Abstract

We investigate the polarizing properties of periodic array of silver nanoellipsoids placed on top of a planar LED structure. The response of the particles is calculated with the periodic layered Green’s tensor in the electrostatic limit with dynamic depolarization and radiation damping corrections. We investigate the degree of polarization and the total extracted power spectra depending on parameters like lattice period, axial ratio and particle size. The proposed model is applicable over a wide range of parameters and appropriate to optimize the given structure. The optimization procedure shows that particles in the size range of 100 nm are optimal to reach 50% degree of polarization and less than 15% absorbance for an uncollimated and unpolarized dipole source.

© 2014 Optical Society of America

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  1. R. Otte, L. P. de Joung, and A. H. M. van Roermund, Low-power Wireless Infrared Communications (Kluwer Academic Publishers, 1999).
    [CrossRef]
  2. J. C. Ramella-Roman, K. Lee, S. A. Prahl, and S. L. Jacques, “Polarized light imaging with a handheld camera,” Proc. SPIE 5068, 284–293 (2003).
    [CrossRef]
  3. J. S. Baba, S. S. Gleason, J. S. Goddard, and J. M. Paulus, “Application of polarization for optical motion-registered SPECT functional imaging of tumors in mice,” Proc. SPIE 5702, 97–103 (2005).
    [CrossRef]
  4. P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley, Canada, 1999).
  5. M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett. 91, 051117 (2007).
    [CrossRef]
  6. J. H. Oh, S. J. Yang, and Y. R. Do, “Polarized white light from LEDs using remote-phosphor layer sandwiched between reflective polarizer and light-recycling dichroic filter,” Opt. Express 21, A765–A773 (2013).
    [CrossRef] [PubMed]
  7. Ö. Sepsi, I. Szanda, and P. Koppa, “Investigation of polarized light emitting diodes with integrated wire grid polarizer,” Opt. Express 18, 14547–14552 (2010).
    [CrossRef] [PubMed]
  8. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
    [CrossRef]
  9. S. G. Moiseev, “Thin-film polarizer made of heterogeneous medium with uniformly oriented silver nanoparticles,” Appl. Phys. A 103, 775–777 (2011).
    [CrossRef]
  10. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
    [CrossRef]
  11. B. Gallinet, A. M. Kern, and O. J. F. Martin, “Accurate and versatile modeling of electromagnetic scattering on periodic nanostructures with a surface integral approach,” J. Opt. Soc. Am. A 27, 2261–2271 (2010).
    [CrossRef]
  12. M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
    [CrossRef]
  13. U. Kreibig, “Electronic properties of small silver particles, the optical constant and their temperature dependence,” J. Phys. F: Metal Phys 4, 999 (1974).
    [CrossRef]
  14. K. Kambe, “Theory of Electron Diffraction by Crystals. Green’s function and integral equation,” Z. Naturforschg. 22a, 422–431 (1967).
  15. N. A. Sanford, A. Munkholm, M. R. Krames, A. Shapiro, I. Levin, A. V. Davydov, S. Sayan, L. S. Wielunski, and T. E. Madey, “Refractive index and birefringence of InxGa1-xN films grown by MOCVD,” phys. stat. sol. (C) 2, 2783–2786 (2005).
    [CrossRef]
  16. L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
    [CrossRef]

2013

2011

S. G. Moiseev, “Thin-film polarizer made of heterogeneous medium with uniformly oriented silver nanoparticles,” Appl. Phys. A 103, 775–777 (2011).
[CrossRef]

2010

2007

M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett. 91, 051117 (2007).
[CrossRef]

2005

J. S. Baba, S. S. Gleason, J. S. Goddard, and J. M. Paulus, “Application of polarization for optical motion-registered SPECT functional imaging of tumors in mice,” Proc. SPIE 5702, 97–103 (2005).
[CrossRef]

N. A. Sanford, A. Munkholm, M. R. Krames, A. Shapiro, I. Levin, A. V. Davydov, S. Sayan, L. S. Wielunski, and T. E. Madey, “Refractive index and birefringence of InxGa1-xN films grown by MOCVD,” phys. stat. sol. (C) 2, 2783–2786 (2005).
[CrossRef]

2003

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

J. C. Ramella-Roman, K. Lee, S. A. Prahl, and S. L. Jacques, “Polarized light imaging with a handheld camera,” Proc. SPIE 5068, 284–293 (2003).
[CrossRef]

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

2000

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[CrossRef]

1974

U. Kreibig, “Electronic properties of small silver particles, the optical constant and their temperature dependence,” J. Phys. F: Metal Phys 4, 999 (1974).
[CrossRef]

1967

K. Kambe, “Theory of Electron Diffraction by Crystals. Green’s function and integral equation,” Z. Naturforschg. 22a, 422–431 (1967).

Baba, J. S.

J. S. Baba, S. S. Gleason, J. S. Goddard, and J. M. Paulus, “Application of polarization for optical motion-registered SPECT functional imaging of tumors in mice,” Proc. SPIE 5702, 97–103 (2005).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Chhajed, S.

M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett. 91, 051117 (2007).
[CrossRef]

Cho, J.

M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett. 91, 051117 (2007).
[CrossRef]

Coronado, E.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Davydov, A. V.

N. A. Sanford, A. Munkholm, M. R. Krames, A. Shapiro, I. Levin, A. V. Davydov, S. Sayan, L. S. Wielunski, and T. E. Madey, “Refractive index and birefringence of InxGa1-xN films grown by MOCVD,” phys. stat. sol. (C) 2, 2783–2786 (2005).
[CrossRef]

de Joung, L. P.

R. Otte, L. P. de Joung, and A. H. M. van Roermund, Low-power Wireless Infrared Communications (Kluwer Academic Publishers, 1999).
[CrossRef]

Do, Y. R.

Gallinet, B.

Gay-Balmaz, P.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[CrossRef]

Gleason, S. S.

J. S. Baba, S. S. Gleason, J. S. Goddard, and J. M. Paulus, “Application of polarization for optical motion-registered SPECT functional imaging of tumors in mice,” Proc. SPIE 5702, 97–103 (2005).
[CrossRef]

Goddard, J. S.

J. S. Baba, S. S. Gleason, J. S. Goddard, and J. M. Paulus, “Application of polarization for optical motion-registered SPECT functional imaging of tumors in mice,” Proc. SPIE 5702, 97–103 (2005).
[CrossRef]

Gu, C.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley, Canada, 1999).

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Jacques, S. L.

J. C. Ramella-Roman, K. Lee, S. A. Prahl, and S. L. Jacques, “Polarized light imaging with a handheld camera,” Proc. SPIE 5068, 284–293 (2003).
[CrossRef]

Kambe, K.

K. Kambe, “Theory of Electron Diffraction by Crystals. Green’s function and integral equation,” Z. Naturforschg. 22a, 422–431 (1967).

Kelly, K. L.

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Kern, A. M.

Kim, J. K.

M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett. 91, 051117 (2007).
[CrossRef]

Koppa, P.

Krames, M. R.

N. A. Sanford, A. Munkholm, M. R. Krames, A. Shapiro, I. Levin, A. V. Davydov, S. Sayan, L. S. Wielunski, and T. E. Madey, “Refractive index and birefringence of InxGa1-xN films grown by MOCVD,” phys. stat. sol. (C) 2, 2783–2786 (2005).
[CrossRef]

Kreibig, U.

U. Kreibig, “Electronic properties of small silver particles, the optical constant and their temperature dependence,” J. Phys. F: Metal Phys 4, 999 (1974).
[CrossRef]

Lee, K.

J. C. Ramella-Roman, K. Lee, S. A. Prahl, and S. L. Jacques, “Polarized light imaging with a handheld camera,” Proc. SPIE 5068, 284–293 (2003).
[CrossRef]

Levin, I.

N. A. Sanford, A. Munkholm, M. R. Krames, A. Shapiro, I. Levin, A. V. Davydov, S. Sayan, L. S. Wielunski, and T. E. Madey, “Refractive index and birefringence of InxGa1-xN films grown by MOCVD,” phys. stat. sol. (C) 2, 2783–2786 (2005).
[CrossRef]

Madey, T. E.

N. A. Sanford, A. Munkholm, M. R. Krames, A. Shapiro, I. Levin, A. V. Davydov, S. Sayan, L. S. Wielunski, and T. E. Madey, “Refractive index and birefringence of InxGa1-xN films grown by MOCVD,” phys. stat. sol. (C) 2, 2783–2786 (2005).
[CrossRef]

Martin, O. J. F.

B. Gallinet, A. M. Kern, and O. J. F. Martin, “Accurate and versatile modeling of electromagnetic scattering on periodic nanostructures with a surface integral approach,” J. Opt. Soc. Am. A 27, 2261–2271 (2010).
[CrossRef]

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[CrossRef]

Moiseev, S. G.

S. G. Moiseev, “Thin-film polarizer made of heterogeneous medium with uniformly oriented silver nanoparticles,” Appl. Phys. A 103, 775–777 (2011).
[CrossRef]

Munkholm, A.

N. A. Sanford, A. Munkholm, M. R. Krames, A. Shapiro, I. Levin, A. V. Davydov, S. Sayan, L. S. Wielunski, and T. E. Madey, “Refractive index and birefringence of InxGa1-xN films grown by MOCVD,” phys. stat. sol. (C) 2, 2783–2786 (2005).
[CrossRef]

Oh, J. H.

Otte, R.

R. Otte, L. P. de Joung, and A. H. M. van Roermund, Low-power Wireless Infrared Communications (Kluwer Academic Publishers, 1999).
[CrossRef]

Paulus, J. M.

J. S. Baba, S. S. Gleason, J. S. Goddard, and J. M. Paulus, “Application of polarization for optical motion-registered SPECT functional imaging of tumors in mice,” Proc. SPIE 5702, 97–103 (2005).
[CrossRef]

Paulus, M.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[CrossRef]

Prahl, S. A.

J. C. Ramella-Roman, K. Lee, S. A. Prahl, and S. L. Jacques, “Polarized light imaging with a handheld camera,” Proc. SPIE 5068, 284–293 (2003).
[CrossRef]

Ramella-Roman, J. C.

J. C. Ramella-Roman, K. Lee, S. A. Prahl, and S. L. Jacques, “Polarized light imaging with a handheld camera,” Proc. SPIE 5068, 284–293 (2003).
[CrossRef]

Sanford, N. A.

N. A. Sanford, A. Munkholm, M. R. Krames, A. Shapiro, I. Levin, A. V. Davydov, S. Sayan, L. S. Wielunski, and T. E. Madey, “Refractive index and birefringence of InxGa1-xN films grown by MOCVD,” phys. stat. sol. (C) 2, 2783–2786 (2005).
[CrossRef]

Sayan, S.

N. A. Sanford, A. Munkholm, M. R. Krames, A. Shapiro, I. Levin, A. V. Davydov, S. Sayan, L. S. Wielunski, and T. E. Madey, “Refractive index and birefringence of InxGa1-xN films grown by MOCVD,” phys. stat. sol. (C) 2, 2783–2786 (2005).
[CrossRef]

Schatz, G. C.

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Schubert, E. F.

M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett. 91, 051117 (2007).
[CrossRef]

Schubert, M. F.

M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett. 91, 051117 (2007).
[CrossRef]

Sepsi, Ö.

Shapiro, A.

N. A. Sanford, A. Munkholm, M. R. Krames, A. Shapiro, I. Levin, A. V. Davydov, S. Sayan, L. S. Wielunski, and T. E. Madey, “Refractive index and birefringence of InxGa1-xN films grown by MOCVD,” phys. stat. sol. (C) 2, 2783–2786 (2005).
[CrossRef]

Szanda, I.

van Roermund, A. H. M.

R. Otte, L. P. de Joung, and A. H. M. van Roermund, Low-power Wireless Infrared Communications (Kluwer Academic Publishers, 1999).
[CrossRef]

Wielunski, L. S.

N. A. Sanford, A. Munkholm, M. R. Krames, A. Shapiro, I. Levin, A. V. Davydov, S. Sayan, L. S. Wielunski, and T. E. Madey, “Refractive index and birefringence of InxGa1-xN films grown by MOCVD,” phys. stat. sol. (C) 2, 2783–2786 (2005).
[CrossRef]

Yang, S. J.

Yeh, P.

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley, Canada, 1999).

Zhao, L.

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

Zhao, L. L.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Appl. Phys. A

S. G. Moiseev, “Thin-film polarizer made of heterogeneous medium with uniformly oriented silver nanoparticles,” Appl. Phys. A 103, 775–777 (2011).
[CrossRef]

Appl. Phys. Lett.

M. F. Schubert, S. Chhajed, J. K. Kim, E. F. Schubert, and J. Cho, “Polarization of light emission by 460 nm GaInN/GaN light-emitting diodes grown on (0001) oriented sapphire substrates,” Appl. Phys. Lett. 91, 051117 (2007).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. Chem. B

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

J. Phys. F: Metal Phys

U. Kreibig, “Electronic properties of small silver particles, the optical constant and their temperature dependence,” J. Phys. F: Metal Phys 4, 999 (1974).
[CrossRef]

Opt. Express

Phys. Rev. E

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[CrossRef]

phys. stat. sol. (C)

N. A. Sanford, A. Munkholm, M. R. Krames, A. Shapiro, I. Levin, A. V. Davydov, S. Sayan, L. S. Wielunski, and T. E. Madey, “Refractive index and birefringence of InxGa1-xN films grown by MOCVD,” phys. stat. sol. (C) 2, 2783–2786 (2005).
[CrossRef]

Proc. SPIE

J. C. Ramella-Roman, K. Lee, S. A. Prahl, and S. L. Jacques, “Polarized light imaging with a handheld camera,” Proc. SPIE 5068, 284–293 (2003).
[CrossRef]

J. S. Baba, S. S. Gleason, J. S. Goddard, and J. M. Paulus, “Application of polarization for optical motion-registered SPECT functional imaging of tumors in mice,” Proc. SPIE 5702, 97–103 (2005).
[CrossRef]

Z. Naturforschg.

K. Kambe, “Theory of Electron Diffraction by Crystals. Green’s function and integral equation,” Z. Naturforschg. 22a, 422–431 (1967).

Other

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley, Canada, 1999).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

R. Otte, L. P. de Joung, and A. H. M. van Roermund, Low-power Wireless Infrared Communications (Kluwer Academic Publishers, 1999).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Geometry of the investigated planar LED structure with silver nanoellipsoids on top.

Fig. 2
Fig. 2

Degree of polarization (top left), transmittance (top right), absorbance (bottom left) and reflectance (bottom right) spectra of periodic array of silver nanospheroids placed on an LED chip. The major semi-axis values are presented in the legend of the figure, the AR is constant 2 and the period of the lattice is 2lx + 5 nm.

Fig. 3
Fig. 3

Degree of polarization (left) and absorbance (right) spectra of periodic array of silver nanospheroids placed on an LED chip. The major semi-axis was lx = 25 nm, the axial ratio was equal to 2. The lattice period is presented in the legend of the figure.

Fig. 4
Fig. 4

DOP, absorbance, transmittance and reflectance at 620 nm as function of particle semi-major axis. The axial ratio was equal to 2.2, the period was p = 2.1lx.

Equations (6)

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

p = ε h α ̳ E ( r 0 ) ,
α ̳ i j = 4 π l x l y l z 3 ε p ε h ε h + L i ( ε p ε h ) δ i j ,
α ˜ ̳ i j = α ̳ i j ( 1 k h 2 4 π l i α ̳ i j i 1 6 π k h 3 α ̳ i j ) 1 ,
E ( r ) = E inc ( r ) + ω 2 μ 0 j G ̳ ( r , r j ) p j ,
p j = e i K ( r j r 0 ) ( I ̳ ε h α ˜ ̳ ω 2 μ 0 G ̳ lat ( r 0 ) ) 1 ε h α ˜ ̳ E inc ( r 0 ) ,
G ̳ lat ( r 0 ) = j G ̳ ( r 0 , r j ) e i K ( r j r 0 ) .

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