Abstract

Using numerical modeling, it is shown that chains of dielectric spheres and cylinders act as polarizers. The mechanism is based on gradual filtering of periodically focused modes with a certain polarization propagating with minimal losses due to Brewster angles conditions, whereas orthogonally polarized modes are strongly attenuated. It is shown that chains of cylinders filter linearly polarized beams, whereas chains of spheres filter radially polarized beams. In the geometrical optics limit, we show that in a range of sphere refractive indices 1.68–1.80 a degree of radial polarization in excess of 0.9 can be obtained in 10-sphere-long chains.

© 2013 Optical Society of America

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  1. A. Darafsheh and V. N. Astratov, Appl. Phys. Lett. 100, 061123 (2012).
    [CrossRef]
  2. V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
    [CrossRef]
  3. S. Deng, W. Cai, and V. N. Astratov, Opt. Express 12, 6468 (2004).
    [CrossRef]
  4. Z. Chen, A. Taflove, and V. Backman, Opt. Express 12, 1214 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. Z. Chen, A. Taflove, and V. Backman, Opt. Lett. 31, 389 (2006).
    [CrossRef]
  9. A. M. Kapitonov and V. N. Astratov, Opt. Lett. 32, 409 (2007).
    [CrossRef]
  10. S. Yang and V. N. Astratov, Appl. Phys. Lett. 92, 261111 (2008).
    [CrossRef]
  11. T. Mitsui, Y. Wakayama, T. Onodera, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Adv. Mater. 22, 3022 (2010).
    [CrossRef]
  12. T. Mitsui, T. Onodera, Y. Wakayama, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Opt. Express 19, 22258 (2011).
    [CrossRef]
  13. O. Lecarme, T. P. Rivera, L. Arbez, T. Honeggar, K. Berton, and D. Peyrade, J. Vac. Sci. Technol. B 28, C6O11 (2010).
    [CrossRef]
  14. C.-Y. Liu, Phys. Lett. A 376, 3261 (2012).
    [CrossRef]
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    [CrossRef]
  16. Q. Zhan, Adv. Opt. Photonics 1, 1 (2009).
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    [CrossRef]
  18. T. C. Hutchens, A. Darafsheh, A. Fardad, A. N. Antoszyk, H. S. Ying, V. N. Astratov, and N. M. Fried, J. Biomed. Opt. 17, 068004 (2012).
    [CrossRef]
  19. E. Mcleod and C. B. Arnold, Nat. Nanotechnol. 3, 413 (2008).
    [CrossRef]
  20. V. N. Astratov, in Photonic Microresonator Research and Applications, I. Chremmos, O. Schwelb, and N. Uzunoglu, eds. (Springer, 2010), pp. 423–457.
  21. A. Darafsheh, “Optical super-resolution and periodical focusing effects by dielectric microspheres,” Ph.D. dissertation (University of North Carolina at Charlotte, 2013).
  22. E. Hecht, Optics, 4th ed. (Addison, 2001).
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    [CrossRef]
  24. A. Al-Qasimi, O. Korotkova, D. James, and E. Wolf, Opt. Lett. 32, 1015 (2007).
    [CrossRef]

2012 (4)

A. Darafsheh and V. N. Astratov, Appl. Phys. Lett. 100, 061123 (2012).
[CrossRef]

C.-Y. Liu, Phys. Lett. A 376, 3261 (2012).
[CrossRef]

T. C. Hutchens, A. Darafsheh, A. Fardad, A. N. Antoszyk, H. S. Ying, V. N. Astratov, and N. M. Fried, J. Biomed. Opt. 17, 068004 (2012).
[CrossRef]

D. McCloskey, J. J. Wang, and J. F. Donegan, Opt. Express 20, 128 (2012).
[CrossRef]

2011 (2)

2010 (2)

O. Lecarme, T. P. Rivera, L. Arbez, T. Honeggar, K. Berton, and D. Peyrade, J. Vac. Sci. Technol. B 28, C6O11 (2010).
[CrossRef]

T. Mitsui, Y. Wakayama, T. Onodera, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Adv. Mater. 22, 3022 (2010).
[CrossRef]

2009 (2)

Q. Zhan, Adv. Opt. Photonics 1, 1 (2009).

A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, J. Comp. Theor. Nanosci. 6, 1979 (2009).

2008 (3)

E. Mcleod and C. B. Arnold, Nat. Nanotechnol. 3, 413 (2008).
[CrossRef]

S. Yang and V. N. Astratov, Appl. Phys. Lett. 92, 261111 (2008).
[CrossRef]

P. Ferrand, J. Wenger, A. Devilez, M. Pianta, B. Stout, N. Bonod, E. Popov, and H. Rigneault, Opt. Express 16, 6930 (2008).
[CrossRef]

2007 (2)

2006 (2)

Z. Chen, A. Taflove, and V. Backman, Opt. Lett. 31, 389 (2006).
[CrossRef]

A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
[CrossRef]

2004 (3)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Al-Qasimi, A.

Antoszyk, A. N.

T. C. Hutchens, A. Darafsheh, A. Fardad, A. N. Antoszyk, H. S. Ying, V. N. Astratov, and N. M. Fried, J. Biomed. Opt. 17, 068004 (2012).
[CrossRef]

A. Darafsheh, A. Fardad, N. M. Fried, A. N. Antoszyk, H. S. Ying, and V. N. Astratov, Opt. Express 19, 3440 (2011).
[CrossRef]

Arbez, L.

O. Lecarme, T. P. Rivera, L. Arbez, T. Honeggar, K. Berton, and D. Peyrade, J. Vac. Sci. Technol. B 28, C6O11 (2010).
[CrossRef]

Arnold, C. B.

E. Mcleod and C. B. Arnold, Nat. Nanotechnol. 3, 413 (2008).
[CrossRef]

Ashili, S. P.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

Astratov, V. N.

A. Darafsheh and V. N. Astratov, Appl. Phys. Lett. 100, 061123 (2012).
[CrossRef]

T. C. Hutchens, A. Darafsheh, A. Fardad, A. N. Antoszyk, H. S. Ying, V. N. Astratov, and N. M. Fried, J. Biomed. Opt. 17, 068004 (2012).
[CrossRef]

A. Darafsheh, A. Fardad, N. M. Fried, A. N. Antoszyk, H. S. Ying, and V. N. Astratov, Opt. Express 19, 3440 (2011).
[CrossRef]

S. Yang and V. N. Astratov, Appl. Phys. Lett. 92, 261111 (2008).
[CrossRef]

A. M. Kapitonov and V. N. Astratov, Opt. Lett. 32, 409 (2007).
[CrossRef]

A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
[CrossRef]

S. Deng, W. Cai, and V. N. Astratov, Opt. Express 12, 6468 (2004).
[CrossRef]

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

V. N. Astratov, in Photonic Microresonator Research and Applications, I. Chremmos, O. Schwelb, and N. Uzunoglu, eds. (Springer, 2010), pp. 423–457.

Backman, V.

A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, J. Comp. Theor. Nanosci. 6, 1979 (2009).

Z. Chen, A. Taflove, and V. Backman, Opt. Lett. 31, 389 (2006).
[CrossRef]

Z. Chen, A. Taflove, and V. Backman, Opt. Express 12, 1214 (2004).
[CrossRef]

Berton, K.

O. Lecarme, T. P. Rivera, L. Arbez, T. Honeggar, K. Berton, and D. Peyrade, J. Vac. Sci. Technol. B 28, C6O11 (2010).
[CrossRef]

Bonod, N.

Cai, W.

A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
[CrossRef]

S. Deng, W. Cai, and V. N. Astratov, Opt. Express 12, 6468 (2004).
[CrossRef]

Chen, Z.

Darafsheh, A.

T. C. Hutchens, A. Darafsheh, A. Fardad, A. N. Antoszyk, H. S. Ying, V. N. Astratov, and N. M. Fried, J. Biomed. Opt. 17, 068004 (2012).
[CrossRef]

A. Darafsheh and V. N. Astratov, Appl. Phys. Lett. 100, 061123 (2012).
[CrossRef]

A. Darafsheh, A. Fardad, N. M. Fried, A. N. Antoszyk, H. S. Ying, and V. N. Astratov, Opt. Express 19, 3440 (2011).
[CrossRef]

A. Darafsheh, “Optical super-resolution and periodical focusing effects by dielectric microspheres,” Ph.D. dissertation (University of North Carolina at Charlotte, 2013).

Deng, S.

Devilez, A.

Donegan, J. F.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Fardad, A.

T. C. Hutchens, A. Darafsheh, A. Fardad, A. N. Antoszyk, H. S. Ying, V. N. Astratov, and N. M. Fried, J. Biomed. Opt. 17, 068004 (2012).
[CrossRef]

A. Darafsheh, A. Fardad, N. M. Fried, A. N. Antoszyk, H. S. Ying, and V. N. Astratov, Opt. Express 19, 3440 (2011).
[CrossRef]

Ferrand, P.

Franchak, J. P.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

Fried, N. M.

T. C. Hutchens, A. Darafsheh, A. Fardad, A. N. Antoszyk, H. S. Ying, V. N. Astratov, and N. M. Fried, J. Biomed. Opt. 17, 068004 (2012).
[CrossRef]

A. Darafsheh, A. Fardad, N. M. Fried, A. N. Antoszyk, H. S. Ying, and V. N. Astratov, Opt. Express 19, 3440 (2011).
[CrossRef]

Hayashi, T.

T. Mitsui, T. Onodera, Y. Wakayama, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Opt. Express 19, 22258 (2011).
[CrossRef]

T. Mitsui, Y. Wakayama, T. Onodera, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Adv. Mater. 22, 3022 (2010).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison, 2001).

Heifetz, A.

A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, J. Comp. Theor. Nanosci. 6, 1979 (2009).

Honeggar, T.

O. Lecarme, T. P. Rivera, L. Arbez, T. Honeggar, K. Berton, and D. Peyrade, J. Vac. Sci. Technol. B 28, C6O11 (2010).
[CrossRef]

Hutchens, T. C.

T. C. Hutchens, A. Darafsheh, A. Fardad, A. N. Antoszyk, H. S. Ying, V. N. Astratov, and N. M. Fried, J. Biomed. Opt. 17, 068004 (2012).
[CrossRef]

Ikeda, N.

T. Mitsui, T. Onodera, Y. Wakayama, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Opt. Express 19, 22258 (2011).
[CrossRef]

T. Mitsui, Y. Wakayama, T. Onodera, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Adv. Mater. 22, 3022 (2010).
[CrossRef]

James, D.

Kanaev, A. V.

A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
[CrossRef]

Kapitonov, A. M.

Kong, S. C.

A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, J. Comp. Theor. Nanosci. 6, 1979 (2009).

Korotkova, O.

Lecarme, O.

O. Lecarme, T. P. Rivera, L. Arbez, T. Honeggar, K. Berton, and D. Peyrade, J. Vac. Sci. Technol. B 28, C6O11 (2010).
[CrossRef]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Liu, C.-Y.

C.-Y. Liu, Phys. Lett. A 376, 3261 (2012).
[CrossRef]

McCloskey, D.

Mcleod, E.

E. Mcleod and C. B. Arnold, Nat. Nanotechnol. 3, 413 (2008).
[CrossRef]

Mitsui, T.

T. Mitsui, T. Onodera, Y. Wakayama, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Opt. Express 19, 22258 (2011).
[CrossRef]

T. Mitsui, Y. Wakayama, T. Onodera, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Adv. Mater. 22, 3022 (2010).
[CrossRef]

Oikawa, H.

T. Mitsui, T. Onodera, Y. Wakayama, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Opt. Express 19, 22258 (2011).
[CrossRef]

T. Mitsui, Y. Wakayama, T. Onodera, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Adv. Mater. 22, 3022 (2010).
[CrossRef]

Onodera, T.

T. Mitsui, T. Onodera, Y. Wakayama, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Opt. Express 19, 22258 (2011).
[CrossRef]

T. Mitsui, Y. Wakayama, T. Onodera, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Adv. Mater. 22, 3022 (2010).
[CrossRef]

Peyrade, D.

O. Lecarme, T. P. Rivera, L. Arbez, T. Honeggar, K. Berton, and D. Peyrade, J. Vac. Sci. Technol. B 28, C6O11 (2010).
[CrossRef]

Pianta, M.

Popov, E.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Rigneault, H.

Rivera, T. P.

O. Lecarme, T. P. Rivera, L. Arbez, T. Honeggar, K. Berton, and D. Peyrade, J. Vac. Sci. Technol. B 28, C6O11 (2010).
[CrossRef]

Sahakian, A. V.

A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, J. Comp. Theor. Nanosci. 6, 1979 (2009).

Stout, B.

Sugimoto, Y.

T. Mitsui, T. Onodera, Y. Wakayama, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Opt. Express 19, 22258 (2011).
[CrossRef]

T. Mitsui, Y. Wakayama, T. Onodera, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Adv. Mater. 22, 3022 (2010).
[CrossRef]

Taflove, A.

A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, J. Comp. Theor. Nanosci. 6, 1979 (2009).

Z. Chen, A. Taflove, and V. Backman, Opt. Lett. 31, 389 (2006).
[CrossRef]

Z. Chen, A. Taflove, and V. Backman, Opt. Express 12, 1214 (2004).
[CrossRef]

Takamasu, T.

T. Mitsui, T. Onodera, Y. Wakayama, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Opt. Express 19, 22258 (2011).
[CrossRef]

T. Mitsui, Y. Wakayama, T. Onodera, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Adv. Mater. 22, 3022 (2010).
[CrossRef]

Wakayama, Y.

T. Mitsui, T. Onodera, Y. Wakayama, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Opt. Express 19, 22258 (2011).
[CrossRef]

T. Mitsui, Y. Wakayama, T. Onodera, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Adv. Mater. 22, 3022 (2010).
[CrossRef]

Wang, J. J.

Wenger, J.

Wolf, E.

Yang, S.

S. Yang and V. N. Astratov, Appl. Phys. Lett. 92, 261111 (2008).
[CrossRef]

Ying, H. S.

T. C. Hutchens, A. Darafsheh, A. Fardad, A. N. Antoszyk, H. S. Ying, V. N. Astratov, and N. M. Fried, J. Biomed. Opt. 17, 068004 (2012).
[CrossRef]

A. Darafsheh, A. Fardad, N. M. Fried, A. N. Antoszyk, H. S. Ying, and V. N. Astratov, Opt. Express 19, 3440 (2011).
[CrossRef]

Zhan, Q.

Q. Zhan, Adv. Opt. Photonics 1, 1 (2009).

Adv. Mater. (1)

T. Mitsui, Y. Wakayama, T. Onodera, T. Hayashi, N. Ikeda, Y. Sugimoto, T. Takamasu, and H. Oikawa, Adv. Mater. 22, 3022 (2010).
[CrossRef]

Adv. Opt. Photonics (1)

Q. Zhan, Adv. Opt. Photonics 1, 1 (2009).

Appl. Phys. Lett. (4)

A. Darafsheh and V. N. Astratov, Appl. Phys. Lett. 100, 061123 (2012).
[CrossRef]

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
[CrossRef]

S. Yang and V. N. Astratov, Appl. Phys. Lett. 92, 261111 (2008).
[CrossRef]

J. Biomed. Opt. (1)

T. C. Hutchens, A. Darafsheh, A. Fardad, A. N. Antoszyk, H. S. Ying, V. N. Astratov, and N. M. Fried, J. Biomed. Opt. 17, 068004 (2012).
[CrossRef]

J. Comp. Theor. Nanosci. (1)

A. Heifetz, S. C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, J. Comp. Theor. Nanosci. 6, 1979 (2009).

J. Vac. Sci. Technol. B (1)

O. Lecarme, T. P. Rivera, L. Arbez, T. Honeggar, K. Berton, and D. Peyrade, J. Vac. Sci. Technol. B 28, C6O11 (2010).
[CrossRef]

Nat. Nanotechnol. (1)

E. Mcleod and C. B. Arnold, Nat. Nanotechnol. 3, 413 (2008).
[CrossRef]

Opt. Express (6)

Opt. Lett. (3)

Phys. Lett. A (1)

C.-Y. Liu, Phys. Lett. A 376, 3261 (2012).
[CrossRef]

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Other (3)

V. N. Astratov, in Photonic Microresonator Research and Applications, I. Chremmos, O. Schwelb, and N. Uzunoglu, eds. (Springer, 2010), pp. 423–457.

A. Darafsheh, “Optical super-resolution and periodical focusing effects by dielectric microspheres,” Ph.D. dissertation (University of North Carolina at Charlotte, 2013).

E. Hecht, Optics, 4th ed. (Addison, 2001).

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Figures (5)

Fig. 1.
Fig. 1.

2D electric field intensity maps calculated for touching cylinders with D=3μm and n=3 at λ=0.53μm for the incident plane waves with electric field oscillating along the (a) y axis and (b) z axis. (c) The intensity profiles of the focused beams calculated 0.62 μm away from the tip of the end cylinder showing stronger peak transmission in case (a) compared to (b).

Fig. 2.
Fig. 2.

(a) Ray tracing in an array of identical touching spheres under the condition of periodic propagation. (b) Transmittance and (c) loss in chains of N=1, 5, 10 and 20 spheres as a function of n for TE and TM polarizations of the incident ray. In a geometrical optics limit (D10λ) the results are not dependent on D and λ.

Fig. 3.
Fig. 3.

Three different types of coupling to the PFMs. (a) Collimated rays, (b) spherical emitter, and (c) a multimode fiber inserted inside a hollow waveguide.

Fig. 4.
Fig. 4.

(a) Intensity distribution produced by a 20-sphere-long chain with n=3 as a result of illumination with collimated rays. (b) Linear polarizer (along x) placed between the end-sphere and the detectors. (c) Intensity distribution with the polarizer installed also showing positions of two detectors (dashed rectangles) used for DOP calculations.

Fig. 5.
Fig. 5.

(a)–(c) Degree of radial polarization versus n calculated for three types of ray sources illustrated in Figs. 3(a)3(c), respectively.

Equations (3)

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RTE=sin2(θi/2)sin2(3θi/2),
RTM=tan2(θi/2)tan2(3θi/2).
Q(r)=|Ix(r)Iy(r)|Ix(r)+Iy(r),

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