Abstract

We use two-beam second-harmonic generation to address thin films of silicon nitride (SiN). This technique is able to distinguish between the dipolar and higher-multipolar (magnetic and quadrupolar) contributions to the nonlinearity, as earlier shown for bulk samples. Our results for the SiN films exhibit strong multipolar signatures. Nevertheless, the results can be fully explained by the strong dipolar response of SiN once multiple reflections of the fundamental and second-harmonic fields within the film are properly taken into account. The results show that the recognition of multipolar nonlinearities requires extreme care for samples typically used for the characterization of new materials.

© 2016 Optical Society of America

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References

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  1. K. L. Sly, S.-W. Mok, and J. C. Conboy, “Second harmonic correlation spectroscopy: a method for determining surface binding kinetics and thermodynamics,” Anal. Chem. 85(17), 8429–8435 (2013).
    [Crossref] [PubMed]
  2. D. E. Wilcox, M. E. Sykes, A. Niedringhaus, M. Shtein, and J. P. Ogilvie, “Heterodyne-detected and ultrafast time-resolved second-harmonic generation for sensitive measurements of charge transfer,” Opt. Lett. 39(14), 4274–4277 (2014).
    [Crossref] [PubMed]
  3. Y. R. Shen, “Surface nonlinear optics: a historical perspective,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1375–1379 (2000).
    [Crossref]
  4. L. Alloatti, C. Kieninger, A. Froelich, M. Lauermann, T. Frenzel, K. Köhnle, W. Freude, J. Leuthold, M. Wegener, and C. Koos, “Second-order nonlinear optical metamaterials: ABC-type nanolaminates,” Appl. Phys. Lett. 107(12), 121903 (2015).
    [Crossref]
  5. S. Clemmen, A. Hermans, E. Solano, J. Dendooven, K. Koskinen, M. Kauranen, E. Brainis, C. Detavernier, and R. Baets, “Atomic layer deposited second-order nonlinear optical metamaterial for back-end integration with CMOS-compatible nanophotonic circuitry,” Opt. Lett. 40(22), 5371–5374 (2015).
    [Crossref] [PubMed]
  6. P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter 33(12), 8254–8263 (1986).
    [Crossref] [PubMed]
  7. P. Guyot-Sionnest and Y. R. Shen, “Local and nonlocal surface nonlinearities for surface optical second-harmonic generation,” Phys. Rev. B Condens. Matter 35(9), 4420–4426 (1987).
    [Crossref] [PubMed]
  8. J. E. Sipe, V. Mizrahi, and G. I. Stegeman, “Fundamental difficulty in the use of second-harmonic generation as a strictly surface probe,” Phys. Rev. B Condens. Matter 35(17), 9091–9094 (1987).
    [Crossref] [PubMed]
  9. N. Bloembergen, R. Chang, S. Jha, and C. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174(3), 813–822 (1968).
    [Crossref]
  10. F. Wang, F. Rodríguez, W. Albers, and M. Kauranen, “Enhancement of bulk-type multipolar second-harmonic generation arising from surface morphology of metals,” New J. Phys. 12(6), 063009 (2010).
    [Crossref]
  11. S. Kruk, M. Weismann, A. Y. Bykov, E. A. Mamonov, I. A. Kolmychek, T. Murzina, N. C. Panoiu, D. N. Neshev, and Y. S. Kivshar, “Enhanced magnetic second-harmonic generation from resonant metasurfaces,” ACS Photonics 2(8), 1007–1012 (2015).
    [Crossref]
  12. I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
    [Crossref] [PubMed]
  13. J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
    [Crossref] [PubMed]
  14. M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
    [Crossref] [PubMed]
  15. P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, “Single-beam and enhanced two-beam second-harmonic generation from silicon nanocrystals by use of spatially inhomogeneous femtosecond pulses,” Phys. Rev. Lett. 94(4), 047401 (2005).
    [Crossref] [PubMed]
  16. S. Cattaneo and M. Kauranen, “Polarization-based identification of bulk contributions in surface nonlinear optics,” Phys. Rev. B 72(3), 033412 (2005).
    [Crossref]
  17. F. J. Rodríguez, F. X. Wang, B. K. Canfield, S. Cattaneo, and M. Kauranen, “Multipolar tensor analysis of second-order nonlinear optical response of surface and bulk of glass,” Opt. Express 15(14), 8695–8701 (2007).
    [Crossref] [PubMed]
  18. F. J. Rodriguez, F. X. Wang, and M. Kauranen, “Calibration of the second-order nonlinear optical susceptibility of surface and bulk of glass,” Opt. Express 16(12), 8704–8710 (2008).
    [Crossref] [PubMed]
  19. F. X. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
    [Crossref]
  20. Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, and Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61(2), 145 (1992).
    [Crossref]
  21. T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100(16), 161902 (2012).
    [Crossref]
  22. J. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. B 4(4), 481–498 (1987).
    [Crossref]

2015 (3)

L. Alloatti, C. Kieninger, A. Froelich, M. Lauermann, T. Frenzel, K. Köhnle, W. Freude, J. Leuthold, M. Wegener, and C. Koos, “Second-order nonlinear optical metamaterials: ABC-type nanolaminates,” Appl. Phys. Lett. 107(12), 121903 (2015).
[Crossref]

S. Clemmen, A. Hermans, E. Solano, J. Dendooven, K. Koskinen, M. Kauranen, E. Brainis, C. Detavernier, and R. Baets, “Atomic layer deposited second-order nonlinear optical metamaterial for back-end integration with CMOS-compatible nanophotonic circuitry,” Opt. Lett. 40(22), 5371–5374 (2015).
[Crossref] [PubMed]

S. Kruk, M. Weismann, A. Y. Bykov, E. A. Mamonov, I. A. Kolmychek, T. Murzina, N. C. Panoiu, D. N. Neshev, and Y. S. Kivshar, “Enhanced magnetic second-harmonic generation from resonant metasurfaces,” ACS Photonics 2(8), 1007–1012 (2015).
[Crossref]

2014 (3)

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

D. E. Wilcox, M. E. Sykes, A. Niedringhaus, M. Shtein, and J. P. Ogilvie, “Heterodyne-detected and ultrafast time-resolved second-harmonic generation for sensitive measurements of charge transfer,” Opt. Lett. 39(14), 4274–4277 (2014).
[Crossref] [PubMed]

2013 (1)

K. L. Sly, S.-W. Mok, and J. C. Conboy, “Second harmonic correlation spectroscopy: a method for determining surface binding kinetics and thermodynamics,” Anal. Chem. 85(17), 8429–8435 (2013).
[Crossref] [PubMed]

2012 (2)

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100(16), 161902 (2012).
[Crossref]

2010 (1)

F. Wang, F. Rodríguez, W. Albers, and M. Kauranen, “Enhancement of bulk-type multipolar second-harmonic generation arising from surface morphology of metals,” New J. Phys. 12(6), 063009 (2010).
[Crossref]

2009 (1)

F. X. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
[Crossref]

2008 (1)

2007 (1)

2005 (2)

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, “Single-beam and enhanced two-beam second-harmonic generation from silicon nanocrystals by use of spatially inhomogeneous femtosecond pulses,” Phys. Rev. Lett. 94(4), 047401 (2005).
[Crossref] [PubMed]

S. Cattaneo and M. Kauranen, “Polarization-based identification of bulk contributions in surface nonlinear optics,” Phys. Rev. B 72(3), 033412 (2005).
[Crossref]

2000 (1)

Y. R. Shen, “Surface nonlinear optics: a historical perspective,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1375–1379 (2000).
[Crossref]

1992 (1)

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, and Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61(2), 145 (1992).
[Crossref]

1987 (3)

P. Guyot-Sionnest and Y. R. Shen, “Local and nonlocal surface nonlinearities for surface optical second-harmonic generation,” Phys. Rev. B Condens. Matter 35(9), 4420–4426 (1987).
[Crossref] [PubMed]

J. E. Sipe, V. Mizrahi, and G. I. Stegeman, “Fundamental difficulty in the use of second-harmonic generation as a strictly surface probe,” Phys. Rev. B Condens. Matter 35(17), 9091–9094 (1987).
[Crossref] [PubMed]

J. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. B 4(4), 481–498 (1987).
[Crossref]

1986 (1)

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter 33(12), 8254–8263 (1986).
[Crossref] [PubMed]

1968 (1)

N. Bloembergen, R. Chang, S. Jha, and C. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174(3), 813–822 (1968).
[Crossref]

Ahorinta, R.

F. X. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
[Crossref]

Albers, W.

F. Wang, F. Rodríguez, W. Albers, and M. Kauranen, “Enhancement of bulk-type multipolar second-harmonic generation arising from surface morphology of metals,” New J. Phys. 12(6), 063009 (2010).
[Crossref]

Albers, W. M.

F. X. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
[Crossref]

Alloatti, L.

L. Alloatti, C. Kieninger, A. Froelich, M. Lauermann, T. Frenzel, K. Köhnle, W. Freude, J. Leuthold, M. Wegener, and C. Koos, “Second-order nonlinear optical metamaterials: ABC-type nanolaminates,” Appl. Phys. Lett. 107(12), 121903 (2015).
[Crossref]

Baets, R.

Benichou, E.

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

Bloembergen, N.

N. Bloembergen, R. Chang, S. Jha, and C. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174(3), 813–822 (1968).
[Crossref]

Brainis, E.

Brener, I.

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Brevet, P.-F.

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

Butet, J.

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

Bykov, A. Y.

S. Kruk, M. Weismann, A. Y. Bykov, E. A. Mamonov, I. A. Kolmychek, T. Murzina, N. C. Panoiu, D. N. Neshev, and Y. S. Kivshar, “Enhanced magnetic second-harmonic generation from resonant metasurfaces,” ACS Photonics 2(8), 1007–1012 (2015).
[Crossref]

Canfield, B. K.

Castro-López, M.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

Cattaneo, S.

Chang, R.

N. Bloembergen, R. Chang, S. Jha, and C. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174(3), 813–822 (1968).
[Crossref]

Chen, W.

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter 33(12), 8254–8263 (1986).
[Crossref] [PubMed]

Clemmen, S.

Conboy, J. C.

K. L. Sly, S.-W. Mok, and J. C. Conboy, “Second harmonic correlation spectroscopy: a method for determining surface binding kinetics and thermodynamics,” Anal. Chem. 85(17), 8429–8435 (2013).
[Crossref] [PubMed]

Curto, A. G.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

Decker, M.

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Dendooven, J.

Detavernier, C.

Downer, M. C.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, “Single-beam and enhanced two-beam second-harmonic generation from silicon nanocrystals by use of spatially inhomogeneous femtosecond pulses,” Phys. Rev. Lett. 94(4), 047401 (2005).
[Crossref] [PubMed]

Ezhov, A. A.

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Fedyanin, A. A.

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Figliozzi, P.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, “Single-beam and enhanced two-beam second-harmonic generation from silicon nanocrystals by use of spatially inhomogeneous femtosecond pulses,” Phys. Rev. Lett. 94(4), 047401 (2005).
[Crossref] [PubMed]

Frenzel, T.

L. Alloatti, C. Kieninger, A. Froelich, M. Lauermann, T. Frenzel, K. Köhnle, W. Freude, J. Leuthold, M. Wegener, and C. Koos, “Second-order nonlinear optical metamaterials: ABC-type nanolaminates,” Appl. Phys. Lett. 107(12), 121903 (2015).
[Crossref]

Freude, W.

L. Alloatti, C. Kieninger, A. Froelich, M. Lauermann, T. Frenzel, K. Köhnle, W. Freude, J. Leuthold, M. Wegener, and C. Koos, “Second-order nonlinear optical metamaterials: ABC-type nanolaminates,” Appl. Phys. Lett. 107(12), 121903 (2015).
[Crossref]

Froelich, A.

L. Alloatti, C. Kieninger, A. Froelich, M. Lauermann, T. Frenzel, K. Köhnle, W. Freude, J. Leuthold, M. Wegener, and C. Koos, “Second-order nonlinear optical metamaterials: ABC-type nanolaminates,” Appl. Phys. Lett. 107(12), 121903 (2015).
[Crossref]

Genty, G.

T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100(16), 161902 (2012).
[Crossref]

Guyot-Sionnest, P.

P. Guyot-Sionnest and Y. R. Shen, “Local and nonlocal surface nonlinearities for surface optical second-harmonic generation,” Phys. Rev. B Condens. Matter 35(9), 4420–4426 (1987).
[Crossref] [PubMed]

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter 33(12), 8254–8263 (1986).
[Crossref] [PubMed]

Hancu, I. M.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

Hase, Y.

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, and Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61(2), 145 (1992).
[Crossref]

Hermans, A.

Hopkins, B.

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Hyvärinen, O.

T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100(16), 161902 (2012).
[Crossref]

Ito, R.

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, and Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61(2), 145 (1992).
[Crossref]

Jha, S.

N. Bloembergen, R. Chang, S. Jha, and C. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174(3), 813–822 (1968).
[Crossref]

Jiang, Y.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, “Single-beam and enhanced two-beam second-harmonic generation from silicon nanocrystals by use of spatially inhomogeneous femtosecond pulses,” Phys. Rev. Lett. 94(4), 047401 (2005).
[Crossref] [PubMed]

Jonin, C.

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

Kano, S. S.

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, and Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61(2), 145 (1992).
[Crossref]

Kauranen, M.

S. Clemmen, A. Hermans, E. Solano, J. Dendooven, K. Koskinen, M. Kauranen, E. Brainis, C. Detavernier, and R. Baets, “Atomic layer deposited second-order nonlinear optical metamaterial for back-end integration with CMOS-compatible nanophotonic circuitry,” Opt. Lett. 40(22), 5371–5374 (2015).
[Crossref] [PubMed]

T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100(16), 161902 (2012).
[Crossref]

F. Wang, F. Rodríguez, W. Albers, and M. Kauranen, “Enhancement of bulk-type multipolar second-harmonic generation arising from surface morphology of metals,” New J. Phys. 12(6), 063009 (2010).
[Crossref]

F. X. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
[Crossref]

F. J. Rodriguez, F. X. Wang, and M. Kauranen, “Calibration of the second-order nonlinear optical susceptibility of surface and bulk of glass,” Opt. Express 16(12), 8704–8710 (2008).
[Crossref] [PubMed]

F. J. Rodríguez, F. X. Wang, B. K. Canfield, S. Cattaneo, and M. Kauranen, “Multipolar tensor analysis of second-order nonlinear optical response of surface and bulk of glass,” Opt. Express 15(14), 8695–8701 (2007).
[Crossref] [PubMed]

S. Cattaneo and M. Kauranen, “Polarization-based identification of bulk contributions in surface nonlinear optics,” Phys. Rev. B 72(3), 033412 (2005).
[Crossref]

Kieninger, C.

L. Alloatti, C. Kieninger, A. Froelich, M. Lauermann, T. Frenzel, K. Köhnle, W. Freude, J. Leuthold, M. Wegener, and C. Koos, “Second-order nonlinear optical metamaterials: ABC-type nanolaminates,” Appl. Phys. Lett. 107(12), 121903 (2015).
[Crossref]

Kivshar, Y. S.

S. Kruk, M. Weismann, A. Y. Bykov, E. A. Mamonov, I. A. Kolmychek, T. Murzina, N. C. Panoiu, D. N. Neshev, and Y. S. Kivshar, “Enhanced magnetic second-harmonic generation from resonant metasurfaces,” ACS Photonics 2(8), 1007–1012 (2015).
[Crossref]

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Köhnle, K.

L. Alloatti, C. Kieninger, A. Froelich, M. Lauermann, T. Frenzel, K. Köhnle, W. Freude, J. Leuthold, M. Wegener, and C. Koos, “Second-order nonlinear optical metamaterials: ABC-type nanolaminates,” Appl. Phys. Lett. 107(12), 121903 (2015).
[Crossref]

Kolmychek, I. A.

S. Kruk, M. Weismann, A. Y. Bykov, E. A. Mamonov, I. A. Kolmychek, T. Murzina, N. C. Panoiu, D. N. Neshev, and Y. S. Kivshar, “Enhanced magnetic second-harmonic generation from resonant metasurfaces,” ACS Photonics 2(8), 1007–1012 (2015).
[Crossref]

Kondo, T.

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, and Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61(2), 145 (1992).
[Crossref]

Koos, C.

L. Alloatti, C. Kieninger, A. Froelich, M. Lauermann, T. Frenzel, K. Köhnle, W. Freude, J. Leuthold, M. Wegener, and C. Koos, “Second-order nonlinear optical metamaterials: ABC-type nanolaminates,” Appl. Phys. Lett. 107(12), 121903 (2015).
[Crossref]

Koskinen, K.

Kruk, S.

S. Kruk, M. Weismann, A. Y. Bykov, E. A. Mamonov, I. A. Kolmychek, T. Murzina, N. C. Panoiu, D. N. Neshev, and Y. S. Kivshar, “Enhanced magnetic second-harmonic generation from resonant metasurfaces,” ACS Photonics 2(8), 1007–1012 (2015).
[Crossref]

Kumata, K.

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, and Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61(2), 145 (1992).
[Crossref]

Kuttge, M.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

Lascoux, N.

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

Lauermann, M.

L. Alloatti, C. Kieninger, A. Froelich, M. Lauermann, T. Frenzel, K. Köhnle, W. Freude, J. Leuthold, M. Wegener, and C. Koos, “Second-order nonlinear optical metamaterials: ABC-type nanolaminates,” Appl. Phys. Lett. 107(12), 121903 (2015).
[Crossref]

Lee, C.

N. Bloembergen, R. Chang, S. Jha, and C. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174(3), 813–822 (1968).
[Crossref]

Leuthold, J.

L. Alloatti, C. Kieninger, A. Froelich, M. Lauermann, T. Frenzel, K. Köhnle, W. Freude, J. Leuthold, M. Wegener, and C. Koos, “Second-order nonlinear optical metamaterials: ABC-type nanolaminates,” Appl. Phys. Lett. 107(12), 121903 (2015).
[Crossref]

Mamonov, E. A.

S. Kruk, M. Weismann, A. Y. Bykov, E. A. Mamonov, I. A. Kolmychek, T. Murzina, N. C. Panoiu, D. N. Neshev, and Y. S. Kivshar, “Enhanced magnetic second-harmonic generation from resonant metasurfaces,” ACS Photonics 2(8), 1007–1012 (2015).
[Crossref]

Matlis, N.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, “Single-beam and enhanced two-beam second-harmonic generation from silicon nanocrystals by use of spatially inhomogeneous femtosecond pulses,” Phys. Rev. Lett. 94(4), 047401 (2005).
[Crossref] [PubMed]

Mattern, B.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, “Single-beam and enhanced two-beam second-harmonic generation from silicon nanocrystals by use of spatially inhomogeneous femtosecond pulses,” Phys. Rev. Lett. 94(4), 047401 (2005).
[Crossref] [PubMed]

Melik-Gaykazyan, E. V.

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Mendoza, B. S.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, “Single-beam and enhanced two-beam second-harmonic generation from silicon nanocrystals by use of spatially inhomogeneous femtosecond pulses,” Phys. Rev. Lett. 94(4), 047401 (2005).
[Crossref] [PubMed]

Miroshnichenko, A. E.

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Mizrahi, V.

J. E. Sipe, V. Mizrahi, and G. I. Stegeman, “Fundamental difficulty in the use of second-harmonic generation as a strictly surface probe,” Phys. Rev. B Condens. Matter 35(17), 9091–9094 (1987).
[Crossref] [PubMed]

Mochán, W. L.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, “Single-beam and enhanced two-beam second-harmonic generation from silicon nanocrystals by use of spatially inhomogeneous femtosecond pulses,” Phys. Rev. Lett. 94(4), 047401 (2005).
[Crossref] [PubMed]

Mok, S.-W.

K. L. Sly, S.-W. Mok, and J. C. Conboy, “Second harmonic correlation spectroscopy: a method for determining surface binding kinetics and thermodynamics,” Anal. Chem. 85(17), 8429–8435 (2013).
[Crossref] [PubMed]

Murzina, T.

S. Kruk, M. Weismann, A. Y. Bykov, E. A. Mamonov, I. A. Kolmychek, T. Murzina, N. C. Panoiu, D. N. Neshev, and Y. S. Kivshar, “Enhanced magnetic second-harmonic generation from resonant metasurfaces,” ACS Photonics 2(8), 1007–1012 (2015).
[Crossref]

Neshev, D. N.

S. Kruk, M. Weismann, A. Y. Bykov, E. A. Mamonov, I. A. Kolmychek, T. Murzina, N. C. Panoiu, D. N. Neshev, and Y. S. Kivshar, “Enhanced magnetic second-harmonic generation from resonant metasurfaces,” ACS Photonics 2(8), 1007–1012 (2015).
[Crossref]

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Niedringhaus, A.

Ning, T.

T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100(16), 161902 (2012).
[Crossref]

Ogilvie, J. P.

Ohashi, M.

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, and Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61(2), 145 (1992).
[Crossref]

Panoiu, N. C.

S. Kruk, M. Weismann, A. Y. Bykov, E. A. Mamonov, I. A. Kolmychek, T. Murzina, N. C. Panoiu, D. N. Neshev, and Y. S. Kivshar, “Enhanced magnetic second-harmonic generation from resonant metasurfaces,” ACS Photonics 2(8), 1007–1012 (2015).
[Crossref]

Pietarinen, H.

T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100(16), 161902 (2012).
[Crossref]

Rodriguez, F. J.

Rodríguez, F.

F. Wang, F. Rodríguez, W. Albers, and M. Kauranen, “Enhancement of bulk-type multipolar second-harmonic generation arising from surface morphology of metals,” New J. Phys. 12(6), 063009 (2010).
[Crossref]

Rodríguez, F. J.

F. X. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
[Crossref]

F. J. Rodríguez, F. X. Wang, B. K. Canfield, S. Cattaneo, and M. Kauranen, “Multipolar tensor analysis of second-order nonlinear optical response of surface and bulk of glass,” Opt. Express 15(14), 8695–8701 (2007).
[Crossref] [PubMed]

Russier-Antoine, I.

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

Shcherbakov, M. R.

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Shen, Y. R.

Y. R. Shen, “Surface nonlinear optics: a historical perspective,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1375–1379 (2000).
[Crossref]

P. Guyot-Sionnest and Y. R. Shen, “Local and nonlocal surface nonlinearities for surface optical second-harmonic generation,” Phys. Rev. B Condens. Matter 35(9), 4420–4426 (1987).
[Crossref] [PubMed]

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter 33(12), 8254–8263 (1986).
[Crossref] [PubMed]

Shiraki, Y.

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, and Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61(2), 145 (1992).
[Crossref]

Shorokhov, A. S.

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Shtein, M.

Simonen, J.

T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100(16), 161902 (2012).
[Crossref]

Sipe, J.

F. X. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
[Crossref]

J. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. B 4(4), 481–498 (1987).
[Crossref]

Sipe, J. E.

J. E. Sipe, V. Mizrahi, and G. I. Stegeman, “Fundamental difficulty in the use of second-harmonic generation as a strictly surface probe,” Phys. Rev. B Condens. Matter 35(17), 9091–9094 (1987).
[Crossref] [PubMed]

Sly, K. L.

K. L. Sly, S.-W. Mok, and J. C. Conboy, “Second harmonic correlation spectroscopy: a method for determining surface binding kinetics and thermodynamics,” Anal. Chem. 85(17), 8429–8435 (2013).
[Crossref] [PubMed]

Solano, E.

Staude, I.

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Stegeman, G. I.

J. E. Sipe, V. Mizrahi, and G. I. Stegeman, “Fundamental difficulty in the use of second-harmonic generation as a strictly surface probe,” Phys. Rev. B Condens. Matter 35(17), 9091–9094 (1987).
[Crossref] [PubMed]

Sun, L.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, “Single-beam and enhanced two-beam second-harmonic generation from silicon nanocrystals by use of spatially inhomogeneous femtosecond pulses,” Phys. Rev. Lett. 94(4), 047401 (2005).
[Crossref] [PubMed]

Sykes, M. E.

van Hulst, N. F.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

Wang, F.

F. Wang, F. Rodríguez, W. Albers, and M. Kauranen, “Enhancement of bulk-type multipolar second-harmonic generation arising from surface morphology of metals,” New J. Phys. 12(6), 063009 (2010).
[Crossref]

Wang, F. X.

Wegener, M.

L. Alloatti, C. Kieninger, A. Froelich, M. Lauermann, T. Frenzel, K. Köhnle, W. Freude, J. Leuthold, M. Wegener, and C. Koos, “Second-order nonlinear optical metamaterials: ABC-type nanolaminates,” Appl. Phys. Lett. 107(12), 121903 (2015).
[Crossref]

Weismann, M.

S. Kruk, M. Weismann, A. Y. Bykov, E. A. Mamonov, I. A. Kolmychek, T. Murzina, N. C. Panoiu, D. N. Neshev, and Y. S. Kivshar, “Enhanced magnetic second-harmonic generation from resonant metasurfaces,” ACS Photonics 2(8), 1007–1012 (2015).
[Crossref]

White, C. W.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, “Single-beam and enhanced two-beam second-harmonic generation from silicon nanocrystals by use of spatially inhomogeneous femtosecond pulses,” Phys. Rev. Lett. 94(4), 047401 (2005).
[Crossref] [PubMed]

Wilcox, D. E.

Withrow, S. P.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, “Single-beam and enhanced two-beam second-harmonic generation from silicon nanocrystals by use of spatially inhomogeneous femtosecond pulses,” Phys. Rev. Lett. 94(4), 047401 (2005).
[Crossref] [PubMed]

ACS Photonics (1)

S. Kruk, M. Weismann, A. Y. Bykov, E. A. Mamonov, I. A. Kolmychek, T. Murzina, N. C. Panoiu, D. N. Neshev, and Y. S. Kivshar, “Enhanced magnetic second-harmonic generation from resonant metasurfaces,” ACS Photonics 2(8), 1007–1012 (2015).
[Crossref]

Anal. Chem. (1)

K. L. Sly, S.-W. Mok, and J. C. Conboy, “Second harmonic correlation spectroscopy: a method for determining surface binding kinetics and thermodynamics,” Anal. Chem. 85(17), 8429–8435 (2013).
[Crossref] [PubMed]

Appl. Phys. Lett. (3)

L. Alloatti, C. Kieninger, A. Froelich, M. Lauermann, T. Frenzel, K. Köhnle, W. Freude, J. Leuthold, M. Wegener, and C. Koos, “Second-order nonlinear optical metamaterials: ABC-type nanolaminates,” Appl. Phys. Lett. 107(12), 121903 (2015).
[Crossref]

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, and Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61(2), 145 (1992).
[Crossref]

T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100(16), 161902 (2012).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

Y. R. Shen, “Surface nonlinear optics: a historical perspective,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1375–1379 (2000).
[Crossref]

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

Nano Lett. (3)

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, “Multipolar interference for directed light emission,” Nano Lett. 14(1), 166–171 (2014).
[Crossref] [PubMed]

J. Butet, I. Russier-Antoine, C. Jonin, N. Lascoux, E. Benichou, and P.-F. Brevet, “Sensing with multipolar second harmonic generation from spherical metallic nanoparticles,” Nano Lett. 12(3), 1697–1701 (2012).
[Crossref] [PubMed]

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

New J. Phys. (1)

F. Wang, F. Rodríguez, W. Albers, and M. Kauranen, “Enhancement of bulk-type multipolar second-harmonic generation arising from surface morphology of metals,” New J. Phys. 12(6), 063009 (2010).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. (1)

N. Bloembergen, R. Chang, S. Jha, and C. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev. 174(3), 813–822 (1968).
[Crossref]

Phys. Rev. B (2)

F. X. Wang, F. J. Rodríguez, W. M. Albers, R. Ahorinta, J. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B 80(23), 233402 (2009).
[Crossref]

S. Cattaneo and M. Kauranen, “Polarization-based identification of bulk contributions in surface nonlinear optics,” Phys. Rev. B 72(3), 033412 (2005).
[Crossref]

Phys. Rev. B Condens. Matter (3)

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter 33(12), 8254–8263 (1986).
[Crossref] [PubMed]

P. Guyot-Sionnest and Y. R. Shen, “Local and nonlocal surface nonlinearities for surface optical second-harmonic generation,” Phys. Rev. B Condens. Matter 35(9), 4420–4426 (1987).
[Crossref] [PubMed]

J. E. Sipe, V. Mizrahi, and G. I. Stegeman, “Fundamental difficulty in the use of second-harmonic generation as a strictly surface probe,” Phys. Rev. B Condens. Matter 35(17), 9091–9094 (1987).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, “Single-beam and enhanced two-beam second-harmonic generation from silicon nanocrystals by use of spatially inhomogeneous femtosecond pulses,” Phys. Rev. Lett. 94(4), 047401 (2005).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 Schematic of two-beam SHG measurement and the used notation.
Fig. 2
Fig. 2 Schematic of the two main consequences of reflections in thin samples. a) Multiple reflections contributing to the total field strength. b) SHG generated into two directions in the nonlinear medium.
Fig. 3
Fig. 3 Three simulations of a measurement: a) reflections neglected, no multipole contribution; b) reflections neglected, 10% multipole contribution; c) 5° phase difference between h s and ks , no multipole contribution.
Fig. 4
Fig. 4 Experimental data fitted in three different ways: a) traditional model without multipole contribution; b) traditional model with multipole contribution and c) detailed model without multipole contribution.

Equations (10)

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

P s d = 2 χ x x z ( a s b p sin θ b + a p b s sin θ a ) ,
P MP = β e ( e ) + γ ( e e ) + δ ' ( e ) e ,
P s δ ' = i k δ ' sin ( θ a θ b ) ( a s b p a p b s ) ,
C + = t 13 r 32 e 2 i | w | D 1 r 31 r 32 e 2 i | w | D , and C = t 13 1 r 31 r 32 e 2 i | w | D .
E s α , β { + , } [ P s d ( a α , b β ) + P s δ ' ( a α , b β ) ] ( G α , β + R 31 s G ' α , β ) ,
G α , β = 1 exp ( i ( w a , α + w b , β + W ) D ) i ( w a , α + w b , β + W ) , and G ' α , β = 1 exp ( i ( w a , α + w b , β W ) D ) i ( w a , α + w b , β W )
E s h s a p b s + k s a s b p ,
[ h s k s ] = [ m 11 m 12 m 21 m 22 ] [ χ x x z k δ ' ] , where
m 11 = 2 sin ( θ a ) α , β { + , } C α a , p C β b , s ( G α , β + R 31 s G ' α , β ) m 12 = i α , β { + , } C α a , p C β b , s ( G α , β + R 31 s G ' α , β ) 1 β sin ( θ a 1 α 1 β θ b ) , m 21 = 2 sin ( θ b ) α , β { + , } C α a , s C β b , p ( G α , β + R 31 s G ' α , β ) m 22 = i α , β { + , } C α a , s C β b , p ( G α , β + R 31 s G ' α , β ) 1 β sin ( θ a 1 α 1 β θ b )
h s = [ 2 χ x x z sin ( θ a ) i k δ ' sin ( θ a θ b ) ] t 13 a , p t 13 b , s , k s = [ 2 χ x x z sin ( θ b ) + i k δ ' sin ( θ a θ b ) ] t 13 a , s t 13 b , p

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