Abstract

We develop a generalized model to describe thin film interference in interface-specific nonlinear optical spectroscopies of ideal isotropic stratified systems that enables the separation of this effect from the individual interfacial nonlinear responses. The model utilizes a property of the transfer matrix formalism that allows for simplification of an arbitrary layered system to a single layer with newly defined coefficients of reflection and transmission. In addition to the already well known internal transfer coefficients that relate incident fields to internal fields, we define external transfer coefficients that describe how internally generated fields propagate out of the system. By applying the usual boundary conditions we are able to analytically describe the local and induced fields immediately adjacent to an arbitrary interface, followed by transfer of the generated fields out of the system. The model provides a complete and easily implemented approach to calculating the observables from interface-specific spectroscopies on arbitrary layered thin film systems in a concise way.

© 2013 Optical Society of America

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  1. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
  2. X. D. Zhu, H. Suhr, and Y. R. Shen, “Surface vibrational spectroscopy by infrared-visible sum frequency generation,” Phys. Rev. B 35, 3047–3050 (1987).
    [CrossRef]
  3. Z. Chen, Y. R. Shen, and G. A. Somorjai, “Studies of polymer surfaces by sum frequency generation vibrational spectroscopy,” Annu. Rev. Phys. Chem. 53, 437–465 (2002).
    [CrossRef]
  4. F. Vidal and A. Tadjeddine, “Sum-frequency generation spectroscopy of interfaces,” Rep. Prog. Phys. 68, 1095–1127 (2005).
    [CrossRef]
  5. A. Ghosh, M. Smits, M. Sovago, J. Bredenbeck, M. Muller, and M. Bonn, “Ultrafast vibrational dynamics of interfacial water,” Chem. Phys. 350, 23–30 (2008).
    [CrossRef]
  6. T. C. Anglin, D. B. O’Brien, and A. M. Massari, “Monitoring the charge accumulation process in polymeric field-effect transistors via in situ sum frequency generation,” J. Phys. Chem. C 114, 17629–17637 (2010).
    [CrossRef]
  7. D. B. O’Brien, T. C. Anglin, and A. M. Massari, “Surface chemistry and annealing-driven interfacial changes in organic semiconducting thin films on silica surfaces,” Langmuir 27, 13940–13949 (2011).
    [CrossRef]
  8. G. Li, A. Dhinojwala, and M. S. Yeganeh, “Interfacial structure and melting temperature of alcohol and alkane molecules in contact with polystyrene films,” J. Phys. Chem. B 113, 2739–2747 (2009).
    [CrossRef]
  9. G. P. Harp, K. S. Gautam, and A. Dhinojwala, “Probing polymer/polymer interfaces,” J. Am. Chem. Soc. 124, 7908–7909 (2002).
    [CrossRef]
  10. K. S. Gautam, A. D. Schwab, A. Dhinojwala, D. Zhang, S. M. Dougal, and M. S. Yeganeh, “Molecular structure of polystyrene at air/polymer and solid/polymer interfaces,” Phys. Rev. Lett. 85, 3854–3857 (2000).
    [CrossRef]
  11. A. G. Lambert, D. J. Neivandt, A. M. Briggs, E. W. Usadi, and P. B. Davies, “Interference effects in sum frequency spectra from monolayers on composite dielectric/metal substrates,” J. Phys. Chem. B 106, 5461–5469 (2002).
    [CrossRef]
  12. M. Feller, W. Chen, and Y. Shen, “Investigation of surface-induced alignment of liquid-crystal molecules by optical second-harmonic generation,” Phys. Rev. A 43, 6778–6792 (1991).
    [CrossRef]
  13. C. Hirose, H. Ishida, K. Iwatsu, N. Watanabe, and J. Kubota, “In situ SFG spectroscopy of film growth. I. General formulation and the analysis of the signal observed during the deposition,” Chem. Phys. 108, 5948–5956 (1998).
    [CrossRef]
  14. Y. Tong, Y. Zhao, N. Li, M. Osawa, P. B. Davies, and S. Ye, “Interference effects in the sum frequency generation spectra of thin organic films. I. Theoretical modeling and simulation,” J. Chem. Phys. 133, 034704 (2010).
    [CrossRef]
  15. X. Lu, M. L. Clarke, D. Li, X. Wang, G. Xue, and Z. Chen, “A sum frequency generation vibrational study of the interference effect in poly(n-butyl methacrylate) thin films sandwiched between silica and water,” J. Phys. Chem. C 115, 13759–13767 (2011).
    [CrossRef]
  16. E. H. G. Backus, N. Garcia-Araez, M. Bonn, and H. J. Bakker, “On the role of Fresnel factors in sum-frequency generation spectroscopy of metal–water and metal-oxide–water interfaces,” J. Phys. Chem. C 116, 23351–23361 (2012).
    [CrossRef]
  17. G. Li, A. Dhinojwala, and M. S. Yeganeh, “Interference effect from buried interfaces investigated by angular-dependent infrared–visible sum frequency generation technique,” J. Phys. Chem. C 115, 7554–7561 (2011).
    [CrossRef]
  18. J. E. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481 (1987).
    [CrossRef]
  19. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).
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    [CrossRef]
  21. P. T. Wilson, K. A. Briggman, W. E. Wallace, J. C. Stephenson, and L. J. Richter, “Selective study of polymer/dielectric interfaces with vibrationally resonant sum frequency generation via thin-film interference,” Appl. Phys. Lett. 80, 3084–3086 (2002).
    [CrossRef]
  22. M. Born, E. Wolf, and A. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
  23. Z. Knittl, Optics of Thin Films (Wiley, 1976).
  24. Y. R. Shen, “Optical second harmonic generation at interfaces,” Annu. Rev. Phys. Chem. 40, 327–350 (1989).
    [CrossRef]
  25. N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
    [CrossRef]
  26. T. F. Heinz, “Second-order nonlinear optical effects at surfaces and interfaces,” in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, eds. (Elsevier, 1991).
  27. H.-F. Wang, W. Gan, R. Lu, Y. Rao, and B.-H. Wu, “Quantitative spectral and orientational analysis in surface sum frequency generation vibrational spectroscopy (SFG-VS),” Int. Rev. Phys. Chem. 24, 191–256 (2005).
    [CrossRef]
  28. D. B. O’Brien and A. M. Massari, “Simulated vibrational sum frequency generation from a multilayer thin film system with two active interfaces,” J. Chem. Phys. 138, 154708 (2013).
    [CrossRef]
  29. X. Zhuang, P. Miranda, D. Kim, and Y. Shen, “Mapping molecular orientation and conformation at interfaces by surface nonlinear optics,” Phys. Rev. B 59, 12632–12640 (1999).
    [CrossRef]
  30. C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced second-harmonic generation and Raman scattering,” Phys. Rev. B 27, 1965–1979 (1983).
    [CrossRef]
  31. X. Wei, S.-C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, “Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries,” J. Phys. Chem. B 104, 3349–3354 (2000).
    [CrossRef]
  32. D.-S. Zheng, Y. Wang, A.-A. Liu, and H.-F. Wang, “Microscopic molecular optics theory of surface second harmonic generation and sum-frequency generation spectroscopy based on the discrete dipole lattice model,” Int. Rev. Phys. Chem. 27, 629–664 (2008).
    [CrossRef]
  33. N. J. Begue, A. J. Moad, and G. J. Simpson, “Nonlinear optical stokes ellipsometry. 1. Theoretical framework,” J. Phys. Chem. C 113, 10158–10165 (2009).
    [CrossRef]
  34. N. J. Begue, R. M. Everly, V. J. Hall, L. Haupert, and G. J. Simpson, “Nonlinear optical stokes ellipsometry. II. Experimental demonstration,” J. Phys. Chem. C 113, 10166–10175 (2009).
    [CrossRef]

2013 (1)

D. B. O’Brien and A. M. Massari, “Simulated vibrational sum frequency generation from a multilayer thin film system with two active interfaces,” J. Chem. Phys. 138, 154708 (2013).
[CrossRef]

2012 (1)

E. H. G. Backus, N. Garcia-Araez, M. Bonn, and H. J. Bakker, “On the role of Fresnel factors in sum-frequency generation spectroscopy of metal–water and metal-oxide–water interfaces,” J. Phys. Chem. C 116, 23351–23361 (2012).
[CrossRef]

2011 (3)

G. Li, A. Dhinojwala, and M. S. Yeganeh, “Interference effect from buried interfaces investigated by angular-dependent infrared–visible sum frequency generation technique,” J. Phys. Chem. C 115, 7554–7561 (2011).
[CrossRef]

X. Lu, M. L. Clarke, D. Li, X. Wang, G. Xue, and Z. Chen, “A sum frequency generation vibrational study of the interference effect in poly(n-butyl methacrylate) thin films sandwiched between silica and water,” J. Phys. Chem. C 115, 13759–13767 (2011).
[CrossRef]

D. B. O’Brien, T. C. Anglin, and A. M. Massari, “Surface chemistry and annealing-driven interfacial changes in organic semiconducting thin films on silica surfaces,” Langmuir 27, 13940–13949 (2011).
[CrossRef]

2010 (2)

Y. Tong, Y. Zhao, N. Li, M. Osawa, P. B. Davies, and S. Ye, “Interference effects in the sum frequency generation spectra of thin organic films. I. Theoretical modeling and simulation,” J. Chem. Phys. 133, 034704 (2010).
[CrossRef]

T. C. Anglin, D. B. O’Brien, and A. M. Massari, “Monitoring the charge accumulation process in polymeric field-effect transistors via in situ sum frequency generation,” J. Phys. Chem. C 114, 17629–17637 (2010).
[CrossRef]

2009 (3)

G. Li, A. Dhinojwala, and M. S. Yeganeh, “Interfacial structure and melting temperature of alcohol and alkane molecules in contact with polystyrene films,” J. Phys. Chem. B 113, 2739–2747 (2009).
[CrossRef]

N. J. Begue, A. J. Moad, and G. J. Simpson, “Nonlinear optical stokes ellipsometry. 1. Theoretical framework,” J. Phys. Chem. C 113, 10158–10165 (2009).
[CrossRef]

N. J. Begue, R. M. Everly, V. J. Hall, L. Haupert, and G. J. Simpson, “Nonlinear optical stokes ellipsometry. II. Experimental demonstration,” J. Phys. Chem. C 113, 10166–10175 (2009).
[CrossRef]

2008 (2)

D.-S. Zheng, Y. Wang, A.-A. Liu, and H.-F. Wang, “Microscopic molecular optics theory of surface second harmonic generation and sum-frequency generation spectroscopy based on the discrete dipole lattice model,” Int. Rev. Phys. Chem. 27, 629–664 (2008).
[CrossRef]

A. Ghosh, M. Smits, M. Sovago, J. Bredenbeck, M. Muller, and M. Bonn, “Ultrafast vibrational dynamics of interfacial water,” Chem. Phys. 350, 23–30 (2008).
[CrossRef]

2005 (2)

F. Vidal and A. Tadjeddine, “Sum-frequency generation spectroscopy of interfaces,” Rep. Prog. Phys. 68, 1095–1127 (2005).
[CrossRef]

H.-F. Wang, W. Gan, R. Lu, Y. Rao, and B.-H. Wu, “Quantitative spectral and orientational analysis in surface sum frequency generation vibrational spectroscopy (SFG-VS),” Int. Rev. Phys. Chem. 24, 191–256 (2005).
[CrossRef]

2002 (4)

P. T. Wilson, K. A. Briggman, W. E. Wallace, J. C. Stephenson, and L. J. Richter, “Selective study of polymer/dielectric interfaces with vibrationally resonant sum frequency generation via thin-film interference,” Appl. Phys. Lett. 80, 3084–3086 (2002).
[CrossRef]

Z. Chen, Y. R. Shen, and G. A. Somorjai, “Studies of polymer surfaces by sum frequency generation vibrational spectroscopy,” Annu. Rev. Phys. Chem. 53, 437–465 (2002).
[CrossRef]

G. P. Harp, K. S. Gautam, and A. Dhinojwala, “Probing polymer/polymer interfaces,” J. Am. Chem. Soc. 124, 7908–7909 (2002).
[CrossRef]

A. G. Lambert, D. J. Neivandt, A. M. Briggs, E. W. Usadi, and P. B. Davies, “Interference effects in sum frequency spectra from monolayers on composite dielectric/metal substrates,” J. Phys. Chem. B 106, 5461–5469 (2002).
[CrossRef]

2000 (2)

K. S. Gautam, A. D. Schwab, A. Dhinojwala, D. Zhang, S. M. Dougal, and M. S. Yeganeh, “Molecular structure of polystyrene at air/polymer and solid/polymer interfaces,” Phys. Rev. Lett. 85, 3854–3857 (2000).
[CrossRef]

X. Wei, S.-C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, “Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries,” J. Phys. Chem. B 104, 3349–3354 (2000).
[CrossRef]

1999 (1)

X. Zhuang, P. Miranda, D. Kim, and Y. Shen, “Mapping molecular orientation and conformation at interfaces by surface nonlinear optics,” Phys. Rev. B 59, 12632–12640 (1999).
[CrossRef]

1998 (1)

C. Hirose, H. Ishida, K. Iwatsu, N. Watanabe, and J. Kubota, “In situ SFG spectroscopy of film growth. I. General formulation and the analysis of the signal observed during the deposition,” Chem. Phys. 108, 5948–5956 (1998).
[CrossRef]

1995 (1)

1991 (1)

M. Feller, W. Chen, and Y. Shen, “Investigation of surface-induced alignment of liquid-crystal molecules by optical second-harmonic generation,” Phys. Rev. A 43, 6778–6792 (1991).
[CrossRef]

1989 (1)

Y. R. Shen, “Optical second harmonic generation at interfaces,” Annu. Rev. Phys. Chem. 40, 327–350 (1989).
[CrossRef]

1987 (2)

J. E. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481 (1987).
[CrossRef]

X. D. Zhu, H. Suhr, and Y. R. Shen, “Surface vibrational spectroscopy by infrared-visible sum frequency generation,” Phys. Rev. B 35, 3047–3050 (1987).
[CrossRef]

1983 (1)

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced second-harmonic generation and Raman scattering,” Phys. Rev. B 27, 1965–1979 (1983).
[CrossRef]

1962 (1)

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

Anglin, T. C.

D. B. O’Brien, T. C. Anglin, and A. M. Massari, “Surface chemistry and annealing-driven interfacial changes in organic semiconducting thin films on silica surfaces,” Langmuir 27, 13940–13949 (2011).
[CrossRef]

T. C. Anglin, D. B. O’Brien, and A. M. Massari, “Monitoring the charge accumulation process in polymeric field-effect transistors via in situ sum frequency generation,” J. Phys. Chem. C 114, 17629–17637 (2010).
[CrossRef]

Backus, E. H. G.

E. H. G. Backus, N. Garcia-Araez, M. Bonn, and H. J. Bakker, “On the role of Fresnel factors in sum-frequency generation spectroscopy of metal–water and metal-oxide–water interfaces,” J. Phys. Chem. C 116, 23351–23361 (2012).
[CrossRef]

Bakker, H. J.

E. H. G. Backus, N. Garcia-Araez, M. Bonn, and H. J. Bakker, “On the role of Fresnel factors in sum-frequency generation spectroscopy of metal–water and metal-oxide–water interfaces,” J. Phys. Chem. C 116, 23351–23361 (2012).
[CrossRef]

Begue, N. J.

N. J. Begue, A. J. Moad, and G. J. Simpson, “Nonlinear optical stokes ellipsometry. 1. Theoretical framework,” J. Phys. Chem. C 113, 10158–10165 (2009).
[CrossRef]

N. J. Begue, R. M. Everly, V. J. Hall, L. Haupert, and G. J. Simpson, “Nonlinear optical stokes ellipsometry. II. Experimental demonstration,” J. Phys. Chem. C 113, 10166–10175 (2009).
[CrossRef]

Bhatia, A.

M. Born, E. Wolf, and A. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

Bloembergen, N.

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

Bonn, M.

E. H. G. Backus, N. Garcia-Araez, M. Bonn, and H. J. Bakker, “On the role of Fresnel factors in sum-frequency generation spectroscopy of metal–water and metal-oxide–water interfaces,” J. Phys. Chem. C 116, 23351–23361 (2012).
[CrossRef]

A. Ghosh, M. Smits, M. Sovago, J. Bredenbeck, M. Muller, and M. Bonn, “Ultrafast vibrational dynamics of interfacial water,” Chem. Phys. 350, 23–30 (2008).
[CrossRef]

Born, M.

M. Born, E. Wolf, and A. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

Bredenbeck, J.

A. Ghosh, M. Smits, M. Sovago, J. Bredenbeck, M. Muller, and M. Bonn, “Ultrafast vibrational dynamics of interfacial water,” Chem. Phys. 350, 23–30 (2008).
[CrossRef]

Briggman, K. A.

P. T. Wilson, K. A. Briggman, W. E. Wallace, J. C. Stephenson, and L. J. Richter, “Selective study of polymer/dielectric interfaces with vibrationally resonant sum frequency generation via thin-film interference,” Appl. Phys. Lett. 80, 3084–3086 (2002).
[CrossRef]

Briggs, A. M.

A. G. Lambert, D. J. Neivandt, A. M. Briggs, E. W. Usadi, and P. B. Davies, “Interference effects in sum frequency spectra from monolayers on composite dielectric/metal substrates,” J. Phys. Chem. B 106, 5461–5469 (2002).
[CrossRef]

Chen, C. K.

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced second-harmonic generation and Raman scattering,” Phys. Rev. B 27, 1965–1979 (1983).
[CrossRef]

Chen, W.

M. Feller, W. Chen, and Y. Shen, “Investigation of surface-induced alignment of liquid-crystal molecules by optical second-harmonic generation,” Phys. Rev. A 43, 6778–6792 (1991).
[CrossRef]

Chen, Z.

X. Lu, M. L. Clarke, D. Li, X. Wang, G. Xue, and Z. Chen, “A sum frequency generation vibrational study of the interference effect in poly(n-butyl methacrylate) thin films sandwiched between silica and water,” J. Phys. Chem. C 115, 13759–13767 (2011).
[CrossRef]

Z. Chen, Y. R. Shen, and G. A. Somorjai, “Studies of polymer surfaces by sum frequency generation vibrational spectroscopy,” Annu. Rev. Phys. Chem. 53, 437–465 (2002).
[CrossRef]

Clarke, M. L.

X. Lu, M. L. Clarke, D. Li, X. Wang, G. Xue, and Z. Chen, “A sum frequency generation vibrational study of the interference effect in poly(n-butyl methacrylate) thin films sandwiched between silica and water,” J. Phys. Chem. C 115, 13759–13767 (2011).
[CrossRef]

Davies, P. B.

Y. Tong, Y. Zhao, N. Li, M. Osawa, P. B. Davies, and S. Ye, “Interference effects in the sum frequency generation spectra of thin organic films. I. Theoretical modeling and simulation,” J. Chem. Phys. 133, 034704 (2010).
[CrossRef]

A. G. Lambert, D. J. Neivandt, A. M. Briggs, E. W. Usadi, and P. B. Davies, “Interference effects in sum frequency spectra from monolayers on composite dielectric/metal substrates,” J. Phys. Chem. B 106, 5461–5469 (2002).
[CrossRef]

Dhinojwala, A.

G. Li, A. Dhinojwala, and M. S. Yeganeh, “Interference effect from buried interfaces investigated by angular-dependent infrared–visible sum frequency generation technique,” J. Phys. Chem. C 115, 7554–7561 (2011).
[CrossRef]

G. Li, A. Dhinojwala, and M. S. Yeganeh, “Interfacial structure and melting temperature of alcohol and alkane molecules in contact with polystyrene films,” J. Phys. Chem. B 113, 2739–2747 (2009).
[CrossRef]

G. P. Harp, K. S. Gautam, and A. Dhinojwala, “Probing polymer/polymer interfaces,” J. Am. Chem. Soc. 124, 7908–7909 (2002).
[CrossRef]

K. S. Gautam, A. D. Schwab, A. Dhinojwala, D. Zhang, S. M. Dougal, and M. S. Yeganeh, “Molecular structure of polystyrene at air/polymer and solid/polymer interfaces,” Phys. Rev. Lett. 85, 3854–3857 (2000).
[CrossRef]

Dougal, S. M.

K. S. Gautam, A. D. Schwab, A. Dhinojwala, D. Zhang, S. M. Dougal, and M. S. Yeganeh, “Molecular structure of polystyrene at air/polymer and solid/polymer interfaces,” Phys. Rev. Lett. 85, 3854–3857 (2000).
[CrossRef]

Everly, R. M.

N. J. Begue, R. M. Everly, V. J. Hall, L. Haupert, and G. J. Simpson, “Nonlinear optical stokes ellipsometry. II. Experimental demonstration,” J. Phys. Chem. C 113, 10166–10175 (2009).
[CrossRef]

Feller, M.

M. Feller, W. Chen, and Y. Shen, “Investigation of surface-induced alignment of liquid-crystal molecules by optical second-harmonic generation,” Phys. Rev. A 43, 6778–6792 (1991).
[CrossRef]

Gan, W.

H.-F. Wang, W. Gan, R. Lu, Y. Rao, and B.-H. Wu, “Quantitative spectral and orientational analysis in surface sum frequency generation vibrational spectroscopy (SFG-VS),” Int. Rev. Phys. Chem. 24, 191–256 (2005).
[CrossRef]

Garcia-Araez, N.

E. H. G. Backus, N. Garcia-Araez, M. Bonn, and H. J. Bakker, “On the role of Fresnel factors in sum-frequency generation spectroscopy of metal–water and metal-oxide–water interfaces,” J. Phys. Chem. C 116, 23351–23361 (2012).
[CrossRef]

Gautam, K. S.

G. P. Harp, K. S. Gautam, and A. Dhinojwala, “Probing polymer/polymer interfaces,” J. Am. Chem. Soc. 124, 7908–7909 (2002).
[CrossRef]

K. S. Gautam, A. D. Schwab, A. Dhinojwala, D. Zhang, S. M. Dougal, and M. S. Yeganeh, “Molecular structure of polystyrene at air/polymer and solid/polymer interfaces,” Phys. Rev. Lett. 85, 3854–3857 (2000).
[CrossRef]

Ghosh, A.

A. Ghosh, M. Smits, M. Sovago, J. Bredenbeck, M. Muller, and M. Bonn, “Ultrafast vibrational dynamics of interfacial water,” Chem. Phys. 350, 23–30 (2008).
[CrossRef]

Hall, V. J.

N. J. Begue, R. M. Everly, V. J. Hall, L. Haupert, and G. J. Simpson, “Nonlinear optical stokes ellipsometry. II. Experimental demonstration,” J. Phys. Chem. C 113, 10166–10175 (2009).
[CrossRef]

Harp, G. P.

G. P. Harp, K. S. Gautam, and A. Dhinojwala, “Probing polymer/polymer interfaces,” J. Am. Chem. Soc. 124, 7908–7909 (2002).
[CrossRef]

Hashizume, N.

Haupert, L.

N. J. Begue, R. M. Everly, V. J. Hall, L. Haupert, and G. J. Simpson, “Nonlinear optical stokes ellipsometry. II. Experimental demonstration,” J. Phys. Chem. C 113, 10166–10175 (2009).
[CrossRef]

Heinz, T. F.

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced second-harmonic generation and Raman scattering,” Phys. Rev. B 27, 1965–1979 (1983).
[CrossRef]

T. F. Heinz, “Second-order nonlinear optical effects at surfaces and interfaces,” in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, eds. (Elsevier, 1991).

Held, H.

X. Wei, S.-C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, “Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries,” J. Phys. Chem. B 104, 3349–3354 (2000).
[CrossRef]

Hirose, C.

C. Hirose, H. Ishida, K. Iwatsu, N. Watanabe, and J. Kubota, “In situ SFG spectroscopy of film growth. I. General formulation and the analysis of the signal observed during the deposition,” Chem. Phys. 108, 5948–5956 (1998).
[CrossRef]

Hong, S.-C.

X. Wei, S.-C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, “Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries,” J. Phys. Chem. B 104, 3349–3354 (2000).
[CrossRef]

Ishida, H.

C. Hirose, H. Ishida, K. Iwatsu, N. Watanabe, and J. Kubota, “In situ SFG spectroscopy of film growth. I. General formulation and the analysis of the signal observed during the deposition,” Chem. Phys. 108, 5948–5956 (1998).
[CrossRef]

Ito, R.

Iwatsu, K.

C. Hirose, H. Ishida, K. Iwatsu, N. Watanabe, and J. Kubota, “In situ SFG spectroscopy of film growth. I. General formulation and the analysis of the signal observed during the deposition,” Chem. Phys. 108, 5948–5956 (1998).
[CrossRef]

Kim, D.

X. Zhuang, P. Miranda, D. Kim, and Y. Shen, “Mapping molecular orientation and conformation at interfaces by surface nonlinear optics,” Phys. Rev. B 59, 12632–12640 (1999).
[CrossRef]

Knittl, Z.

Z. Knittl, Optics of Thin Films (Wiley, 1976).

Kondo, T.

Kubota, J.

C. Hirose, H. Ishida, K. Iwatsu, N. Watanabe, and J. Kubota, “In situ SFG spectroscopy of film growth. I. General formulation and the analysis of the signal observed during the deposition,” Chem. Phys. 108, 5948–5956 (1998).
[CrossRef]

Lambert, A. G.

A. G. Lambert, D. J. Neivandt, A. M. Briggs, E. W. Usadi, and P. B. Davies, “Interference effects in sum frequency spectra from monolayers on composite dielectric/metal substrates,” J. Phys. Chem. B 106, 5461–5469 (2002).
[CrossRef]

Li, D.

X. Lu, M. L. Clarke, D. Li, X. Wang, G. Xue, and Z. Chen, “A sum frequency generation vibrational study of the interference effect in poly(n-butyl methacrylate) thin films sandwiched between silica and water,” J. Phys. Chem. C 115, 13759–13767 (2011).
[CrossRef]

Li, G.

G. Li, A. Dhinojwala, and M. S. Yeganeh, “Interference effect from buried interfaces investigated by angular-dependent infrared–visible sum frequency generation technique,” J. Phys. Chem. C 115, 7554–7561 (2011).
[CrossRef]

G. Li, A. Dhinojwala, and M. S. Yeganeh, “Interfacial structure and melting temperature of alcohol and alkane molecules in contact with polystyrene films,” J. Phys. Chem. B 113, 2739–2747 (2009).
[CrossRef]

Li, N.

Y. Tong, Y. Zhao, N. Li, M. Osawa, P. B. Davies, and S. Ye, “Interference effects in the sum frequency generation spectra of thin organic films. I. Theoretical modeling and simulation,” J. Chem. Phys. 133, 034704 (2010).
[CrossRef]

Liu, A.-A.

D.-S. Zheng, Y. Wang, A.-A. Liu, and H.-F. Wang, “Microscopic molecular optics theory of surface second harmonic generation and sum-frequency generation spectroscopy based on the discrete dipole lattice model,” Int. Rev. Phys. Chem. 27, 629–664 (2008).
[CrossRef]

Lu, R.

H.-F. Wang, W. Gan, R. Lu, Y. Rao, and B.-H. Wu, “Quantitative spectral and orientational analysis in surface sum frequency generation vibrational spectroscopy (SFG-VS),” Int. Rev. Phys. Chem. 24, 191–256 (2005).
[CrossRef]

Lu, X.

X. Lu, M. L. Clarke, D. Li, X. Wang, G. Xue, and Z. Chen, “A sum frequency generation vibrational study of the interference effect in poly(n-butyl methacrylate) thin films sandwiched between silica and water,” J. Phys. Chem. C 115, 13759–13767 (2011).
[CrossRef]

Lvovsky, A. I.

X. Wei, S.-C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, “Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries,” J. Phys. Chem. B 104, 3349–3354 (2000).
[CrossRef]

Massari, A. M.

D. B. O’Brien and A. M. Massari, “Simulated vibrational sum frequency generation from a multilayer thin film system with two active interfaces,” J. Chem. Phys. 138, 154708 (2013).
[CrossRef]

D. B. O’Brien, T. C. Anglin, and A. M. Massari, “Surface chemistry and annealing-driven interfacial changes in organic semiconducting thin films on silica surfaces,” Langmuir 27, 13940–13949 (2011).
[CrossRef]

T. C. Anglin, D. B. O’Brien, and A. M. Massari, “Monitoring the charge accumulation process in polymeric field-effect transistors via in situ sum frequency generation,” J. Phys. Chem. C 114, 17629–17637 (2010).
[CrossRef]

Miranda, P.

X. Zhuang, P. Miranda, D. Kim, and Y. Shen, “Mapping molecular orientation and conformation at interfaces by surface nonlinear optics,” Phys. Rev. B 59, 12632–12640 (1999).
[CrossRef]

Moad, A. J.

N. J. Begue, A. J. Moad, and G. J. Simpson, “Nonlinear optical stokes ellipsometry. 1. Theoretical framework,” J. Phys. Chem. C 113, 10158–10165 (2009).
[CrossRef]

Muller, M.

A. Ghosh, M. Smits, M. Sovago, J. Bredenbeck, M. Muller, and M. Bonn, “Ultrafast vibrational dynamics of interfacial water,” Chem. Phys. 350, 23–30 (2008).
[CrossRef]

Neivandt, D. J.

A. G. Lambert, D. J. Neivandt, A. M. Briggs, E. W. Usadi, and P. B. Davies, “Interference effects in sum frequency spectra from monolayers on composite dielectric/metal substrates,” J. Phys. Chem. B 106, 5461–5469 (2002).
[CrossRef]

O’Brien, D. B.

D. B. O’Brien and A. M. Massari, “Simulated vibrational sum frequency generation from a multilayer thin film system with two active interfaces,” J. Chem. Phys. 138, 154708 (2013).
[CrossRef]

D. B. O’Brien, T. C. Anglin, and A. M. Massari, “Surface chemistry and annealing-driven interfacial changes in organic semiconducting thin films on silica surfaces,” Langmuir 27, 13940–13949 (2011).
[CrossRef]

T. C. Anglin, D. B. O’Brien, and A. M. Massari, “Monitoring the charge accumulation process in polymeric field-effect transistors via in situ sum frequency generation,” J. Phys. Chem. C 114, 17629–17637 (2010).
[CrossRef]

Ohashi, M.

Osawa, M.

Y. Tong, Y. Zhao, N. Li, M. Osawa, P. B. Davies, and S. Ye, “Interference effects in the sum frequency generation spectra of thin organic films. I. Theoretical modeling and simulation,” J. Chem. Phys. 133, 034704 (2010).
[CrossRef]

Pershan, P. S.

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

Rao, Y.

H.-F. Wang, W. Gan, R. Lu, Y. Rao, and B.-H. Wu, “Quantitative spectral and orientational analysis in surface sum frequency generation vibrational spectroscopy (SFG-VS),” Int. Rev. Phys. Chem. 24, 191–256 (2005).
[CrossRef]

Ricard, D.

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced second-harmonic generation and Raman scattering,” Phys. Rev. B 27, 1965–1979 (1983).
[CrossRef]

Richter, L. J.

P. T. Wilson, K. A. Briggman, W. E. Wallace, J. C. Stephenson, and L. J. Richter, “Selective study of polymer/dielectric interfaces with vibrationally resonant sum frequency generation via thin-film interference,” Appl. Phys. Lett. 80, 3084–3086 (2002).
[CrossRef]

Schwab, A. D.

K. S. Gautam, A. D. Schwab, A. Dhinojwala, D. Zhang, S. M. Dougal, and M. S. Yeganeh, “Molecular structure of polystyrene at air/polymer and solid/polymer interfaces,” Phys. Rev. Lett. 85, 3854–3857 (2000).
[CrossRef]

Shen, Y.

X. Zhuang, P. Miranda, D. Kim, and Y. Shen, “Mapping molecular orientation and conformation at interfaces by surface nonlinear optics,” Phys. Rev. B 59, 12632–12640 (1999).
[CrossRef]

M. Feller, W. Chen, and Y. Shen, “Investigation of surface-induced alignment of liquid-crystal molecules by optical second-harmonic generation,” Phys. Rev. A 43, 6778–6792 (1991).
[CrossRef]

Shen, Y. R.

Z. Chen, Y. R. Shen, and G. A. Somorjai, “Studies of polymer surfaces by sum frequency generation vibrational spectroscopy,” Annu. Rev. Phys. Chem. 53, 437–465 (2002).
[CrossRef]

X. Wei, S.-C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, “Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries,” J. Phys. Chem. B 104, 3349–3354 (2000).
[CrossRef]

Y. R. Shen, “Optical second harmonic generation at interfaces,” Annu. Rev. Phys. Chem. 40, 327–350 (1989).
[CrossRef]

X. D. Zhu, H. Suhr, and Y. R. Shen, “Surface vibrational spectroscopy by infrared-visible sum frequency generation,” Phys. Rev. B 35, 3047–3050 (1987).
[CrossRef]

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced second-harmonic generation and Raman scattering,” Phys. Rev. B 27, 1965–1979 (1983).
[CrossRef]

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

Simpson, G. J.

N. J. Begue, A. J. Moad, and G. J. Simpson, “Nonlinear optical stokes ellipsometry. 1. Theoretical framework,” J. Phys. Chem. C 113, 10158–10165 (2009).
[CrossRef]

N. J. Begue, R. M. Everly, V. J. Hall, L. Haupert, and G. J. Simpson, “Nonlinear optical stokes ellipsometry. II. Experimental demonstration,” J. Phys. Chem. C 113, 10166–10175 (2009).
[CrossRef]

Sipe, J. E.

Smits, M.

A. Ghosh, M. Smits, M. Sovago, J. Bredenbeck, M. Muller, and M. Bonn, “Ultrafast vibrational dynamics of interfacial water,” Chem. Phys. 350, 23–30 (2008).
[CrossRef]

Somorjai, G. A.

Z. Chen, Y. R. Shen, and G. A. Somorjai, “Studies of polymer surfaces by sum frequency generation vibrational spectroscopy,” Annu. Rev. Phys. Chem. 53, 437–465 (2002).
[CrossRef]

Sovago, M.

A. Ghosh, M. Smits, M. Sovago, J. Bredenbeck, M. Muller, and M. Bonn, “Ultrafast vibrational dynamics of interfacial water,” Chem. Phys. 350, 23–30 (2008).
[CrossRef]

Stephenson, J. C.

P. T. Wilson, K. A. Briggman, W. E. Wallace, J. C. Stephenson, and L. J. Richter, “Selective study of polymer/dielectric interfaces with vibrationally resonant sum frequency generation via thin-film interference,” Appl. Phys. Lett. 80, 3084–3086 (2002).
[CrossRef]

Suhr, H.

X. D. Zhu, H. Suhr, and Y. R. Shen, “Surface vibrational spectroscopy by infrared-visible sum frequency generation,” Phys. Rev. B 35, 3047–3050 (1987).
[CrossRef]

Tadjeddine, A.

F. Vidal and A. Tadjeddine, “Sum-frequency generation spectroscopy of interfaces,” Rep. Prog. Phys. 68, 1095–1127 (2005).
[CrossRef]

Tong, Y.

Y. Tong, Y. Zhao, N. Li, M. Osawa, P. B. Davies, and S. Ye, “Interference effects in the sum frequency generation spectra of thin organic films. I. Theoretical modeling and simulation,” J. Chem. Phys. 133, 034704 (2010).
[CrossRef]

Usadi, E. W.

A. G. Lambert, D. J. Neivandt, A. M. Briggs, E. W. Usadi, and P. B. Davies, “Interference effects in sum frequency spectra from monolayers on composite dielectric/metal substrates,” J. Phys. Chem. B 106, 5461–5469 (2002).
[CrossRef]

Vidal, F.

F. Vidal and A. Tadjeddine, “Sum-frequency generation spectroscopy of interfaces,” Rep. Prog. Phys. 68, 1095–1127 (2005).
[CrossRef]

Wallace, W. E.

P. T. Wilson, K. A. Briggman, W. E. Wallace, J. C. Stephenson, and L. J. Richter, “Selective study of polymer/dielectric interfaces with vibrationally resonant sum frequency generation via thin-film interference,” Appl. Phys. Lett. 80, 3084–3086 (2002).
[CrossRef]

Wang, H.-F.

D.-S. Zheng, Y. Wang, A.-A. Liu, and H.-F. Wang, “Microscopic molecular optics theory of surface second harmonic generation and sum-frequency generation spectroscopy based on the discrete dipole lattice model,” Int. Rev. Phys. Chem. 27, 629–664 (2008).
[CrossRef]

H.-F. Wang, W. Gan, R. Lu, Y. Rao, and B.-H. Wu, “Quantitative spectral and orientational analysis in surface sum frequency generation vibrational spectroscopy (SFG-VS),” Int. Rev. Phys. Chem. 24, 191–256 (2005).
[CrossRef]

Wang, X.

X. Lu, M. L. Clarke, D. Li, X. Wang, G. Xue, and Z. Chen, “A sum frequency generation vibrational study of the interference effect in poly(n-butyl methacrylate) thin films sandwiched between silica and water,” J. Phys. Chem. C 115, 13759–13767 (2011).
[CrossRef]

Wang, Y.

D.-S. Zheng, Y. Wang, A.-A. Liu, and H.-F. Wang, “Microscopic molecular optics theory of surface second harmonic generation and sum-frequency generation spectroscopy based on the discrete dipole lattice model,” Int. Rev. Phys. Chem. 27, 629–664 (2008).
[CrossRef]

Watanabe, N.

C. Hirose, H. Ishida, K. Iwatsu, N. Watanabe, and J. Kubota, “In situ SFG spectroscopy of film growth. I. General formulation and the analysis of the signal observed during the deposition,” Chem. Phys. 108, 5948–5956 (1998).
[CrossRef]

Wei, X.

X. Wei, S.-C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, “Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries,” J. Phys. Chem. B 104, 3349–3354 (2000).
[CrossRef]

Wilson, P. T.

P. T. Wilson, K. A. Briggman, W. E. Wallace, J. C. Stephenson, and L. J. Richter, “Selective study of polymer/dielectric interfaces with vibrationally resonant sum frequency generation via thin-film interference,” Appl. Phys. Lett. 80, 3084–3086 (2002).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, and A. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

Wu, B.-H.

H.-F. Wang, W. Gan, R. Lu, Y. Rao, and B.-H. Wu, “Quantitative spectral and orientational analysis in surface sum frequency generation vibrational spectroscopy (SFG-VS),” Int. Rev. Phys. Chem. 24, 191–256 (2005).
[CrossRef]

Xue, G.

X. Lu, M. L. Clarke, D. Li, X. Wang, G. Xue, and Z. Chen, “A sum frequency generation vibrational study of the interference effect in poly(n-butyl methacrylate) thin films sandwiched between silica and water,” J. Phys. Chem. C 115, 13759–13767 (2011).
[CrossRef]

Ye, S.

Y. Tong, Y. Zhao, N. Li, M. Osawa, P. B. Davies, and S. Ye, “Interference effects in the sum frequency generation spectra of thin organic films. I. Theoretical modeling and simulation,” J. Chem. Phys. 133, 034704 (2010).
[CrossRef]

Yeganeh, M. S.

G. Li, A. Dhinojwala, and M. S. Yeganeh, “Interference effect from buried interfaces investigated by angular-dependent infrared–visible sum frequency generation technique,” J. Phys. Chem. C 115, 7554–7561 (2011).
[CrossRef]

G. Li, A. Dhinojwala, and M. S. Yeganeh, “Interfacial structure and melting temperature of alcohol and alkane molecules in contact with polystyrene films,” J. Phys. Chem. B 113, 2739–2747 (2009).
[CrossRef]

K. S. Gautam, A. D. Schwab, A. Dhinojwala, D. Zhang, S. M. Dougal, and M. S. Yeganeh, “Molecular structure of polystyrene at air/polymer and solid/polymer interfaces,” Phys. Rev. Lett. 85, 3854–3857 (2000).
[CrossRef]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Zhang, D.

K. S. Gautam, A. D. Schwab, A. Dhinojwala, D. Zhang, S. M. Dougal, and M. S. Yeganeh, “Molecular structure of polystyrene at air/polymer and solid/polymer interfaces,” Phys. Rev. Lett. 85, 3854–3857 (2000).
[CrossRef]

Zhao, Y.

Y. Tong, Y. Zhao, N. Li, M. Osawa, P. B. Davies, and S. Ye, “Interference effects in the sum frequency generation spectra of thin organic films. I. Theoretical modeling and simulation,” J. Chem. Phys. 133, 034704 (2010).
[CrossRef]

Zheng, D.-S.

D.-S. Zheng, Y. Wang, A.-A. Liu, and H.-F. Wang, “Microscopic molecular optics theory of surface second harmonic generation and sum-frequency generation spectroscopy based on the discrete dipole lattice model,” Int. Rev. Phys. Chem. 27, 629–664 (2008).
[CrossRef]

Zhu, X. D.

X. D. Zhu, H. Suhr, and Y. R. Shen, “Surface vibrational spectroscopy by infrared-visible sum frequency generation,” Phys. Rev. B 35, 3047–3050 (1987).
[CrossRef]

Zhuang, X.

X. Zhuang, P. Miranda, D. Kim, and Y. Shen, “Mapping molecular orientation and conformation at interfaces by surface nonlinear optics,” Phys. Rev. B 59, 12632–12640 (1999).
[CrossRef]

Annu. Rev. Phys. Chem. (2)

Z. Chen, Y. R. Shen, and G. A. Somorjai, “Studies of polymer surfaces by sum frequency generation vibrational spectroscopy,” Annu. Rev. Phys. Chem. 53, 437–465 (2002).
[CrossRef]

Y. R. Shen, “Optical second harmonic generation at interfaces,” Annu. Rev. Phys. Chem. 40, 327–350 (1989).
[CrossRef]

Appl. Phys. Lett. (1)

P. T. Wilson, K. A. Briggman, W. E. Wallace, J. C. Stephenson, and L. J. Richter, “Selective study of polymer/dielectric interfaces with vibrationally resonant sum frequency generation via thin-film interference,” Appl. Phys. Lett. 80, 3084–3086 (2002).
[CrossRef]

Chem. Phys. (2)

A. Ghosh, M. Smits, M. Sovago, J. Bredenbeck, M. Muller, and M. Bonn, “Ultrafast vibrational dynamics of interfacial water,” Chem. Phys. 350, 23–30 (2008).
[CrossRef]

C. Hirose, H. Ishida, K. Iwatsu, N. Watanabe, and J. Kubota, “In situ SFG spectroscopy of film growth. I. General formulation and the analysis of the signal observed during the deposition,” Chem. Phys. 108, 5948–5956 (1998).
[CrossRef]

Int. Rev. Phys. Chem. (2)

H.-F. Wang, W. Gan, R. Lu, Y. Rao, and B.-H. Wu, “Quantitative spectral and orientational analysis in surface sum frequency generation vibrational spectroscopy (SFG-VS),” Int. Rev. Phys. Chem. 24, 191–256 (2005).
[CrossRef]

D.-S. Zheng, Y. Wang, A.-A. Liu, and H.-F. Wang, “Microscopic molecular optics theory of surface second harmonic generation and sum-frequency generation spectroscopy based on the discrete dipole lattice model,” Int. Rev. Phys. Chem. 27, 629–664 (2008).
[CrossRef]

J. Am. Chem. Soc. (1)

G. P. Harp, K. S. Gautam, and A. Dhinojwala, “Probing polymer/polymer interfaces,” J. Am. Chem. Soc. 124, 7908–7909 (2002).
[CrossRef]

J. Chem. Phys. (2)

Y. Tong, Y. Zhao, N. Li, M. Osawa, P. B. Davies, and S. Ye, “Interference effects in the sum frequency generation spectra of thin organic films. I. Theoretical modeling and simulation,” J. Chem. Phys. 133, 034704 (2010).
[CrossRef]

D. B. O’Brien and A. M. Massari, “Simulated vibrational sum frequency generation from a multilayer thin film system with two active interfaces,” J. Chem. Phys. 138, 154708 (2013).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. Chem. B (3)

A. G. Lambert, D. J. Neivandt, A. M. Briggs, E. W. Usadi, and P. B. Davies, “Interference effects in sum frequency spectra from monolayers on composite dielectric/metal substrates,” J. Phys. Chem. B 106, 5461–5469 (2002).
[CrossRef]

G. Li, A. Dhinojwala, and M. S. Yeganeh, “Interfacial structure and melting temperature of alcohol and alkane molecules in contact with polystyrene films,” J. Phys. Chem. B 113, 2739–2747 (2009).
[CrossRef]

X. Wei, S.-C. Hong, A. I. Lvovsky, H. Held, and Y. R. Shen, “Evaluation of surface vs bulk contributions in sum-frequency vibrational spectroscopy using reflection and transmission geometries,” J. Phys. Chem. B 104, 3349–3354 (2000).
[CrossRef]

J. Phys. Chem. C (6)

N. J. Begue, A. J. Moad, and G. J. Simpson, “Nonlinear optical stokes ellipsometry. 1. Theoretical framework,” J. Phys. Chem. C 113, 10158–10165 (2009).
[CrossRef]

N. J. Begue, R. M. Everly, V. J. Hall, L. Haupert, and G. J. Simpson, “Nonlinear optical stokes ellipsometry. II. Experimental demonstration,” J. Phys. Chem. C 113, 10166–10175 (2009).
[CrossRef]

X. Lu, M. L. Clarke, D. Li, X. Wang, G. Xue, and Z. Chen, “A sum frequency generation vibrational study of the interference effect in poly(n-butyl methacrylate) thin films sandwiched between silica and water,” J. Phys. Chem. C 115, 13759–13767 (2011).
[CrossRef]

E. H. G. Backus, N. Garcia-Araez, M. Bonn, and H. J. Bakker, “On the role of Fresnel factors in sum-frequency generation spectroscopy of metal–water and metal-oxide–water interfaces,” J. Phys. Chem. C 116, 23351–23361 (2012).
[CrossRef]

G. Li, A. Dhinojwala, and M. S. Yeganeh, “Interference effect from buried interfaces investigated by angular-dependent infrared–visible sum frequency generation technique,” J. Phys. Chem. C 115, 7554–7561 (2011).
[CrossRef]

T. C. Anglin, D. B. O’Brien, and A. M. Massari, “Monitoring the charge accumulation process in polymeric field-effect transistors via in situ sum frequency generation,” J. Phys. Chem. C 114, 17629–17637 (2010).
[CrossRef]

Langmuir (1)

D. B. O’Brien, T. C. Anglin, and A. M. Massari, “Surface chemistry and annealing-driven interfacial changes in organic semiconducting thin films on silica surfaces,” Langmuir 27, 13940–13949 (2011).
[CrossRef]

Phys. Rev. (1)

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

Phys. Rev. A (1)

M. Feller, W. Chen, and Y. Shen, “Investigation of surface-induced alignment of liquid-crystal molecules by optical second-harmonic generation,” Phys. Rev. A 43, 6778–6792 (1991).
[CrossRef]

Phys. Rev. B (3)

X. D. Zhu, H. Suhr, and Y. R. Shen, “Surface vibrational spectroscopy by infrared-visible sum frequency generation,” Phys. Rev. B 35, 3047–3050 (1987).
[CrossRef]

X. Zhuang, P. Miranda, D. Kim, and Y. Shen, “Mapping molecular orientation and conformation at interfaces by surface nonlinear optics,” Phys. Rev. B 59, 12632–12640 (1999).
[CrossRef]

C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, “Surface-enhanced second-harmonic generation and Raman scattering,” Phys. Rev. B 27, 1965–1979 (1983).
[CrossRef]

Phys. Rev. Lett. (1)

K. S. Gautam, A. D. Schwab, A. Dhinojwala, D. Zhang, S. M. Dougal, and M. S. Yeganeh, “Molecular structure of polystyrene at air/polymer and solid/polymer interfaces,” Phys. Rev. Lett. 85, 3854–3857 (2000).
[CrossRef]

Rep. Prog. Phys. (1)

F. Vidal and A. Tadjeddine, “Sum-frequency generation spectroscopy of interfaces,” Rep. Prog. Phys. 68, 1095–1127 (2005).
[CrossRef]

Other (5)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

M. Born, E. Wolf, and A. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

Z. Knittl, Optics of Thin Films (Wiley, 1976).

T. F. Heinz, “Second-order nonlinear optical effects at surfaces and interfaces,” in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, eds. (Elsevier, 1991).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of model and definitions of variables for an arbitrary layered thin film system.

Fig. 2.
Fig. 2.

Definition of the layer phase calculation showing planes of constant phase.

Fig. 3.
Fig. 3.

Graphical depiction of the effective boundaries of subsystems I and II for layer v showing partial system transfer coefficients as the newly defined transmission and reflection coefficients at the boundaries.

Fig. 4.
Fig. 4.

A simple demonstration for applying the model, showing (a) an illustration of the system, (b) simulated ssp data, and (c) simulated sps data. The plots in (b) and (c) include I0αβγ (solid black), |T1ijk|2 (dashed gray), |T2ijk|2 (dashed black), and |χ1ijk|2 (green, short dashes) all scaled on the left. The interference term is solid red and scaled on the right.

Equations (75)

Equations on this page are rendered with MathJax. Learn more.

E=Ee^exp[i(k·rωt)].
I0/k+1|v=1k+1E⃗v,0/k+1NL|2.
E⃗v,0/k+1NL=T⃗v,0/k+1PvNL,
PvNL=χvNL:m=1nEvm,local,
Evm,local=T⃖0/k+1,vmE⃖0/k+1m.
Wv1,v=1tv1,v[1rv1,vrv1,v1],
[EvEv+]=Wv1,v[EvEv+].
rv1,vp=nv1cos(θv)nvcos(θv1)nv1cos(θv)+nvcos(θv1),
rv1,vs=nv1cos(θv1)nvcos(θv)nv1cos(θv1)+nvcos(θv),
tv1,vp=2nv1cos(θv1)nv1cos(θv)+nvcos(θv1),
tv1,vs=2nv1cos(θv1)nv1cos(θv1)+nvcos(θv),
Φv=[exp(iϕv)00exp(iϕv)],
[EvEv+]=Φv[Ev+1Ev+1+],
ϕv=|kv·Δrv||kvzdv|=2πnvλdvcos(θv),
S=(v=0k1Wv,v+1Φv+1)Wk,k+1,
[E1E1+]=S[Ek+1Ek+1+].
r0,sys=E⃗0E⃖0=s(21)s(11),
t0,sys=E⃗k+1E⃖0=1s(11),
rk+1,sys=E⃗k+1E⃖k+1=s(12)s(11),
tk+1,sys=E⃗0E⃖k+1=|S|s(11).
SvI=(i=0v2Wi,i+1Φi+1)Wv1,v,
SvII=(i=vk1Wi,i+1Φi+1)Wk,k+1,
[τ0,vτ0,v+]=ΦvSvII[t0,sys0],
[τ0,vτ0,v+]=Sv1II[t0,sys0],
[τk+1,vτk+1,v+]=ΦvSvII[rk+1,sys1],
[τk+1,vτk+1,v+]=Sv1II[rk+1,sys1].
t0,I=εvE⃖0=1sv,(11)I,
rv,I=εvεv+=sv,(12)Isv,(11)I,
tk+1,II=εv+1+E⃖k+1=|SvII|sv,(11)II,
rv,II=εv+1+εv+1=sv,(21)IIsv,(11)II,
τ0,v=EvE⃖0=t0,Ij=0[rv,Irv,IIexp(2iϕv)]j=t0,I1rv,Irv,IIexp(2iϕv),
τ0,v+=Ev+E⃖0=τ0,vrv,IIexp(2iϕv),
τ0,v=EvE⃖0=τ0,v1exp(iϕv1),
τ0,v+=Ev+E⃖0=τ0,v1+exp(iϕv1),
τk+1,v=EvE⃖k+1=τk+1,v+rv,I,
τk+1,v+=Ev+E⃖k+1=tk+1,IIexp(iϕv)j=0[rv,Irv,IIexp(2iϕv)]j=tk+1,IIexp(iϕv)1rv,Irv,IIexp(2iϕv),
τk+1,v=EvE⃖k+1=τk+1,v1exp(iϕv1),
τk+1,v+=Ev+E⃖k+1=τk+1,v1+exp(iϕv1).
tv,I=ε1+εv+=|SvI|sv,(11)I.
tv,II=εk+1εv+1=1sv,(11)I.
τv,0=E⃗0εv=tv,Irv,IIexp(2iϕv)j=0[rv,Irv,IIexp(2iϕv)]j=tv,Irv,IIexp(2iϕv)1rv,Irv,IIexp(2iϕv),
τv,0+=E⃗0εv+=tv1,Iexp(iϕv1)j=0[rv1,Irv1,IIexp(2iϕv1)]j=tv1,Iexp(iϕv1)1rv1,Irv1,IIexp(2iϕv1),
τv,k+1+=E⃗k+1εv+=tv1,IIrv1,Iexp(2iϕv1)i=0[rv1,Irv1,IIexp(2iϕv1)]j=tv1,IIrv1,Iexp(2iϕv1)1rv1,Irv1,IIexp(2iϕv1),
τv,k+1=E⃗k+1εv=tv,IIexp(iϕv)j=0[rv,Irv,IIexp(2iϕv)]j=tv,IIexp(iϕv)1rv,Irv,IIexp(2iϕv),
[Evm,local,xEvm,local,yEvm,local,z]=T⃖0/k+1,vm[E⃖0/k+1m,pE⃖0/k+1m,s0],
Pr(θv)=[cos(θv)00010sin(θv)00],
[ExEyEz]=Pr(θv)[EpEs0],
Evlocal,x=cos(θv1)(Ev,p+Ev+,p),
Evlocal,y=Ev,s+Ev+,s,
n¯v2Evlocal,z=nv12sin(θv1)(Ev,pEv+,p).
f⃖0/k+1,v+/=[t0/k+1,v+/,p000t0/k+1,v+/,s0000],
Jv=[10001000(nv1/n¯v)2],
T⃖0/k+1,v=Jv(Pr(θv1)f⃖0/k+1,v++Pr(θv1)f⃖0/k+1,v),
f⃖0/k+1,v+/=[t0/k+1,v+/,p000t0/k+1,v+/,s0000],
Jv=[10001000(nv/n¯v)2],
T⃖0/k+1,v=Jv[Pr(θv)f⃖0/k+1,v++Pr(θv)f⃖0/k+1,v].
Rz(φ)=[cos(φ)sin(φ)0sin(φ)cos(φ)0001],
T⃖0/k+1,v=Rz(φ)T⃖0/k+1,vrot.
[E⃗v,0/k+1NL,pE⃗v,0/k+1NL,s0]=T⃗v,0/k+1[PvNL,xPvNL,yPvNL,z].
E⃗v,0/k+1NL=(pv+T⃗v,0/k+1++pvT⃗v,0/k+1)PvNL.
pv+=i2πsec(θv1)cλnv1,
pv=i2πsec(θv)cλnv.
T⃗v,0/k+1+/=f⃗v,0/k+1+/Lv+/.
[εvNL,+/,pεvNL,+/,s0]=pv+/Lv+/[PvNL,xPvNL,yPvNL,z],
kvNL=±kv1±kv2±kvn.
Lv+=[Pr(θv1)T+fv1,vPr(θv1)T]Jv,
Lv=[Pr(θv)T+fv,v1Pr(θv)T]Jv,
fi,j=[ri,jp000ri,js0000].
E⃗v,0/k+1NL=E⃗v,0/k+1NL,++E⃗v,0/k+1NL,=εvNL,+tv,0/k+1++εvNL,tv,0/k+1,
f⃗v,0/k+1+/=[tv,0/k+1+/,p000tv,0/k+1+/,s0000],
I0ssp|(v=12Tvyyzχv(2),yyz)E⃖0vis,sE⃖0mIR,p|2,
I0sps|(v=12Tvyzyχv(2),yzy)E⃖0vis,pE⃖0mIR,s|2,
Tvyyzt⃗v,0,(22)VSFGt⃖0,v,(22)vist⃖0,v,(31)mIR,
Tvyzyt⃗v,0,(22)VSFGt⃖0,v,(31)vist⃖0,v,(22)mIR.
I0αβγ|χ1(2),ijkT1ijk|2+|χ2(2),ijkT2ijk|2+2|χ1(2),ijkT1ijkχ2(2),ijkT2ijk|cos(ϕT12ijk)|χ1(2),ijk|2[|T1ijk|2+|T2ijk|2+2|T1ijk||T2ijk|cos(ϕT12ijk)].

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