Abstract

We study the transmission properties of a one-dimensional array with intersite side-coupled defect and demonstrate that, as the system undergoes sharp Fano resonance, it exhibits geometry-induced vorticity of the energy flux. The optical vortex inverts its handedness at the Fano resonance, revealing a strong link between two phenomena, both being of interference origin. Our approach is quite general and can be applied to a variety of systems; as an example we demonstrate a similar effect in photonic crystal structure.

© 2012 Optical Society of America

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References

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  1. E. Wolf and M. Born, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Cambridge Univ., 1998).
  2. M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 52, 293 (2009).
    [CrossRef]
  3. J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. Ser. A: Math. Phys. Eng. Sci. 336, 165 (1974).
    [CrossRef]
  4. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
    [CrossRef]
  5. A. A. Sukhorukov, S. Ha, A. S. Desyatnikov, A. V. Lavrinenko, and Yu. S. Kivshar, J. Opt. A 11, 094016 (2009).
    [CrossRef]
  6. E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 85, 165305 (2012).
    [CrossRef]
  7. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
    [CrossRef]
  8. N. Shitrit, S. Nechayev, V. Kleiner, and E. Hasman, Nano Lett. 12, 1620 (2012).
    [CrossRef]
  9. S. V. Boriskina and B. M. Reinhard, Nanoscale 4, 76 (2012).
    [CrossRef]
  10. U. Fano, Phys. Rev. 124, 1866 (1961).
    [CrossRef]
  11. A. E. Miroshnichenko, S. Flach, and Yu. S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
    [CrossRef]
  12. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
    [CrossRef]
  13. A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, Phys. Rev. E 71, 036626 (2005).
    [CrossRef]
  14. B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
    [CrossRef]
  15. A. S. Desyatnikov, M. R. Dennis, and A. Ferrando, Phys. Rev. A 83, 063822 (2011).
    [CrossRef]
  16. S. F. Mingaleev and Y. S. Kivshar, Phys. Rev. Lett. 86, 5474 (2001).
    [CrossRef]
  17. S. F. Mingaleev, A. E. Miroshnichenko, and Yu. S. Kivshar, Opt. Express 16, 11647 (2008).
    [CrossRef]
  18. A. E. Miroshnichenko and Yu. S. Kivshar, Appl. Phys. Lett. 95, 121109 (2009).
    [CrossRef]
  19. Y. Xu and A. E. Miroshnichenko, Phys. Rev. A 84, 033828 (2011).
    [CrossRef]
  20. Y. Xu and A. E. Miroshnichenko, Europhys. Lett. 97, 44007 (2012).
    [CrossRef]

2012 (4)

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 85, 165305 (2012).
[CrossRef]

N. Shitrit, S. Nechayev, V. Kleiner, and E. Hasman, Nano Lett. 12, 1620 (2012).
[CrossRef]

S. V. Boriskina and B. M. Reinhard, Nanoscale 4, 76 (2012).
[CrossRef]

Y. Xu and A. E. Miroshnichenko, Europhys. Lett. 97, 44007 (2012).
[CrossRef]

2011 (3)

Y. Xu and A. E. Miroshnichenko, Phys. Rev. A 84, 033828 (2011).
[CrossRef]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

A. S. Desyatnikov, M. R. Dennis, and A. Ferrando, Phys. Rev. A 83, 063822 (2011).
[CrossRef]

2010 (2)

A. E. Miroshnichenko, S. Flach, and Yu. S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

2009 (3)

A. E. Miroshnichenko and Yu. S. Kivshar, Appl. Phys. Lett. 95, 121109 (2009).
[CrossRef]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 52, 293 (2009).
[CrossRef]

A. A. Sukhorukov, S. Ha, A. S. Desyatnikov, A. V. Lavrinenko, and Yu. S. Kivshar, J. Opt. A 11, 094016 (2009).
[CrossRef]

2008 (1)

2005 (2)

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, Phys. Rev. E 71, 036626 (2005).
[CrossRef]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

2001 (2)

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

S. F. Mingaleev and Y. S. Kivshar, Phys. Rev. Lett. 86, 5474 (2001).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. Ser. A: Math. Phys. Eng. Sci. 336, 165 (1974).
[CrossRef]

1961 (1)

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Berry, M. V.

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. Ser. A: Math. Phys. Eng. Sci. 336, 165 (1974).
[CrossRef]

Boriskina, S. V.

S. V. Boriskina and B. M. Reinhard, Nanoscale 4, 76 (2012).
[CrossRef]

Born, M.

E. Wolf and M. Born, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Cambridge Univ., 1998).

Bulgakov, E. N.

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 85, 165305 (2012).
[CrossRef]

Capasso, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Dennis, M. R.

A. S. Desyatnikov, M. R. Dennis, and A. Ferrando, Phys. Rev. A 83, 063822 (2011).
[CrossRef]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 52, 293 (2009).
[CrossRef]

Desyatnikov, A. S.

A. S. Desyatnikov, M. R. Dennis, and A. Ferrando, Phys. Rev. A 83, 063822 (2011).
[CrossRef]

A. A. Sukhorukov, S. Ha, A. S. Desyatnikov, A. V. Lavrinenko, and Yu. S. Kivshar, J. Opt. A 11, 094016 (2009).
[CrossRef]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

Fano, U.

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Ferrando, A.

A. S. Desyatnikov, M. R. Dennis, and A. Ferrando, Phys. Rev. A 83, 063822 (2011).
[CrossRef]

Flach, S.

A. E. Miroshnichenko, S. Flach, and Yu. S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, Phys. Rev. E 71, 036626 (2005).
[CrossRef]

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Giessen, H.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Ha, S.

A. A. Sukhorukov, S. Ha, A. S. Desyatnikov, A. V. Lavrinenko, and Yu. S. Kivshar, J. Opt. A 11, 094016 (2009).
[CrossRef]

Halas, N. J.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Hasman, E.

N. Shitrit, S. Nechayev, V. Kleiner, and E. Hasman, Nano Lett. 12, 1620 (2012).
[CrossRef]

Kats, M. A.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Kevrekidis, P. G.

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Kivshar, Y. S.

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, Phys. Rev. E 71, 036626 (2005).
[CrossRef]

S. F. Mingaleev and Y. S. Kivshar, Phys. Rev. Lett. 86, 5474 (2001).
[CrossRef]

Kivshar, Yu. S.

A. E. Miroshnichenko, S. Flach, and Yu. S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

A. A. Sukhorukov, S. Ha, A. S. Desyatnikov, A. V. Lavrinenko, and Yu. S. Kivshar, J. Opt. A 11, 094016 (2009).
[CrossRef]

A. E. Miroshnichenko and Yu. S. Kivshar, Appl. Phys. Lett. 95, 121109 (2009).
[CrossRef]

S. F. Mingaleev, A. E. Miroshnichenko, and Yu. S. Kivshar, Opt. Express 16, 11647 (2008).
[CrossRef]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

Kleiner, V.

N. Shitrit, S. Nechayev, V. Kleiner, and E. Hasman, Nano Lett. 12, 1620 (2012).
[CrossRef]

Lavrinenko, A. V.

A. A. Sukhorukov, S. Ha, A. S. Desyatnikov, A. V. Lavrinenko, and Yu. S. Kivshar, J. Opt. A 11, 094016 (2009).
[CrossRef]

Luk’yanchuk, B.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Maier, S. A.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Malomed, B. A.

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Mingaleev, S. F.

S. F. Mingaleev, A. E. Miroshnichenko, and Yu. S. Kivshar, Opt. Express 16, 11647 (2008).
[CrossRef]

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, Phys. Rev. E 71, 036626 (2005).
[CrossRef]

S. F. Mingaleev and Y. S. Kivshar, Phys. Rev. Lett. 86, 5474 (2001).
[CrossRef]

Miroshnichenko, A. E.

Y. Xu and A. E. Miroshnichenko, Europhys. Lett. 97, 44007 (2012).
[CrossRef]

Y. Xu and A. E. Miroshnichenko, Phys. Rev. A 84, 033828 (2011).
[CrossRef]

A. E. Miroshnichenko, S. Flach, and Yu. S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

A. E. Miroshnichenko and Yu. S. Kivshar, Appl. Phys. Lett. 95, 121109 (2009).
[CrossRef]

S. F. Mingaleev, A. E. Miroshnichenko, and Yu. S. Kivshar, Opt. Express 16, 11647 (2008).
[CrossRef]

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, Phys. Rev. E 71, 036626 (2005).
[CrossRef]

Nechayev, S.

N. Shitrit, S. Nechayev, V. Kleiner, and E. Hasman, Nano Lett. 12, 1620 (2012).
[CrossRef]

Nordlander, P.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. Ser. A: Math. Phys. Eng. Sci. 336, 165 (1974).
[CrossRef]

O’Holleran, K.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 52, 293 (2009).
[CrossRef]

Padgett, M. J.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 52, 293 (2009).
[CrossRef]

Reinhard, B. M.

S. V. Boriskina and B. M. Reinhard, Nanoscale 4, 76 (2012).
[CrossRef]

Sadreev, A. F.

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 85, 165305 (2012).
[CrossRef]

Shitrit, N.

N. Shitrit, S. Nechayev, V. Kleiner, and E. Hasman, Nano Lett. 12, 1620 (2012).
[CrossRef]

Sukhorukov, A. A.

A. A. Sukhorukov, S. Ha, A. S. Desyatnikov, A. V. Lavrinenko, and Yu. S. Kivshar, J. Opt. A 11, 094016 (2009).
[CrossRef]

Tetienne, J.-P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Torner, L.

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

Wolf, E.

E. Wolf and M. Born, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Cambridge Univ., 1998).

Xu, Y.

Y. Xu and A. E. Miroshnichenko, Europhys. Lett. 97, 44007 (2012).
[CrossRef]

Y. Xu and A. E. Miroshnichenko, Phys. Rev. A 84, 033828 (2011).
[CrossRef]

Yu, N.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Zheludev, N. I.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

A. E. Miroshnichenko and Yu. S. Kivshar, Appl. Phys. Lett. 95, 121109 (2009).
[CrossRef]

Europhys. Lett. (1)

Y. Xu and A. E. Miroshnichenko, Europhys. Lett. 97, 44007 (2012).
[CrossRef]

J. Opt. A (1)

A. A. Sukhorukov, S. Ha, A. S. Desyatnikov, A. V. Lavrinenko, and Yu. S. Kivshar, J. Opt. A 11, 094016 (2009).
[CrossRef]

Nano Lett. (1)

N. Shitrit, S. Nechayev, V. Kleiner, and E. Hasman, Nano Lett. 12, 1620 (2012).
[CrossRef]

Nanoscale (1)

S. V. Boriskina and B. M. Reinhard, Nanoscale 4, 76 (2012).
[CrossRef]

Nat. Mater. (1)

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Mater. 9, 707 (2010).
[CrossRef]

Opt. Express (1)

Phys. Rev. (1)

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Phys. Rev. A (2)

Y. Xu and A. E. Miroshnichenko, Phys. Rev. A 84, 033828 (2011).
[CrossRef]

A. S. Desyatnikov, M. R. Dennis, and A. Ferrando, Phys. Rev. A 83, 063822 (2011).
[CrossRef]

Phys. Rev. B (1)

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 85, 165305 (2012).
[CrossRef]

Phys. Rev. E (2)

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Y. S. Kivshar, Phys. Rev. E 71, 036626 (2005).
[CrossRef]

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

S. F. Mingaleev and Y. S. Kivshar, Phys. Rev. Lett. 86, 5474 (2001).
[CrossRef]

Proc. R. Soc. Lond. Ser. A: Math. Phys. Eng. Sci. (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. Ser. A: Math. Phys. Eng. Sci. 336, 165 (1974).
[CrossRef]

Prog. Opt. (2)

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Prog. Opt. 52, 293 (2009).
[CrossRef]

Rev. Mod. Phys. (1)

A. E. Miroshnichenko, S. Flach, and Yu. S. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

Science (1)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Other (1)

E. Wolf and M. Born, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Cambridge Univ., 1998).

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Figures (3)

Fig. 1.
Fig. 1.

Scheme of the discrete system Eq. (1). The arrows show the positive directions of indicated currents.

Fig. 2.
Fig. 2.

(a) Transmission and (b) currents of the discrete array in Fig. 1. (c) Sketches of the energy flows corresponding to three regions distinguished in (a) by shading: (i) no vortex, L=0, (ii) antivortex, L=1, and (iii) vortex, L=+1. (d) Power spectrum of the triangle, |fl|2; see Eq. (5).

Fig. 3.
Fig. 3.

PCW with a defect: 2D PC consists of dielectric rods with n=3.4 and radius=0.18a, and side-coupled defect rod with n=1.6 and radius=0.1ain vacuum; a is the lattice constant. The Poynting vector is shown for two different frequencies (units of 2πc/a, c is the speed of light): (a) Ω=0.3790 and (b) Ω=0.3807, marked by dots in the transmission graph (c). The amplitude of the Poynting vector is color-coded in (a), (b) and the direction map is shown with the streamlines. The insets show schematic of the major flow to help the eye; cf. discrete model in Fig. 2(c).

Equations (6)

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

idEndt+En1+En+1+(δn,m+δn,m+1)F=0,idFdt+Em+Em+1=0.
dPndt=Jn1Jn+δn,mJ0,m+δn,m+1J0,m+1,dP0dt=J0,m+1J0,m,
En=eiωt{eiqn+Reiqn,nm,Teiqn,nm+1,
T=sin(3q/2)sin(3q/2)icos(q/2),
L=12π[arg(F*Em)+arg(Em*Em+1)+arg(Em+1*F)],
fl=13Δj=13Δjei2πlj/3.

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