner distribution techniques,” J. Phys. B: At. Mol. Opt. Phys. 39(22), 4747–4758 (2006).
[Crossref]

J. Phys. Chem. (1)

S. D. McClure, D. B. Turner, P. C. Arpin, T. Mirkovic, and G. D. Scholes, “Coherent oscillations in the PC577 cryptophyte antenna occur in the excited electronic state,” J. Phys. Chem. 118(5), 1296–1308 (2014).
[Crossref]

J. Phys. Chem. A (1)

S. Phillips, R. J. Gledhill, J. W. Essex, and C. M. Edge, “Application of the Hilbert-Huang transform to the analysis of molecular dynamics simulations,” J. Phys. Chem. A 107(24), 4869–4876 (2003).
[Crossref]

J. R. Stat. Soc. B (1)

Y.-C. Chen, M. Y. Cheng, and H. T. Wu, “Nonparametric and adaptive modeling of dynamic periodicity and trend with heteroscedastic and dependent errors,” J. R. Stat. Soc. B 76(3), 651–682 (2014).
[Crossref]

Nat. Chem. (1)

C. Y. Wong, R. M. Alvey, D. B. Turner, K. E. Wilk, D. A. Bryant, P. M. G. Curmi, R. J. Silbey, and G. D. Scholes, “Electronic coherence lineshapes reveal hidden excitonic correlations in photosynthetic light harvesting,” Nat. Chem. 4(5), 396–404 (2012).
[Crossref] [PubMed]

Nat. Comm. (1)

P.-C. Li, Y.-L. Sheu, C. Laughlin, and S.-I Chu, “Dynamical origin of near- and below-threshold harmonic generation of Cs in an intense mid-infrared laser field,” Nat. Comm. 6, 7178 (2015).
[Crossref]

Nature Photon. (1)

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in a Keldysh-scaled system,” Nature Photon. 4(6), 352–356 (2010).
[Crossref]

Opt. Express (1)

Phys. Chem. Chem. Phys. (3)

L. Wang, W. Liu, and C. Fang, “Elucidating low-frequency vibrational dynamics in calcite and water with time-resolved third-harmonic generation spectroscopy,” Phys. Chem. Chem. Phys. 17(26), 17034 (2015).
[Crossref] [PubMed]

D. B. Turner, R. Dinshaw, K.-K. Lee, M. S. Belsley, K. E. Wilk, P. M. G. Curmic, and G. D. Scholes, “Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis,” Phys. Chem. Chem. Phys. 14, 4857–4874 (2012).
[Crossref] [PubMed]

L. Y. Hsu and H. Rabitz, “Coherent light-driven electron transport through polycyclic aromatic hydrocarbon: laser frequency, field intensity, and polarization angle dependence,” Phys. Chem. Chem. Phys. 17(32), 20617–20629 (2015).
[Crossref] [PubMed]

Phys. Rev. A (9)

F. Risoud, J. Caillat, A. Maquet, R. Taieb, and C. Leveque, “Quantitative extraction of the emission times of high-order harmonics via the determination of instantaneous frequencies,” Phys. Rev. A 88(4), 043415 (2013).
[Crossref]

P.-C. Li, Y.-L. Sheu, C. Laughlin, and S.-I Chu, “Role of laser-driven electron-multirescattering in resonance-enhanced below-threshold harmonic generation in He atoms,” Phys. Rev. A 90(4), 041401(R) (2014).
[Crossref]

C. C. Chirila, I. Dreissigacker, E. V. van der Zwan, and M. Lein, “Emission times in high-order harmonic generation,” Phys. Rev. A 81(3), 033412 (2010).
[Crossref]

C. Figueira de Morisson Faria, M. Dorr, W. Becker, and W. Sandner, “Time-frequency analysis of two-color high-harmonic generation,” Phys. Rev. A 60(2), 1377–1384 (1999).
[Crossref]

P. Antoine, B. Piraux, D. B. Milosevic, and M. Gajda, “Generation of ultrashort pulses of harmonics,” Phys. Rev. A 54(3), R1761–R1764 (1996).
[Crossref] [PubMed]

X. M. Tong and Shih I. Chu, “Probing the spectral and temporal structures of high-order harmonic generation in intense laser pulses,” Phys. Rev. A 61(2), 021802(R) (2000).
[Crossref]

X. Chu, S. I. Chu, and C. Laughlin, “Spectral and temporal structures of high-order harmonic generation of Na in intense mid-ir laser fields,” Phys. Rev. A 64(1), 013406 (2001).
[Crossref]

M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wave packet,” Phys. Rev. A 54(1), R37 (1996).
[Crossref] [PubMed]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994).
[Crossref] [PubMed]

Phys. Rev. B (1)

J. H. Shirley, “Solution of the Schrodinger equation with a hamiltonian periodic in time,” Phys. Rev. B 138(4B), B979–B987 (1965).
[Crossref]

Phys. Rev. Lett. (3)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993).
[Crossref] [PubMed]

Y. F. Suprunenko, P. T. Clemson, and A. Stefanovska, “Chronotaxic systems: a new class of self-sustained nonautonomous oscillators,” Phys. Rev. Lett. 111(2), 024101 (2013).
[Crossref] [PubMed]

A. Ludwig, J. Maurer, B. M. Mayer, C. R. Phillips, L. Gallmann, and U. Keller, “Breakdown of the dipole approximation in strong-field ionization,” Phys. Rev. Lett. 113(24), 243001 (2014).
[Crossref] [PubMed]

Proc. IEE (1)

D. Gabor, “Theory of communication,” Proc. IEE,  93, 429–457 (1946).

Proc. R. Soc. A (1)

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time Series analysis,” Proc. R. Soc. A 454(1971), 903–995 (1998).
[Crossref]

Rev. Mod. Phys. (1)

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009).
[Crossref]

Other (12)

Y. Deng, Q. Sun, F. Liu, C. Wang, and Q. Xing, “Terahertz time-resolved spectroscopy with wavelet-transform,” in International Congress on Image and Signal Processing (IEEE, 2010), pp. 3462–3464.
[Crossref]

P. Flandrin, Time-frequency/time-scale analysis, wavelet analysis and its applications (Academic, 1999).

I. Daubechies, Ten lectures on wavelets (Society for Industrial and Applied Mathematics, 1992).
[Crossref]

Z. Chang, Fundamentals of attosecond optics (CRC, 2011).
[Crossref]

B. Boashash and B. Ristich, “Polynomial Wigner-Ville distributions and time-varying higher-order spectra,” in Time-Frequency and Time-Scale Analysis, in Proceedings of IEEE-SP Int. Symp. (1992), pp. 31–34.

P. Flandrin, F. Auger, and E. Chassande-Mottin, Time-frequency signal processing (CRC, 2003).

S. H. Lin, Advances in multi-photon processes and spectroscopy (World Scientific Publishing, 2010), Vol. 19.

L. Cohen, Time-frequency analysis, signal processing series (Prentice-Hall, 1995).

H. T. Wu, Adaptive analysis of complex data sets Doctoral dissertation (Princeton University, 2011).

K. C. Kulander, K. J. Schafer, and J. L. Krause, in Proceedings of the Workshop on Super-Intense Laser Atom Physics (SILAP) III. (Plenum, 1993).

M. Gavrila, Atoms in intense laser fields (Academic, 1992).

P. Gibbon, Short pulse laser interactions with matter (Imperial College, 2005).

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Figures (9)

Fig. 1
Fig. 1 The simulation of laser-driven hydrogen in the multiphoton ionization regime. The laser wavelength is 880 nm, and the laser intensity I0 = 1013 W/cm2, corresponding to the Keldysh parameter of γK = 3.07. (a) The laser profile. (b) The induced dipole moment dL(t). (c) The power spectrum of the laser profile. (d) The power spectrum of dL(t). Note that the laser profile and dL(t) are very similar, yet very different in their spectral components.
Fig. 2
Fig. 2 TF representations in the multiphoton ionization regime by the (a) GT, (b) MWT, (c) WVD, and (d) SPWVD. The lines indicating odd harmonics in the GT and MWT are subject to broadening issues arising from a window. Although the broadening artifact can be alleviated by the WVD, the evoked interference artifacts in the TF representation result in incomprehensible analysis. By applying additional filters, the SPWVD can moderate the interference patterns, at the price of broadening of the features in the TF representation.
Fig. 3
Fig. 3 TF representations in the multiphoton ionization regime by the (a) RM-GT and (b) RM-SPWVD. The broadening caused by the window in the GT and filter functions in SPWVD is removed. Note that the frequency shift in the beginning 10 cycles corresponds to the AC Stark effect. TF representations in the multiphoton ionization regime by the (c) SST-GT and (d) SST-MWT. The broadening issue caused by the window in GT and MWT are removed. Note that the frequency shift in the beginning 10 cycles corresponds the AC Stark effect.
Fig. 4
Fig. 4 The AC Stark effect revealed by the (a) RM-GT, (b) SST-GT and (c) SST-MWT. (d) Comparison of the frequency shift caused by the AC Stark effect computed by the SST-GT (gray scale) and the Floquet method.
Fig. 5
Fig. 5 Illustration for the (a) AC-Stark effect and (b) the high-order harmonic process.
Fig. 6
Fig. 6 The simulation of laser-driven hydrogen in the tunneling ionization regime. The laser wavelength is 800 nm, and the laser intensity 3.5 × 1014 W/cm2, corresponding to the Keldysh parameter of γK = 0.57. (a) The laser profile. (b) The induced dipole moment dA(t).
Fig. 7
Fig. 7 TF representations in the tunneling ionization regime by the (a) GT, (b) MWT, (c) WVD, and (d) SPWVD. The repeating arches suggest that excitation of the harmonics is strongly correlated with the laser field. In the representations of the GT and MWT, the arches are broaden by the window, leading to the difficulty to differentiate the intricate structures inside the arches. The representation of the WVD is obscured by the interference pattern, and it is difficult to remove the interference pattern with filters in the SPWVD.
Fig. 8
Fig. 8 TF representations in the tunneling ionization regime by the (a) RM-GT and (b) RM-SPWVD. The broadening artifacts caused by the window in both methods are eliminated, but it is difficult to remove the interference pattern in the SPWVD. TF representations in the tunneling ionization regime by the (c) SST-GT and (d) SST-MWT. The broadening artifacts caused by the window in both methods are alleviated. (e) TF representation in the tunneling ionization regime by the second order SST-GT. Note that the diffusive pattern in the SST-GT is modified for the arches. (f) Comparison of the TF representation of the SST-GT and the trajectory of an electron released between the 1T and 1.5T (denoted by red circles) computed by the standard semiclassical approach suggested independently by Corkum [56] and Kulander et al. [57].
Fig. 9
Fig. 9 (a) TF representation in the tunneling ionization regime of the EMD-HS algorithm, which contains all IMF modes extracted by EMD. (b) TF representation in the tunneling ionization regime of the first two IMFs extracted by EMD. To enhance the visualization, the curves are thickened. (c) Comparison of the first two IMFs with the TF representation by the SST-GT. According to the semiclassical trajectory, the first IMF is the first return and the second IMF is the second return. (d) The first IMF and (e) the second IMF analyzed by the SST-GT.

Tables (3)

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Table 1 Summary of TF methods in this Study

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Table 2 Comparison of TF methods in the multiphoton ionization regime

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Table 3 Comparison of TF methods in the tunneling ionization regime

Equations (33)

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i ψ ( r , t ) t = ( 1 2 2 1 r z E ( t ) ) ψ ( r , t ) ,
d L ( t ) = ψ * ( r , t ) z ψ ( r , t ) d r .
d A ( t ) = ψ * ( r , t ) d 2 z d t 2 ψ ( r , t ) d r .
STFT x g ( t , ω ) = x ( ζ ) g * ( ζ t ) e i ω ( ζ t ) d ζ .
GT x g ( t , ω ) = x ( ζ ) e ( ζ t ) 2 2 σ 2 e i ω ( ζ t ) d ζ .
CWT x g ( t , a ) = x ( ζ ) 1 a g * ( ζ t a ) d ζ ,
MWT x g ( t , ω ) = x ( ζ ) ω g * ( ω ( ζ t ) ) d ζ ,
WVD x ( t , ω ) = x ( t + ζ / 2 ) x * ( t ζ / 2 ) e i ω ζ d ζ .
| STFT x g ( t , ω ) | 2 = WVD x ( ζ , η ) WVD g ( ζ t , η ω ) d ζ d η .
C x ( t , ω ) = x ( s + ζ / 2 ) x * ( s ζ / 2 ) e i ω ζ e i ξ ( s t ) f ( ξ , ζ ) d ξ d s d ζ ,
SPWVD x g , h ( t , ω ) = g ( t s ) h ( ζ ) x ( s + ζ / 2 ) x * ( s ζ / 2 ) e i ω ζ d ζ d s
= WVD x ( s , ξ ) W h ( s t , ξ ω ) d s d ξ ,
t ^ x ( t , ω ) = { { STFT x t g ( t , ω ) ( STFT x g ( t , ω ) ) * } | STFT x g ( t , ω ) | 2 , when STFT x g ( t , ω ) 0 , when STFT x g ( t , ω ) = 0 .
ω ^ x ( t , ω ) = { { STFT x d g ( t , ω ) ( STFT x g ( t , ω ) ) * } | STFT x g ( t , ω ) | 2 , when STFT x g ( t , ω ) 0 , when STFT x g ( t , ω ) = 0 .
RM-STFT x g ( t ^ x , ω ^ x ) = | STFT x g ( t , ω ) | 2 δ ( t ^ x ( t , ω ) t , ω ^ x ( t , ω ) ω ) d t d ω .
RM-SPWVD x ( t ^ x , ω ^ x ) = SPWVD x g ( t , ω ) δ ( t ^ x ( t , ω ) t , ω ^ x ( t , ω ) ω ) d t d ω .
t ^ x ( t , ω ) = s WVD x ( s , ξ ) W h ( s t , ξ ω ) d s d ξ
ω ^ x ( t , ω ) = ξ WVD x ( s , ξ ) W h ( s t , ξ ω ) d s d ξ .
SST-STFT x g ( t , ω ) = STFT x g ( t , η ) 1 α π e | ω ω ^ x ( t , η ) | 2 α d η ,
ω ^ x ( t , η ) = { i t STFT x g ( t , η ) STFT x g ( t , η ) when STFT x g ( t , η ) 0 when STFT x g ( t , η ) = 0 .
ω ̌ x ( t , η ) = { ω ^ x ( t , η ) + c ( t , η ) ( t t ^ x ( t , η ) ) when η t ^ x ( t , η ) 0 ω ^ x ( t , η ) otherwise ,
t ^ x ( t , η ) = t + i η STFT x g ( t , η ) STFT x g ( t , η ) and c ( t , η ) = t ω ^ x ( t , η ) η t ^ x ( t , η ) .
x k ( t ) = { C g 1 ω k ( t ) ε 2 ω k ( t ) + ε 2 SST-STFT x g ( t , ω ) d ω }
SST-CWT x g ( t , ω ) = η 3 / 2 CWT x g ( t , η ) 1 α π e | ω ω ^ x ( t , η ) | 2 α d η ,
ω ^ x ( t , η ) = { i t CWT x g ( t , η ) CWT x g ( t , η ) when CWT x g ( t , η ) 0 when CWT x g ( t , η ) = 0 .
x k ( t ) = { R g 1 ω k ( t ) ε 2 ω k ( t ) + ε 2 a 3 / 2 SST-CWT x g ( t , a ) d a }
x ˜ ( t ) = x ( t ) + i ( x ( t ) ) = a ( t ) e i Φ ( t ) ,
ω ( t ) = 1 2 π d Φ ( t ) d t .
HS x ( t , ω ) = k a k ( t ) δ ( ω ω k ( t ) ) ,
F ( t ) = { sin 2 ( π t 10 T ) when 0 t T 1 when T t 9 T sin 2 ( π t 10 T ) when 9 T t 10 T ,
{ A C 1 ( ) L ( ) , ϕ C 3 ( ) , inf t A ( t ) c 1 , inf t ϕ ( t ) c 1 , sup t A ( t ) c 2 , sup t ϕ ( t ) c 2 , sup t | ϕ ( t ) | c 3 , | A ( t ) | ε ϕ ( t ) , | ϕ ( t ) | ε ϕ ( t ) for all t ,
n l m k n l m k | H ^ F | n l m k ϕ λ ξ n l m k = ε λ ξ ϕ λ ξ n l m k ,
n l m k | H ^ F | n l m k = E n l m δ n n δ l l δ m m δ k k n l m | z | n l m e E 0 2 ( δ k , k + 1 + δ k , k 1 ) + k h ¯ ω δ n n δ l l δ m m δ k k

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