1
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Dhamija S, Bhutani G, Jayachandran A, De AK. A Revisit on Impulsive Stimulated Raman Spectroscopy: Importance of Spectral Dispersion of Chirped Broadband Probe. J Phys Chem A 2022; 126:1019-1032. [PMID: 35142494 DOI: 10.1021/acs.jpca.1c10566] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The usefulness of a chirped broadband probe and spectral dispersion to obtain Raman spectra under nonresonant/resonant impulsive excitation is revisited. A general methodology is presented that inherently takes care of phasing the time-domain low-frequency oscillations without probe pulse compression and retrieves the absolute phase of the oscillations. As test beds, neat solvents (CCl4, CHCl3, and CH2Cl2) are used. Observation of periodic intensity modulation along detection wavelengths for particular modes is explained using a simple electric field interaction picture. This method is extended to diatomic molecule (iodine) and polyatomic molecules (Nile blue and methylene blue) to assign vibrational frequencies in ground/excited electronic state that are supported by density functional theory calculations. A comparison between frequency-domain and time-domain counterparts, i.e., stimulated Raman scattering and impulsive stimulated Raman scattering using degenerate pump-probe pairs is presented, and most importantly, it is shown how impulsive stimulated Raman scattering using chirped broadband probe retains unique advantages offered by both.
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Affiliation(s)
- Shaina Dhamija
- Condensed Phase Dynamics Group, Department of Chemical Sciences, Indian Institute of Science Education and Research Mohali, Knowledge City, Sector 81, SAS Nagar, Punjab 140306, India
| | - Garima Bhutani
- Condensed Phase Dynamics Group, Department of Chemical Sciences, Indian Institute of Science Education and Research Mohali, Knowledge City, Sector 81, SAS Nagar, Punjab 140306, India
| | - Ajay Jayachandran
- Condensed Phase Dynamics Group, Department of Chemical Sciences, Indian Institute of Science Education and Research Mohali, Knowledge City, Sector 81, SAS Nagar, Punjab 140306, India
| | - Arijit K De
- Condensed Phase Dynamics Group, Department of Chemical Sciences, Indian Institute of Science Education and Research Mohali, Knowledge City, Sector 81, SAS Nagar, Punjab 140306, India
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2
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Dobryakov AL, Krohn OA, Quick M, Ioffe I, Kovalenko SA. Positive and Negative Signal and Line-Shape in Stimulated Raman Spectroscopy: Resonance Femtosecond Raman Spectra of Diphenylbutadiene. J Chem Phys 2022; 156:084304. [DOI: 10.1063/5.0075116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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3
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van Stokkum IHM, Kloz M, Polli D, Viola D, Weißenborn J, Peerbooms E, Cerullo G, Kennis JTM. Vibronic dynamics resolved by global and target analysis of ultrafast transient absorption spectra. J Chem Phys 2021; 155:114113. [PMID: 34551543 DOI: 10.1063/5.0060672] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a methodology that provides a complete parametric description of the time evolution of the electronically and vibrationally excited states as detected by ultrafast transient absorption (TA). Differently from previous approaches, which started fitting the data after ≈100 fs, no data are left out in our methodology, and the "coherent artifact" and the instrument response function are fully taken into account. In case studies, the method is applied to solvents, the dye Nile blue, and all-trans β-carotene in cyclohexane solution. The estimated Damped Oscillation Associated Spectra (DOAS) and phases express the most important vibrational frequencies present in the molecular system. By global fit alone of the experimental data, it is difficult to interpret in detail the underlying dynamics. Since it is unfeasible to directly fit the data by a theoretical simulation, our enhanced DOAS methodology thus provides a useful "middle ground" where the theoretical description and the fit of the experimental data can meet. β-carotene in cyclohexane was complementarily studied with femtosecond stimulated Raman spectroscopy (FSRS). The fs-ps dynamics of β-carotene in cyclohexane in TA and FSRS experiments can be described by a sequential scheme S2 → hot S1 → S1' → S1 → S0 with lifetimes of 167 fs (fixed), 0.35, 1.1, and 9.6 ps. The correspondence of DOAS decaying concomitantly with hot S1 and the Species Associated Difference Spectra of hot S1 in TA and FSRS suggest that we observe here features of the vibrational relaxation and nuclear reorganization responsible for the hot S1 to S1 transition.
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Affiliation(s)
- Ivo H M van Stokkum
- Department of Physics and Astronomy and LaserLaB, Faculty of Science, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - Miroslav Kloz
- Institute of Physics, ELI Beamlines, Academy of Sciences of the Czech Republic, CZ-18221 Prague, Czech Republic
| | - Dario Polli
- IFN-CNR, Department of Physics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - Daniele Viola
- IFN-CNR, Department of Physics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - Jörn Weißenborn
- Department of Physics and Astronomy and LaserLaB, Faculty of Science, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - Ebo Peerbooms
- Department of Physics and Astronomy and LaserLaB, Faculty of Science, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - Giulio Cerullo
- IFN-CNR, Department of Physics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - John T M Kennis
- Department of Physics and Astronomy and LaserLaB, Faculty of Science, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
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van Stokkum IHM, Jumper CC, Lee TS, Myahkostupov M, Castellano FN, Scholes GD. Vibronic and excitonic dynamics in perylenediimide dimers and tetramer. J Chem Phys 2020; 153:224101. [PMID: 33317279 DOI: 10.1063/5.0024530] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Broad-band pump-probe spectroscopy combined with global and target analysis is employed to study the vibronic and excitonic dynamics of two dimers and a tetramer of perylenediimides. A simultaneous analysis is developed for two systems that have been measured in the same conditions. This enhances the resolvability of the vibronic and excitonic dynamics of the systems, and the solvent contributions that are common in the experiments. We resolve two oscillations of 1399 cm-1 or 311 cm-1 damped with ≈30/ps involved in vibrational relaxation and two more oscillations of 537 cm-1 or 136 cm-1 damped with ≈3/ps. A relaxation process with a rate of 2.1/ps-3.2/ps that is positively correlated with the excitonic coupling was discovered in all three model systems, attributed to annihilation of the one but lowest exciton state.
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Affiliation(s)
- Ivo H M van Stokkum
- Institute for Lasers, Life and Biophotonics, Faculty of Sciences, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - Chanelle C Jumper
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Tia S Lee
- Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204, USA
| | - Mykhaylo Myahkostupov
- Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204, USA
| | - Felix N Castellano
- Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204, USA
| | - Gregory D Scholes
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
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Cherepanov DA, Brady NG, Shelaev IV, Nguyen J, Gostev FE, Mamedov MD, Nadtochenko VA, Bruce BD. PSI-SMALP, a Detergent-free Cyanobacterial Photosystem I, Reveals Faster Femtosecond Photochemistry. Biophys J 2020; 118:337-351. [PMID: 31882247 PMCID: PMC6976803 DOI: 10.1016/j.bpj.2019.11.3391] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2019] [Revised: 11/17/2019] [Accepted: 11/26/2019] [Indexed: 12/12/2022] Open
Abstract
Cyanobacterial photosystem I (PSI) functions as a light-driven cyt c6-ferredoxin/oxidoreductase located in the thylakoid membrane. In this work, the energy and charge transfer processes in PSI complexes isolated from Thermosynechococcus elongatus via conventional n-dodecyl-β-D-maltoside solubilization (DM-PSI) and a, to our knowledge, new detergent-free method using styrene-maleic acid copolymers (SMA-PSI) have been investigated by pump-to-probe femtosecond laser spectroscopy. In DM-PSI preparations excited at 740 nm, the excitation remained localized on the long-wavelength chlorophyll forms within 0.1-20 ps and revealed little or no charge separation and oxidation of the special pair, P700. The formation of ion-radical pair P700+A1- occurred with a characteristic time of 36 ps, being kinetically controlled by energy transfer from the long-wavelength chlorophyll to P700. Quite surprisingly, the detergent-free SMA-PSI complexes upon excitation by these long-wave pulses undergo an ultrafast (<100 fs) charge separation in ∼45% of particles. In the remaining complexes (∼55%), the energy transfer to P700 occurred at ∼36 ps, similar to the DM-PSI. Both isolation methods result in a trimeric form of PSI, yet the SMA-PSI complexes display a heterogenous kinetic behavior. The much faster rate of charge separation suggests the existence of an ultrafast pathway for charge separation in the SMA-PSI that may be disrupted during detergent isolation.
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Affiliation(s)
- Dmitry A Cherepanov
- N. N. Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences, Moscow, Russia
| | - Nathan G Brady
- Biochemistry and Cellular and Molecular Biology Department, University of Tennessee, Knoxville, Tennessee
| | - Ivan V Shelaev
- N. N. Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences, Moscow, Russia
| | - Jon Nguyen
- Biochemistry and Cellular and Molecular Biology Department, University of Tennessee, Knoxville, Tennessee
| | - Fedor E Gostev
- N. N. Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences, Moscow, Russia
| | - Mahir D Mamedov
- A. N. Belozersky Institute of Physical-Chemical Biology, Moscow State University, Moscow, Russia
| | - Victor A Nadtochenko
- N. N. Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences, Moscow, Russia.
| | - Barry D Bruce
- Biochemistry and Cellular and Molecular Biology Department, University of Tennessee, Knoxville, Tennessee; Energy Science & Engineering Program, The Bredesen Center, University of Tennessee, Knoxville, Tennessee.
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van Thor JJ. Advances and opportunities in ultrafast X-ray crystallography and ultrafast structural optical crystallography of nuclear and electronic protein dynamics. STRUCTURAL DYNAMICS (MELVILLE, N.Y.) 2019; 6:050901. [PMID: 31559317 PMCID: PMC6759419 DOI: 10.1063/1.5110685] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2019] [Accepted: 08/29/2019] [Indexed: 05/02/2023]
Abstract
Both nuclear and electronic dynamics contribute to protein function and need multiple and complementary techniques to reveal their ultrafast structural dynamics response. Real-space information obtained from the measurement of electron density dynamics by X-ray crystallography provides aspects of both, while the molecular physics of coherence parameters and frequency-frequency correlation needs spectroscopy methods. Ultrafast pump-probe applications of protein dynamics in crystals provide real-space information through direct X-ray crystallographic structure analysis or through structural optical crystallographic analysis. A discussion of methods of analysis using ultrafast macromolecular X-ray crystallography and ultrafast nonlinear structural optical crystallography is presented. The current and future high repetition rate capabilities provided by X-ray free electron lasers for ultrafast diffraction studies provide opportunities for optical control and optical selection of nuclear coherence which may develop to access higher frequency dynamics through improvements of sensitivity and time resolution to reveal coherence directly. Specific selection of electronic coherence requires optical probes, which can provide real-space structural information through photoselection of oriented samples and specifically in birefringent crystals. Ultrafast structural optical crystallography of photosynthetic energy transfer has been demonstrated, and the theory of two-dimensional structural optical crystallography has shown a method for accessing the structural selection of electronic coherence.
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Affiliation(s)
- Jasper J. van Thor
- Molecular Biophysics, Imperial College London, London SW7 2AZ, United Kingdom
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7
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Gdor I, Ghosh T, Lioubashevski O, Ruhman S. Nonresonant Raman Effects on Femtosecond Pump-Probe with Chirped White Light: Challenges and Opportunities. J Phys Chem Lett 2017; 8:1920-1924. [PMID: 28388046 DOI: 10.1021/acs.jpclett.7b00559] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Impulsive Raman excitation in neat organic liquids far from resonance is followed using chirped broad-band supercontinuum probe pulses. Spectral modulations due to impulsively induced coherent vibrations vary in intensity 10-fold as a function of the probe's linear chirp. Simulations clarify why the vibrational signature is maximized for a group delay dispersion (GDD) in reduced units of νvib-2 = 0.5 while a probe GDD of twice that quenches the same spectral modulations. Accordingly, recent claims that chirped white-light probe pulses provide equivalent information on material response to their compressed analogues must be taken with caution. In particular, interactions that induce spectral shifts in the probe depend crucially on the arrival chronology of the continuum colors. On one hand, this presents limitations to application of chirped continuum radiation as-is in pump-probe experiments. It also presents the opportunity for using this dependence to control the relative amplitude of nonresonant interactions in pump-probe signals such as that of solvent vibrations.
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Affiliation(s)
- Itay Gdor
- Institute of Chemistry, The Hebrew University , Jerusalem 9190401, Israel
| | - Tufan Ghosh
- Institute of Chemistry, The Hebrew University , Jerusalem 9190401, Israel
| | - Oleg Lioubashevski
- Institute of Chemistry, The Hebrew University , Jerusalem 9190401, Israel
| | - Sanford Ruhman
- Institute of Chemistry, The Hebrew University , Jerusalem 9190401, Israel
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Schnedermann C, Muders V, Ehrenberg D, Schlesinger R, Kukura P, Heberle J. Vibronic Dynamics of the Ultrafast all-trans to 13-cis Photoisomerization of Retinal in Channelrhodopsin-1. J Am Chem Soc 2016; 138:4757-62. [DOI: 10.1021/jacs.5b12251] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Christoph Schnedermann
- Physical
and Theoretical Chemistry Laboratory, University of Oxford, South Parks
Road, Oxford OX1 3QZ, United Kingdom
| | | | | | | | - Philipp Kukura
- Physical
and Theoretical Chemistry Laboratory, University of Oxford, South Parks
Road, Oxford OX1 3QZ, United Kingdom
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Liebel M, Schnedermann C, Wende T, Kukura P. Principles and Applications of Broadband Impulsive Vibrational Spectroscopy. J Phys Chem A 2015; 119:9506-17. [DOI: 10.1021/acs.jpca.5b05948] [Citation(s) in RCA: 83] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- M. Liebel
- Physical and Theoretical
Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QZ Oxford, U.K
| | - C. Schnedermann
- Physical and Theoretical
Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QZ Oxford, U.K
| | - T. Wende
- Physical and Theoretical
Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QZ Oxford, U.K
| | - P. Kukura
- Physical and Theoretical
Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QZ Oxford, U.K
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Son M, Park KH, Yoon MC, Kim P, Kim D. Excited-State Vibrational Coherence in Perylene Bisimide Probed by Femtosecond Broadband Pump-Probe Spectroscopy. J Phys Chem A 2015; 119:6275-82. [PMID: 25992707 DOI: 10.1021/acs.jpca.5b03571] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
Broadband laser pulses with ultrashort duration are capable of triggering impulsive excitation of the superposition of vibrational eigenstates, giving rise to quantum beating signals originating from coherent wave packet motions along the potential energy surface. In this work, coherent vibrational wave packet dynamics of an N,N'-bis(2,6-dimethylphenyl)perylene bisimide (DMP-PBI) were investigated by femtosecond broadband pump-probe spectroscopy which features fast and balanced data acquisition with a wide spectral coverage of >200 nm. Clear modulations were observed in the envelope of the stimulated emission decay profiles of DMP-PBI with the oscillation frequencies of 140 and 275 cm(-1). Fast Fourier transform analysis of each oscillatory mode revealed characteristic phase jumps near the maxima of the steady-state fluorescence, indicating that the observed vibrational coherence originates from an excited-state wave packet motion. Quantum calculations of the normal modes at the low-frequency region suggest that low-frequency C-C (C═C) stretching motions accompanied by deformation of the dimethylphenyl substituents are responsible for the manifestation of such coherent wave packet dynamics.
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Affiliation(s)
- Minjung Son
- Spectroscopy Laboratory for Functional π-Electronic Systems and Department of Chemistry, Yonsei University, Seoul 120-749, Korea
| | - Kyu Hyung Park
- Spectroscopy Laboratory for Functional π-Electronic Systems and Department of Chemistry, Yonsei University, Seoul 120-749, Korea
| | - Min-Chul Yoon
- Spectroscopy Laboratory for Functional π-Electronic Systems and Department of Chemistry, Yonsei University, Seoul 120-749, Korea
| | - Pyosang Kim
- Spectroscopy Laboratory for Functional π-Electronic Systems and Department of Chemistry, Yonsei University, Seoul 120-749, Korea
| | - Dongho Kim
- Spectroscopy Laboratory for Functional π-Electronic Systems and Department of Chemistry, Yonsei University, Seoul 120-749, Korea
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Zhang B, Stratt RM. Vibrational energy relaxation of large-amplitude vibrations in liquids. J Chem Phys 2012; 137:024506. [PMID: 22803546 DOI: 10.1063/1.4733392] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Given the limited intermolecular spaces available in dense liquids, the large amplitudes of highly excited, low frequency vibrational modes pose an interesting dilemma for large molecules in solution. We carry out molecular dynamics calculations of the lowest frequency ("warping") mode of perylene dissolved in liquid argon, and demonstrate that vibrational excitation of this mode should cause identifiable changes in local solvation shell structure. But while the same kinds of solvent structural rearrangements can cause the non-equilibrium relaxation dynamics of highly excited diatomic rotors in liquids to differ substantially from equilibrium dynamics, our simulations also indicate that the non-equilibrium vibrational energy relaxation of large-amplitude vibrational overtones in liquids should show no such deviations from linear response. This observation seems to be a generic feature of large-moment-arm vibrational degrees of freedom and is therefore probably not specific to our choice of model system: The lowest frequency (largest amplitude) cases probably dissipate energy too quickly and the higher frequency (more slowly relaxing) cases most likely have solvent displacements too small to generate significant nonlinearities in simple nonpolar solvents. Vibrational kinetic energy relaxation, in particular, seems to be especially and surprisingly linear.
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Affiliation(s)
- Baofeng Zhang
- Department of Chemistry, Brown University, Providence, Rhode Island 02912, USA
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Wand A, Rozin R, Eliash T, Jung KH, Sheves M, Ruhman S. Asymmetric Toggling of a Natural Photoswitch: Ultrafast Spectroscopy of Anabaena Sensory Rhodopsin. J Am Chem Soc 2011; 133:20922-32. [DOI: 10.1021/ja208371g] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Amir Wand
- Institute of Chemistry and Farkash Center for Light-Induced Processes, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Rinat Rozin
- Department of Organic Chemistry, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - Tamar Eliash
- Department of Organic Chemistry, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - Kwang-Hwan Jung
- Department of Life Science and Institute of Biological Interfaces, Sogang University, Shinsu-Dong 1, Mapo-Gu, Seoul 121-742, South Korea
| | - Mordechai Sheves
- Department of Organic Chemistry, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - Sanford Ruhman
- Institute of Chemistry and Farkash Center for Light-Induced Processes, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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Liu J, Kida Y, Teramoto T, Kobayashi T. Generation of stable sub-10 fs pulses at 400 nm in a hollow fiber for UV pump-probe experiment. OPTICS EXPRESS 2010; 18:4664-4672. [PMID: 20389478 DOI: 10.1364/oe.18.004664] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
Stable sub-10-fs pulses useful for many pump-probe experiments with center wavelength at 400 nm were obtained using a hollow-fiber compression technique with a beam-pointing stabilizing system. The output power stability was improved by around 2-times with the beam-pointing stabilizer. A 1-mm-thick cell sample of perylene dissolved in cyclohexane was used to test the pulse using for the pump-probe experiment. Even the high C-H stretching of vibration mode at around 2860 cm(-1), 2916 cm(-1), and 2955 cm(-1) were real-time resolved with vibrational phase information.
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Affiliation(s)
- Jun Liu
- International Cooperative Research Project, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan.
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Wand A, Kallush S, Shoshanim O, Bismuth O, Kosloff R, Ruhman S. Chirp effects on impulsive vibrational spectroscopy: a multimode perspective. Phys Chem Chem Phys 2010; 12:2149-63. [DOI: 10.1039/b920356g] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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