Abstract

We study light scattering by cylindrical multilayer structures containing Kerr-type nonlinear materials. We develop a new semi-analytical method for solving such nonlinear problems by reducing the original 2D system by a 1D nonlinear Helmholtz equation. We apply our method for the case of wave scattering by the core-shell metal-dielectric nanowire and show that the nonlinearity allows us to control scattering cross section, which in the resonant regime demonstrates optical bistability. We compare our method with the finite-difference time-domain (FDTD) approach and find that the new approach is accurate and is 105 times faster and more numerically robust than the FDTD.

© 2014 Optical Society of America

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  1. J. Dorfmuller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010).
    [CrossRef]
  2. G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. Gómez Rivas, “Nanowire antenna emission,” Nano Lett. 12, 5481–5486 (2012).
    [CrossRef]
  3. L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
    [CrossRef]
  4. Y. Zhan, J. Zhao, C. Zhou, M. Alemayehu, Y. Li, and Y. Li, “Enhanced photon absorption of single nanowire α-Si solar cells modulated by silver core,” Opt. Express 20, 11506–11516 (2012).
    [CrossRef]
  5. T. J. Kempa, J. F. Cahoon, S. Kim, R. W. Day, D. C. Bell, H. Park, and C. M. Lieber, “Coaxial multishell nanowires with high-quality electronic interfaces and tunable optical cavities for ultrathin photovoltaics,” Proc. Natl. Acad. Sci. USA 109, 1407–1412 (2012).
    [CrossRef]
  6. A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901 (2008).
    [CrossRef]
  7. A. Mirzaei, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Cloaking and enhanced scattering of core-shell plasmonic nanowires,” Opt. Express 21, 10454–10459 (2013).
    [CrossRef]
  8. Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett. 105, 013901 (2010).
    [CrossRef]
  9. L. Schächter, Beam-wave Interaction in Periodic and Quasi-Periodic Structures (Springer, 2011).
  10. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).
  11. N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 02885 (2013).
    [CrossRef]
  12. X. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood, S. Assefa, Y. A. Vlasov, and W. M. J. Green, “Self-phase modulation and nonlinear loss in silicon nanophotonic wires near the mid-infrared two-photon absorption edge,” Opt. Express 19, 7778–7789 (2011).
    [CrossRef]
  13. A. Taflove and S. C. Hagness, Computational Electrodynamics the Finite Difference Time Domain Method (Artech House, 2005).
  14. R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A 13, 483–493 (1996).
    [CrossRef]
  15. C. I. Valencia, E. R. Méndez, and B. S. Mendoza, “Second-harmonic generation in the scattering of light by an infinite cylinder,” J. Opt. Soc. Am. B 21, 36–44 (2004).
    [CrossRef]
  16. M. A. Hasan, “Electromagnetic scattering from nonlinear anisotropic cylinders—part 1: fundamental frequency,” IEEE Trans. Antennas Propag. 38, 523–533 (1990).
    [CrossRef]
  17. S. Caorsi, A. Massa, and M. Pastorino, “Approximate solutions to the scattering by nonlinear isotropic dielectric cylinders of circular cross sections under TM illumination,” IEEE Trans. Antennas Propag. 43, 1262–1269 (1995).
  18. S. Caorsi, A. Massa, and M. Pastorino, “Bistatic scattering-width computation for weakly nonlinear dielectric cylinders of arbitrary inhomogeneous cross-section shapes under transverse-magnetic wave illumination,” J. Opt. Soc. Am. A 12, 2482–2490 (1995).
    [CrossRef]
  19. S. Caorsi, A. Massa, and M. Pastorino, “Rytov approximation: application to scattering by two-dimensional weakly nonlinear dielectrics,” J. Opt. Soc. Am. A 13, 509–516 (1996).
    [CrossRef]
  20. R. W. Boyd, Nonlinear Optics (Elsevier, 2008).
  21. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).
  22. A. Vial, “Implementation of the critical points model in the recursive convolution method for modelling dispersive media with the finite-difference time domain method,” J. Opt. A 9, 745–748 (2007).
    [CrossRef]

2013 (2)

A. Mirzaei, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Cloaking and enhanced scattering of core-shell plasmonic nanowires,” Opt. Express 21, 10454–10459 (2013).
[CrossRef]

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 02885 (2013).
[CrossRef]

2012 (3)

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. Gómez Rivas, “Nanowire antenna emission,” Nano Lett. 12, 5481–5486 (2012).
[CrossRef]

Y. Zhan, J. Zhao, C. Zhou, M. Alemayehu, Y. Li, and Y. Li, “Enhanced photon absorption of single nanowire α-Si solar cells modulated by silver core,” Opt. Express 20, 11506–11516 (2012).
[CrossRef]

T. J. Kempa, J. F. Cahoon, S. Kim, R. W. Day, D. C. Bell, H. Park, and C. M. Lieber, “Coaxial multishell nanowires with high-quality electronic interfaces and tunable optical cavities for ultrathin photovoltaics,” Proc. Natl. Acad. Sci. USA 109, 1407–1412 (2012).
[CrossRef]

2011 (1)

2010 (3)

Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett. 105, 013901 (2010).
[CrossRef]

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

J. Dorfmuller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010).
[CrossRef]

2008 (1)

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef]

2007 (1)

A. Vial, “Implementation of the critical points model in the recursive convolution method for modelling dispersive media with the finite-difference time domain method,” J. Opt. A 9, 745–748 (2007).
[CrossRef]

2004 (1)

1996 (2)

1995 (2)

S. Caorsi, A. Massa, and M. Pastorino, “Approximate solutions to the scattering by nonlinear isotropic dielectric cylinders of circular cross sections under TM illumination,” IEEE Trans. Antennas Propag. 43, 1262–1269 (1995).

S. Caorsi, A. Massa, and M. Pastorino, “Bistatic scattering-width computation for weakly nonlinear dielectric cylinders of arbitrary inhomogeneous cross-section shapes under transverse-magnetic wave illumination,” J. Opt. Soc. Am. A 12, 2482–2490 (1995).
[CrossRef]

1990 (1)

M. A. Hasan, “Electromagnetic scattering from nonlinear anisotropic cylinders—part 1: fundamental frequency,” IEEE Trans. Antennas Propag. 38, 523–533 (1990).
[CrossRef]

Alemayehu, M.

Alu, A.

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef]

Assefa, S.

Badding, J. V.

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 02885 (2013).
[CrossRef]

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

Barten, T.

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. Gómez Rivas, “Nanowire antenna emission,” Nano Lett. 12, 5481–5486 (2012).
[CrossRef]

Bell, D. C.

T. J. Kempa, J. F. Cahoon, S. Kim, R. W. Day, D. C. Bell, H. Park, and C. M. Lieber, “Coaxial multishell nanowires with high-quality electronic interfaces and tunable optical cavities for ultrathin photovoltaics,” Proc. Natl. Acad. Sci. USA 109, 1407–1412 (2012).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).

Borghi, R.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Elsevier, 2008).

Brongersma, M. L.

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Cahoon, J. F.

T. J. Kempa, J. F. Cahoon, S. Kim, R. W. Day, D. C. Bell, H. Park, and C. M. Lieber, “Coaxial multishell nanowires with high-quality electronic interfaces and tunable optical cavities for ultrathin photovoltaics,” Proc. Natl. Acad. Sci. USA 109, 1407–1412 (2012).
[CrossRef]

Cai, W.

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Cao, L.

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Caorsi, S.

Dadap, J. I.

Day, R. W.

T. J. Kempa, J. F. Cahoon, S. Kim, R. W. Day, D. C. Bell, H. Park, and C. M. Lieber, “Coaxial multishell nanowires with high-quality electronic interfaces and tunable optical cavities for ultrathin photovoltaics,” Proc. Natl. Acad. Sci. USA 109, 1407–1412 (2012).
[CrossRef]

Day, T. D.

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 02885 (2013).
[CrossRef]

Dorfmuller, J.

J. Dorfmuller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010).
[CrossRef]

Driscoll, J. B.

Engheta, N.

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef]

Etrich, C.

J. Dorfmuller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010).
[CrossRef]

Fan, P.

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Fan, S.

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett. 105, 013901 (2010).
[CrossRef]

Fontana, Y.

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. Gómez Rivas, “Nanowire antenna emission,” Nano Lett. 12, 5481–5486 (2012).
[CrossRef]

Frezza, F.

Gómez Rivas, J.

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. Gómez Rivas, “Nanowire antenna emission,” Nano Lett. 12, 5481–5486 (2012).
[CrossRef]

Gori, F.

Green, W. M. J.

Grzela, G.

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. Gómez Rivas, “Nanowire antenna emission,” Nano Lett. 12, 5481–5486 (2012).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics the Finite Difference Time Domain Method (Artech House, 2005).

Hasan, M. A.

M. A. Hasan, “Electromagnetic scattering from nonlinear anisotropic cylinders—part 1: fundamental frequency,” IEEE Trans. Antennas Propag. 38, 523–533 (1990).
[CrossRef]

Healy, N.

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 02885 (2013).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).

Kempa, T. J.

T. J. Kempa, J. F. Cahoon, S. Kim, R. W. Day, D. C. Bell, H. Park, and C. M. Lieber, “Coaxial multishell nanowires with high-quality electronic interfaces and tunable optical cavities for ultrathin photovoltaics,” Proc. Natl. Acad. Sci. USA 109, 1407–1412 (2012).
[CrossRef]

Kern, K.

J. Dorfmuller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010).
[CrossRef]

Khunsin, W.

J. Dorfmuller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010).
[CrossRef]

Kim, S.

T. J. Kempa, J. F. Cahoon, S. Kim, R. W. Day, D. C. Bell, H. Park, and C. M. Lieber, “Coaxial multishell nanowires with high-quality electronic interfaces and tunable optical cavities for ultrathin photovoltaics,” Proc. Natl. Acad. Sci. USA 109, 1407–1412 (2012).
[CrossRef]

Kivshar, Y. S.

Li, Y.

Lieber, C. M.

T. J. Kempa, J. F. Cahoon, S. Kim, R. W. Day, D. C. Bell, H. Park, and C. M. Lieber, “Coaxial multishell nanowires with high-quality electronic interfaces and tunable optical cavities for ultrathin photovoltaics,” Proc. Natl. Acad. Sci. USA 109, 1407–1412 (2012).
[CrossRef]

Liu, X.

Massa, A.

Mehta, P.

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 02885 (2013).
[CrossRef]

Méndez, E. R.

Mendoza, B. S.

Miroshnichenko, A. E.

Mirzaei, A.

Osgood, R. M.

Paniagua-Domínguez, R.

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. Gómez Rivas, “Nanowire antenna emission,” Nano Lett. 12, 5481–5486 (2012).
[CrossRef]

Park, H.

T. J. Kempa, J. F. Cahoon, S. Kim, R. W. Day, D. C. Bell, H. Park, and C. M. Lieber, “Coaxial multishell nanowires with high-quality electronic interfaces and tunable optical cavities for ultrathin photovoltaics,” Proc. Natl. Acad. Sci. USA 109, 1407–1412 (2012).
[CrossRef]

Pastorino, M.

Peacock, A. C.

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 02885 (2013).
[CrossRef]

Rockstuhl, C.

J. Dorfmuller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010).
[CrossRef]

Ruan, Z.

Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett. 105, 013901 (2010).
[CrossRef]

Sánchez-Gil, J. A.

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. Gómez Rivas, “Nanowire antenna emission,” Nano Lett. 12, 5481–5486 (2012).
[CrossRef]

Santarsiero, M.

Schächter, L.

L. Schächter, Beam-wave Interaction in Periodic and Quasi-Periodic Structures (Springer, 2011).

Schettini, G.

Schuller, J. A.

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Shadrivov, I. V.

Suhailin, F. H.

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 02885 (2013).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics the Finite Difference Time Domain Method (Artech House, 2005).

Valencia, C. I.

Vasudev, A. P.

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Vial, A.

A. Vial, “Implementation of the critical points model in the recursive convolution method for modelling dispersive media with the finite-difference time domain method,” J. Opt. A 9, 745–748 (2007).
[CrossRef]

Vlasov, Y. A.

Vogelgesang, R.

J. Dorfmuller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010).
[CrossRef]

Vukovic, N.

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 02885 (2013).
[CrossRef]

White, J. S.

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Yu, Z.

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Zhan, Y.

Zhao, J.

Zhou, C.

IEEE Trans. Antennas Propag. (2)

M. A. Hasan, “Electromagnetic scattering from nonlinear anisotropic cylinders—part 1: fundamental frequency,” IEEE Trans. Antennas Propag. 38, 523–533 (1990).
[CrossRef]

S. Caorsi, A. Massa, and M. Pastorino, “Approximate solutions to the scattering by nonlinear isotropic dielectric cylinders of circular cross sections under TM illumination,” IEEE Trans. Antennas Propag. 43, 1262–1269 (1995).

J. Opt. A (1)

A. Vial, “Implementation of the critical points model in the recursive convolution method for modelling dispersive media with the finite-difference time domain method,” J. Opt. A 9, 745–748 (2007).
[CrossRef]

J. Opt. Soc. Am. A (3)

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

Nano Lett. (3)

J. Dorfmuller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010).
[CrossRef]

G. Grzela, R. Paniagua-Domínguez, T. Barten, Y. Fontana, J. A. Sánchez-Gil, and J. Gómez Rivas, “Nanowire antenna emission,” Nano Lett. 12, 5481–5486 (2012).
[CrossRef]

L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. 10, 439–445 (2010).
[CrossRef]

Opt. Express (3)

Phys. Rev. Lett. (2)

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef]

Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett. 105, 013901 (2010).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

T. J. Kempa, J. F. Cahoon, S. Kim, R. W. Day, D. C. Bell, H. Park, and C. M. Lieber, “Coaxial multishell nanowires with high-quality electronic interfaces and tunable optical cavities for ultrathin photovoltaics,” Proc. Natl. Acad. Sci. USA 109, 1407–1412 (2012).
[CrossRef]

Sci. Rep. (1)

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 02885 (2013).
[CrossRef]

Other (5)

A. Taflove and S. C. Hagness, Computational Electrodynamics the Finite Difference Time Domain Method (Artech House, 2005).

R. W. Boyd, Nonlinear Optics (Elsevier, 2008).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).

L. Schächter, Beam-wave Interaction in Periodic and Quasi-Periodic Structures (Springer, 2011).

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

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Figures (7)

Fig. 1.
Fig. 1.

Schematics of the problem: TM polarized plane wave is scattered on a multilayer cylindrical structure.

Fig. 2.
Fig. 2.

Flowchart of the iterative algorithm used for the solution of the nonlinear problem.

Fig. 3.
Fig. 3.

(a) Core-shell structure and incident plane wave, r1=18nm and r2=73nm. (b) Far-field radiation pattern for linear and nonlinear cases. (c) Field profile outside the structure in two linear and nonlinear regimes. The gray circle in the middle indicates the structure.

Fig. 4.
Fig. 4.

Field profile inside the structure for λ=800nm; both linear and nonlinear regimes using the first eight excited modes. Total value of Eφ and Er are plotted separately to demonstrate how they change in the boundaries. Eφ in mode n=5 is also plotted as an example of how higher modes are excited in the structure in nonlinear regime.

Fig. 5.
Fig. 5.

Change of the SCS spectrum with the increase of the incident field amplitude E0. The numbers on the curves indicate the value of αE02. The inset shows dependence of the SCS on the incident power at 800 and 811 nm.

Fig. 6.
Fig. 6.

Dependency of hysteresis loop properties on the wavelength of the incident plane wave. The difference between increasing and decreasing edges indicates the width of the loop. The hysteresis loop is plotted for two wavelengths in inset of Fig. 5.

Fig. 7.
Fig. 7.

Scattering cross-section of the core-shell nanowire as a function of incident power at λ=800nm. Solid line shows results of the semi-analytical method, while circles show results of the FDTD simulations.

Equations (19)

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

1rr(rHzr)+1r22Hzφ2+k2Hz=0.
Hz(r,φ)=a^zH0n=0+N(n)in[τlnJn(r¯)+ρlnHn(1)(r¯)]cos(nφ)=a^zH0n=0+N(n)Hzn(r)cos(nφ),
Eφ(r,φ)=a^φE0n=0+N(n)i(n+1)ε(r,λ)1/2[τlnJn(r¯)+ρlnHn(1)(r¯)]cos(nφ)=a^φE0n=0+N(n)Eφn(r)cos(nφ),
Er(r,φ)=a^rE0n=0+nN(n)i(n+1)(k0rε(r,λ))1[τlnJn(r¯)+ρlnHn(1)(r¯)]sin(nφ)=a^rE0n=0+N(n)Ern(r)sin(nφ),
SCS=2λπ(|ρL+10|2+2n=1+|ρL+1n|2).
Δε(r,φ)=α|Etotal(r,φ)|2.
Δε(r,φ)=δε0(r)+m=1+δεm(r)cos(mφ).
δεm(r)=N(m)π0πα|Etotal(r,φ)|2cos(mφ)dφ,
|Etotal|2=|E⃗φ|2+|E⃗r|2=(EφR)2+(EφI)2+(ErR)2+(ErI)2,
(EφR,I)2=E02i=0j=0N(i)N(j)Eφi,R,IEφj,R,Icos(iφ)cos(jφ),
(ErR,I)2=E02i=0j=0N(i)N(j)Eri,R,IErj,R,Isin(iφ)sin(jφ).
(EφR,I)2=E02i=0DEφi,R,I(r)cos(iφ),
(ErR,I)2=E02i=0DEri,R,I(r)cos(iφ),
DEφi,R,I(r)=12j=0(N(ij)N(j)Eφij,R,IEφj,R,I+2N(i+j)N(j)3N(i)Eφi+j,R,IEφj,R,I),
DEri,R,I(r)=12j=0(N(ij)N(j)Erij,R,IErj,R,I+2N(i+j)N(j)3N(i)Eri+j,R,IErj,R,I).
δεm(r)=αE02(DEφm,R+DEφm,I+DErm,R+DErm,I).
1rr(rHznr)+[k02(εL+δε0)n2r2]Hzn+k02SHznN(n)=0,
SHzn(r)=N(n)π0π(Δε(r,φ)δε0(r))Hz(r,φ)cos(nφ)dφ.
δεn(r)=(1β)δεprevn(r)+βδεnewn(r),

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