Abstract

We present a set of techniques that enhances a previously developed time domain simulation of wave propagation and allows the study of the optical response of a broad range of dielectric photonic structures. This method is particularly suitable for dealing with complex biological structures, especially due to the simple and intuitive way of defining the setup and the photonic structure to be simulated, which can be done via a digital image of the structure. The presented techniques include a direction filter that permits the decoupling of waves traveling simultaneously in different directions, a dynamic differential absorber to cancel the waves reflected at the edges of the simulation space, and a multifrequency excitation scheme. We also show how the simulation can be adapted to apply a near to far field method in order to evaluate the resulting wavefield outside the simulation domain. We validate these techniques, and, as an example, we apply the method to the complex structure of a microorganism called Diachea leucopoda, which exhibits a multicolor iridescent appearance.

© 2013 Optical Society of America

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    [CrossRef]
  37. P. J. Cobelli, A. Maurel, V. Pagneux, and P. Petitjeans, “Global measurement of water waves by Fourier transform profilometry,” Exp. Fluids 46, 1037–1047 (2009).
    [CrossRef]
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    [CrossRef]
  40. R. L. Higdon, “Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation,” Math. Comp. 47, 437–459 (1986).
  41. R. L. Higdon, “Numerical absorbing boundary conditions for the wave equation,” Math. Comp. 49, 65–90 (1987).
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    [CrossRef]

2012 (2)

2011 (1)

G. Schmidt and B. H. Kleemann, “Integral equation methods from grating theory to photonics: an overview and new approaches for conical diffraction,” J. Mod. Opt. 58, 407–423 (2011).
[CrossRef]

2010 (4)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[CrossRef]

A. E. Luna, D. C. Skigin, M. Inchaussandague, and A. R. Alsina, “Structural color in beetles of South America,” Proc. SPIE 7782, 778205 (2010).
[CrossRef]

M. Inchaussandague, D. Skigin, C. Carmaran, and S. Rosenfeldt, “Structural color in myxomycetes,” Opt. Express 18, 16055–16063 (2010).
[CrossRef]

2009 (4)

P. J. Cobelli, A. Maurel, V. Pagneux, and P. Petitjeans, “Global measurement of water waves by Fourier transform profilometry,” Exp. Fluids 46, 1037–1047 (2009).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef]

A. E. Dolinko, “From Newton’s second law to Huygens’s principle: visualizing waves in a large array of masses joined by springs,” Eur. J. Phys. 30, 1217–1228 (2009).
[CrossRef]

M. Lester, D. C. Skigin, and R. A. Depine, “Blaze produced by a dual-period array of subwavelength cylinders,” J. Opt. A 11, 045705 (2009).
[CrossRef]

2008 (1)

2007 (3)

2005 (1)

2004 (1)

A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92, 117403 (2004).
[CrossRef]

2003 (4)

L. Jensen, Z. Lei, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[CrossRef]

P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424, 852–855 (2003).
[CrossRef]

S. Huntington, J. Katsifolis, B. Gibson, J. Canning, K. Lyytikainen, J. Zagari, L. Cahill, and J. Love, “Retaining and characterising nano-structure within tapered air-silica structured optical fibers,” Opt. Express 11, 98–104 (2003).
[CrossRef]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

1998 (1)

1997 (1)

D. C. Skigin and R. A. Depine, “The multilayer modal method for electromagnetic scattering from surfaces with several arbitrarily shaped grooves,” J. Mod. Opt. 44, 1023–1036 (1997).
[CrossRef]

1994 (2)

J. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Physiol. 114, 185–200 (1994).

R. A. Depine and M. E. Inchaussandague, “Corrugated diffraction gratings in uniaxial crystals,” J. Opt. Soc. Am. A 11, 173–180 (1994).
[CrossRef]

1990 (1)

A. A. Maradudin, T. R. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

1987 (1)

R. L. Higdon, “Numerical absorbing boundary conditions for the wave equation,” Math. Comp. 49, 65–90 (1987).

1986 (1)

R. L. Higdon, “Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation,” Math. Comp. 47, 437–459 (1986).

1982 (1)

1981 (1)

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. A 71, 811–818 (1981).
[CrossRef]

1979 (2)

B. Engquist and A. Majda, “Numerical absorbing boundary conditions for the wave equation,” Commun. Pure Appl. Math 32, 313–357 (1979).
[CrossRef]

J. R. Andrewartha, J. R. Fox, and I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[CrossRef]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

1966 (1)

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).

1949 (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. Inst. Radio Eng. 37, 10–21 (1949).
[CrossRef]

1928 (1)

R. Courant, K. Friedrichs, and H. Lewy, “Über die partiellen Differenzengleichungen der mathematischen Physik,” Math. Ann. 100, 32–74 (1928).
[CrossRef]

Alsina, A. R.

A. E. Luna, D. C. Skigin, M. Inchaussandague, and A. R. Alsina, “Structural color in beetles of South America,” Proc. SPIE 7782, 778205 (2010).
[CrossRef]

Andrewartha, J. R.

J. R. Andrewartha, J. R. Fox, and I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[CrossRef]

Bader, D. A.

M. F. Su, I. El-Kady, D. A. Bader, and S. Lin, “A novel FDTD application featuring OpenMP-MPI hybrid parallelization,” in Proceedings of the 33rd International Conference on Parallel Processing (ICPP), Montreal, 2004, pp. 373–379.

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef]

Berenger, J.

J. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Physiol. 114, 185–200 (1994).

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Berthier, S.

S. Berthier, Iridescences, the Physical Colours of Insects (Springer, 2007).

Brenner, P.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[CrossRef]

Cahill, L.

Canning, J.

Carmaran, C.

Chan, C. T.

L. Jensen, Z. Lei, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Chandezon, J.

Cobelli, P. J.

P. J. Cobelli, A. Maurel, V. Pagneux, and P. Petitjeans, “Global measurement of water waves by Fourier transform profilometry,” Exp. Fluids 46, 1037–1047 (2009).
[CrossRef]

Cornet, G.

Courant, R.

R. Courant, K. Friedrichs, and H. Lewy, “Über die partiellen Differenzengleichungen der mathematischen Physik,” Math. Ann. 100, 32–74 (1928).
[CrossRef]

Depine, R. A.

M. Lester, D. C. Skigin, and R. A. Depine, “Blaze produced by a dual-period array of subwavelength cylinders,” J. Opt. A 11, 045705 (2009).
[CrossRef]

R. A. Depine and D. C. Skigin, “Multilayer modal method for diffraction from dielectric inhomogeneous apertures,” J. Opt. Soc. Am. A 15, 675–683 (1998).
[CrossRef]

D. C. Skigin and R. A. Depine, “The multilayer modal method for electromagnetic scattering from surfaces with several arbitrarily shaped grooves,” J. Mod. Opt. 44, 1023–1036 (1997).
[CrossRef]

R. A. Depine and M. E. Inchaussandague, “Corrugated diffraction gratings in uniaxial crystals,” J. Opt. Soc. Am. A 11, 173–180 (1994).
[CrossRef]

Dolinko, A.

Dolinko, A. E.

A. E. Dolinko, “From Newton’s second law to Huygens’s principle: visualizing waves in a large array of masses joined by springs,” Eur. J. Phys. 30, 1217–1228 (2009).
[CrossRef]

Dupuis, M.

Eleftheriades, G. V.

A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92, 117403 (2004).
[CrossRef]

El-Kady, I.

M. F. Su, I. El-Kady, D. A. Bader, and S. Lin, “A novel FDTD application featuring OpenMP-MPI hybrid parallelization,” in Proceedings of the 33rd International Conference on Parallel Processing (ICPP), Montreal, 2004, pp. 373–379.

Engelen, R.

Engquist, B.

B. Engquist and A. Majda, “Numerical absorbing boundary conditions for the wave equation,” Commun. Pure Appl. Math 32, 313–357 (1979).
[CrossRef]

Ergin, T.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[CrossRef]

Fox, J. R.

J. R. Andrewartha, J. R. Fox, and I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[CrossRef]

Friedrichs, K.

R. Courant, K. Friedrichs, and H. Lewy, “Über die partiellen Differenzengleichungen der mathematischen Physik,” Math. Ann. 100, 32–74 (1928).
[CrossRef]

Gaylord, T. K.

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. A 71, 811–818 (1981).
[CrossRef]

Gibson, B.

Gomez-Iglesias, A.

D. O’Brien, A. Gomez-Iglesias, M. D. Settle, A. Michaeli, M. Salib, and T. F. Krauss, “Tunable optical delay using photonic crystal heterostructure nanocavities,” Phys. Rev. B 76, 115110 (2007).
[CrossRef]

Grbic, A.

A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92, 117403 (2004).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech, 2005).

Hennelly, B.

Higdon, R. L.

R. L. Higdon, “Numerical absorbing boundary conditions for the wave equation,” Math. Comp. 49, 65–90 (1987).

R. L. Higdon, “Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation,” Math. Comp. 47, 437–459 (1986).

Huang, Y.-T.

Huntington, S.

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Inchaussandague, M.

Inchaussandague, M. E.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

Jensen, L.

L. Jensen, Z. Lei, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Joannopoulos, J.

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton University, 1995).

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Katsifolis, J.

Kinoshita, S.

S. Kinoshita, Structural Colors in the Realm of Nature (World Scientific, 2008).

Kleemann, B. H.

G. Schmidt and B. H. Kleemann, “Integral equation methods from grating theory to photonics: an overview and new approaches for conical diffraction,” J. Mod. Opt. 58, 407–423 (2011).
[CrossRef]

Kolle, M.

M. Kolle, Photonic Structures Inspired by Nature (Springer-Verlag, 2011).

Krauss, T. F.

D. O’Brien, A. Gomez-Iglesias, M. D. Settle, A. Michaeli, M. Salib, and T. F. Krauss, “Tunable optical delay using photonic crystal heterostructure nanocavities,” Phys. Rev. B 76, 115110 (2007).
[CrossRef]

M. Settle, R. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15, 219–226 (2007).
[CrossRef]

Kuipers, L.

Lei, Z.

L. Jensen, Z. Lei, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Lester, M.

M. Lester, D. C. Skigin, and R. A. Depine, “Blaze produced by a dual-period array of subwavelength cylinders,” J. Opt. A 11, 045705 (2009).
[CrossRef]

Lewy, H.

R. Courant, K. Friedrichs, and H. Lewy, “Über die partiellen Differenzengleichungen der mathematischen Physik,” Math. Ann. 100, 32–74 (1928).
[CrossRef]

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef]

Lin, S.

M. F. Su, I. El-Kady, D. A. Bader, and S. Lin, “A novel FDTD application featuring OpenMP-MPI hybrid parallelization,” in Proceedings of the 33rd International Conference on Parallel Processing (ICPP), Montreal, 2004, pp. 373–379.

Love, J.

Luna, A. E.

A. E. Luna, D. C. Skigin, M. Inchaussandague, and A. R. Alsina, “Structural color in beetles of South America,” Proc. SPIE 7782, 778205 (2010).
[CrossRef]

Lyytikainen, K.

Majda, A.

B. Engquist and A. Majda, “Numerical absorbing boundary conditions for the wave equation,” Commun. Pure Appl. Math 32, 313–357 (1979).
[CrossRef]

Maradudin, A. A.

A. A. Maradudin, T. R. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

Martelli, C.

Maurel, A.

P. J. Cobelli, A. Maurel, V. Pagneux, and P. Petitjeans, “Global measurement of water waves by Fourier transform profilometry,” Exp. Fluids 46, 1037–1047 (2009).
[CrossRef]

Maystre, D.

McGurn, A. R.

A. A. Maradudin, T. R. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

Meade, R.

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton University, 1995).

Méndez, E. R.

A. A. Maradudin, T. R. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

Michaeli, A.

M. Settle, R. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15, 219–226 (2007).
[CrossRef]

D. O’Brien, A. Gomez-Iglesias, M. D. Settle, A. Michaeli, M. Salib, and T. F. Krauss, “Tunable optical delay using photonic crystal heterostructure nanocavities,” Phys. Rev. B 76, 115110 (2007).
[CrossRef]

Michel, T. R.

A. A. Maradudin, T. R. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
[CrossRef]

Moharam, M. G.

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. A 71, 811–818 (1981).
[CrossRef]

O’Brien, D.

D. O’Brien, A. Gomez-Iglesias, M. D. Settle, A. Michaeli, M. Salib, and T. F. Krauss, “Tunable optical delay using photonic crystal heterostructure nanocavities,” Phys. Rev. B 76, 115110 (2007).
[CrossRef]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Pagneux, V.

P. J. Cobelli, A. Maurel, V. Pagneux, and P. Petitjeans, “Global measurement of water waves by Fourier transform profilometry,” Exp. Fluids 46, 1037–1047 (2009).
[CrossRef]

Pei, T.-H.

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T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

Petitjeans, P.

P. J. Cobelli, A. Maurel, V. Pagneux, and P. Petitjeans, “Global measurement of water waves by Fourier transform profilometry,” Exp. Fluids 46, 1037–1047 (2009).
[CrossRef]

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Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Russell, P.

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[CrossRef]

Salib, M.

D. O’Brien, A. Gomez-Iglesias, M. D. Settle, A. Michaeli, M. Salib, and T. F. Krauss, “Tunable optical delay using photonic crystal heterostructure nanocavities,” Phys. Rev. B 76, 115110 (2007).
[CrossRef]

M. Settle, R. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15, 219–226 (2007).
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P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424, 852–855 (2003).
[CrossRef]

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G. Schmidt and B. H. Kleemann, “Integral equation methods from grating theory to photonics: an overview and new approaches for conical diffraction,” J. Mod. Opt. 58, 407–423 (2011).
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Settle, M. D.

D. O’Brien, A. Gomez-Iglesias, M. D. Settle, A. Michaeli, M. Salib, and T. F. Krauss, “Tunable optical delay using photonic crystal heterostructure nanocavities,” Phys. Rev. B 76, 115110 (2007).
[CrossRef]

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[CrossRef]

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L. Jensen, Z. Lei, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

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A. E. Luna, D. C. Skigin, M. Inchaussandague, and A. R. Alsina, “Structural color in beetles of South America,” Proc. SPIE 7782, 778205 (2010).
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M. F. Su, I. El-Kady, D. A. Bader, and S. Lin, “A novel FDTD application featuring OpenMP-MPI hybrid parallelization,” in Proceedings of the 33rd International Conference on Parallel Processing (ICPP), Montreal, 2004, pp. 373–379.

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P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424, 852–855 (2003).
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T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
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J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
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J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
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[CrossRef]

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A. E. Dolinko, “From Newton’s second law to Huygens’s principle: visualizing waves in a large array of masses joined by springs,” Eur. J. Phys. 30, 1217–1228 (2009).
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[CrossRef]

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K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).

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J. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Physiol. 114, 185–200 (1994).

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D. C. Skigin and R. A. Depine, “The multilayer modal method for electromagnetic scattering from surfaces with several arbitrarily shaped grooves,” J. Mod. Opt. 44, 1023–1036 (1997).
[CrossRef]

G. Schmidt and B. H. Kleemann, “Integral equation methods from grating theory to photonics: an overview and new approaches for conical diffraction,” J. Mod. Opt. 58, 407–423 (2011).
[CrossRef]

J. Opt. A (1)

M. Lester, D. C. Skigin, and R. A. Depine, “Blaze produced by a dual-period array of subwavelength cylinders,” J. Opt. A 11, 045705 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

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Nat. Mater. (1)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef]

Nature (1)

P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424, 852–855 (2003).
[CrossRef]

Opt. Acta (1)

J. R. Andrewartha, J. R. Fox, and I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[CrossRef]

Opt. Express (5)

Phys. Rev. B (1)

D. O’Brien, A. Gomez-Iglesias, M. D. Settle, A. Michaeli, M. Salib, and T. F. Krauss, “Tunable optical delay using photonic crystal heterostructure nanocavities,” Phys. Rev. B 76, 115110 (2007).
[CrossRef]

Phys. Rev. Lett. (3)

L. Jensen, Z. Lei, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92, 117403 (2004).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

Proc. Inst. Radio Eng. (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. Inst. Radio Eng. 37, 10–21 (1949).
[CrossRef]

Proc. SPIE (1)

A. E. Luna, D. C. Skigin, M. Inchaussandague, and A. R. Alsina, “Structural color in beetles of South America,” Proc. SPIE 7782, 778205 (2010).
[CrossRef]

Science (2)

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[CrossRef]

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[CrossRef]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

Other (7)

M. Kolle, Photonic Structures Inspired by Nature (Springer-Verlag, 2011).

M. F. Su, I. El-Kady, D. A. Bader, and S. Lin, “A novel FDTD application featuring OpenMP-MPI hybrid parallelization,” in Proceedings of the 33rd International Conference on Parallel Processing (ICPP), Montreal, 2004, pp. 373–379.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

S. Kinoshita, Structural Colors in the Realm of Nature (World Scientific, 2008).

S. Berthier, Iridescences, the Physical Colours of Insects (Springer, 2007).

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton University, 1995).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech, 2005).

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Figures (18)

Fig. 1.
Fig. 1.

Particle array representing the physical model of the simulation.

Fig. 2.
Fig. 2.

Geometric representation of the action performed by the positive DF operator.

Fig. 3.
Fig. 3.

Angle α between the direction of propagation of the plane wave (along vw) and the filtering direction (along v).

Fig. 4.
Fig. 4.

Attenuation of the plane wave as a function of the angle α between its direction of propagation and the filtering direction.

Fig. 5.
Fig. 5.

Angular effect of the DF on a circular wavefront.

Fig. 6.
Fig. 6.

(a) Source emitting Gaussian waves in directions +x and x. (b) Secondary plane of the DF that cancels waves traveling toward the +x direction. (c) Secondary plane of the DF that cancels waves traveling toward the x direction. Arrows show the wavefront propagation directions.

Fig. 7.
Fig. 7.

Amplitude of a propagating wave at two fixed points located in x=xa and x=xb.

Fig. 8.
Fig. 8.

Effective wavelength λeff and effective phase velocity veff of an obliquely incident wave forming an angle α with the normal to the simulation space edge.

Fig. 9.
Fig. 9.

Delay versus angle of incidence: discretized (solid line) and calculated (dashed line).

Fig. 10.
Fig. 10.

Location of the absorbing and the reading points for a 2D simulation space. The distance Δd is also indicated.

Fig. 11.
Fig. 11.

Numerical experiment with the ADDA: Reflectance versus angle of incidence α for δd=2 (blue solid line), δd=4 (green dashed line), and δd=8 (red dotted line).

Fig. 12.
Fig. 12.

Attenuation versus angle of incidence α for δd=2 (blue solid line), δd=4 (green dashed line), and δd=8 (red dotted line).

Fig. 13.
Fig. 13.

Intensity diagram of a Gaussian beam forming an angle α=20° with the normal to the lower horizontal edge of the simulation space for the case δd=4. (a) Without ADDA and (b) with ADDA.

Fig. 14.
Fig. 14.

Schematic diagram of the TF implementation.

Fig. 15.
Fig. 15.

Simulated intensity diagram of a multifrequency plane wave scattered by an opaque cylinder of a diameter of 620 nm. (a) The multifrequency wavefield, (b) λ=780nm component, (c) λ=570nm component, and (d) λ=380nm component.

Fig. 16.
Fig. 16.

(a) Diachea leucopoda observed under the optical microscope and (b) TEM image of the peridium cross section.

Fig. 17.
Fig. 17.

Reflected near field intensity diagram produced by the peridium of the Diachea leucopoda obtained with the simulation method, for a wavelength of 380 nm. Brighter regions correspond to higher intensities.

Fig. 18.
Fig. 18.

Far field reflectance (R) as a function of the observation angle α and of the wavelength λ for the peridium of the Diachea leucopoda.

Equations (46)

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

2At2=Tμ2AγμAt+Etμ,
Mphys=m0+Mmp,
Dphys=Dμp,
Ephys=rp(E128),
Et=Ephyssin(ωτnnc+φ),
τn=vdvphysσp,
ωd=ωvdσpc.
vdσp<πcω.
F(+)[A(x,t)]=A(x,t+Δt)A(xvΔt,t),
A(x,t+Δt)=A(xvΔt,t).
F(+)[A(x,t)]=A(xvΔt,t)A(xvΔt,t)=0t.
A(xvΔt,t)=B+(xvΔt,t)+B(xvΔt,t)
A(x,t+Δt)=B+(x,t+Δt)+B(x,t+Δt),
F(+)[A(x,t)]=B+(x,t+Δt)+B(x,t+Δt)B+(xvΔt,t)B(xvΔt,t).
B+(x,t+Δt)=B+(xvΔt,t)
B(x,t+Δt)=B(x+vΔt,t).
F(+)[A(x,t)]=B(x+vΔt,t)B(xvΔt,t).
F(+)[A(xvΔt,t)]=B(x,t)B(x,t2Δt),
F(+)[A(x,t)]2ΔtB(x+vΔt,t)t.
F2(v,δ)[A2(r,t)]=A2(r,t+δ)A2(rvδ,t).
A2(r,t)=Aeikw(rvwt),
|F2(v,δ)(α)|=A|eiωδeiωδcos(α)|,
μa(α)=1|F2(v,δ)(α)|/|F2(v,δ)|max,
μa(α)=12[cos(α)+1].
F=(ϕx,ϕy)
Ab(t1)=Aa(t0),
AM(nc)=AM1(nc2),
A1(nc)=A2(nc2),
λeff=λw/cos(α),
veff=ωkeff=λefff
δeff=1veff=cos(α)vw=δdcos(α),
α=arctan(ϕyϕx).
Et=i=1ftotEisin(ωiτnnc+φi),
nctot=2p2+q2vd0.
Fextm=d2zdt2+γdodzdt+ωdo2z,
Δωγdo,
ωr=ωdo2γdo22ωdo,
Q=ωdoγdo.
tMFE=tSFE(1+δMFEftot),
ncStot>(1+δMFEftot)ncMtot,
vdσp=ωdcωπcω
εr(λe)=100|IMFE(λe)ISFE(λe)|ISFE(λe)|,
Zt(r)=Ca[G(r|r)n^a·Zt(r)Zt(r)n^a·G(r|r)]dC,
G(r|r)=i4H0(2)(k|rr|)
Zr(t)=Ar(t)eiωt=Ar(t)cos(ωt)iAr(t)sin(ωt),
ZI(r,t)=ddt{ZR(r,t)}.

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