Abstract

We propose a scheme for high precision position sensing based on coherent perfect absorption (CPA) in a five-layered structure comprising three layers of metal-dielectric composites and two spacer (air) layers. Both the outermost interfaces of the five layered medium are irradiated by two identical coherent light waves at the same angle of incidence. We first investigate the occurrence of CPA in a symmetric layered structure as a function of different system parameters for oblique incidence. Thereafter, by shifting the middle layer, beginning from one end of the structure to the other, we observe the periodic occurrence of extremely narrow CPA resonances at several positions of the middle layer. Moreover this phenomenon is seen to recur even at many other wavelengths. We discuss how the position sensitivity of this phenomenon can be utilized for designing a CPA based high precision position sensing device.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. J. Militky, M. Kadulova, and P. Hlubina, “Highly sensitive displacement measurement based on spectral interferometry and Vernier effect,” Opt. Commun. 366, 335–339 (2016).
    [Crossref]
  2. M. M. Brundavanam, N. K. Viswanathan, and D. N. Rao, “Nonodisplacement measurement using spectral shift in a white-light interferometer,” Appl. Opt. 47(34), 6334–6339 (2008).
    [Crossref] [PubMed]
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    [Crossref]
  5. G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photon. 4(4), 441–471 (2012).
    [Crossref]
  6. Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  23. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983) p. 77.
  24. W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010) p. 25.
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    [Crossref]
  26. E.D. Palik, Handbook of Optical Constant of Solids (Academic, 1998) p. 81.
  27. P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, 1988) p. 83.
  28. M. Born and E. Wolf, Principle of Optics, 7th ed. (Cambridge University, 2005) p. 75.

2016 (2)

J. Militky, M. Kadulova, and P. Hlubina, “Highly sensitive displacement measurement based on spectral interferometry and Vernier effect,” Opt. Commun. 366, 335–339 (2016).
[Crossref]

W. Zhu, F. Xiao, M. Kang, and M. Premaratne, “Coherent perfect absorption in an all-dielectric metasurface,” Appl. Phy. Lett. 108, 121901 (2016).
[Crossref]

2015 (2)

S. Dey, “Coherent perfect absorption using Gaussian beams,” Opt. Commun. 356, 515–521 (2015).
[Crossref]

Y. Fan, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

2014 (1)

2012 (5)

2011 (3)

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[Crossref] [PubMed]

J. Hao, L. Zhou, and M. Qiu, “Nearly total absorption of light and heat generation by plasmonic metamaterials,” Phys. Rev. B 83, 165107 (2011).
[Crossref]

J. Sun, L. Liu, G. Dong, and J. Zhou, “An extremely broad band metamaterial absorber based on destructive interference,” Opt. Express 19, 21155-21162 (2011).
[Crossref] [PubMed]

2010 (4)

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010).
[Crossref] [PubMed]

X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near unity absorbance,” Phys. Rev. Lett. 104, 207403 (2010).
[Crossref]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

C. F. Gmachl, “Suckers for light,” Nature 467, 37–39 (2010).
[Crossref] [PubMed]

2008 (3)

M. M. Brundavanam, N. K. Viswanathan, and D. N. Rao, “Nonodisplacement measurement using spectral shift in a white-light interferometer,” Appl. Opt. 47(34), 6334–6339 (2008).
[Crossref] [PubMed]

G. Berkovic, E. Shafir, M. A. Golub, M. Bril, and V. Shurman, “Multiple-fiber and multiple wavelength confocal sensing with diffractive optical elements,” IEEE Sens. J. 8(7), 1089–1092 (2008).
[Crossref]

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
[Crossref] [PubMed]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Agarwal, G. S.

Bakke, T.

T. Bakke and I. R. Johansen, “PZT micromirror with integrated piezoresistive position sensors,” in 2012 International Conference on Optical MEMS and Nanophotonics (2012), paper 6318868.

Berkovic, G.

G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photon. 4(4), 441–471 (2012).
[Crossref]

G. Berkovic, E. Shafir, M. A. Golub, M. Bril, and V. Shurman, “Multiple-fiber and multiple wavelength confocal sensing with diffractive optical elements,” IEEE Sens. J. 8(7), 1089–1092 (2008).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983) p. 77.

Born, M.

M. Born and E. Wolf, Principle of Optics, 7th ed. (Cambridge University, 2005) p. 75.

Bril, M.

G. Berkovic, E. Shafir, M. A. Golub, M. Bril, and V. Shurman, “Multiple-fiber and multiple wavelength confocal sensing with diffractive optical elements,” IEEE Sens. J. 8(7), 1089–1092 (2008).
[Crossref]

Brundavanam, M. M.

Cai, W.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010) p. 25.

Cao, H.

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
[Crossref] [PubMed]

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
[Crossref] [PubMed]

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

Chong, Y.

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
[Crossref] [PubMed]

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
[Crossref] [PubMed]

Chong, Y. D.

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Dey, S.

S. Dey, “Coherent perfect absorption using Gaussian beams,” Opt. Commun. 356, 515–521 (2015).
[Crossref]

S. Dey and S. Singh, “Coherent perfect absorption with Gaussian beams,” in 2013 Workshop on Recent Advances in Photonics, (2013), paper 6917665.

Dong, G.

Duttagupta, S.

Fan, Y.

Y. Fan, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Feng, Q.

Ge, L.

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

Giessen, H.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010).
[Crossref] [PubMed]

Gmachl, C. F.

C. F. Gmachl, “Suckers for light,” Nature 467, 37–39 (2010).
[Crossref] [PubMed]

Golub, M. A.

G. Berkovic, E. Shafir, M. A. Golub, M. Bril, and V. Shurman, “Multiple-fiber and multiple wavelength confocal sensing with diffractive optical elements,” IEEE Sens. J. 8(7), 1089–1092 (2008).
[Crossref]

Gupta, S. D.

Hao, J.

J. Hao, L. Zhou, and M. Qiu, “Nearly total absorption of light and heat generation by plasmonic metamaterials,” Phys. Rev. B 83, 165107 (2011).
[Crossref]

Hentschel, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010).
[Crossref] [PubMed]

Hlubina, P.

J. Militky, M. Kadulova, and P. Hlubina, “Highly sensitive displacement measurement based on spectral interferometry and Vernier effect,” Opt. Commun. 366, 335–339 (2016).
[Crossref]

Hu, C.

Huang, C.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983) p. 77.

Johansen, I. R.

T. Bakke and I. R. Johansen, “PZT micromirror with integrated piezoresistive position sensors,” in 2012 International Conference on Optical MEMS and Nanophotonics (2012), paper 6318868.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Kadulova, M.

J. Militky, M. Kadulova, and P. Hlubina, “Highly sensitive displacement measurement based on spectral interferometry and Vernier effect,” Opt. Commun. 366, 335–339 (2016).
[Crossref]

Kang, M.

W. Zhu, F. Xiao, M. Kang, and M. Premaratne, “Coherent perfect absorption in an all-dielectric metasurface,” Appl. Phy. Lett. 108, 121901 (2016).
[Crossref]

Landy, N. I.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
[Crossref] [PubMed]

Liu, L.

Liu, N.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010).
[Crossref] [PubMed]

Liu, X.

X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near unity absorbance,” Phys. Rev. Lett. 104, 207403 (2010).
[Crossref]

Luo, X.

Ma, X.

Martin, O. J. F.

Mesch, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010).
[Crossref] [PubMed]

Militky, J.

J. Militky, M. Kadulova, and P. Hlubina, “Highly sensitive displacement measurement based on spectral interferometry and Vernier effect,” Opt. Commun. 366, 335–339 (2016).
[Crossref]

Mock, J. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
[Crossref] [PubMed]

Noh, H.

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
[Crossref] [PubMed]

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
[Crossref] [PubMed]

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[Crossref] [PubMed]

Padilla, W. J.

X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near unity absorbance,” Phys. Rev. Lett. 104, 207403 (2010).
[Crossref]

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
[Crossref] [PubMed]

Palik, E.D.

E.D. Palik, Handbook of Optical Constant of Solids (Academic, 1998) p. 81.

Premaratne, M.

W. Zhu, F. Xiao, M. Kang, and M. Premaratne, “Coherent perfect absorption in an all-dielectric metasurface,” Appl. Phy. Lett. 108, 121901 (2016).
[Crossref]

Pu, M.

Qiu, M.

J. Hao, L. Zhou, and M. Qiu, “Nearly total absorption of light and heat generation by plasmonic metamaterials,” Phys. Rev. B 83, 165107 (2011).
[Crossref]

Rao, D. N.

Sajuyigbe, S.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
[Crossref] [PubMed]

Shafir, E.

G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photon. 4(4), 441–471 (2012).
[Crossref]

G. Berkovic, E. Shafir, M. A. Golub, M. Bril, and V. Shurman, “Multiple-fiber and multiple wavelength confocal sensing with diffractive optical elements,” IEEE Sens. J. 8(7), 1089–1092 (2008).
[Crossref]

Shalaev, V.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010) p. 25.

Shurman, V.

G. Berkovic, E. Shafir, M. A. Golub, M. Bril, and V. Shurman, “Multiple-fiber and multiple wavelength confocal sensing with diffractive optical elements,” IEEE Sens. J. 8(7), 1089–1092 (2008).
[Crossref]

Singh, S.

S. Dey and S. Singh, “Coherent perfect absorption with Gaussian beams,” in 2013 Workshop on Recent Advances in Photonics, (2013), paper 6917665.

Smith, D. R.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
[Crossref] [PubMed]

Starr, A. F.

X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near unity absorbance,” Phys. Rev. Lett. 104, 207403 (2010).
[Crossref]

Starr, T.

X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near unity absorbance,” Phys. Rev. Lett. 104, 207403 (2010).
[Crossref]

Stone, A. D.

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
[Crossref] [PubMed]

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
[Crossref] [PubMed]

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

Sun, J.

Viswanathan, N. K.

Wan, W.

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[Crossref] [PubMed]

Wang, C.

Wang, M.

Weiss, T.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010).
[Crossref] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principle of Optics, 7th ed. (Cambridge University, 2005) p. 75.

Xiao, F.

W. Zhu, F. Xiao, M. Kang, and M. Premaratne, “Coherent perfect absorption in an all-dielectric metasurface,” Appl. Phy. Lett. 108, 121901 (2016).
[Crossref]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, 1988) p. 83.

Zhang, J.

Zhao, Z.

Zhou, J.

Zhou, L.

J. Hao, L. Zhou, and M. Qiu, “Nearly total absorption of light and heat generation by plasmonic metamaterials,” Phys. Rev. B 83, 165107 (2011).
[Crossref]

Zhu, W.

W. Zhu, F. Xiao, M. Kang, and M. Premaratne, “Coherent perfect absorption in an all-dielectric metasurface,” Appl. Phy. Lett. 108, 121901 (2016).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phy. Lett. (1)

W. Zhu, F. Xiao, M. Kang, and M. Premaratne, “Coherent perfect absorption in an all-dielectric metasurface,” Appl. Phy. Lett. 108, 121901 (2016).
[Crossref]

IEEE Sens. J. (1)

G. Berkovic, E. Shafir, M. A. Golub, M. Bril, and V. Shurman, “Multiple-fiber and multiple wavelength confocal sensing with diffractive optical elements,” IEEE Sens. J. 8(7), 1089–1092 (2008).
[Crossref]

Nano Lett. (1)

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010).
[Crossref] [PubMed]

Nature (1)

C. F. Gmachl, “Suckers for light,” Nature 467, 37–39 (2010).
[Crossref] [PubMed]

Opt. Commun. (2)

J. Militky, M. Kadulova, and P. Hlubina, “Highly sensitive displacement measurement based on spectral interferometry and Vernier effect,” Opt. Commun. 366, 335–339 (2016).
[Crossref]

S. Dey, “Coherent perfect absorption using Gaussian beams,” Opt. Commun. 356, 515–521 (2015).
[Crossref]

Opt. Express (4)

Phys. Rev. B (2)

J. Hao, L. Zhou, and M. Qiu, “Nearly total absorption of light and heat generation by plasmonic metamaterials,” Phys. Rev. B 83, 165107 (2011).
[Crossref]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Phys. Rev. Lett. (5)

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
[Crossref] [PubMed]

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
[Crossref] [PubMed]

X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near unity absorbance,” Phys. Rev. Lett. 104, 207403 (2010).
[Crossref]

Sci. Rep. (1)

Y. Fan, “Tunable mid-infrared coherent perfect absorption in a graphene meta-surface,” Sci. Rep. 5, 13956 (2015).
[Crossref] [PubMed]

Science (1)

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[Crossref] [PubMed]

Other (7)

S. Dey and S. Singh, “Coherent perfect absorption with Gaussian beams,” in 2013 Workshop on Recent Advances in Photonics, (2013), paper 6917665.

T. Bakke and I. R. Johansen, “PZT micromirror with integrated piezoresistive position sensors,” in 2012 International Conference on Optical MEMS and Nanophotonics (2012), paper 6318868.

E.D. Palik, Handbook of Optical Constant of Solids (Academic, 1998) p. 81.

P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, 1988) p. 83.

M. Born and E. Wolf, Principle of Optics, 7th ed. (Cambridge University, 2005) p. 75.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983) p. 77.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010) p. 25.

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Figures (10)

Fig. 1
Fig. 1 Schematic view of the layered medium. Two identical light waves focus (or incident) on opposite interfaces of the system on CM and air layered medium. Here, rL (tL) and rR (tR) are reflection (transmission) coefficient at the left hand side (LHS) and right hand side (RHS) of the interfaces respectively. Various layers thickness (are not scaled) and the coordinate systems are shown in the figure.
Fig. 2
Fig. 2 First and second rows of the figure depict the real (a, b and e) and imaginary (b, d and f) values of permittivity of respective medium. First, second and third columns show the permittivity of gold (Au) (a and b), silica (SiO2) (c and d) and composite medium (CM) (e and f with volume fraction fm = 0.00641) in the optical region respectively.
Fig. 3
Fig. 3 (a) Plot of Log10|SI| as a function of volume fraction (fm) for a fixed wavelength, λ = 590.03 nm. (b) Absolute values of the amplitude of reflection (|rL|) (solid line) and transmission (|tR|) (dash line) coefficients and (c) phase difference, ∆ϕ (units of π) between the right transmitted ( Φ t R ) and left reflected ( Φ t L ) plane waves.
Fig. 4
Fig. 4 Variation of Log10 |SI| as a function of d2 (width of spacer layer) for fixed values of wavelength, λ (= 590.03 nm) and metal volume fraction, fm (=0.00641). Note that width d2 of spacer layer is actually the position of CM layer d3 from the first CM layer d1. Also shown is the case (red dashed line) when widths of all three CM layers are unequal, i.e., d1d3d5.
Fig. 5
Fig. 5 (a) Plot of log10|SI| as a function of wavelength (λ) for a fixed value of volume fraction fm = 0.00641. (b) Absolute values of reflected (|rL|) (solid line) and transmitted (|tR|) (dash line) amplitudes and (c) phase difference, ∆Φ (scale of π) between the right transmitted ( Φ t R ) and left reflected ( Φ t L ) plane waves.
Fig. 6
Fig. 6 Scattering Log10|SI| plotted as functions of (a) wavelength (λ) and spacing d2 caused by translation of middle layer d3 relative to first (d1) layer. (b) Log10|SI| plotted as a functions of function of the position of middle layer (d2). Here, volume fraction fm = 0.00641, angle of incidence θi = 45° and CPA observed at λG = 587.4 nm, λY = 590.0 nm, λO = 610.5 nm and λR = 614.0 nm.
Fig. 7
Fig. 7 Log10|SI| plotted as a function of position of the middle d3 layer for 45° angles of incidence.
Fig. 8
Fig. 8 Variation of scattering intensity ((Log10|SI|) as a function of (a) wavelength λ and (b) position of middle layer relative to d1. Width of CM layers is d1 = d3 = d5 = 0.1 mm and total spacer width is d2 + d4 = 0.02 mm. The angle of incidence θi = 45°, λ = 644 nm and fm = 0.001164. Here HWHM of CPA resonances is around 10 nm.
Fig. 9
Fig. 9 log10|SI| is plotted as a function of position of the middle layer for normal incidence (dash line, λ = 589.1 nm and fm = 0.00552 and oblique incidence (solid line, λ = 590 nm and fm = 0.00641)).
Fig. 10
Fig. 10 Top view of proposed setup for high precision position sensing device based on CPA in multilayered structure. BS1, BS2 and BS3 are 50% - 50% beam splitters, M is a mirror, PD1 and PD2 are photodetectors. One end of the piezoelectric transducer (PZT) is rigidly fixed to the device wall while the other movable end is in contact with both the device whose position is to be monitored and the central movable CM slab d3 mounted on a ring. A narrow slots is cut along the length of the wall of the tube so that the shaft connected through it to the movable central CM slab can move freely along the length of the tube between the other two CM slabs d1 and d5 fixed to both ends of the CM tube.

Equations (4)

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ϵ C M = 1 4 { ( 3 f 1 1 ) ϵ 1 + ( 3 f 2 1 ) ϵ 2 ± [ ( 3 f 1 1 ) ϵ 1 + ( 3 f 2 1 ) ϵ 2 ] 2 + 8 ϵ 1 ϵ 2 } ,
D j ( z ) = [ e i k j z z e i k j z z k j z k 0 e i k j z z k j z k 0 e i k j z z ]
[ α i + α i ] = [ D i 1 ( 0 ) D 1 ( 0 ) ] [ D 1 1 ( d 1 ) D 2 ( d 1 ) ] [ D 5 1 ( d ) D f ( d ) ] [ α f + 0 ] = [ M 11 M 21 ] α f +
[ α f + α f ] = [ D f 1 ( d ) D 5 ( d ) ] [ D 5 1 ( d d 5 ) D 4 ( d d 5 ) ] [ D 1 1 ( 0 ) D i ( 0 ) ] [ 0 α i ] = [ M 12 M 22 ] α i

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