Sum-frequency generation at molecule-nanostructure interfaces from diagrammatic theory of nonlinear optics

Diagrammatic methods; Dipolar energy; Energy exchanges; First order; General method; Molecular hyperpolarizabilities; Molecular response; Response functions; Sum frequency; Sum frequency generation; Electronic, Optical and Magnetic Materials; Condensed Matter Physics

Abstract :

[en] We apply the loop diagrammatic method for linear and nonlinear optics to the calculation of the sum-frequency response of a molecule-nanostructure composite system. The presence of the nanostructure modifies the molecular response through dipolar energy exchange, and the molecular hyperpolarizability is factorized by nanostructure response functions of increasing orders. We provide a general method to transform these functions into products of first-order nanostructure polarizabilities, accounting for enhancements of the molecular response by coupling to plasmonic or excitonic resonances. In particular, we show how the diagrams may be directly read to determine the response functions and their factorization without explicit calculation. The methodology provides a frame for various applications to other systems, interactions, and nonlinear optical processes.

Disciplines :

Physics

Author, co-author :

Noblet, Thomas ; Université de Liège - ULiège > Département de physique > Biophotonique

Busson, Bertrand ; Université Paris-Saclay, CNRS, Institut de Chimie Physique, UMR 8000, Orsay, France

Language :

English

Title :

Sum-frequency generation at molecule-nanostructure interfaces from diagrammatic theory of nonlinear optics

Publication date :

15 May 2022

Journal title :

Physical Review. B

ISSN :

2469-9950

eISSN :

2469-9969

Publisher :

American Physical Society

Volume :

105

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://link.aps.org/article/10.1103/PhysRevB.105.205420

Available on ORBi :

since 26 September 2022

Statistics

Number of views

20 (1 by ULiège)

Number of downloads

16 (0 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

Bibliography

E. H. G. Backus, A. Eichler, A. W. Kleyn, and M. Bonn, Real-time observation of molecular motion on a surface, Science 310, 1790 (2005) 0036-8075 10.1126/science.1120693.
H. Arnolds, Vibrational dynamics of adsorbates-Quo vadis? Prog. Surf. Sci. 86, 1 (2011) 0079-6816 10.1016/j.progsurf.2010.10.001.
G. Rupprechter, A surface science approach to ambient pressure catalytic reactions, Catal. Today 126, 3 (2007) 0920-5861 10.1016/j.cattod.2006.12.005.
C.-S. Hsieh, R. K. Campen, M. Okuno, E. H. G. Backus, Y. Nagata, and M. Bonn, Mechanism of vibrational energy dissipation of free OH groups at the air-water interface., Proc. Natl. Acad. Sci. USA 110, 18780 (2013) 0027-8424 10.1073/pnas.1314770110.
R. Khatib, E. H. G. Backus, M. Bonn, M.-J. Perez-Haro, M.-P. Gaigeot, and M. Sulpizi, Water orientation and hydrogen-bond structure at the fluorite/water interface, Sci. Rep. 6, 24287 (2016) 2045-2322 10.1038/srep24287.
D. Hu, A. Mafi, and K. C. Chou, Revisiting the thermodynamics of water surfaces and the effects of surfactant head group, J. Phys. Chem. B 120, 2257 (2016) 1520-6106 10.1021/acs.jpcb.5b11717.
P. E. Ohno, H. f. Wang, and F. M. Geiger, Second-order spectral lineshapes from charged interfaces, Nat. Commun. 8, 1032 (2017) 2041-1723 10.1038/s41467-017-01088-0.
L. Dalstein, A. Revel, C. Humbert, and B. Busson, Nonlinear optical response of a gold surface in the visible range: A study by two-color sum-frequency generation spectroscopy. I. Experimental determination, J. Chem. Phys. 148, 134701 (2018) 0021-9606 10.1063/1.5021553.
L. Dalstein, C. Humbert, M. Ben Haddada, S. Boujday, G. Barbillon, and B. Busson, The prevailing role of hotspots in plasmon-enhanced sum-frequency generation spectroscopy, J. Phys. Chem. Lett. 10, 7706 (2019) 1948-7185 10.1021/acs.jpclett.9b03064.
N. Alyabyeva, A. Ouvrard, A.-M. Zakaria, and B. Bourguignon, Probing nanoparticle geometry down to subnanometer size: The benefits of vibrational spectroscopy, J. Phys. Chem. Lett. 10, 624 (2019) 1948-7185 10.1021/acs.jpclett.8b03830.
P. Guyot-Sionnest, J. H. Hunt, and Y. R. Shen, Sum-frequency Vibrational Spectroscopy of a Langmuir Film: Study of Molecular Orientation of a Two-dimensional System, Phys. Rev. Lett. 59, 1597 (1987) 0031-9007 10.1103/PhysRevLett.59.1597.
Y. R. Shen, Nonlinear optical studies of surfaces, Appl. Phys. A 59, 541 (1994) 0721-7250 10.1007/BF00348272.
A. N. Bordenyuk, C. Weeraman, A. Yatawara, H. D. Jayathilake, I. Stiopkin, Y. Liu, and A. V. Benderskii, Vibrational sum frequency generation spectroscopy of dodecanethiol on metal nanoparticles, J. Phys. Chem. C 111, 8925 (2007) 1932-7447 10.1021/jp069062n.
D. Lis, Y. Caudano, M. Henry, S. Demoustier-Champagne, E. Ferain, and F. Cecchet, Selective plasmonic platforms based on nanopillars to enhance vibrational sum-frequency generation spectroscopy, Adv. Opt. Mater. 1, 244 (2013) 2195-1071 10.1002/adom.201200034.
L. Dalstein, M. B. Haddada, G. Barbillon, C. Humbert, A. Tadjeddine, S. Boujday, and B. Busson, Revealing the interplay between adsorbed molecular layers and gold nanoparticles by linear and nonlinear optical properties, J. Phys. Chem. C 119, 17146 (2015) 1932-7447 10.1021/acs.jpcc.5b03601.
C. Humbert, A. Dahi, L. Dalstein, B. Busson, M. Lismont, P. Colson, and L. Dreesen, Linear and nonlinear optical properties of functionalized CdSe quantum dots prepared by plasma sputtering and wet chemistry, J. Colloid Interface Sci. 445, 69 (2015) 10.1016/j.jcis.2014.12.075.
T. Noblet, L. Dreesen, S. Boujday, C. Méthivier, B. Busson, A. Tadjeddine, and C. Humbert, Semiconductor quantum dots reveal dipolar coupling from exciton to ligand vibration, Commun. Chem. 1, 76 (2018) 2399-3669 10.1038/s42004-018-0079-y.
C. Humbert, T. Noblet, L. Dalstein, B. Busson, and G. Barbillon, Sum-frequency generation spectroscopy of plasmonic nanomaterials: A review, Materials 12, 836 (2019) 1996-1944 10.3390/ma12050836.
M. Linke, M. Hille, M. Lackner, L. Schumacher, S. Schlücker, and E. Hasselbrink, Plasmonic effects of Au nanoparticles on the vibrational sum frequency spectrum of 4-nitrothiophenol, J. Phys. Chem. C 123, 24234 (2019) 1932-7447 10.1021/acs.jpcc.9b05207.
T. Noblet, S. Boujday, C. Méthivier, M. Erard, J. Hottechamps, B. Busson, and C. Humbert, Two-dimensional layers of colloidal CdTe quantum dots: Assembly, optical properties, and vibroelectronic coupling, J. Phys. Chem. C 124, 25873 (2020) 1932-7447 10.1021/acs.jpcc.0c08191.
T. Noblet, B. Busson, and C. Humbert, Diagrammatic theory of linear and nonlinear optics for composite systems, Phys. Rev. A 104, 063504 (2021) 2469-9926 10.1103/PhysRevA.104.063504.
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.105.205420 for mathematical details and theoretical foundations of the relation between the Matsubara formalism and optics, the Feynman rules for computing diagrams, the definitions of (non)linear optical response functions, the procedure of factorization within diagrams, and the method to pair and sum bipartite diagrams.
A. M. Zagoskin, Quantum Theory of Many-body Systems: Techniques and Applications (Springer, Berlin, 1998).
G. D. Mahan, Many-particle Physics, 2nd ed. (Plenum, New York, 1990).
D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics: An Introduction to Radiation-molecule Interaction (Academic, New York, 1984).
R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, New York, 2003).
B. Busson and L. Dalstein, Sum-frequency spectroscopy amplified by plasmonics: The small particle case, J. Phys. Chem. C 123, 26597 (2019) 1932-7447 10.1021/acs.jpcc.9b06334.
Y. He, H. Ren, E.-M. You, P. M. Radjenovic, S.-G. Sun, Z.-Q. Tian, J.-F. Li, and Z. Wang, Polarization-and Wavelength-Dependent Shell-Isolated-Nanoparticle-Enhanced Sum-Frequency Generation with High Sensitivity, Phys. Rev. Lett. 125, 047401 (2020) 0031-9007 10.1103/PhysRevLett.125.047401.
C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, Weinheim, 1983).
J. A. Creighton, Surface raman electromagnetic enhancement factors for molecules at the surface of small isolated metal spheres: the determination of adsorbate orientation from sers relative intensities, Surf. Sci. 124, 209 (1983) 0039-6028 10.1016/0039-6028(83)90345-X.
In Ref. [27], Eq. (4) should be corrected: (Equation presented) should appear instead of (Equation presented).
S. H. Lin and A. A. Villaeys, Theoretical description of steady-state sum-frequency generation in molecular adsorbates, Phys. Rev. A 50, 5134 (1994) 1050-2947 10.1103/PhysRevA.50.5134.
C. Noguez, Surface plasmons on metal nanoparticles: The influence of shape and physical environment, J. Phys. Chem. C 111, 3806 (2007) 1932-7447 10.1021/jp066539m.
M. A. Yurkin and A. G. Hoekstra, The discrete-dipole-approximation code adda: Capabilities and known limitations, J. Quant. Spectrosc. Radiat. Transf. 112, 2234 (2011) 0022-4073 10.1016/j.jqsrt.2011.01.031.
A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, Artech House Antennas and Propagation Library (Artech House, Norwood, 2005).
R. Rodríguez-Oliveros and J. A. Sánchez-Gil, Gold nanostars as thermoplasmonic nanoparticles for optical heating, Opt. Express 20, 621 (2012) 1094-4087 10.1364/OE.20.000621.
S. Roy, K.-K. Hung, U. Stege, and D. K. Hore, Rotations, projections, direction cosines, and vibrational spectra, Appl. Spectrosc. Rev. 49, 233 (2014) 0570-4928 10.1080/05704928.2013.819810.
S. Roke, M. Bonn, and A. V. Petukhov, Nonlinear optical scattering: The concept of effective susceptibility, Phys. Rev. B 70, 115106 (2004) 1098-0121 10.1103/PhysRevB.70.115106.
H. B. de Aguiar, R. Scheu, K. C. Jena, A. G. F. de Beer, and S. Roke, Comparison of scattering and reflection sfg: a question of phase-matching, Phys. Chem. Chem. Phys. 14, 6826 (2012) 1463-9076 10.1039/c2cp40324b.
A. B. Evlyukhin, C. Reinhardt, U. Zywietz, and B. N. Chichkov, Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions, Phys. Rev. B 85, 245411 (2012) 1098-0121 10.1103/PhysRevB.85.245411.
N. G. Bastús, J. Piella, and V. Puntes, Quantifying the sensitivity of multipolar (dipolar, quadrupolar, and octapolar) surface plasmon resonances in silver nanoparticles: The effect of size, composition, and surface coating, Langmuir 32, 290 (2016) 0743-7463 10.1021/acs.langmuir.5b03859.
Q. Sun, H. Yu, K. Ueno, A. Kubo, Y. Matsuo, and H. Misawa, Dissecting the few-femtosecond dephasing time of dipole and quadrupole modes in gold nanoparticles using polarized photoemission electron microscopy, ACS Nano 10, 3835 (2016) 1936-0851 10.1021/acsnano.6b00715.
J. Gao, H. Gu, and B. Xu, Multifunctional magnetic nanoparticles: Design, synthesis, and biomedical applications, Acc. Chem. Res. 42, 1097 (2009) 0001-4842 10.1021/ar9000026.
R. E. Raab and O. L. de Lange, Multipole Theory in Electromagnetism (Oxford University Press, Oxford, 2005).
A. G. F. de Beer and S. Roke, Nonlinear mie theory for second-harmonic and sum-frequency scattering, Phys. Rev. B 79, 155420 (2009) 1098-0121 10.1103/PhysRevB.79.155420.
S. Van Elshocht, T. Verbiest, M. Kauranen, A. Persoons, B. M. W. Langeveld-Voss, and E. W. Meijer, Direct evidence of the failure of electric-dipole approximation in second-harmonic generation from a chiral polymer film, J. Chem. Phys. 107, 8201 (1997) 0021-9606 10.1063/1.475223.
M. C. Schanne-Klein, F. Hache, A. Roy, C. Flytzanis, and C. Payrastre, Off resonance second order optical activity of isotropic layers of chiral molecules: Observation of electric and magnetic contributions, J. Chem. Phys. 108, 9436 (1998) 0021-9606 10.1063/1.476394.
C. Neipert, B. Space, and A. B. Roney, Generalized computational time correlation function approach: Quantifying quadrupole contributions to vibrationally resonant second-order interface-specific optical spectroscopies, J. Phys. Chem. C 111, 8749 (2007) 1932-7447 10.1021/jp066934c.
W. Mori, L. Wang, Y. Sato, and A. Morita, Development of quadrupole susceptibility automatic calculator in sum frequency generation spectroscopy and application to methyl C-H vibrations, J. Chem. Phys. 153, 174705 (2020) 0021-9606 10.1063/5.0026341.