Abstract

This work describes a 3-D Finite-Difference Time-Domain (FDTD) computational approach for the optical characterization of an opal photonic crystal. To fully validate the approach we compare the computed transmittance of a crystal model with the transmittance of an actual crystal sample, as measured over the 400 ÷ 750 nm wavelength range. The opal photonic crystal considered has a face-centered cubic (FCC) lattice structure of spherical particles made of polystyrene (a non-absorptive material with constant relative dielectric permittivity). Light-matter interaction is described by numerically solving Maxwell’s equations via a parallelized FDTD code. Periodic boundary conditions (PBCs) at the outer edges of the crystal are used to effectively enforce an infinite lateral extension of the sample. A method to study the propagating Bloch modes inside the crystal bulk is also proposed, which allows the reconstruction of the ω-k dispersion curve for k sweeping discretely the Brillouin zone of the crystal.

© 2014 Optical Society of America

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References

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  1. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
    [Crossref]
  2. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  3. A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel FDTD modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
    [Crossref]
  4. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals. Molding the Flow of Light, 2nd ed. (Princeton University, 2008), Appendix B.
  5. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), Chap. VIII.
  6. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998), Chap. 9.
  7. W. Gropp, E. L. Lusk, and A. Skjellum, Using MPI. Portable Parallel Programming With the Message Passing Interface, 2nd ed. (MIT, 1999).
  8. W. Gropp, E. L. Lusk, and R. Thakur, Using MPI-2. Advanced Features in the Message Passing Interface (MIT, 1999).
  9. P. Pacheco, Parallel Programming with MPI (Morgan Kaufmann, 1997).
  10. A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. 23, 623–630 (1975).
    [Crossref]
  11. J. A. Roden and S. D. Gedney, “Convolution PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Tech. Lett. 27(5), 334–339 (2000).
    [Crossref]
  12. R. Pontalti, L. Cristoforetti, and L. Cescatti, “The frequency dependent FD-TD method for multi-frequency results in microwave hypertermia treatment simulation,” Phys. Med. Biol. 38, 1283–1298 (1993).
    [Crossref]
  13. R. Pontalti, J. Nadobny, P. Wust, A. Vaccari, and D. Sullivan, “Investigation of static and quasi-static fields inherent to the pulsed FDTD method,” IEEE Trans. Microwave Theory Tech.50(8), (2002).
    [Crossref]
  14. A. Vaccari, R. Pontalti, C. Malacarne, and L. Cristoforetti, “A robust and efficient subgridding algorithm for finite-difference time-domain simulations of Maxwell’s equations,” J. Comput. Phys. 194, 117–139 (2004).
    [Crossref]
  15. A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
    [Crossref]

2014 (1)

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel FDTD modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

2009 (1)

A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
[Crossref]

2004 (1)

A. Vaccari, R. Pontalti, C. Malacarne, and L. Cristoforetti, “A robust and efficient subgridding algorithm for finite-difference time-domain simulations of Maxwell’s equations,” J. Comput. Phys. 194, 117–139 (2004).
[Crossref]

2000 (1)

J. A. Roden and S. D. Gedney, “Convolution PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Tech. Lett. 27(5), 334–339 (2000).
[Crossref]

1993 (1)

R. Pontalti, L. Cristoforetti, and L. Cescatti, “The frequency dependent FD-TD method for multi-frequency results in microwave hypertermia treatment simulation,” Phys. Med. Biol. 38, 1283–1298 (1993).
[Crossref]

1975 (1)

A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. 23, 623–630 (1975).
[Crossref]

1966 (1)

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

Almeida, R. M.

A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
[Crossref]

Armellini, C.

A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
[Crossref]

Bozzoli, A.

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel FDTD modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

Brodwin, M. E.

A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. 23, 623–630 (1975).
[Crossref]

Calà Lesina, A.

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel FDTD modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

Calliari, L.

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel FDTD modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

Cescatti, L.

R. Pontalti, L. Cristoforetti, and L. Cescatti, “The frequency dependent FD-TD method for multi-frequency results in microwave hypertermia treatment simulation,” Phys. Med. Biol. 38, 1283–1298 (1993).
[Crossref]

Chiappini, A.

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel FDTD modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
[Crossref]

Chiasera, A.

A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
[Crossref]

Conti, G. N.

A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
[Crossref]

Cristoforetti, L.

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel FDTD modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

A. Vaccari, R. Pontalti, C. Malacarne, and L. Cristoforetti, “A robust and efficient subgridding algorithm for finite-difference time-domain simulations of Maxwell’s equations,” J. Comput. Phys. 194, 117–139 (2004).
[Crossref]

R. Pontalti, L. Cristoforetti, and L. Cescatti, “The frequency dependent FD-TD method for multi-frequency results in microwave hypertermia treatment simulation,” Phys. Med. Biol. 38, 1283–1298 (1993).
[Crossref]

Ferrari, M.

A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
[Crossref]

Fortes, L.

A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
[Crossref]

Gedney, S. D.

J. A. Roden and S. D. Gedney, “Convolution PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Tech. Lett. 27(5), 334–339 (2000).
[Crossref]

Gonçalves, M. C.

A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
[Crossref]

Gropp, W.

W. Gropp, E. L. Lusk, and A. Skjellum, Using MPI. Portable Parallel Programming With the Message Passing Interface, 2nd ed. (MIT, 1999).

W. Gropp, E. L. Lusk, and R. Thakur, Using MPI-2. Advanced Features in the Message Passing Interface (MIT, 1999).

Guider, R.

A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
[Crossref]

Hagness, S. C.

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

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998), Chap. 9.

Jestin, Y.

A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
[Crossref]

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals. Molding the Flow of Light, 2nd ed. (Princeton University, 2008), Appendix B.

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals. Molding the Flow of Light, 2nd ed. (Princeton University, 2008), Appendix B.

Lusk, E. L.

W. Gropp, E. L. Lusk, and R. Thakur, Using MPI-2. Advanced Features in the Message Passing Interface (MIT, 1999).

W. Gropp, E. L. Lusk, and A. Skjellum, Using MPI. Portable Parallel Programming With the Message Passing Interface, 2nd ed. (MIT, 1999).

Malacarne, C.

A. Vaccari, R. Pontalti, C. Malacarne, and L. Cristoforetti, “A robust and efficient subgridding algorithm for finite-difference time-domain simulations of Maxwell’s equations,” J. Comput. Phys. 194, 117–139 (2004).
[Crossref]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals. Molding the Flow of Light, 2nd ed. (Princeton University, 2008), Appendix B.

Nadobny, J.

R. Pontalti, J. Nadobny, P. Wust, A. Vaccari, and D. Sullivan, “Investigation of static and quasi-static fields inherent to the pulsed FDTD method,” IEEE Trans. Microwave Theory Tech.50(8), (2002).
[Crossref]

Pacheco, P.

P. Pacheco, Parallel Programming with MPI (Morgan Kaufmann, 1997).

Pelli, S.

A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
[Crossref]

Pontalti, R.

A. Vaccari, R. Pontalti, C. Malacarne, and L. Cristoforetti, “A robust and efficient subgridding algorithm for finite-difference time-domain simulations of Maxwell’s equations,” J. Comput. Phys. 194, 117–139 (2004).
[Crossref]

R. Pontalti, L. Cristoforetti, and L. Cescatti, “The frequency dependent FD-TD method for multi-frequency results in microwave hypertermia treatment simulation,” Phys. Med. Biol. 38, 1283–1298 (1993).
[Crossref]

R. Pontalti, J. Nadobny, P. Wust, A. Vaccari, and D. Sullivan, “Investigation of static and quasi-static fields inherent to the pulsed FDTD method,” IEEE Trans. Microwave Theory Tech.50(8), (2002).
[Crossref]

Prudenzano, F.

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel FDTD modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

Ramunno, L.

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel FDTD modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

Retoux, R.

A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
[Crossref]

Righini, G. C.

A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
[Crossref]

Roden, J. A.

J. A. Roden and S. D. Gedney, “Convolution PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Tech. Lett. 27(5), 334–339 (2000).
[Crossref]

Skjellum, A.

W. Gropp, E. L. Lusk, and A. Skjellum, Using MPI. Portable Parallel Programming With the Message Passing Interface, 2nd ed. (MIT, 1999).

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), Chap. VIII.

Sullivan, D.

R. Pontalti, J. Nadobny, P. Wust, A. Vaccari, and D. Sullivan, “Investigation of static and quasi-static fields inherent to the pulsed FDTD method,” IEEE Trans. Microwave Theory Tech.50(8), (2002).
[Crossref]

Taflove, A.

A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. 23, 623–630 (1975).
[Crossref]

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

Thakur, R.

W. Gropp, E. L. Lusk, and R. Thakur, Using MPI-2. Advanced Features in the Message Passing Interface (MIT, 1999).

Vaccari, A.

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel FDTD modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

A. Vaccari, R. Pontalti, C. Malacarne, and L. Cristoforetti, “A robust and efficient subgridding algorithm for finite-difference time-domain simulations of Maxwell’s equations,” J. Comput. Phys. 194, 117–139 (2004).
[Crossref]

R. Pontalti, J. Nadobny, P. Wust, A. Vaccari, and D. Sullivan, “Investigation of static and quasi-static fields inherent to the pulsed FDTD method,” IEEE Trans. Microwave Theory Tech.50(8), (2002).
[Crossref]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals. Molding the Flow of Light, 2nd ed. (Princeton University, 2008), Appendix B.

Wust, P.

R. Pontalti, J. Nadobny, P. Wust, A. Vaccari, and D. Sullivan, “Investigation of static and quasi-static fields inherent to the pulsed FDTD method,” IEEE Trans. Microwave Theory Tech.50(8), (2002).
[Crossref]

Yee, K. S.

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

IEEE Trans. Antennas Propag. (1)

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

IEEE Trans. Microwave Theory Tech. (1)

A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. 23, 623–630 (1975).
[Crossref]

J. Comput. Phys. (1)

A. Vaccari, R. Pontalti, C. Malacarne, and L. Cristoforetti, “A robust and efficient subgridding algorithm for finite-difference time-domain simulations of Maxwell’s equations,” J. Comput. Phys. 194, 117–139 (2004).
[Crossref]

J. Non-Cryst. Solids (1)

A. Chiappini, C. Armellini, A. Chiasera, M. Ferrari, L. Fortes, M. C. Gonçalves, R. Guider, Y. Jestin, R. Retoux, G. N. Conti, S. Pelli, R. M. Almeida, and G. C. Righini, “An alternative method to obtain direct opal photonic crystal structures,” J. Non-Cryst. Solids 355, 1167–1170 (2009).
[Crossref]

Microw. Opt. Tech. Lett. (1)

J. A. Roden and S. D. Gedney, “Convolution PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Tech. Lett. 27(5), 334–339 (2000).
[Crossref]

Opt. Eng. (1)

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel FDTD modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

Phys. Med. Biol. (1)

R. Pontalti, L. Cristoforetti, and L. Cescatti, “The frequency dependent FD-TD method for multi-frequency results in microwave hypertermia treatment simulation,” Phys. Med. Biol. 38, 1283–1298 (1993).
[Crossref]

Other (8)

R. Pontalti, J. Nadobny, P. Wust, A. Vaccari, and D. Sullivan, “Investigation of static and quasi-static fields inherent to the pulsed FDTD method,” IEEE Trans. Microwave Theory Tech.50(8), (2002).
[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals. Molding the Flow of Light, 2nd ed. (Princeton University, 2008), Appendix B.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), Chap. VIII.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998), Chap. 9.

W. Gropp, E. L. Lusk, and A. Skjellum, Using MPI. Portable Parallel Programming With the Message Passing Interface, 2nd ed. (MIT, 1999).

W. Gropp, E. L. Lusk, and R. Thakur, Using MPI-2. Advanced Features in the Message Passing Interface (MIT, 1999).

P. Pacheco, Parallel Programming with MPI (Morgan Kaufmann, 1997).

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

Supplementary Material (3)

» Media 1: AVI (14660 KB)     
» Media 2: AVI (14061 KB)     
» Media 3: AVI (9096 KB)     

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Figures (12)

Fig. 1
Fig. 1 Lateral xy (top), yz (bottom-left) and front xz (bottom-right) sections of the FCC lattice as modeled in the FDTD code.
Fig. 2
Fig. 2 Two-dimensional scheme of the FDTD modeling with PBCs.
Fig. 3
Fig. 3 Overall spatial mesh decomposition for parallelization.
Fig. 4
Fig. 4 Schematic of FDTD data exchange between contiguous MPI processes.
Fig. 5
Fig. 5 Light-opals interaction: xy (top, see Media 1), yz (bottom-left, see Media 2) and xz (bottom-right, see Media 3) planes.
Fig. 6
Fig. 6 Numerical transmittance (top curve) and reflectance (bottom curve) for a crystal slab made of 20 stacked (1, 1, 1) planes.
Fig. 7
Fig. 7 Numerical transmittance for a crystal slab made of 100 stacked (1, 1, 1) planes (top curve) compared with an experimental result (bottom curve) for a macroscopic sample of the same FCC crystal.
Fig. 8
Fig. 8 Normalized DFT module of E⃗ on a xy plane inside the crystal sample at 500 nm (top), 550 nm (middle) and 600 nm (bottom).
Fig. 9
Fig. 9 Normalized DFT module of E⃗ on a yz plane inside the crystal sample at 500 nm (top), 550 nm (middle) and 600 nm (bottom).
Fig. 10
Fig. 10 Examples of numerically calculated spatial spectra for ω = 2πc/λ, with λ = 400 nm (top-left), 540 nm (top-right) and 700 nm (bottom).
Fig. 11
Fig. 11 Numerical amplitude spatial spectra of z(r⃗; ω) for ω = 2πc/λ, with λ = 700 nm (left curve), 540 nm (middle curve) and 400 nm (right curve).
Fig. 12
Fig. 12 Quantitative reconstruction of the dispersion curve of an opal FCC photonic crystal.

Equations (1)

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E ˜ z ( r ; ω ) e i k r d 3 r ~ , m , n E ˜ z ( , m , n ; ω ) e i k r , m , n .

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