Abstract

A surface plasmon (SP) field excited at the metal–air interface by a TM-polarized laser and perturbed by an unpolarized, weakly absorbing laser beam leads to an understanding of the SP decay field’s contribution to specular reflection at the near field. The locally perturbed near field results in a spatial variation of the magnitude of the SP decay field due to the photo-thermal effect on the excited SP wave. The SP decay field of different magnitude interferes with the specular reflected field, affecting its polarization and phase characteristics. The changes in the resulting far field are polarimetrically analyzed to extract the polarization ellipse parameters and the phase changes in the entire plasmonic field region. The obtained results are promising for potential applications in all-optical polarization modulators and switches for optical computing.

© 2013 Optical Society of America

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2012 (3)

J. Zhang and L. Zhang, “Nanostructures for surface plasmons,” Adv. Opt. Photon. 4, 157–321 (2012).
[CrossRef]

M. Pohl, V. I. Belotelov, I. A. Akimov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, A. K. Zvezdin, D. R. Yakovlev, and M. Bayer, “Plasmonic crystals for ultrafast nanophotonics: optical switching of surface plasmon polaritons,” Phys. Rev. B 85, 081401 (2012).
[CrossRef]

P. Shankar, V. Kumar, and N. K. Viswanathan, “Plasmon-mediated vectorial topological dipole: formation and annihilation,” Opt. Lett. 37, 4233–4235 (2012).
[CrossRef]

2011 (1)

2010 (1)

G. Baffou, R. Quidant, and F. J. García de Abajo, “Nanoscale control of optical heating in complex plasmonic systems,” ACS Nano 4, 709–716 (2010).
[CrossRef]

2009 (1)

2008 (1)

L. J. Berezhinsky, L. S. Maksimenko, I. E. Matyash, S. P. Rudenko, and B. K. Serdega, “Polarization modulation spectroscopy of surface plasmon resonance,” Opt. Spectrosc. 105, 257–264 (2008).
[CrossRef]

2007 (1)

2006 (2)

W. L. Barnes, “Surface plasmon–polariton length scales: a route to sub-wavelength optics,” J. Opt. A 8, S87–S93(2006).
[CrossRef]

M. Rashidi-Huyeh and B. Palpant, “Counterintuitive thermo-optical response of metal-dielectric nanocomposite materials as a result of local electromagnetic field enhancement,” Phys. Rev. B 74, 075405 (2006).
[CrossRef]

2005 (2)

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon sub-wavelength optics,” Nature 424, 824–830 (2003).
[CrossRef]

2001 (1)

H.-P. Chiang, Y.-C. Wang, P. Leung, and W. Tse, “A theoretical model for the temperature-dependent sensitivity of the optical sensor based on surface plasmon resonance,” Opt. Commun. 188, 283–289 (2001).
[CrossRef]

2000 (1)

A. K. Nikitin, “Polarimetric detection of the photon excitation of surface plasmons,” Quantum Electron. 30, 73–77(2000).
[CrossRef]

1999 (2)

T. Velinov, M. G. Somekh, and S. Liu, “Direct far-field observation of surface-plasmon propagation by photoinduced scattering,” Appl. Phys. Lett. 75, 3908–3910 (1999).
[CrossRef]

F. I. Baida, D. V. Labeke, and J. M. Vigoureux, “Theoretical study of near-field surface plasmon excitation, propagation and diffraction,” Opt. Commun. 171, 317–331 (1999).
[CrossRef]

1994 (1)

1993 (1)

1992 (1)

S. Negm and H. Talaat, “Radiative and non-radiative decay of surface plasmons in thin metal films,” Solid State Commun. 84, 133–137 (1992).
[CrossRef]

1990 (1)

S. Herminghaus and P. Leiderer, “Surface plasmon enhanced transient thermoreflectance,” Appl. Phys. A 51, 350–353 (1990).
[CrossRef]

1988 (1)

M. van Exter and A. Lagendijk, “Ultrashort surface-plasmon and phonon dynamics,” Phys. Rev. Lett. 60, 49–52 (1988).
[CrossRef]

1985 (1)

H. Dohi, S. Tago, M. Fukui, and O. Tada, “Spatial dependence of reflected light intensity in ATR geometry: long-range surface plasmon polariton case,” Solid State Commun. 55, 1023–1026 (1985).
[CrossRef]

1976 (1)

W. P. Chen, G. Ritchie, and E. Burstein, “Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations,” Phys. Rev. Lett. 37, 993–997 (1976).
[CrossRef]

Akimov, I. A.

M. Pohl, V. I. Belotelov, I. A. Akimov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, A. K. Zvezdin, D. R. Yakovlev, and M. Bayer, “Plasmonic crystals for ultrafast nanophotonics: optical switching of surface plasmon polaritons,” Phys. Rev. B 85, 081401 (2012).
[CrossRef]

Andaloro, R. V.

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 1st ed. (North Holland, 1988).

Baffou, G.

G. Baffou, R. Quidant, and F. J. García de Abajo, “Nanoscale control of optical heating in complex plasmonic systems,” ACS Nano 4, 709–716 (2010).
[CrossRef]

Baida, F. I.

F. I. Baida, D. V. Labeke, and J. M. Vigoureux, “Theoretical study of near-field surface plasmon excitation, propagation and diffraction,” Opt. Commun. 171, 317–331 (1999).
[CrossRef]

Barnes, W. L.

W. L. Barnes, “Surface plasmon–polariton length scales: a route to sub-wavelength optics,” J. Opt. A 8, S87–S93(2006).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon sub-wavelength optics,” Nature 424, 824–830 (2003).
[CrossRef]

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 1st ed. (North Holland, 1988).

Bayer, M.

M. Pohl, V. I. Belotelov, I. A. Akimov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, A. K. Zvezdin, D. R. Yakovlev, and M. Bayer, “Plasmonic crystals for ultrafast nanophotonics: optical switching of surface plasmon polaritons,” Phys. Rev. B 85, 081401 (2012).
[CrossRef]

Belotelov, V. I.

M. Pohl, V. I. Belotelov, I. A. Akimov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, A. K. Zvezdin, D. R. Yakovlev, and M. Bayer, “Plasmonic crystals for ultrafast nanophotonics: optical switching of surface plasmon polaritons,” Phys. Rev. B 85, 081401 (2012).
[CrossRef]

Berezhinsky, L. J.

L. J. Berezhinsky, L. S. Maksimenko, I. E. Matyash, S. P. Rudenko, and B. K. Serdega, “Polarization modulation spectroscopy of surface plasmon resonance,” Opt. Spectrosc. 105, 257–264 (2008).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Brongersma, M. L.

R. Zia, M. D. Selker, and M. L. Brongersma, “Leaky and bound modes of surface plasmon waveguides,” Phys. Rev. B 71, 165431 (2005).
[CrossRef]

Burstein, E.

W. P. Chen, G. Ritchie, and E. Burstein, “Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations,” Phys. Rev. Lett. 37, 993–997 (1976).
[CrossRef]

Chen, W. P.

W. P. Chen, G. Ritchie, and E. Burstein, “Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations,” Phys. Rev. Lett. 37, 993–997 (1976).
[CrossRef]

Chiang, H.-P.

H.-P. Chiang, Y.-C. Wang, P. Leung, and W. Tse, “A theoretical model for the temperature-dependent sensitivity of the optical sensor based on surface plasmon resonance,” Opt. Commun. 188, 283–289 (2001).
[CrossRef]

Deck, R. T.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon sub-wavelength optics,” Nature 424, 824–830 (2003).
[CrossRef]

Dohi, H.

H. Dohi, S. Tago, M. Fukui, and O. Tada, “Spatial dependence of reflected light intensity in ATR geometry: long-range surface plasmon polariton case,” Solid State Commun. 55, 1023–1026 (1985).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon sub-wavelength optics,” Nature 424, 824–830 (2003).
[CrossRef]

Fukui, M.

H. Dohi, S. Tago, M. Fukui, and O. Tada, “Spatial dependence of reflected light intensity in ATR geometry: long-range surface plasmon polariton case,” Solid State Commun. 55, 1023–1026 (1985).
[CrossRef]

García de Abajo, F. J.

G. Baffou, R. Quidant, and F. J. García de Abajo, “Nanoscale control of optical heating in complex plasmonic systems,” ACS Nano 4, 709–716 (2010).
[CrossRef]

Gopal, A. V.

M. Pohl, V. I. Belotelov, I. A. Akimov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, A. K. Zvezdin, D. R. Yakovlev, and M. Bayer, “Plasmonic crystals for ultrafast nanophotonics: optical switching of surface plasmon polaritons,” Phys. Rev. B 85, 081401 (2012).
[CrossRef]

Herminghaus, S.

S. Herminghaus, M. Klopfleisch, and H. J. Schmidt, “Attenuated total reflectance as a quantum interference phenomenon,” Opt. Lett. 19, 293–295 (1994).
[CrossRef]

S. Herminghaus and P. Leiderer, “Surface plasmon enhanced transient thermoreflectance,” Appl. Phys. A 51, 350–353 (1990).
[CrossRef]

Kamiyama, T.

Kasture, S.

M. Pohl, V. I. Belotelov, I. A. Akimov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, A. K. Zvezdin, D. R. Yakovlev, and M. Bayer, “Plasmonic crystals for ultrafast nanophotonics: optical switching of surface plasmon polaritons,” Phys. Rev. B 85, 081401 (2012).
[CrossRef]

Klopfleisch, M.

Kolomenski, A.

Kolomenskii, A.

Kumar, V.

Labeke, D. V.

F. I. Baida, D. V. Labeke, and J. M. Vigoureux, “Theoretical study of near-field surface plasmon excitation, propagation and diffraction,” Opt. Commun. 171, 317–331 (1999).
[CrossRef]

Lagendijk, A.

M. van Exter and A. Lagendijk, “Ultrashort surface-plasmon and phonon dynamics,” Phys. Rev. Lett. 60, 49–52 (1988).
[CrossRef]

Leiderer, P.

S. Herminghaus and P. Leiderer, “Surface plasmon enhanced transient thermoreflectance,” Appl. Phys. A 51, 350–353 (1990).
[CrossRef]

Leung, P.

H.-P. Chiang, Y.-C. Wang, P. Leung, and W. Tse, “A theoretical model for the temperature-dependent sensitivity of the optical sensor based on surface plasmon resonance,” Opt. Commun. 188, 283–289 (2001).
[CrossRef]

Liu, S.

T. Velinov, M. G. Somekh, and S. Liu, “Direct far-field observation of surface-plasmon propagation by photoinduced scattering,” Appl. Phys. Lett. 75, 3908–3910 (1999).
[CrossRef]

Maksimenko, L. S.

L. J. Berezhinsky, L. S. Maksimenko, I. E. Matyash, S. P. Rudenko, and B. K. Serdega, “Polarization modulation spectroscopy of surface plasmon resonance,” Opt. Spectrosc. 105, 257–264 (2008).
[CrossRef]

Matyash, I. E.

L. J. Berezhinsky, L. S. Maksimenko, I. E. Matyash, S. P. Rudenko, and B. K. Serdega, “Polarization modulation spectroscopy of surface plasmon resonance,” Opt. Spectrosc. 105, 257–264 (2008).
[CrossRef]

Negm, S.

S. Negm and H. Talaat, “Radiative and non-radiative decay of surface plasmons in thin metal films,” Solid State Commun. 84, 133–137 (1992).
[CrossRef]

Nikitin, A. K.

A. K. Nikitin, “Polarimetric detection of the photon excitation of surface plasmons,” Quantum Electron. 30, 73–77(2000).
[CrossRef]

Noel, J.

Okamoto, T.

Palpant, B.

M. Rashidi-Huyeh and B. Palpant, “Counterintuitive thermo-optical response of metal-dielectric nanocomposite materials as a result of local electromagnetic field enhancement,” Phys. Rev. B 74, 075405 (2006).
[CrossRef]

Peng, S.

Pohl, M.

M. Pohl, V. I. Belotelov, I. A. Akimov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, A. K. Zvezdin, D. R. Yakovlev, and M. Bayer, “Plasmonic crystals for ultrafast nanophotonics: optical switching of surface plasmon polaritons,” Phys. Rev. B 85, 081401 (2012).
[CrossRef]

Quidant, R.

G. Baffou, R. Quidant, and F. J. García de Abajo, “Nanoscale control of optical heating in complex plasmonic systems,” ACS Nano 4, 709–716 (2010).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

Rashidi-Huyeh, M.

M. Rashidi-Huyeh and B. Palpant, “Counterintuitive thermo-optical response of metal-dielectric nanocomposite materials as a result of local electromagnetic field enhancement,” Phys. Rev. B 74, 075405 (2006).
[CrossRef]

Ritchie, G.

W. P. Chen, G. Ritchie, and E. Burstein, “Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations,” Phys. Rev. Lett. 37, 993–997 (1976).
[CrossRef]

Rudenko, S. P.

L. J. Berezhinsky, L. S. Maksimenko, I. E. Matyash, S. P. Rudenko, and B. K. Serdega, “Polarization modulation spectroscopy of surface plasmon resonance,” Opt. Spectrosc. 105, 257–264 (2008).
[CrossRef]

Schmidt, H. J.

Schuessler, H.

Selker, M. D.

R. Zia, M. D. Selker, and M. L. Brongersma, “Leaky and bound modes of surface plasmon waveguides,” Phys. Rev. B 71, 165431 (2005).
[CrossRef]

Serdega, B. K.

L. J. Berezhinsky, L. S. Maksimenko, I. E. Matyash, S. P. Rudenko, and B. K. Serdega, “Polarization modulation spectroscopy of surface plasmon resonance,” Opt. Spectrosc. 105, 257–264 (2008).
[CrossRef]

Shankar, P.

Simon, H. J.

Somekh, M. G.

T. Velinov, M. G. Somekh, and S. Liu, “Direct far-field observation of surface-plasmon propagation by photoinduced scattering,” Appl. Phys. Lett. 75, 3908–3910 (1999).
[CrossRef]

Tada, O.

H. Dohi, S. Tago, M. Fukui, and O. Tada, “Spatial dependence of reflected light intensity in ATR geometry: long-range surface plasmon polariton case,” Solid State Commun. 55, 1023–1026 (1985).
[CrossRef]

Tago, S.

H. Dohi, S. Tago, M. Fukui, and O. Tada, “Spatial dependence of reflected light intensity in ATR geometry: long-range surface plasmon polariton case,” Solid State Commun. 55, 1023–1026 (1985).
[CrossRef]

Talaat, H.

S. Negm and H. Talaat, “Radiative and non-radiative decay of surface plasmons in thin metal films,” Solid State Commun. 84, 133–137 (1992).
[CrossRef]

Tse, W.

H.-P. Chiang, Y.-C. Wang, P. Leung, and W. Tse, “A theoretical model for the temperature-dependent sensitivity of the optical sensor based on surface plasmon resonance,” Opt. Commun. 188, 283–289 (2001).
[CrossRef]

van Exter, M.

M. van Exter and A. Lagendijk, “Ultrashort surface-plasmon and phonon dynamics,” Phys. Rev. Lett. 60, 49–52 (1988).
[CrossRef]

Velinov, T.

T. Velinov, M. G. Somekh, and S. Liu, “Direct far-field observation of surface-plasmon propagation by photoinduced scattering,” Appl. Phys. Lett. 75, 3908–3910 (1999).
[CrossRef]

Vengurlekar, A. S.

M. Pohl, V. I. Belotelov, I. A. Akimov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, A. K. Zvezdin, D. R. Yakovlev, and M. Bayer, “Plasmonic crystals for ultrafast nanophotonics: optical switching of surface plasmon polaritons,” Phys. Rev. B 85, 081401 (2012).
[CrossRef]

Vigoureux, J. M.

F. I. Baida, D. V. Labeke, and J. M. Vigoureux, “Theoretical study of near-field surface plasmon excitation, propagation and diffraction,” Opt. Commun. 171, 317–331 (1999).
[CrossRef]

Viswanathan, N. K.

Wang, Y.-C.

H.-P. Chiang, Y.-C. Wang, P. Leung, and W. Tse, “A theoretical model for the temperature-dependent sensitivity of the optical sensor based on surface plasmon resonance,” Opt. Commun. 188, 283–289 (2001).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Yakovlev, D. R.

M. Pohl, V. I. Belotelov, I. A. Akimov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, A. K. Zvezdin, D. R. Yakovlev, and M. Bayer, “Plasmonic crystals for ultrafast nanophotonics: optical switching of surface plasmon polaritons,” Phys. Rev. B 85, 081401 (2012).
[CrossRef]

Yamaguchi, I.

Zhang, J.

Zhang, L.

Zia, R.

R. Zia, M. D. Selker, and M. L. Brongersma, “Leaky and bound modes of surface plasmon waveguides,” Phys. Rev. B 71, 165431 (2005).
[CrossRef]

Zvezdin, A. K.

M. Pohl, V. I. Belotelov, I. A. Akimov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, A. K. Zvezdin, D. R. Yakovlev, and M. Bayer, “Plasmonic crystals for ultrafast nanophotonics: optical switching of surface plasmon polaritons,” Phys. Rev. B 85, 081401 (2012).
[CrossRef]

ACS Nano (1)

G. Baffou, R. Quidant, and F. J. García de Abajo, “Nanoscale control of optical heating in complex plasmonic systems,” ACS Nano 4, 709–716 (2010).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (2)

Appl. Phys. A (1)

S. Herminghaus and P. Leiderer, “Surface plasmon enhanced transient thermoreflectance,” Appl. Phys. A 51, 350–353 (1990).
[CrossRef]

Appl. Phys. Lett. (1)

T. Velinov, M. G. Somekh, and S. Liu, “Direct far-field observation of surface-plasmon propagation by photoinduced scattering,” Appl. Phys. Lett. 75, 3908–3910 (1999).
[CrossRef]

J. Opt. A (1)

W. L. Barnes, “Surface plasmon–polariton length scales: a route to sub-wavelength optics,” J. Opt. A 8, S87–S93(2006).
[CrossRef]

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

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon sub-wavelength optics,” Nature 424, 824–830 (2003).
[CrossRef]

Opt. Commun. (2)

H.-P. Chiang, Y.-C. Wang, P. Leung, and W. Tse, “A theoretical model for the temperature-dependent sensitivity of the optical sensor based on surface plasmon resonance,” Opt. Commun. 188, 283–289 (2001).
[CrossRef]

F. I. Baida, D. V. Labeke, and J. M. Vigoureux, “Theoretical study of near-field surface plasmon excitation, propagation and diffraction,” Opt. Commun. 171, 317–331 (1999).
[CrossRef]

Opt. Lett. (4)

Opt. Spectrosc. (1)

L. J. Berezhinsky, L. S. Maksimenko, I. E. Matyash, S. P. Rudenko, and B. K. Serdega, “Polarization modulation spectroscopy of surface plasmon resonance,” Opt. Spectrosc. 105, 257–264 (2008).
[CrossRef]

Phys. Rev. B (3)

M. Pohl, V. I. Belotelov, I. A. Akimov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, A. K. Zvezdin, D. R. Yakovlev, and M. Bayer, “Plasmonic crystals for ultrafast nanophotonics: optical switching of surface plasmon polaritons,” Phys. Rev. B 85, 081401 (2012).
[CrossRef]

R. Zia, M. D. Selker, and M. L. Brongersma, “Leaky and bound modes of surface plasmon waveguides,” Phys. Rev. B 71, 165431 (2005).
[CrossRef]

M. Rashidi-Huyeh and B. Palpant, “Counterintuitive thermo-optical response of metal-dielectric nanocomposite materials as a result of local electromagnetic field enhancement,” Phys. Rev. B 74, 075405 (2006).
[CrossRef]

Phys. Rev. Lett. (2)

M. van Exter and A. Lagendijk, “Ultrashort surface-plasmon and phonon dynamics,” Phys. Rev. Lett. 60, 49–52 (1988).
[CrossRef]

W. P. Chen, G. Ritchie, and E. Burstein, “Excitation of surface electromagnetic waves in attenuated total-reflection prism configurations,” Phys. Rev. Lett. 37, 993–997 (1976).
[CrossRef]

Quantum Electron. (1)

A. K. Nikitin, “Polarimetric detection of the photon excitation of surface plasmons,” Quantum Electron. 30, 73–77(2000).
[CrossRef]

Solid State Commun. (2)

S. Negm and H. Talaat, “Radiative and non-radiative decay of surface plasmons in thin metal films,” Solid State Commun. 84, 133–137 (1992).
[CrossRef]

H. Dohi, S. Tago, M. Fukui, and O. Tada, “Spatial dependence of reflected light intensity in ATR geometry: long-range surface plasmon polariton case,” Solid State Commun. 55, 1023–1026 (1985).
[CrossRef]

Other (3)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 1st ed. (North Holland, 1988).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic of the Kretschmann–Raether geometry experimental setup. P, GT polarizer; HWP, Half-wave plate; QWP, quarter-wave plates; and D, detector (power meter, CCD). (b) Tilted view of the experimental setup showing the geometrical coordinates and footprint of the exciting laser. (c) Characteristic (R versus θi) surface plasmon resonance (SPR) curve measured for 45nm Au film. Experimental data and theoretical curve fit are shown.

Fig. 2.
Fig. 2.

(a) 3D plot of relative change of reflected far-field intensity (ΔR) as a function of Ar+ laser exposure positions in the xy plane of the footprint. (b) Reflected far-field intensity (R) plotted as a function of Ar+ laser exposure position on the x axis for different Ar+ laser power.

Fig. 3.
Fig. 3.

Line profile of far-field intensity distribution measured from CCD images for different Ar+ laser exposure positions. open square, no irradiation; open triangle, off-center irradiation; and open circle, center irradiation. (i), (ii), and (iii) are the corresponding CCD images of the reflected beam.

Fig. 4.
Fig. 4.

Behavior of polarization parameters corresponding to three selected scan positions: 0, 1.2, and 1.7 mm on the y axis plotted as functions of the Ar+ laser exposure position along the x axis. (a) Ellipse orientation (ψ). (b) Ellipticity (ε). (c1) and (c2) Phase (ϕ) plots corresponding to 0, 1.7, and 1.2 mm scan positions, respectively. The approximate position of the elliptical footprint of the He–Ne laser on the metal–air interface visualized as a colored ellipse in the xy plane.

Equations (3)

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rpmap=[rpmp+rmapexp(2ikzmd)1+rpmprmapexp(2ikzmd)];R=|rpmap|2
rikp=[(kziεikzkεk)/(kziεi+kzkεk)];kzi=[εi(ω/c)2kx2]1/2,
kspp=k0εpεmεp+εm,

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