Abstract

A generalized lock-in detection method is proposed to extract amplitude and phase from optical interferometers when an arbitrary periodic phase or frequency modulation is used. The actual modulation function is used to create the reference signals providing an optimal extraction of the useful information, notably for sinusoidal phase modulation. This simple and efficient approach has been tested and applied to phase sensitive spectroscopy and near-field optical measurements. We analyze the case where the signal amplitude is modulated and we show how to suppress the contribution of unmodulated background field.

© 2014 Optical Society of America

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References

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  1. Y. Shizhuo, F. T. Yu, and P. Ruffin, Fiber Optic Sensors (CRC Press, 1998).
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    [Crossref] [PubMed]
  3. N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
    [Crossref]
  4. M. Vaez-Iravani and R. Toledo-Crow, “Phase contrast and amplitude pseudoheterodyne interference near field scanning optical microscopy,” Appl. Phys. Lett. 62(10), 1044–1046 (1993).
    [Crossref]
  5. R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
    [Crossref] [PubMed]
  6. R. Debdulal, S. Leong, and M. Welland, “Dielectric contrast imaging using apertureless scanning near-field optical microscopy in the reflection mode,” J. Korean Phys. Soc. 47, 140–146 (2005).
  7. Y. Sasaki and H. Sasaki, “Heterodyne detection for the extraction of the probe-scattering signal in scattering-type scanning near-field optical microscope,” Jpn. J. Appl. Phys. 39(4A), L321 (2000).
    [Crossref]
  8. D. Jackson, A. Kersey, M. Corke, and J. Jones, “Pseudoheterodyne detection scheme for optical interferometers,” Electron. Lett. 18(2), 1081–1083 (1982).
    [Crossref]
  9. G. Conforti, M. Brenci, A. Mencaglia, and A. G. Mignani, “Fiber optic vibration sensor for remote monitoring in high power electric machines,” Appl. Opt. 28(23), 5158–5161 (1989).
    [Crossref] [PubMed]
  10. A. Kersey and D. Jackson, “Pseudo-heterodyne detection scheme for the fibre gyroscope,” Electron. Lett. vol.  20(2), 368–370 (1984).
    [Crossref]
  11. A. Dandridge, A. Tveten, and T. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microwave Theory Tech. 30(10), 1635–1641 (1982).
    [Crossref]
  12. B. Lee and Y. Jeong, Fiber Optics Sensors (CRC Press, 2008), Chap. 7.
  13. S. Pilevar, W. Atia, and C. Davis, “Reflection near-field scanning optical microscopy: an interferometric approach,” Ultramicroscopy. 61(1), 233–236 (1995).
    [Crossref]
  14. L. Stern, B. Desiatov, I. Goykhman, G. M. Lerman, and U. Levy, “Near field phase mapping exploiting intrinsic oscillations of aperture NSOM probe,” Opt. Express 19(13), 12014–12020 (2011).
    [Crossref] [PubMed]
  15. B. Deutsch, R. Hillenbrand, and L. Novotny, “Near-field amplitude and phase recovery using phase-shifting interferometry,” Opt. Express 16(2), 494–501 (2008).
    [Crossref] [PubMed]
  16. H. J. Weber, L. Ruby, and G. B. Arfken, Mathematical methods for physicists (Harcourt/Academic, 2000).
  17. C. Elliott, V. Vijayakumar, W. Zink, and R. Hansen, “National instruments LabVIEW: A programming environment for laboratory automation and measurement,” Journal of the Association for Laboratory Automation 12(1), 17–24 (2007).
    [Crossref]
  18. Y. Yao, A. Hoffman, and C. Gmachl, “Mid-infrared quantum cascade lasers,” Nat. Photonics 6, 432–439 (2012).
    [Crossref]
  19. Z. Sedaghat, A. Bruyant, M. Kazan, J. Vaillant, S. Blaize, N. Rochat, N. Chevalier, E. Garcia-Caurel, P. Morin, and P. Royer, “Development of a polarization resolved mid-IR near-field microscope,” Proc. SPIE 7946, 79461N (2011).
    [Crossref]
  20. S. Amarie and F. Keilmann, “Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy,” Phys. Rev. B 83(4), 045404 (2011).
    [Crossref]
  21. Z. Sedaghat, “A near-field study of the probe-sample interaction in near and mid-infrared nanoscopy,” Ph.D. thesis, University of Technology of Troyes (2012).
  22. M. Kazan, A. Bruyant, Z. Sedaghat, L. Arnaud, S. Blaize, and P. Royer, “Temperature and directional dependences of the infrared dielectric function of free standing silicon nanowire,” Phys. Status Solidi C 8(3),1006–1011 (2011).
    [Crossref]
  23. B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4), 321–328 (2000).
    [Crossref]
  24. M. Kulawik, M. Nowicki, G. Thielsch, L. Cramer, H.-P. Rust, H.-J. Freund, T. P. Pearl, and P. S. Weiss, “A double lamellae dropoff etching procedure for tungsten tips attached to tuning fork atomic force microscopy/scanning tunneling microscopy sensors,” Rev. Sci. Instrum. 74(2), 1027–1030 (2003).
    [Crossref]
  25. A. Apuzzo, M. Fvrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13(3), 1000–1006 (2013).
    [Crossref] [PubMed]
  26. R. Salas-Montiel, A. Apuzzo, C. Delacour, Z. Sedaghat, A. Bruyant, P. Grosse, A. Chelnokov, G. Lerondel, and S. Blaize, “Quantitative analysis and near-field observation of strong coupling between plasmonic nanogap and silicon waveguides,” Appl. Phys. Lett.100(23), (2012).
    [Crossref]
  27. A. Bruyant, “Etude de structures photoniques en champ proche par microscopie optique à sonde diffusante,” Ph.D. thesis, University of Technology of Troyes, (2004).

2013 (1)

A. Apuzzo, M. Fvrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13(3), 1000–1006 (2013).
[Crossref] [PubMed]

2012 (2)

Y. Yao, A. Hoffman, and C. Gmachl, “Mid-infrared quantum cascade lasers,” Nat. Photonics 6, 432–439 (2012).
[Crossref]

P. S. Carney, B. Deutsch, A. A. Govyadinov, and R. Hillenbrand, “Phase in nanooptics,” ACS Nano,  6(1), 8–12 (2012).
[Crossref] [PubMed]

2011 (4)

Z. Sedaghat, A. Bruyant, M. Kazan, J. Vaillant, S. Blaize, N. Rochat, N. Chevalier, E. Garcia-Caurel, P. Morin, and P. Royer, “Development of a polarization resolved mid-IR near-field microscope,” Proc. SPIE 7946, 79461N (2011).
[Crossref]

S. Amarie and F. Keilmann, “Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy,” Phys. Rev. B 83(4), 045404 (2011).
[Crossref]

M. Kazan, A. Bruyant, Z. Sedaghat, L. Arnaud, S. Blaize, and P. Royer, “Temperature and directional dependences of the infrared dielectric function of free standing silicon nanowire,” Phys. Status Solidi C 8(3),1006–1011 (2011).
[Crossref]

L. Stern, B. Desiatov, I. Goykhman, G. M. Lerman, and U. Levy, “Near field phase mapping exploiting intrinsic oscillations of aperture NSOM probe,” Opt. Express 19(13), 12014–12020 (2011).
[Crossref] [PubMed]

2008 (1)

2007 (1)

C. Elliott, V. Vijayakumar, W. Zink, and R. Hansen, “National instruments LabVIEW: A programming environment for laboratory automation and measurement,” Journal of the Association for Laboratory Automation 12(1), 17–24 (2007).
[Crossref]

2006 (1)

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
[Crossref]

2005 (1)

R. Debdulal, S. Leong, and M. Welland, “Dielectric contrast imaging using apertureless scanning near-field optical microscopy in the reflection mode,” J. Korean Phys. Soc. 47, 140–146 (2005).

2003 (1)

M. Kulawik, M. Nowicki, G. Thielsch, L. Cramer, H.-P. Rust, H.-J. Freund, T. P. Pearl, and P. S. Weiss, “A double lamellae dropoff etching procedure for tungsten tips attached to tuning fork atomic force microscopy/scanning tunneling microscopy sensors,” Rev. Sci. Instrum. 74(2), 1027–1030 (2003).
[Crossref]

2000 (3)

B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4), 321–328 (2000).
[Crossref]

Y. Sasaki and H. Sasaki, “Heterodyne detection for the extraction of the probe-scattering signal in scattering-type scanning near-field optical microscope,” Jpn. J. Appl. Phys. 39(4A), L321 (2000).
[Crossref]

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
[Crossref] [PubMed]

1995 (1)

S. Pilevar, W. Atia, and C. Davis, “Reflection near-field scanning optical microscopy: an interferometric approach,” Ultramicroscopy. 61(1), 233–236 (1995).
[Crossref]

1993 (1)

M. Vaez-Iravani and R. Toledo-Crow, “Phase contrast and amplitude pseudoheterodyne interference near field scanning optical microscopy,” Appl. Phys. Lett. 62(10), 1044–1046 (1993).
[Crossref]

1989 (1)

1984 (1)

A. Kersey and D. Jackson, “Pseudo-heterodyne detection scheme for the fibre gyroscope,” Electron. Lett. vol.  20(2), 368–370 (1984).
[Crossref]

1982 (2)

A. Dandridge, A. Tveten, and T. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microwave Theory Tech. 30(10), 1635–1641 (1982).
[Crossref]

D. Jackson, A. Kersey, M. Corke, and J. Jones, “Pseudoheterodyne detection scheme for optical interferometers,” Electron. Lett. 18(2), 1081–1083 (1982).
[Crossref]

Amarie, S.

S. Amarie and F. Keilmann, “Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy,” Phys. Rev. B 83(4), 045404 (2011).
[Crossref]

Apuzzo, A.

A. Apuzzo, M. Fvrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13(3), 1000–1006 (2013).
[Crossref] [PubMed]

R. Salas-Montiel, A. Apuzzo, C. Delacour, Z. Sedaghat, A. Bruyant, P. Grosse, A. Chelnokov, G. Lerondel, and S. Blaize, “Quantitative analysis and near-field observation of strong coupling between plasmonic nanogap and silicon waveguides,” Appl. Phys. Lett.100(23), (2012).
[Crossref]

Arfken, G. B.

H. J. Weber, L. Ruby, and G. B. Arfken, Mathematical methods for physicists (Harcourt/Academic, 2000).

Arnaud, L.

M. Kazan, A. Bruyant, Z. Sedaghat, L. Arnaud, S. Blaize, and P. Royer, “Temperature and directional dependences of the infrared dielectric function of free standing silicon nanowire,” Phys. Status Solidi C 8(3),1006–1011 (2011).
[Crossref]

Atia, W.

S. Pilevar, W. Atia, and C. Davis, “Reflection near-field scanning optical microscopy: an interferometric approach,” Ultramicroscopy. 61(1), 233–236 (1995).
[Crossref]

Blaize, S.

A. Apuzzo, M. Fvrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13(3), 1000–1006 (2013).
[Crossref] [PubMed]

M. Kazan, A. Bruyant, Z. Sedaghat, L. Arnaud, S. Blaize, and P. Royer, “Temperature and directional dependences of the infrared dielectric function of free standing silicon nanowire,” Phys. Status Solidi C 8(3),1006–1011 (2011).
[Crossref]

Z. Sedaghat, A. Bruyant, M. Kazan, J. Vaillant, S. Blaize, N. Rochat, N. Chevalier, E. Garcia-Caurel, P. Morin, and P. Royer, “Development of a polarization resolved mid-IR near-field microscope,” Proc. SPIE 7946, 79461N (2011).
[Crossref]

R. Salas-Montiel, A. Apuzzo, C. Delacour, Z. Sedaghat, A. Bruyant, P. Grosse, A. Chelnokov, G. Lerondel, and S. Blaize, “Quantitative analysis and near-field observation of strong coupling between plasmonic nanogap and silicon waveguides,” Appl. Phys. Lett.100(23), (2012).
[Crossref]

Brenci, M.

Bruyant, A.

A. Apuzzo, M. Fvrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13(3), 1000–1006 (2013).
[Crossref] [PubMed]

Z. Sedaghat, A. Bruyant, M. Kazan, J. Vaillant, S. Blaize, N. Rochat, N. Chevalier, E. Garcia-Caurel, P. Morin, and P. Royer, “Development of a polarization resolved mid-IR near-field microscope,” Proc. SPIE 7946, 79461N (2011).
[Crossref]

M. Kazan, A. Bruyant, Z. Sedaghat, L. Arnaud, S. Blaize, and P. Royer, “Temperature and directional dependences of the infrared dielectric function of free standing silicon nanowire,” Phys. Status Solidi C 8(3),1006–1011 (2011).
[Crossref]

A. Bruyant, “Etude de structures photoniques en champ proche par microscopie optique à sonde diffusante,” Ph.D. thesis, University of Technology of Troyes, (2004).

R. Salas-Montiel, A. Apuzzo, C. Delacour, Z. Sedaghat, A. Bruyant, P. Grosse, A. Chelnokov, G. Lerondel, and S. Blaize, “Quantitative analysis and near-field observation of strong coupling between plasmonic nanogap and silicon waveguides,” Appl. Phys. Lett.100(23), (2012).
[Crossref]

Carney, P. S.

P. S. Carney, B. Deutsch, A. A. Govyadinov, and R. Hillenbrand, “Phase in nanooptics,” ACS Nano,  6(1), 8–12 (2012).
[Crossref] [PubMed]

Chelnokov, A.

A. Apuzzo, M. Fvrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13(3), 1000–1006 (2013).
[Crossref] [PubMed]

R. Salas-Montiel, A. Apuzzo, C. Delacour, Z. Sedaghat, A. Bruyant, P. Grosse, A. Chelnokov, G. Lerondel, and S. Blaize, “Quantitative analysis and near-field observation of strong coupling between plasmonic nanogap and silicon waveguides,” Appl. Phys. Lett.100(23), (2012).
[Crossref]

Chevalier, N.

Z. Sedaghat, A. Bruyant, M. Kazan, J. Vaillant, S. Blaize, N. Rochat, N. Chevalier, E. Garcia-Caurel, P. Morin, and P. Royer, “Development of a polarization resolved mid-IR near-field microscope,” Proc. SPIE 7946, 79461N (2011).
[Crossref]

Conforti, G.

Corke, M.

D. Jackson, A. Kersey, M. Corke, and J. Jones, “Pseudoheterodyne detection scheme for optical interferometers,” Electron. Lett. 18(2), 1081–1083 (1982).
[Crossref]

Cramer, L.

M. Kulawik, M. Nowicki, G. Thielsch, L. Cramer, H.-P. Rust, H.-J. Freund, T. P. Pearl, and P. S. Weiss, “A double lamellae dropoff etching procedure for tungsten tips attached to tuning fork atomic force microscopy/scanning tunneling microscopy sensors,” Rev. Sci. Instrum. 74(2), 1027–1030 (2003).
[Crossref]

Dagens, B.

A. Apuzzo, M. Fvrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13(3), 1000–1006 (2013).
[Crossref] [PubMed]

Dandridge, A.

A. Dandridge, A. Tveten, and T. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microwave Theory Tech. 30(10), 1635–1641 (1982).
[Crossref]

Davis, C.

S. Pilevar, W. Atia, and C. Davis, “Reflection near-field scanning optical microscopy: an interferometric approach,” Ultramicroscopy. 61(1), 233–236 (1995).
[Crossref]

Debdulal, R.

R. Debdulal, S. Leong, and M. Welland, “Dielectric contrast imaging using apertureless scanning near-field optical microscopy in the reflection mode,” J. Korean Phys. Soc. 47, 140–146 (2005).

Delacour, C.

R. Salas-Montiel, A. Apuzzo, C. Delacour, Z. Sedaghat, A. Bruyant, P. Grosse, A. Chelnokov, G. Lerondel, and S. Blaize, “Quantitative analysis and near-field observation of strong coupling between plasmonic nanogap and silicon waveguides,” Appl. Phys. Lett.100(23), (2012).
[Crossref]

Desiatov, B.

Deutsch, B.

Elliott, C.

C. Elliott, V. Vijayakumar, W. Zink, and R. Hansen, “National instruments LabVIEW: A programming environment for laboratory automation and measurement,” Journal of the Association for Laboratory Automation 12(1), 17–24 (2007).
[Crossref]

Freund, H.-J.

M. Kulawik, M. Nowicki, G. Thielsch, L. Cramer, H.-P. Rust, H.-J. Freund, T. P. Pearl, and P. S. Weiss, “A double lamellae dropoff etching procedure for tungsten tips attached to tuning fork atomic force microscopy/scanning tunneling microscopy sensors,” Rev. Sci. Instrum. 74(2), 1027–1030 (2003).
[Crossref]

Fvrier, M.

A. Apuzzo, M. Fvrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13(3), 1000–1006 (2013).
[Crossref] [PubMed]

Garcia-Caurel, E.

Z. Sedaghat, A. Bruyant, M. Kazan, J. Vaillant, S. Blaize, N. Rochat, N. Chevalier, E. Garcia-Caurel, P. Morin, and P. Royer, “Development of a polarization resolved mid-IR near-field microscope,” Proc. SPIE 7946, 79461N (2011).
[Crossref]

Giallorenzi, T.

A. Dandridge, A. Tveten, and T. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microwave Theory Tech. 30(10), 1635–1641 (1982).
[Crossref]

Gmachl, C.

Y. Yao, A. Hoffman, and C. Gmachl, “Mid-infrared quantum cascade lasers,” Nat. Photonics 6, 432–439 (2012).
[Crossref]

Govyadinov, A. A.

P. S. Carney, B. Deutsch, A. A. Govyadinov, and R. Hillenbrand, “Phase in nanooptics,” ACS Nano,  6(1), 8–12 (2012).
[Crossref] [PubMed]

Goykhman, I.

Grosse, P.

R. Salas-Montiel, A. Apuzzo, C. Delacour, Z. Sedaghat, A. Bruyant, P. Grosse, A. Chelnokov, G. Lerondel, and S. Blaize, “Quantitative analysis and near-field observation of strong coupling between plasmonic nanogap and silicon waveguides,” Appl. Phys. Lett.100(23), (2012).
[Crossref]

Hansen, R.

C. Elliott, V. Vijayakumar, W. Zink, and R. Hansen, “National instruments LabVIEW: A programming environment for laboratory automation and measurement,” Journal of the Association for Laboratory Automation 12(1), 17–24 (2007).
[Crossref]

Hillenbrand, R.

P. S. Carney, B. Deutsch, A. A. Govyadinov, and R. Hillenbrand, “Phase in nanooptics,” ACS Nano,  6(1), 8–12 (2012).
[Crossref] [PubMed]

B. Deutsch, R. Hillenbrand, and L. Novotny, “Near-field amplitude and phase recovery using phase-shifting interferometry,” Opt. Express 16(2), 494–501 (2008).
[Crossref] [PubMed]

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
[Crossref]

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
[Crossref] [PubMed]

Hoffman, A.

Y. Yao, A. Hoffman, and C. Gmachl, “Mid-infrared quantum cascade lasers,” Nat. Photonics 6, 432–439 (2012).
[Crossref]

Huber, A.

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
[Crossref]

Jackson, D.

A. Kersey and D. Jackson, “Pseudo-heterodyne detection scheme for the fibre gyroscope,” Electron. Lett. vol.  20(2), 368–370 (1984).
[Crossref]

D. Jackson, A. Kersey, M. Corke, and J. Jones, “Pseudoheterodyne detection scheme for optical interferometers,” Electron. Lett. 18(2), 1081–1083 (1982).
[Crossref]

Jeong, Y.

B. Lee and Y. Jeong, Fiber Optics Sensors (CRC Press, 2008), Chap. 7.

Jones, J.

D. Jackson, A. Kersey, M. Corke, and J. Jones, “Pseudoheterodyne detection scheme for optical interferometers,” Electron. Lett. 18(2), 1081–1083 (1982).
[Crossref]

Kazan, M.

Z. Sedaghat, A. Bruyant, M. Kazan, J. Vaillant, S. Blaize, N. Rochat, N. Chevalier, E. Garcia-Caurel, P. Morin, and P. Royer, “Development of a polarization resolved mid-IR near-field microscope,” Proc. SPIE 7946, 79461N (2011).
[Crossref]

M. Kazan, A. Bruyant, Z. Sedaghat, L. Arnaud, S. Blaize, and P. Royer, “Temperature and directional dependences of the infrared dielectric function of free standing silicon nanowire,” Phys. Status Solidi C 8(3),1006–1011 (2011).
[Crossref]

Keilmann, F.

S. Amarie and F. Keilmann, “Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy,” Phys. Rev. B 83(4), 045404 (2011).
[Crossref]

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
[Crossref] [PubMed]

B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4), 321–328 (2000).
[Crossref]

Kersey, A.

A. Kersey and D. Jackson, “Pseudo-heterodyne detection scheme for the fibre gyroscope,” Electron. Lett. vol.  20(2), 368–370 (1984).
[Crossref]

D. Jackson, A. Kersey, M. Corke, and J. Jones, “Pseudoheterodyne detection scheme for optical interferometers,” Electron. Lett. 18(2), 1081–1083 (1982).
[Crossref]

Knoll, B.

B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4), 321–328 (2000).
[Crossref]

Kulawik, M.

M. Kulawik, M. Nowicki, G. Thielsch, L. Cramer, H.-P. Rust, H.-J. Freund, T. P. Pearl, and P. S. Weiss, “A double lamellae dropoff etching procedure for tungsten tips attached to tuning fork atomic force microscopy/scanning tunneling microscopy sensors,” Rev. Sci. Instrum. 74(2), 1027–1030 (2003).
[Crossref]

Lee, B.

B. Lee and Y. Jeong, Fiber Optics Sensors (CRC Press, 2008), Chap. 7.

Leong, S.

R. Debdulal, S. Leong, and M. Welland, “Dielectric contrast imaging using apertureless scanning near-field optical microscopy in the reflection mode,” J. Korean Phys. Soc. 47, 140–146 (2005).

Lerman, G. M.

Lerondel, G.

A. Apuzzo, M. Fvrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13(3), 1000–1006 (2013).
[Crossref] [PubMed]

R. Salas-Montiel, A. Apuzzo, C. Delacour, Z. Sedaghat, A. Bruyant, P. Grosse, A. Chelnokov, G. Lerondel, and S. Blaize, “Quantitative analysis and near-field observation of strong coupling between plasmonic nanogap and silicon waveguides,” Appl. Phys. Lett.100(23), (2012).
[Crossref]

Levy, U.

Mencaglia, A.

Mignani, A. G.

Morin, P.

Z. Sedaghat, A. Bruyant, M. Kazan, J. Vaillant, S. Blaize, N. Rochat, N. Chevalier, E. Garcia-Caurel, P. Morin, and P. Royer, “Development of a polarization resolved mid-IR near-field microscope,” Proc. SPIE 7946, 79461N (2011).
[Crossref]

Novotny, L.

Nowicki, M.

M. Kulawik, M. Nowicki, G. Thielsch, L. Cramer, H.-P. Rust, H.-J. Freund, T. P. Pearl, and P. S. Weiss, “A double lamellae dropoff etching procedure for tungsten tips attached to tuning fork atomic force microscopy/scanning tunneling microscopy sensors,” Rev. Sci. Instrum. 74(2), 1027–1030 (2003).
[Crossref]

Ocelic, N.

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
[Crossref]

Pearl, T. P.

M. Kulawik, M. Nowicki, G. Thielsch, L. Cramer, H.-P. Rust, H.-J. Freund, T. P. Pearl, and P. S. Weiss, “A double lamellae dropoff etching procedure for tungsten tips attached to tuning fork atomic force microscopy/scanning tunneling microscopy sensors,” Rev. Sci. Instrum. 74(2), 1027–1030 (2003).
[Crossref]

Pilevar, S.

S. Pilevar, W. Atia, and C. Davis, “Reflection near-field scanning optical microscopy: an interferometric approach,” Ultramicroscopy. 61(1), 233–236 (1995).
[Crossref]

Rochat, N.

Z. Sedaghat, A. Bruyant, M. Kazan, J. Vaillant, S. Blaize, N. Rochat, N. Chevalier, E. Garcia-Caurel, P. Morin, and P. Royer, “Development of a polarization resolved mid-IR near-field microscope,” Proc. SPIE 7946, 79461N (2011).
[Crossref]

Royer, P.

Z. Sedaghat, A. Bruyant, M. Kazan, J. Vaillant, S. Blaize, N. Rochat, N. Chevalier, E. Garcia-Caurel, P. Morin, and P. Royer, “Development of a polarization resolved mid-IR near-field microscope,” Proc. SPIE 7946, 79461N (2011).
[Crossref]

M. Kazan, A. Bruyant, Z. Sedaghat, L. Arnaud, S. Blaize, and P. Royer, “Temperature and directional dependences of the infrared dielectric function of free standing silicon nanowire,” Phys. Status Solidi C 8(3),1006–1011 (2011).
[Crossref]

Ruby, L.

H. J. Weber, L. Ruby, and G. B. Arfken, Mathematical methods for physicists (Harcourt/Academic, 2000).

Ruffin, P.

Y. Shizhuo, F. T. Yu, and P. Ruffin, Fiber Optic Sensors (CRC Press, 1998).

Rust, H.-P.

M. Kulawik, M. Nowicki, G. Thielsch, L. Cramer, H.-P. Rust, H.-J. Freund, T. P. Pearl, and P. S. Weiss, “A double lamellae dropoff etching procedure for tungsten tips attached to tuning fork atomic force microscopy/scanning tunneling microscopy sensors,” Rev. Sci. Instrum. 74(2), 1027–1030 (2003).
[Crossref]

Salas-Montiel, R.

A. Apuzzo, M. Fvrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13(3), 1000–1006 (2013).
[Crossref] [PubMed]

R. Salas-Montiel, A. Apuzzo, C. Delacour, Z. Sedaghat, A. Bruyant, P. Grosse, A. Chelnokov, G. Lerondel, and S. Blaize, “Quantitative analysis and near-field observation of strong coupling between plasmonic nanogap and silicon waveguides,” Appl. Phys. Lett.100(23), (2012).
[Crossref]

Sasaki, H.

Y. Sasaki and H. Sasaki, “Heterodyne detection for the extraction of the probe-scattering signal in scattering-type scanning near-field optical microscope,” Jpn. J. Appl. Phys. 39(4A), L321 (2000).
[Crossref]

Sasaki, Y.

Y. Sasaki and H. Sasaki, “Heterodyne detection for the extraction of the probe-scattering signal in scattering-type scanning near-field optical microscope,” Jpn. J. Appl. Phys. 39(4A), L321 (2000).
[Crossref]

Sedaghat, Z.

Z. Sedaghat, A. Bruyant, M. Kazan, J. Vaillant, S. Blaize, N. Rochat, N. Chevalier, E. Garcia-Caurel, P. Morin, and P. Royer, “Development of a polarization resolved mid-IR near-field microscope,” Proc. SPIE 7946, 79461N (2011).
[Crossref]

M. Kazan, A. Bruyant, Z. Sedaghat, L. Arnaud, S. Blaize, and P. Royer, “Temperature and directional dependences of the infrared dielectric function of free standing silicon nanowire,” Phys. Status Solidi C 8(3),1006–1011 (2011).
[Crossref]

Z. Sedaghat, “A near-field study of the probe-sample interaction in near and mid-infrared nanoscopy,” Ph.D. thesis, University of Technology of Troyes (2012).

R. Salas-Montiel, A. Apuzzo, C. Delacour, Z. Sedaghat, A. Bruyant, P. Grosse, A. Chelnokov, G. Lerondel, and S. Blaize, “Quantitative analysis and near-field observation of strong coupling between plasmonic nanogap and silicon waveguides,” Appl. Phys. Lett.100(23), (2012).
[Crossref]

Shizhuo, Y.

Y. Shizhuo, F. T. Yu, and P. Ruffin, Fiber Optic Sensors (CRC Press, 1998).

Stern, L.

Thielsch, G.

M. Kulawik, M. Nowicki, G. Thielsch, L. Cramer, H.-P. Rust, H.-J. Freund, T. P. Pearl, and P. S. Weiss, “A double lamellae dropoff etching procedure for tungsten tips attached to tuning fork atomic force microscopy/scanning tunneling microscopy sensors,” Rev. Sci. Instrum. 74(2), 1027–1030 (2003).
[Crossref]

Toledo-Crow, R.

M. Vaez-Iravani and R. Toledo-Crow, “Phase contrast and amplitude pseudoheterodyne interference near field scanning optical microscopy,” Appl. Phys. Lett. 62(10), 1044–1046 (1993).
[Crossref]

Tveten, A.

A. Dandridge, A. Tveten, and T. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microwave Theory Tech. 30(10), 1635–1641 (1982).
[Crossref]

Vaez-Iravani, M.

M. Vaez-Iravani and R. Toledo-Crow, “Phase contrast and amplitude pseudoheterodyne interference near field scanning optical microscopy,” Appl. Phys. Lett. 62(10), 1044–1046 (1993).
[Crossref]

Vaillant, J.

Z. Sedaghat, A. Bruyant, M. Kazan, J. Vaillant, S. Blaize, N. Rochat, N. Chevalier, E. Garcia-Caurel, P. Morin, and P. Royer, “Development of a polarization resolved mid-IR near-field microscope,” Proc. SPIE 7946, 79461N (2011).
[Crossref]

Vijayakumar, V.

C. Elliott, V. Vijayakumar, W. Zink, and R. Hansen, “National instruments LabVIEW: A programming environment for laboratory automation and measurement,” Journal of the Association for Laboratory Automation 12(1), 17–24 (2007).
[Crossref]

Weber, H. J.

H. J. Weber, L. Ruby, and G. B. Arfken, Mathematical methods for physicists (Harcourt/Academic, 2000).

Weiss, P. S.

M. Kulawik, M. Nowicki, G. Thielsch, L. Cramer, H.-P. Rust, H.-J. Freund, T. P. Pearl, and P. S. Weiss, “A double lamellae dropoff etching procedure for tungsten tips attached to tuning fork atomic force microscopy/scanning tunneling microscopy sensors,” Rev. Sci. Instrum. 74(2), 1027–1030 (2003).
[Crossref]

Welland, M.

R. Debdulal, S. Leong, and M. Welland, “Dielectric contrast imaging using apertureless scanning near-field optical microscopy in the reflection mode,” J. Korean Phys. Soc. 47, 140–146 (2005).

Yao, Y.

Y. Yao, A. Hoffman, and C. Gmachl, “Mid-infrared quantum cascade lasers,” Nat. Photonics 6, 432–439 (2012).
[Crossref]

Yu, F. T.

Y. Shizhuo, F. T. Yu, and P. Ruffin, Fiber Optic Sensors (CRC Press, 1998).

Zink, W.

C. Elliott, V. Vijayakumar, W. Zink, and R. Hansen, “National instruments LabVIEW: A programming environment for laboratory automation and measurement,” Journal of the Association for Laboratory Automation 12(1), 17–24 (2007).
[Crossref]

ACS Nano (1)

P. S. Carney, B. Deutsch, A. A. Govyadinov, and R. Hillenbrand, “Phase in nanooptics,” ACS Nano,  6(1), 8–12 (2012).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
[Crossref]

M. Vaez-Iravani and R. Toledo-Crow, “Phase contrast and amplitude pseudoheterodyne interference near field scanning optical microscopy,” Appl. Phys. Lett. 62(10), 1044–1046 (1993).
[Crossref]

Electron. Lett. (2)

D. Jackson, A. Kersey, M. Corke, and J. Jones, “Pseudoheterodyne detection scheme for optical interferometers,” Electron. Lett. 18(2), 1081–1083 (1982).
[Crossref]

A. Kersey and D. Jackson, “Pseudo-heterodyne detection scheme for the fibre gyroscope,” Electron. Lett. vol.  20(2), 368–370 (1984).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

A. Dandridge, A. Tveten, and T. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microwave Theory Tech. 30(10), 1635–1641 (1982).
[Crossref]

J. Korean Phys. Soc. (1)

R. Debdulal, S. Leong, and M. Welland, “Dielectric contrast imaging using apertureless scanning near-field optical microscopy in the reflection mode,” J. Korean Phys. Soc. 47, 140–146 (2005).

Journal of the Association for Laboratory Automation (1)

C. Elliott, V. Vijayakumar, W. Zink, and R. Hansen, “National instruments LabVIEW: A programming environment for laboratory automation and measurement,” Journal of the Association for Laboratory Automation 12(1), 17–24 (2007).
[Crossref]

Jpn. J. Appl. Phys. (1)

Y. Sasaki and H. Sasaki, “Heterodyne detection for the extraction of the probe-scattering signal in scattering-type scanning near-field optical microscope,” Jpn. J. Appl. Phys. 39(4A), L321 (2000).
[Crossref]

Nano Lett. (1)

A. Apuzzo, M. Fvrier, R. Salas-Montiel, A. Bruyant, A. Chelnokov, G. Lerondel, B. Dagens, and S. Blaize, “Observation of near-field dipolar interactions involved in a metal nanoparticle chain waveguide,” Nano Lett. 13(3), 1000–1006 (2013).
[Crossref] [PubMed]

Nat. Photonics (1)

Y. Yao, A. Hoffman, and C. Gmachl, “Mid-infrared quantum cascade lasers,” Nat. Photonics 6, 432–439 (2012).
[Crossref]

Opt. Commun. (1)

B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4), 321–328 (2000).
[Crossref]

Opt. Express (2)

Phys. Rev. B (1)

S. Amarie and F. Keilmann, “Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy,” Phys. Rev. B 83(4), 045404 (2011).
[Crossref]

Phys. Rev. Lett. (1)

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
[Crossref] [PubMed]

Phys. Status Solidi C (1)

M. Kazan, A. Bruyant, Z. Sedaghat, L. Arnaud, S. Blaize, and P. Royer, “Temperature and directional dependences of the infrared dielectric function of free standing silicon nanowire,” Phys. Status Solidi C 8(3),1006–1011 (2011).
[Crossref]

Proc. SPIE (1)

Z. Sedaghat, A. Bruyant, M. Kazan, J. Vaillant, S. Blaize, N. Rochat, N. Chevalier, E. Garcia-Caurel, P. Morin, and P. Royer, “Development of a polarization resolved mid-IR near-field microscope,” Proc. SPIE 7946, 79461N (2011).
[Crossref]

Rev. Sci. Instrum. (1)

M. Kulawik, M. Nowicki, G. Thielsch, L. Cramer, H.-P. Rust, H.-J. Freund, T. P. Pearl, and P. S. Weiss, “A double lamellae dropoff etching procedure for tungsten tips attached to tuning fork atomic force microscopy/scanning tunneling microscopy sensors,” Rev. Sci. Instrum. 74(2), 1027–1030 (2003).
[Crossref]

Ultramicroscopy. (1)

S. Pilevar, W. Atia, and C. Davis, “Reflection near-field scanning optical microscopy: an interferometric approach,” Ultramicroscopy. 61(1), 233–236 (1995).
[Crossref]

Other (6)

R. Salas-Montiel, A. Apuzzo, C. Delacour, Z. Sedaghat, A. Bruyant, P. Grosse, A. Chelnokov, G. Lerondel, and S. Blaize, “Quantitative analysis and near-field observation of strong coupling between plasmonic nanogap and silicon waveguides,” Appl. Phys. Lett.100(23), (2012).
[Crossref]

A. Bruyant, “Etude de structures photoniques en champ proche par microscopie optique à sonde diffusante,” Ph.D. thesis, University of Technology of Troyes, (2004).

B. Lee and Y. Jeong, Fiber Optics Sensors (CRC Press, 2008), Chap. 7.

Y. Shizhuo, F. T. Yu, and P. Ruffin, Fiber Optic Sensors (CRC Press, 1998).

Z. Sedaghat, “A near-field study of the probe-sample interaction in near and mid-infrared nanoscopy,” Ph.D. thesis, University of Technology of Troyes (2012).

H. J. Weber, L. Ruby, and G. B. Arfken, Mathematical methods for physicists (Harcourt/Academic, 2000).

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Figures (5)

Fig. 1
Fig. 1 Test and application of the G-LIA technique. (a) Michelson interferometer operating with arbitrary phase modulation ϕR in the reference arm. (b) Phase measurement obtained with the setup (a) for a sine modulation of the reference mirror. The phase of the signal field follows a triangular function monitored by capacitive sensors (thick line). The simultaneous interferometric measurements obtained with an integration time of 0.05 s are marked with circles. (c) Same setup as (2) with a gas cell in the signal arm and a tunable laser diode. (d) Example of phase resolved spectroscopy obtained with setup (c).
Fig. 2
Fig. 2 Extended G-LIA operation performed in the mid-IR. (a) Experimental setup used for testing. (b) Phase recorded when a triangular phase modulation of about 1 rad is added in the modulated signal arm. (c–f) Phase-sensitive infrared nanoscopy experiments. (c) Schematic of the experimental setup and investigated samples. (d) Amplitude and phase of the signal field scattered by the nano-probe on oxidized copper lines embedded in Si (sample 1). The phase profile along the white dashed line is plotted below (raw signal averaged on 5 lines). (e) Similar experiments performed with a CO2 laser for decreasing probe sizes as shown in the inserts. (f) Amplitude (blue), phase (gray) and topography (dashes) profiles obtained across the gold/polymer grating surface (sample 2) showing a fast signal drop when the gold-probe distance increases.
Fig. 3
Fig. 3 (a) Example of simulated relative error on the phase using G-LIA detection for increasing real values of n. The simulation was made with ϕS = π/4, Ωtint = 20π, a sampling interval equals to 2π/1000, and a = 3. (b) Background field attenuation for increasing values of a and identical background and modulated signal fields values. In this simulation, n = 30, Ωtint = 20π, and the sampling interval is equal to 2π/1000. The background contribution drops to zero for a corresponding to a zero of J0(a) and large n. (c) Simulated comparison of the signal level between G-LIA and a M-LIA approach where the two first sideband harmonics are detected (ΩA + ΩR, ΩA + 2 * ΩR)
Fig. 4
Fig. 4 Orthonormal reference signals (cosϕR, sinϕR) and their Fourier transforms for selected phase modulations ϕR(t): (a) Sawtooth with an amplitude 2π, (b) Sinusoidal with a phase amplitude a1 corresponding to the first zero of J0, and (c) Triangular with an amplitude of π/2 rad.
Fig. 5
Fig. 5 Summary table

Equations (33)

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

I det E S 2 + E R 2 + 2 E R E S cos ( ϕ S ϕ R ) .
I det I 0 + I mod ,
I mod = 2 E R E S [ cos ( ϕ S ) cos ( ϕ R ) + sin ( ϕ S ) sin ( ϕ R ) ] .
X Ω t ( I det ) = 1 Ω t int 0 Ω t int I det cos ( Ω t ) d ( Ω t ) = E R E S cos ( ϕ S )
Y Ω t ( I det ) = 1 Ω t int 0 Ω t int I det sin ( Ω t ) d ( Ω t ) = E R E S sin ( ϕ S ) .
X m Ω t ( I det ) = 2 E R E S cos ( ϕ S ) | J m ( a ) for m even 0 for m odd ,
Y m Ω t ( I det ) = 2 E R E S sin ( ϕ S ) | 0 for m even J m ( a ) for m odd ,
X ϕ R ( I det ) = 1 Ω t int 0 Ω t int I det cos ( ϕ R ) d ( Ω t ) ,
Y ϕ R ( I det ) = 1 Ω t int 0 Ω t int I det sin ( ϕ R ) d ( Ω t ) .
I mod = 2 E R E P cos ( n Ω t ) cos ( ϕ R ϕ S ) ,
I mod = E R E P cos ( n Ω t + ϕ R ϕ S ) + E R E P cos ( n Ω t ϕ R + ϕ S ) ,
I 0 = const . + E p 2 cos 2 ( n Ω t )
X n Ω t ± ϕ R ( I det ) = 1 Ω t int 0 Ω t int I det C ( t ) d ( Ω t ) E S cos ( ϕ S ) ,
Y n Ω t ± ϕ R ( I det ) = 1 Ω t int 0 Ω t int I det S ( t ) d ( Ω t ) E S sin ( ϕ S ) .
X n Ω t ± a sin ( Ω t ) ( I det ) = E R E P cos ϕ ( 1 + J 2 n ( 2 a ) + J 0 ( 2 a ) ) ,
Y n Ω t ± a sin ( Ω t ) ( I det ) = E R E P sin ϕ ( 1 J 2 n ( 2 a ) J 0 ( 2 a ) ) .
C ( t ) = e ¯ Ω A ( t ) cos ( a e ¯ Ω ( t ) )
S ( t ) = e ¯ Ω A ( t ) sin ( a e ¯ Ω ( t ) ) ,
X a sin ( Ω t ) ( I mod ) = k X E R E S cos ( ϕ S ) with k X = ( 1 + J 0 ( 2 a ) ) ,
Y a sin ( Ω t ) ( I mod ) = k Y E R E S sin ( ϕ S ) with k Y = ( 1 J 0 ( 2 a ) ) ,
X a sin ( Ω t ) ( I ˜ det ) = k ˜ X E R E S cos ( ϕ S ) with k ˜ X = ( 1 + J 0 ( 2 a ) 2 J 0 2 ( a ) )
Y a sin ( Ω t ) ( I ˜ det ) = k ˜ Y E R E S sin ( ϕ S ) with k ˜ Y = ( 1 J 0 ( 2 a ) )
X a T r ( Ω t ) ( I mod ) = k X E R E S cos ( ϕ S ) with k X = ( 1 + sin ( a ) cos ( a ) a )
Y a T r ( Ω t ) ( I mod ) = k Y E R E S sin ( ϕ S ) with k Y = ( 1 sin ( a ) cos ( a ) a )
X a T r ( Ω t ) ( I ˜ det ) = k ˜ X E R E S cos ( ϕ S ) with k ˜ X = ( 1 + sin ( a ) cos ( a ) a 2 sin 2 ( a ) a 2 )
Y a T r ( Ω t ) ( I ˜ det ) = k ˜ Y E R E S sin ( ϕ S ) with k ˜ Y = ( 1 sin ( a ) cos ( a ) a )
I mod Bg = 2 E Bg E P cos ( n Ω t ) cos ( ϕ Bg ϕ S ) .
X n Ω t ± ϕ R ( I mod Bg ) = 1 Ω t int 0 Ω t int I mod Bg C ( t ) d ( Ω t )
Y n Ω t ± ϕ R ( I mod Bg ) = 1 Ω t int 0 Ω t int I mod Bg S ( t ) d ( Ω t ) .
X = 0 t max I det cos ( n Ω t ) cos ( ϕ R ) d t and Y = 0 t max I det cos ( n Ω t ) sin ( ϕ R ) d t
X = 0 t max I det sin ( n Ω t ) cos ( ϕ R ) d t and Y = 0 t max I det sin ( n Ω t ) sin ( ϕ R ) d t
X = k X E R E s cos ( ψ ) cos ( ϕ s ) and Y = k Y E R E s cos ( ψ ) sin ( ϕ s ) ,
X = k X E R E s sin ( ψ ) cos ( ϕ s ) and Y = k Y E R E s sin ( ψ ) sin ( ϕ s ) ,

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