Abstract

A new optical configuration is described for sum-frequency generation spectroscopy in which the two fundamental beams approach the interface from different phases. In this geometry one beam approaches the interface at its critical angle in the denser medium, while the other beam approaches the interface in external reflection from the rarer phase. The proposed configuration permits the signal enhancement obtained with total internal reflection sum-frequency generation to be applied to interfaces for which the denser medium is nontransparent in the infrared spectral region. Calculations predict the optimal incident angles for the externally reflecting infrared beam and the internally reflecting visible beam for a series of polarization combinations. Experimental measurements of the sum-frequency intensity as a function of the visible-beam incident angle are presented and compared with the calculated angular dependence. Resulting sum-frequency spectra obtained with a LiNbO3 optical parametric oscillator nanosecond system are shown for a surfactant system at the D2O–air interface.

© 2000 Optical Society of America

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  1. J. Y. Huang and Y. R. Shen, “Sum-frequency generation as a surface probe,” in Laser Spectroscopy and Photochemistry on Metal Surfaces, H.-L. Dai and W. Ho, eds. (World Scientific, Singapore, 1995), pp. 5–53.
  2. J. C. Conboy, M. C. Messmer, and G. L. Richmond, “Effect of alkyl chain length on the conformation and order of simple ionic surfactants adsorbed at the D2O/CCl4 interface as studied by sum-frequency vibrational spectroscopy,” Langmuir 14, 6722–6727 (1998).
    [CrossRef]
  3. S. Baldelli, C. Schnitzer, M. J. Shultz, and D. J. Campbell, “Sum frequency generation investigation of water at the surface of H2O/H2SO4 binary systems,” J. Phys. Chem. B 101, 10, 435–10, 441 (1997).
    [CrossRef]
  4. S. Baldelli, C. Schnitzer, M. J. Shultz, and D. J. Campbell, “Sum frequency generation investigation of glycerol/water surfaces,” J. Phys. Chem. B 101, 4607–4612 (1997).
    [CrossRef]
  5. S. R. Hatch, R. S. Polizzotti, S. Dougal, and P. Rabinowitz, “Surface vibrational spectroscopy of the vapor/solid and liquid/solid interface of acetonitrile on ZrO2,” Chem. Phys. Lett. 196, 97–102 (1992).
    [CrossRef]
  6. M. C. Messmer, J. C. Conboy, and G. L. Richmond, “Observation of molecular ordering at the liquid–liquid interface by resonant sum frequency generation,” J. Am. Chem. Soc. 117, 8039–8040 (1995).
    [CrossRef]
  7. S. R. Hatch, R. S. Polizzotti, S. Dougal, and P. Rabinowitz, “In situ surface vibrational spectroscopy of the vapor/solid and liquid/solid interfaces of acetonitrile on ZrO2,” J. Vac. Sci. Technol. 11, 2232–2238 (1993).
    [CrossRef]
  8. J. C. Conboy, M. C. Messmer, and G. L. Richmond, “Investigation of surfactant conformation and order at the liquid–liquid interface by total internal reflection sum-frequency vibration spectroscopy,” J. Phys. Chem. 100, 7617–7622 (1996).
    [CrossRef]
  9. M. C. Messmer, J. C. Conboy, and G. L. Richmond, “Resonant sum frequency generation studies of surfactant ordering at the oil–water interface,” in Laser Techniques for Surface Science II, J. M. Hicks, W. Ho, and H.-L. Dai, eds., Proc. SPIE 2547, 135–141 (1995).
    [CrossRef]
  10. N. Bloembergen, “Second harmonic reflected light,” Opt. Acta 13, 311–322 (1966).
    [CrossRef]
  11. N. Bloembergen, H. J. Simmon, and C. H. Lee, “Total reflection phenomena in second-harmonic generation of light,” Phys. Rev. 181, 1261–1271 (1969).
    [CrossRef]
  12. N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
    [CrossRef]
  13. B. Dick, A. Gierulski, G. Marowsky, and G. A. Raider, “Determination of the nonlinear optical susceptibility χ(2) of surface layers by sum and difference frequency generation in reflection and transmission,” Appl. Phys. B: 38, 107–116 (1985).
    [CrossRef]
  14. J. Miragliotta, R. S. Polizzotti, P. Rabinowitz, S. D. Cameron, and R. B. Hall, “IR–visible sum-frequency generation study of methanol adsorption and reaction on nickel(100),” Chem. Phys. 143, 123–130 (1990).
    [CrossRef]
  15. R. Fraenkel, G. E. Butterworth, and C. D. Bain, “In situ vibrational spectroscopy of an organic monolayer at the sapphire–quartz interface,” J. Am. Chem. Soc. 120, 203–204 (1998).
    [CrossRef]
  16. D. Zhang, D. H. Gracias, R. Ward, M. Gauckler, Y. Tian, Y. R. Shen, and G. Somorjai, “Surface studies of polymer blends by sum frequency vibrational spectroscopy, atomic force microscopy, and contact angle goniometry,” J. Phys. Chem. 102, 6225–6230 (1998).
    [CrossRef]
  17. D. E. Gragson and G. L. Richmond, “Investigations of the structure and hydrogen bonding of water molecules at liquid surfaces by vibrational sum frequency spectroscopy,” J. Phys. Chem. 102, 3847–3861 (1998).
    [CrossRef]
  18. Y. Goto, N. Akamatsu, K. Domen, and C. Hirose, “Vibration-induced order–disorder transitions in a Langmuir–Blodgett film as investigated by vibrational sum frequency generation spectroscopy,” J. Phys. Chem. 99, 4086–4090 (1995).
    [CrossRef]
  19. B. D. Casson and C. D. Bain, “Phase transitions in mixed monolayers of sodium dodecyl sulfate and dodecanol at the air/water interface,” J. Phys. Chem. 102, 7434–7441 (1998).
    [CrossRef]
  20. Z. Chen, D. H. Gracias, and G. A. Somorjai, “Sum frequency generation (SFG) surface vibrational spectroscopy studies of buried interfaces: catalytic reaction intermediates on transition metal crystal surfaces at high reactant pressures; polymer surface structures at the solid–gas and solid–liquid interfaces,” Appl. Phys. B 68, 549–557 (1999).
    [CrossRef]
  21. K. Wolfrum and A. Laubereau, “Vibrational sum-frequency spectroscopy of an adsorbed monolayer of hexadecanol on water. Destructive interference of adjacent lines,” Chem. Phys. Lett. 228, 83–88 (1994).
    [CrossRef]
  22. J. E. Bertie and Z. Lan, “The refractive index of colorless liquids in the visible and infrared: contributions from the absorption of infrared and ultraviolet radiation and the electronic molar polarizability below 20, 500 cm−1,” J. Chem. Phys. 103, 10, 152–10, 161 (1995).
    [CrossRef]
  23. D. Epperlein, B. Dick, G. Marowsky, and G. A. Reider, “Second-harmonic generation in centro-symmetric media,” Appl. Phys. B 44, 5–10 (1987).
    [CrossRef]
  24. J. Lobau and K. Wolfrum, “Sum-frequency spectroscopy in total internal reflection geometry: signal enhancement and access to molecular properties,” J. Opt. Soc. Am. B 14, 2505–2512 (1997).
    [CrossRef]
  25. T. F. Heinz, “Second-order nonlinear optical effects at surfaces and interfaces,” in Nonlinear Surface Electromagnetic Phenomena, H.-E. Pontah and G. I. Stegeman, eds. (Elsevier, New York, 1991), pp. 353–416.
  26. P. Guyot-Sionnest, Y. R. Shen, and T. F. Heinz, “Comments on ‘Determination of the nonlinear optical susceptibility χ(2) of surface layers’ by B. Dick et al.,” Appl. Phys. B: 42, 237–238 (1987).
    [CrossRef]
  27. B. U. Felderhof and G. Marowsky, “Electromagnetic radiation from a polarization sheet located at an interface between two media,” Appl. Phys. B 44, 11–17 (1987).
    [CrossRef]
  28. R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1993).
  29. Y. J. Yang, R. L. Pizzolatto, M. C. Henry, and M. C. Messmer are preparing a manuscript to be called “Conformational studies of a Gemini surfactant at an air–water interface by sum-frequency generation spectroscopy.”

1999 (1)

Z. Chen, D. H. Gracias, and G. A. Somorjai, “Sum frequency generation (SFG) surface vibrational spectroscopy studies of buried interfaces: catalytic reaction intermediates on transition metal crystal surfaces at high reactant pressures; polymer surface structures at the solid–gas and solid–liquid interfaces,” Appl. Phys. B 68, 549–557 (1999).
[CrossRef]

1998 (5)

B. D. Casson and C. D. Bain, “Phase transitions in mixed monolayers of sodium dodecyl sulfate and dodecanol at the air/water interface,” J. Phys. Chem. 102, 7434–7441 (1998).
[CrossRef]

J. C. Conboy, M. C. Messmer, and G. L. Richmond, “Effect of alkyl chain length on the conformation and order of simple ionic surfactants adsorbed at the D2O/CCl4 interface as studied by sum-frequency vibrational spectroscopy,” Langmuir 14, 6722–6727 (1998).
[CrossRef]

R. Fraenkel, G. E. Butterworth, and C. D. Bain, “In situ vibrational spectroscopy of an organic monolayer at the sapphire–quartz interface,” J. Am. Chem. Soc. 120, 203–204 (1998).
[CrossRef]

D. Zhang, D. H. Gracias, R. Ward, M. Gauckler, Y. Tian, Y. R. Shen, and G. Somorjai, “Surface studies of polymer blends by sum frequency vibrational spectroscopy, atomic force microscopy, and contact angle goniometry,” J. Phys. Chem. 102, 6225–6230 (1998).
[CrossRef]

D. E. Gragson and G. L. Richmond, “Investigations of the structure and hydrogen bonding of water molecules at liquid surfaces by vibrational sum frequency spectroscopy,” J. Phys. Chem. 102, 3847–3861 (1998).
[CrossRef]

1997 (3)

S. Baldelli, C. Schnitzer, M. J. Shultz, and D. J. Campbell, “Sum frequency generation investigation of water at the surface of H2O/H2SO4 binary systems,” J. Phys. Chem. B 101, 10, 435–10, 441 (1997).
[CrossRef]

S. Baldelli, C. Schnitzer, M. J. Shultz, and D. J. Campbell, “Sum frequency generation investigation of glycerol/water surfaces,” J. Phys. Chem. B 101, 4607–4612 (1997).
[CrossRef]

J. Lobau and K. Wolfrum, “Sum-frequency spectroscopy in total internal reflection geometry: signal enhancement and access to molecular properties,” J. Opt. Soc. Am. B 14, 2505–2512 (1997).
[CrossRef]

1996 (1)

J. C. Conboy, M. C. Messmer, and G. L. Richmond, “Investigation of surfactant conformation and order at the liquid–liquid interface by total internal reflection sum-frequency vibration spectroscopy,” J. Phys. Chem. 100, 7617–7622 (1996).
[CrossRef]

1995 (4)

M. C. Messmer, J. C. Conboy, and G. L. Richmond, “Resonant sum frequency generation studies of surfactant ordering at the oil–water interface,” in Laser Techniques for Surface Science II, J. M. Hicks, W. Ho, and H.-L. Dai, eds., Proc. SPIE 2547, 135–141 (1995).
[CrossRef]

M. C. Messmer, J. C. Conboy, and G. L. Richmond, “Observation of molecular ordering at the liquid–liquid interface by resonant sum frequency generation,” J. Am. Chem. Soc. 117, 8039–8040 (1995).
[CrossRef]

Y. Goto, N. Akamatsu, K. Domen, and C. Hirose, “Vibration-induced order–disorder transitions in a Langmuir–Blodgett film as investigated by vibrational sum frequency generation spectroscopy,” J. Phys. Chem. 99, 4086–4090 (1995).
[CrossRef]

J. E. Bertie and Z. Lan, “The refractive index of colorless liquids in the visible and infrared: contributions from the absorption of infrared and ultraviolet radiation and the electronic molar polarizability below 20, 500 cm−1,” J. Chem. Phys. 103, 10, 152–10, 161 (1995).
[CrossRef]

1994 (1)

K. Wolfrum and A. Laubereau, “Vibrational sum-frequency spectroscopy of an adsorbed monolayer of hexadecanol on water. Destructive interference of adjacent lines,” Chem. Phys. Lett. 228, 83–88 (1994).
[CrossRef]

1993 (1)

S. R. Hatch, R. S. Polizzotti, S. Dougal, and P. Rabinowitz, “In situ surface vibrational spectroscopy of the vapor/solid and liquid/solid interfaces of acetonitrile on ZrO2,” J. Vac. Sci. Technol. 11, 2232–2238 (1993).
[CrossRef]

1992 (1)

S. R. Hatch, R. S. Polizzotti, S. Dougal, and P. Rabinowitz, “Surface vibrational spectroscopy of the vapor/solid and liquid/solid interface of acetonitrile on ZrO2,” Chem. Phys. Lett. 196, 97–102 (1992).
[CrossRef]

1990 (1)

J. Miragliotta, R. S. Polizzotti, P. Rabinowitz, S. D. Cameron, and R. B. Hall, “IR–visible sum-frequency generation study of methanol adsorption and reaction on nickel(100),” Chem. Phys. 143, 123–130 (1990).
[CrossRef]

1987 (3)

D. Epperlein, B. Dick, G. Marowsky, and G. A. Reider, “Second-harmonic generation in centro-symmetric media,” Appl. Phys. B 44, 5–10 (1987).
[CrossRef]

P. Guyot-Sionnest, Y. R. Shen, and T. F. Heinz, “Comments on ‘Determination of the nonlinear optical susceptibility χ(2) of surface layers’ by B. Dick et al.,” Appl. Phys. B: 42, 237–238 (1987).
[CrossRef]

B. U. Felderhof and G. Marowsky, “Electromagnetic radiation from a polarization sheet located at an interface between two media,” Appl. Phys. B 44, 11–17 (1987).
[CrossRef]

1985 (1)

B. Dick, A. Gierulski, G. Marowsky, and G. A. Raider, “Determination of the nonlinear optical susceptibility χ(2) of surface layers by sum and difference frequency generation in reflection and transmission,” Appl. Phys. B: 38, 107–116 (1985).
[CrossRef]

1969 (1)

N. Bloembergen, H. J. Simmon, and C. H. Lee, “Total reflection phenomena in second-harmonic generation of light,” Phys. Rev. 181, 1261–1271 (1969).
[CrossRef]

1966 (1)

N. Bloembergen, “Second harmonic reflected light,” Opt. Acta 13, 311–322 (1966).
[CrossRef]

1962 (1)

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

Akamatsu, N.

Y. Goto, N. Akamatsu, K. Domen, and C. Hirose, “Vibration-induced order–disorder transitions in a Langmuir–Blodgett film as investigated by vibrational sum frequency generation spectroscopy,” J. Phys. Chem. 99, 4086–4090 (1995).
[CrossRef]

Bain, C. D.

B. D. Casson and C. D. Bain, “Phase transitions in mixed monolayers of sodium dodecyl sulfate and dodecanol at the air/water interface,” J. Phys. Chem. 102, 7434–7441 (1998).
[CrossRef]

R. Fraenkel, G. E. Butterworth, and C. D. Bain, “In situ vibrational spectroscopy of an organic monolayer at the sapphire–quartz interface,” J. Am. Chem. Soc. 120, 203–204 (1998).
[CrossRef]

Baldelli, S.

S. Baldelli, C. Schnitzer, M. J. Shultz, and D. J. Campbell, “Sum frequency generation investigation of water at the surface of H2O/H2SO4 binary systems,” J. Phys. Chem. B 101, 10, 435–10, 441 (1997).
[CrossRef]

S. Baldelli, C. Schnitzer, M. J. Shultz, and D. J. Campbell, “Sum frequency generation investigation of glycerol/water surfaces,” J. Phys. Chem. B 101, 4607–4612 (1997).
[CrossRef]

Bertie, J. E.

J. E. Bertie and Z. Lan, “The refractive index of colorless liquids in the visible and infrared: contributions from the absorption of infrared and ultraviolet radiation and the electronic molar polarizability below 20, 500 cm−1,” J. Chem. Phys. 103, 10, 152–10, 161 (1995).
[CrossRef]

Bloembergen, N.

N. Bloembergen, H. J. Simmon, and C. H. Lee, “Total reflection phenomena in second-harmonic generation of light,” Phys. Rev. 181, 1261–1271 (1969).
[CrossRef]

N. Bloembergen, “Second harmonic reflected light,” Opt. Acta 13, 311–322 (1966).
[CrossRef]

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

Butterworth, G. E.

R. Fraenkel, G. E. Butterworth, and C. D. Bain, “In situ vibrational spectroscopy of an organic monolayer at the sapphire–quartz interface,” J. Am. Chem. Soc. 120, 203–204 (1998).
[CrossRef]

Cameron, S. D.

J. Miragliotta, R. S. Polizzotti, P. Rabinowitz, S. D. Cameron, and R. B. Hall, “IR–visible sum-frequency generation study of methanol adsorption and reaction on nickel(100),” Chem. Phys. 143, 123–130 (1990).
[CrossRef]

Campbell, D. J.

S. Baldelli, C. Schnitzer, M. J. Shultz, and D. J. Campbell, “Sum frequency generation investigation of glycerol/water surfaces,” J. Phys. Chem. B 101, 4607–4612 (1997).
[CrossRef]

S. Baldelli, C. Schnitzer, M. J. Shultz, and D. J. Campbell, “Sum frequency generation investigation of water at the surface of H2O/H2SO4 binary systems,” J. Phys. Chem. B 101, 10, 435–10, 441 (1997).
[CrossRef]

Casson, B. D.

B. D. Casson and C. D. Bain, “Phase transitions in mixed monolayers of sodium dodecyl sulfate and dodecanol at the air/water interface,” J. Phys. Chem. 102, 7434–7441 (1998).
[CrossRef]

Chen, Z.

Z. Chen, D. H. Gracias, and G. A. Somorjai, “Sum frequency generation (SFG) surface vibrational spectroscopy studies of buried interfaces: catalytic reaction intermediates on transition metal crystal surfaces at high reactant pressures; polymer surface structures at the solid–gas and solid–liquid interfaces,” Appl. Phys. B 68, 549–557 (1999).
[CrossRef]

Conboy, J. C.

J. C. Conboy, M. C. Messmer, and G. L. Richmond, “Effect of alkyl chain length on the conformation and order of simple ionic surfactants adsorbed at the D2O/CCl4 interface as studied by sum-frequency vibrational spectroscopy,” Langmuir 14, 6722–6727 (1998).
[CrossRef]

J. C. Conboy, M. C. Messmer, and G. L. Richmond, “Investigation of surfactant conformation and order at the liquid–liquid interface by total internal reflection sum-frequency vibration spectroscopy,” J. Phys. Chem. 100, 7617–7622 (1996).
[CrossRef]

M. C. Messmer, J. C. Conboy, and G. L. Richmond, “Resonant sum frequency generation studies of surfactant ordering at the oil–water interface,” in Laser Techniques for Surface Science II, J. M. Hicks, W. Ho, and H.-L. Dai, eds., Proc. SPIE 2547, 135–141 (1995).
[CrossRef]

M. C. Messmer, J. C. Conboy, and G. L. Richmond, “Observation of molecular ordering at the liquid–liquid interface by resonant sum frequency generation,” J. Am. Chem. Soc. 117, 8039–8040 (1995).
[CrossRef]

Dick, B.

D. Epperlein, B. Dick, G. Marowsky, and G. A. Reider, “Second-harmonic generation in centro-symmetric media,” Appl. Phys. B 44, 5–10 (1987).
[CrossRef]

B. Dick, A. Gierulski, G. Marowsky, and G. A. Raider, “Determination of the nonlinear optical susceptibility χ(2) of surface layers by sum and difference frequency generation in reflection and transmission,” Appl. Phys. B: 38, 107–116 (1985).
[CrossRef]

Domen, K.

Y. Goto, N. Akamatsu, K. Domen, and C. Hirose, “Vibration-induced order–disorder transitions in a Langmuir–Blodgett film as investigated by vibrational sum frequency generation spectroscopy,” J. Phys. Chem. 99, 4086–4090 (1995).
[CrossRef]

Dougal, S.

S. R. Hatch, R. S. Polizzotti, S. Dougal, and P. Rabinowitz, “In situ surface vibrational spectroscopy of the vapor/solid and liquid/solid interfaces of acetonitrile on ZrO2,” J. Vac. Sci. Technol. 11, 2232–2238 (1993).
[CrossRef]

S. R. Hatch, R. S. Polizzotti, S. Dougal, and P. Rabinowitz, “Surface vibrational spectroscopy of the vapor/solid and liquid/solid interface of acetonitrile on ZrO2,” Chem. Phys. Lett. 196, 97–102 (1992).
[CrossRef]

Epperlein, D.

D. Epperlein, B. Dick, G. Marowsky, and G. A. Reider, “Second-harmonic generation in centro-symmetric media,” Appl. Phys. B 44, 5–10 (1987).
[CrossRef]

Felderhof, B. U.

B. U. Felderhof and G. Marowsky, “Electromagnetic radiation from a polarization sheet located at an interface between two media,” Appl. Phys. B 44, 11–17 (1987).
[CrossRef]

Fraenkel, R.

R. Fraenkel, G. E. Butterworth, and C. D. Bain, “In situ vibrational spectroscopy of an organic monolayer at the sapphire–quartz interface,” J. Am. Chem. Soc. 120, 203–204 (1998).
[CrossRef]

Gauckler, M.

D. Zhang, D. H. Gracias, R. Ward, M. Gauckler, Y. Tian, Y. R. Shen, and G. Somorjai, “Surface studies of polymer blends by sum frequency vibrational spectroscopy, atomic force microscopy, and contact angle goniometry,” J. Phys. Chem. 102, 6225–6230 (1998).
[CrossRef]

Gierulski, A.

B. Dick, A. Gierulski, G. Marowsky, and G. A. Raider, “Determination of the nonlinear optical susceptibility χ(2) of surface layers by sum and difference frequency generation in reflection and transmission,” Appl. Phys. B: 38, 107–116 (1985).
[CrossRef]

Goto, Y.

Y. Goto, N. Akamatsu, K. Domen, and C. Hirose, “Vibration-induced order–disorder transitions in a Langmuir–Blodgett film as investigated by vibrational sum frequency generation spectroscopy,” J. Phys. Chem. 99, 4086–4090 (1995).
[CrossRef]

Gracias, D. H.

Z. Chen, D. H. Gracias, and G. A. Somorjai, “Sum frequency generation (SFG) surface vibrational spectroscopy studies of buried interfaces: catalytic reaction intermediates on transition metal crystal surfaces at high reactant pressures; polymer surface structures at the solid–gas and solid–liquid interfaces,” Appl. Phys. B 68, 549–557 (1999).
[CrossRef]

D. Zhang, D. H. Gracias, R. Ward, M. Gauckler, Y. Tian, Y. R. Shen, and G. Somorjai, “Surface studies of polymer blends by sum frequency vibrational spectroscopy, atomic force microscopy, and contact angle goniometry,” J. Phys. Chem. 102, 6225–6230 (1998).
[CrossRef]

Gragson, D. E.

D. E. Gragson and G. L. Richmond, “Investigations of the structure and hydrogen bonding of water molecules at liquid surfaces by vibrational sum frequency spectroscopy,” J. Phys. Chem. 102, 3847–3861 (1998).
[CrossRef]

Guyot-Sionnest, P.

P. Guyot-Sionnest, Y. R. Shen, and T. F. Heinz, “Comments on ‘Determination of the nonlinear optical susceptibility χ(2) of surface layers’ by B. Dick et al.,” Appl. Phys. B: 42, 237–238 (1987).
[CrossRef]

Hall, R. B.

J. Miragliotta, R. S. Polizzotti, P. Rabinowitz, S. D. Cameron, and R. B. Hall, “IR–visible sum-frequency generation study of methanol adsorption and reaction on nickel(100),” Chem. Phys. 143, 123–130 (1990).
[CrossRef]

Hatch, S. R.

S. R. Hatch, R. S. Polizzotti, S. Dougal, and P. Rabinowitz, “In situ surface vibrational spectroscopy of the vapor/solid and liquid/solid interfaces of acetonitrile on ZrO2,” J. Vac. Sci. Technol. 11, 2232–2238 (1993).
[CrossRef]

S. R. Hatch, R. S. Polizzotti, S. Dougal, and P. Rabinowitz, “Surface vibrational spectroscopy of the vapor/solid and liquid/solid interface of acetonitrile on ZrO2,” Chem. Phys. Lett. 196, 97–102 (1992).
[CrossRef]

Heinz, T. F.

P. Guyot-Sionnest, Y. R. Shen, and T. F. Heinz, “Comments on ‘Determination of the nonlinear optical susceptibility χ(2) of surface layers’ by B. Dick et al.,” Appl. Phys. B: 42, 237–238 (1987).
[CrossRef]

Hirose, C.

Y. Goto, N. Akamatsu, K. Domen, and C. Hirose, “Vibration-induced order–disorder transitions in a Langmuir–Blodgett film as investigated by vibrational sum frequency generation spectroscopy,” J. Phys. Chem. 99, 4086–4090 (1995).
[CrossRef]

Lan, Z.

J. E. Bertie and Z. Lan, “The refractive index of colorless liquids in the visible and infrared: contributions from the absorption of infrared and ultraviolet radiation and the electronic molar polarizability below 20, 500 cm−1,” J. Chem. Phys. 103, 10, 152–10, 161 (1995).
[CrossRef]

Laubereau, A.

K. Wolfrum and A. Laubereau, “Vibrational sum-frequency spectroscopy of an adsorbed monolayer of hexadecanol on water. Destructive interference of adjacent lines,” Chem. Phys. Lett. 228, 83–88 (1994).
[CrossRef]

Lee, C. H.

N. Bloembergen, H. J. Simmon, and C. H. Lee, “Total reflection phenomena in second-harmonic generation of light,” Phys. Rev. 181, 1261–1271 (1969).
[CrossRef]

Lobau, J.

Marowsky, G.

D. Epperlein, B. Dick, G. Marowsky, and G. A. Reider, “Second-harmonic generation in centro-symmetric media,” Appl. Phys. B 44, 5–10 (1987).
[CrossRef]

B. U. Felderhof and G. Marowsky, “Electromagnetic radiation from a polarization sheet located at an interface between two media,” Appl. Phys. B 44, 11–17 (1987).
[CrossRef]

B. Dick, A. Gierulski, G. Marowsky, and G. A. Raider, “Determination of the nonlinear optical susceptibility χ(2) of surface layers by sum and difference frequency generation in reflection and transmission,” Appl. Phys. B: 38, 107–116 (1985).
[CrossRef]

Messmer, M. C.

J. C. Conboy, M. C. Messmer, and G. L. Richmond, “Effect of alkyl chain length on the conformation and order of simple ionic surfactants adsorbed at the D2O/CCl4 interface as studied by sum-frequency vibrational spectroscopy,” Langmuir 14, 6722–6727 (1998).
[CrossRef]

J. C. Conboy, M. C. Messmer, and G. L. Richmond, “Investigation of surfactant conformation and order at the liquid–liquid interface by total internal reflection sum-frequency vibration spectroscopy,” J. Phys. Chem. 100, 7617–7622 (1996).
[CrossRef]

M. C. Messmer, J. C. Conboy, and G. L. Richmond, “Resonant sum frequency generation studies of surfactant ordering at the oil–water interface,” in Laser Techniques for Surface Science II, J. M. Hicks, W. Ho, and H.-L. Dai, eds., Proc. SPIE 2547, 135–141 (1995).
[CrossRef]

M. C. Messmer, J. C. Conboy, and G. L. Richmond, “Observation of molecular ordering at the liquid–liquid interface by resonant sum frequency generation,” J. Am. Chem. Soc. 117, 8039–8040 (1995).
[CrossRef]

Miragliotta, J.

J. Miragliotta, R. S. Polizzotti, P. Rabinowitz, S. D. Cameron, and R. B. Hall, “IR–visible sum-frequency generation study of methanol adsorption and reaction on nickel(100),” Chem. Phys. 143, 123–130 (1990).
[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]

Polizzotti, R. S.

S. R. Hatch, R. S. Polizzotti, S. Dougal, and P. Rabinowitz, “In situ surface vibrational spectroscopy of the vapor/solid and liquid/solid interfaces of acetonitrile on ZrO2,” J. Vac. Sci. Technol. 11, 2232–2238 (1993).
[CrossRef]

S. R. Hatch, R. S. Polizzotti, S. Dougal, and P. Rabinowitz, “Surface vibrational spectroscopy of the vapor/solid and liquid/solid interface of acetonitrile on ZrO2,” Chem. Phys. Lett. 196, 97–102 (1992).
[CrossRef]

J. Miragliotta, R. S. Polizzotti, P. Rabinowitz, S. D. Cameron, and R. B. Hall, “IR–visible sum-frequency generation study of methanol adsorption and reaction on nickel(100),” Chem. Phys. 143, 123–130 (1990).
[CrossRef]

Rabinowitz, P.

S. R. Hatch, R. S. Polizzotti, S. Dougal, and P. Rabinowitz, “In situ surface vibrational spectroscopy of the vapor/solid and liquid/solid interfaces of acetonitrile on ZrO2,” J. Vac. Sci. Technol. 11, 2232–2238 (1993).
[CrossRef]

S. R. Hatch, R. S. Polizzotti, S. Dougal, and P. Rabinowitz, “Surface vibrational spectroscopy of the vapor/solid and liquid/solid interface of acetonitrile on ZrO2,” Chem. Phys. Lett. 196, 97–102 (1992).
[CrossRef]

J. Miragliotta, R. S. Polizzotti, P. Rabinowitz, S. D. Cameron, and R. B. Hall, “IR–visible sum-frequency generation study of methanol adsorption and reaction on nickel(100),” Chem. Phys. 143, 123–130 (1990).
[CrossRef]

Raider, G. A.

B. Dick, A. Gierulski, G. Marowsky, and G. A. Raider, “Determination of the nonlinear optical susceptibility χ(2) of surface layers by sum and difference frequency generation in reflection and transmission,” Appl. Phys. B: 38, 107–116 (1985).
[CrossRef]

Reider, G. A.

D. Epperlein, B. Dick, G. Marowsky, and G. A. Reider, “Second-harmonic generation in centro-symmetric media,” Appl. Phys. B 44, 5–10 (1987).
[CrossRef]

Richmond, G. L.

D. E. Gragson and G. L. Richmond, “Investigations of the structure and hydrogen bonding of water molecules at liquid surfaces by vibrational sum frequency spectroscopy,” J. Phys. Chem. 102, 3847–3861 (1998).
[CrossRef]

J. C. Conboy, M. C. Messmer, and G. L. Richmond, “Effect of alkyl chain length on the conformation and order of simple ionic surfactants adsorbed at the D2O/CCl4 interface as studied by sum-frequency vibrational spectroscopy,” Langmuir 14, 6722–6727 (1998).
[CrossRef]

J. C. Conboy, M. C. Messmer, and G. L. Richmond, “Investigation of surfactant conformation and order at the liquid–liquid interface by total internal reflection sum-frequency vibration spectroscopy,” J. Phys. Chem. 100, 7617–7622 (1996).
[CrossRef]

M. C. Messmer, J. C. Conboy, and G. L. Richmond, “Resonant sum frequency generation studies of surfactant ordering at the oil–water interface,” in Laser Techniques for Surface Science II, J. M. Hicks, W. Ho, and H.-L. Dai, eds., Proc. SPIE 2547, 135–141 (1995).
[CrossRef]

M. C. Messmer, J. C. Conboy, and G. L. Richmond, “Observation of molecular ordering at the liquid–liquid interface by resonant sum frequency generation,” J. Am. Chem. Soc. 117, 8039–8040 (1995).
[CrossRef]

Schnitzer, C.

S. Baldelli, C. Schnitzer, M. J. Shultz, and D. J. Campbell, “Sum frequency generation investigation of water at the surface of H2O/H2SO4 binary systems,” J. Phys. Chem. B 101, 10, 435–10, 441 (1997).
[CrossRef]

S. Baldelli, C. Schnitzer, M. J. Shultz, and D. J. Campbell, “Sum frequency generation investigation of glycerol/water surfaces,” J. Phys. Chem. B 101, 4607–4612 (1997).
[CrossRef]

Shen, Y. R.

D. Zhang, D. H. Gracias, R. Ward, M. Gauckler, Y. Tian, Y. R. Shen, and G. Somorjai, “Surface studies of polymer blends by sum frequency vibrational spectroscopy, atomic force microscopy, and contact angle goniometry,” J. Phys. Chem. 102, 6225–6230 (1998).
[CrossRef]

P. Guyot-Sionnest, Y. R. Shen, and T. F. Heinz, “Comments on ‘Determination of the nonlinear optical susceptibility χ(2) of surface layers’ by B. Dick et al.,” Appl. Phys. B: 42, 237–238 (1987).
[CrossRef]

Shultz, M. J.

S. Baldelli, C. Schnitzer, M. J. Shultz, and D. J. Campbell, “Sum frequency generation investigation of glycerol/water surfaces,” J. Phys. Chem. B 101, 4607–4612 (1997).
[CrossRef]

S. Baldelli, C. Schnitzer, M. J. Shultz, and D. J. Campbell, “Sum frequency generation investigation of water at the surface of H2O/H2SO4 binary systems,” J. Phys. Chem. B 101, 10, 435–10, 441 (1997).
[CrossRef]

Simmon, H. J.

N. Bloembergen, H. J. Simmon, and C. H. Lee, “Total reflection phenomena in second-harmonic generation of light,” Phys. Rev. 181, 1261–1271 (1969).
[CrossRef]

Somorjai, G.

D. Zhang, D. H. Gracias, R. Ward, M. Gauckler, Y. Tian, Y. R. Shen, and G. Somorjai, “Surface studies of polymer blends by sum frequency vibrational spectroscopy, atomic force microscopy, and contact angle goniometry,” J. Phys. Chem. 102, 6225–6230 (1998).
[CrossRef]

Somorjai, G. A.

Z. Chen, D. H. Gracias, and G. A. Somorjai, “Sum frequency generation (SFG) surface vibrational spectroscopy studies of buried interfaces: catalytic reaction intermediates on transition metal crystal surfaces at high reactant pressures; polymer surface structures at the solid–gas and solid–liquid interfaces,” Appl. Phys. B 68, 549–557 (1999).
[CrossRef]

Tian, Y.

D. Zhang, D. H. Gracias, R. Ward, M. Gauckler, Y. Tian, Y. R. Shen, and G. Somorjai, “Surface studies of polymer blends by sum frequency vibrational spectroscopy, atomic force microscopy, and contact angle goniometry,” J. Phys. Chem. 102, 6225–6230 (1998).
[CrossRef]

Ward, R.

D. Zhang, D. H. Gracias, R. Ward, M. Gauckler, Y. Tian, Y. R. Shen, and G. Somorjai, “Surface studies of polymer blends by sum frequency vibrational spectroscopy, atomic force microscopy, and contact angle goniometry,” J. Phys. Chem. 102, 6225–6230 (1998).
[CrossRef]

Wolfrum, K.

J. Lobau and K. Wolfrum, “Sum-frequency spectroscopy in total internal reflection geometry: signal enhancement and access to molecular properties,” J. Opt. Soc. Am. B 14, 2505–2512 (1997).
[CrossRef]

K. Wolfrum and A. Laubereau, “Vibrational sum-frequency spectroscopy of an adsorbed monolayer of hexadecanol on water. Destructive interference of adjacent lines,” Chem. Phys. Lett. 228, 83–88 (1994).
[CrossRef]

Zhang, D.

D. Zhang, D. H. Gracias, R. Ward, M. Gauckler, Y. Tian, Y. R. Shen, and G. Somorjai, “Surface studies of polymer blends by sum frequency vibrational spectroscopy, atomic force microscopy, and contact angle goniometry,” J. Phys. Chem. 102, 6225–6230 (1998).
[CrossRef]

Appl. Phys. B (3)

Z. Chen, D. H. Gracias, and G. A. Somorjai, “Sum frequency generation (SFG) surface vibrational spectroscopy studies of buried interfaces: catalytic reaction intermediates on transition metal crystal surfaces at high reactant pressures; polymer surface structures at the solid–gas and solid–liquid interfaces,” Appl. Phys. B 68, 549–557 (1999).
[CrossRef]

D. Epperlein, B. Dick, G. Marowsky, and G. A. Reider, “Second-harmonic generation in centro-symmetric media,” Appl. Phys. B 44, 5–10 (1987).
[CrossRef]

B. U. Felderhof and G. Marowsky, “Electromagnetic radiation from a polarization sheet located at an interface between two media,” Appl. Phys. B 44, 11–17 (1987).
[CrossRef]

Appl. Phys. B: (2)

P. Guyot-Sionnest, Y. R. Shen, and T. F. Heinz, “Comments on ‘Determination of the nonlinear optical susceptibility χ(2) of surface layers’ by B. Dick et al.,” Appl. Phys. B: 42, 237–238 (1987).
[CrossRef]

B. Dick, A. Gierulski, G. Marowsky, and G. A. Raider, “Determination of the nonlinear optical susceptibility χ(2) of surface layers by sum and difference frequency generation in reflection and transmission,” Appl. Phys. B: 38, 107–116 (1985).
[CrossRef]

Chem. Phys. (1)

J. Miragliotta, R. S. Polizzotti, P. Rabinowitz, S. D. Cameron, and R. B. Hall, “IR–visible sum-frequency generation study of methanol adsorption and reaction on nickel(100),” Chem. Phys. 143, 123–130 (1990).
[CrossRef]

Chem. Phys. Lett. (2)

K. Wolfrum and A. Laubereau, “Vibrational sum-frequency spectroscopy of an adsorbed monolayer of hexadecanol on water. Destructive interference of adjacent lines,” Chem. Phys. Lett. 228, 83–88 (1994).
[CrossRef]

S. R. Hatch, R. S. Polizzotti, S. Dougal, and P. Rabinowitz, “Surface vibrational spectroscopy of the vapor/solid and liquid/solid interface of acetonitrile on ZrO2,” Chem. Phys. Lett. 196, 97–102 (1992).
[CrossRef]

J. Am. Chem. Soc. (2)

M. C. Messmer, J. C. Conboy, and G. L. Richmond, “Observation of molecular ordering at the liquid–liquid interface by resonant sum frequency generation,” J. Am. Chem. Soc. 117, 8039–8040 (1995).
[CrossRef]

R. Fraenkel, G. E. Butterworth, and C. D. Bain, “In situ vibrational spectroscopy of an organic monolayer at the sapphire–quartz interface,” J. Am. Chem. Soc. 120, 203–204 (1998).
[CrossRef]

J. Chem. Phys. (1)

J. E. Bertie and Z. Lan, “The refractive index of colorless liquids in the visible and infrared: contributions from the absorption of infrared and ultraviolet radiation and the electronic molar polarizability below 20, 500 cm−1,” J. Chem. Phys. 103, 10, 152–10, 161 (1995).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. Chem. (5)

D. Zhang, D. H. Gracias, R. Ward, M. Gauckler, Y. Tian, Y. R. Shen, and G. Somorjai, “Surface studies of polymer blends by sum frequency vibrational spectroscopy, atomic force microscopy, and contact angle goniometry,” J. Phys. Chem. 102, 6225–6230 (1998).
[CrossRef]

D. E. Gragson and G. L. Richmond, “Investigations of the structure and hydrogen bonding of water molecules at liquid surfaces by vibrational sum frequency spectroscopy,” J. Phys. Chem. 102, 3847–3861 (1998).
[CrossRef]

Y. Goto, N. Akamatsu, K. Domen, and C. Hirose, “Vibration-induced order–disorder transitions in a Langmuir–Blodgett film as investigated by vibrational sum frequency generation spectroscopy,” J. Phys. Chem. 99, 4086–4090 (1995).
[CrossRef]

B. D. Casson and C. D. Bain, “Phase transitions in mixed monolayers of sodium dodecyl sulfate and dodecanol at the air/water interface,” J. Phys. Chem. 102, 7434–7441 (1998).
[CrossRef]

J. C. Conboy, M. C. Messmer, and G. L. Richmond, “Investigation of surfactant conformation and order at the liquid–liquid interface by total internal reflection sum-frequency vibration spectroscopy,” J. Phys. Chem. 100, 7617–7622 (1996).
[CrossRef]

J. Phys. Chem. B (2)

S. Baldelli, C. Schnitzer, M. J. Shultz, and D. J. Campbell, “Sum frequency generation investigation of water at the surface of H2O/H2SO4 binary systems,” J. Phys. Chem. B 101, 10, 435–10, 441 (1997).
[CrossRef]

S. Baldelli, C. Schnitzer, M. J. Shultz, and D. J. Campbell, “Sum frequency generation investigation of glycerol/water surfaces,” J. Phys. Chem. B 101, 4607–4612 (1997).
[CrossRef]

J. Vac. Sci. Technol. (1)

S. R. Hatch, R. S. Polizzotti, S. Dougal, and P. Rabinowitz, “In situ surface vibrational spectroscopy of the vapor/solid and liquid/solid interfaces of acetonitrile on ZrO2,” J. Vac. Sci. Technol. 11, 2232–2238 (1993).
[CrossRef]

Langmuir (1)

J. C. Conboy, M. C. Messmer, and G. L. Richmond, “Effect of alkyl chain length on the conformation and order of simple ionic surfactants adsorbed at the D2O/CCl4 interface as studied by sum-frequency vibrational spectroscopy,” Langmuir 14, 6722–6727 (1998).
[CrossRef]

Opt. Acta (1)

N. Bloembergen, “Second harmonic reflected light,” Opt. Acta 13, 311–322 (1966).
[CrossRef]

Phys. Rev. (2)

N. Bloembergen, H. J. Simmon, and C. H. Lee, “Total reflection phenomena in second-harmonic generation of light,” Phys. Rev. 181, 1261–1271 (1969).
[CrossRef]

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

Proc. SPIE (1)

M. C. Messmer, J. C. Conboy, and G. L. Richmond, “Resonant sum frequency generation studies of surfactant ordering at the oil–water interface,” in Laser Techniques for Surface Science II, J. M. Hicks, W. Ho, and H.-L. Dai, eds., Proc. SPIE 2547, 135–141 (1995).
[CrossRef]

Other (4)

J. Y. Huang and Y. R. Shen, “Sum-frequency generation as a surface probe,” in Laser Spectroscopy and Photochemistry on Metal Surfaces, H.-L. Dai and W. Ho, eds. (World Scientific, Singapore, 1995), pp. 5–53.

T. F. Heinz, “Second-order nonlinear optical effects at surfaces and interfaces,” in Nonlinear Surface Electromagnetic Phenomena, H.-E. Pontah and G. I. Stegeman, eds. (Elsevier, New York, 1991), pp. 353–416.

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1993).

Y. J. Yang, R. L. Pizzolatto, M. C. Henry, and M. C. Messmer are preparing a manuscript to be called “Conformational studies of a Gemini surfactant at an air–water interface by sum-frequency generation spectroscopy.”

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Figures (7)

Fig. 1
Fig. 1

Experimental laser system used for sum-frequency generation (SFG) spectroscopy. A LiNbO3 optical parametric oscillator generates the tunable infrared light in the 2600–3200-cm-1 region. A KDP crystal is used to generate the visible 532-nm beam. FI, Faraday isolator; L, lens; VC, vacuum cell; λ/2, half-waveplate; TFP, thin-film polarizer; CP, cube polarizer; IC, input coupler; OC, output coupler; BS, beam splitter; F, filter; SBC, Soleil–Babinet compensator; HBS, harmonic beam splitter; I, iris.

Fig. 2
Fig. 2

Sample setup for internal–external reflection SFG spectroscopy using an infrared approach from the low-index phase. The visible 532-nm beam (ω1) approaches the interface from the high-index phase at its critical angle. The infrared beam (ω2) approaches the surface at an angle of approximately 63° from the normal. An infrared grade fused quartz cell of 5-cm diameter holds the sample. A 7.5-cm CaF2 lens (L) focuses the infrared beam at the interface, and a λ/2 waveplate is used to change the polarization of the visible beam. A photomultiplier tube (PMT) is used to detect the sum-frequency (ω3) signal.

Fig. 3
Fig. 3

Incident and transmitted angles θi and θt for the visible (ω1), infrared (ω2), and SF (ω3) beams in the xz plane for the three geometries examined: (a) internal–internal reflection, (b) external–external reflection, (c) internal–external reflection. The denser medium has an index of refraction nhigh, and the rarer medium has an index of refraction of nlow.

Fig. 4
Fig. 4

Comparison of SF intensities I(ω3) calculated by using Eqs. (25)–(27) in the internal–internal (solid curve), internal–external (dotted–dashed curves), and external–external (dotted curves) reflection geometries as a function of the infrared incident angle θ2,i (in degrees) for (a) ssp, (b) sps, and (c) ppp polarizations. Insets show the log of the SF intensity as a function of the infrared incident angle θ2,i (in degrees). Equations (25)–(27) were evaluated in Gaussian units, and the results were converted into SI units.

Fig. 5
Fig. 5

Plot of SF intensity I(ω3) versus visible incident angle θ1,i and infrared incident angle θ2,i for (a) ssp, (b) sps, and (c) ppp polarization combinations.

Fig. 6
Fig. 6

SF spectra of TMDD adsorbed at the D2O–air interface with the use of internal reflection for the visible and external reflection for the infrared for (a) ssp and (b) sps polarization combinations. The solid curve is a fit to the data with the use of a Voigt line shape. Curve (a) is offset along the y axis by 0.5.

Fig. 7
Fig. 7

Plot of calculated intensity I(ω3) (left-hand axis) and normalized measured SF intensity (right-hand axis) versus visible incident angle θ1,i (in degrees) with the use of an internal–external reflection geometry (infrared angle=63°). Symbols represent experimental measurements taken from the CH3 symmetric stretch of the distal isopropyl groups of the TMDD spectrum in D2O.

Tables (1)

Tables Icon

Table 1 Calculated Angles for the Visible, Infrared, and Sum-Frequency (SF) Beams in the Incident Medium at the Maximum SF Intensity for an Internal–External Reflection Geometry

Equations (27)

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Pj(2)(ω3=ω1+ω2)=klχjkl(2) Ek(ω1)El(ω2),
Ex=Ifx cos θi cos γ,
Ey=Ify sin γ,
Ez=Ifz sin θi cos γ,
I=UAτ,
A=A0cos θi,
χ(2)=00χxxz000χxzx0000000χyyz0χyzy0χzxx000χzyy000χzzz,
fω,x=2nω,i cos θω,tnω,t cos θω,i+nω,i cos θω,t,
fω,y=2nω,i cos θω,inω,t cos θω,t+nω,i cos θω,i,
fω,z=2(nω,i2/nω,t2)nω,t cos θω,inω,t cos θω,i+nω,i cos θω,t,
Px(ω3)=I1I2[(cos θ1,i sin θ2,i cos γ1 cos γ2)χxxzf1,xf2,z+(sin θ1,i cos θ2,i cos γ1 cos γ2)χxzxf1,zf2,x],
Py(ω3)=I1I2[(sin θ2,i sin γ1 cos γ2)χxxzf1,yf2,z+(sin θ1,i cos γ1 sin γ2)χxzxf1,zf2,y],
Pz(ω3)=I1I2[(cos θ1,i cos θ2,i cos γ1 cos γ2)χzxxf1,xf2,x+(sin γ1 sin γ2)χzxxf1,yf2,y+(sin θ1,i sin θ2,i cos γ1 cos γ2)χzzzf1,zf2,z],
Pyssp(ω3)=I1I2(sin θ2,i)χxxzf1,yf2,z,
Pysps(ω3)=I1I2(sin θ1,i)χxzxf1,zf2,y,
Pxppp(ω3)=I1I2[(cos θ1,i sin θ2,i)χxxzf1,xf2,z+(sin θ1,i cos θ2,i)χxzxf1,zf2,x],
Pzppp(ω3)=I1I2[(cos θ1,i cos θ2,i)χzxxf1,xf2,x+(sin θ1,i sin θ2,i)χzzzf1,zf2,z].
E(ω3)f˜P(2)(ω3),
f˜x=cos θ3,tn3,i2 cos θ3,t+n3,in3,t cos θ3,i,
f˜y=1n3,i cos θ3,i+n3,t cos θ3,t,
f˜z=sin θ3,in3,in3,t cos θ3,t+n3,t2 cos θ3,i,
Essp(ω3)=4πi ω3cf˜yPyssp(ω3),
Esps(ω3)=4πi ω3cf˜yPysps(ω3),
Eppp(ω3)=4πi ω3cn3,i[f˜xPxppp(ω3)+f˜zPzppp(ω3)],
Issp(ω3)=n3,ic2π|Essp(ω3)|2,
Isps(ω3)=n3,ic2π|Esps(ω3)|2,
Ippp(ω3)=n3,ic2π|Eppp(ω3)|2.

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