Abstract

Control of electromagnetic fields using graded photonic crystals (GPhCs) is explored using equations of Hamiltonian optics. Contrary to previous works devoted to the long-wavelength regime enabling homogenization of photonic metamaterials, attention is paid to short-wavelength light propagation for the possible use of dispersive phenomena and light path reconfiguring with wavelength. An analytical description of the dispersion diagram of a square PhCs is extracted using plane wave expansion calculations, making possible the description of arbitrary light paths in 2-D GPhC structures and fast optimization to find the conditions suited to make light follow prescribed paths. The validity of the approach is validated by comparison with finite-difference time-domain simulation. For purpose and illustration, a wavelength demultiplexing structure with four channels and an overall surface of 60 µm x $60 µm is proposed. The described methodology is applicable to the generalized 2-D chirp of PhC lattice or filling ratio parameters for electromagnetic field shaping.

© 2011 IEEE

PDF Article

References

  • View by:
  • |
  • |

  1. S. A. Cummer, B.-I. Popa, D. Schuring, D. R. Smith, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621-1-036621-5 (2006).
  2. J. B. Pendry, D. Schurig, D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
  3. U. Leonhardt, T. Tyc, "Broadband invisibility by non-euclidean cloaking," Science 323, 110-112 (2009).
  4. N. I. Landry, W. J. Padilla, "Guiding light with conformal transformations," Opt. Exp. 17, 14872-14879 (2009).
  5. J. Li, J. B. Pendry, "Hiding under the carpet: A new strategy for cloaking," Phys. Rev. Lett. 101, 203901-1-203901-3 (2008).
  6. L. H. Gabrielli, J. Cardenas, C. B. Poitras, M. Lipson, "Silicon nanostructure cloak operating at optical frequencies," Nature Photon. (Lett.) 3, 1-3 (2009).
  7. J. Valentine, J. Li, T. Zentgraf, G. Bartal, X. Zhang, "An optical cloak made of dielectrics," Nature Mater. 8, 568-571 (2009).
  8. A. Lupu, E. Cassan, S. Laval, L. El Melhaoui, P. Lyan, J. Fedeli, "Experimental evidence for superprism phenomena in SOI photonic crystals," Opt. Exp. 12, 5690-5696 (2004).
  9. T. Matsumoto, S. Fujita, T. Baba, "Wavelength demultiplexer consisting of photonic crystal superprism and superlens," Opt. Exp. 13, 10768-10776 (2005).
  10. D. Bernier, X. Le Roux, A. Lupu, D. Marris-Morini, L. Vivien, E. Cassan, "Compact, low cross-talk CWDM demultiplexer using photonic crystal superprism," Opt. Exp. 16, 17209-17214 (2008).
  11. N. Fabre, L. Lalouat, B. Cluzel, X. Mélique, D. Lippens, F. de Fornel, O. Vanbésien, "Optical near-field microscopy of light focusing through a photonic crystal flat lens," Phys. Rev. Lett. 101, 073901-1-073901-4 (2008).
  12. P. S. J. Russell, "Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures," J. Modern. Optics 38, 1599-1619 (1991).
  13. P. S. J. Russell, T. A. Birks, "Hamiltonian approach of non-uniform photonic crystals," J. Lightw. Technol. 17, 1982-1988 (1999).
  14. Jiao, S. Fan, D. A. B. Miller, "Designing for beam propagation in periodic and nonperiodic nanostructures: Extended Hamiltonian method," Phys. Rev. E 70, 036612-1-036612-9 (2004).
  15. E. Centeno, D. Cassagne, "Graded photonic crystals," Opt. Lett. 30, 2278-2280 (2005).
  16. E. Centeno, D. Cassagne, J.-P. Albert, "Mirage and superbending effect in two-dimensional graded photonic crystals," Phys. Rev. B 73, 235119-1-235119-5 (2006).
  17. E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, J.-M. Lourtioz, "Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect," Appl. Phys. Lett. 92, 133501-1-133501-3 (2008).
  18. S. Kawakami, "Analytically solvable model of photonic crystal structures and novel phenomena," J. Lightw. Technol. 20, 1644-1650 (2002).
  19. http://ab-initio.mit.edu/wiki/index.php/MIT_Photonic_Bands.
  20. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, "MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method," Comput. Phys. Commun. 181, 687-702 (2009).

2009 (5)

U. Leonhardt, T. Tyc, "Broadband invisibility by non-euclidean cloaking," Science 323, 110-112 (2009).

N. I. Landry, W. J. Padilla, "Guiding light with conformal transformations," Opt. Exp. 17, 14872-14879 (2009).

L. H. Gabrielli, J. Cardenas, C. B. Poitras, M. Lipson, "Silicon nanostructure cloak operating at optical frequencies," Nature Photon. (Lett.) 3, 1-3 (2009).

J. Valentine, J. Li, T. Zentgraf, G. Bartal, X. Zhang, "An optical cloak made of dielectrics," Nature Mater. 8, 568-571 (2009).

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, "MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method," Comput. Phys. Commun. 181, 687-702 (2009).

2008 (4)

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, J.-M. Lourtioz, "Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect," Appl. Phys. Lett. 92, 133501-1-133501-3 (2008).

D. Bernier, X. Le Roux, A. Lupu, D. Marris-Morini, L. Vivien, E. Cassan, "Compact, low cross-talk CWDM demultiplexer using photonic crystal superprism," Opt. Exp. 16, 17209-17214 (2008).

N. Fabre, L. Lalouat, B. Cluzel, X. Mélique, D. Lippens, F. de Fornel, O. Vanbésien, "Optical near-field microscopy of light focusing through a photonic crystal flat lens," Phys. Rev. Lett. 101, 073901-1-073901-4 (2008).

J. Li, J. B. Pendry, "Hiding under the carpet: A new strategy for cloaking," Phys. Rev. Lett. 101, 203901-1-203901-3 (2008).

2006 (3)

S. A. Cummer, B.-I. Popa, D. Schuring, D. R. Smith, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621-1-036621-5 (2006).

J. B. Pendry, D. Schurig, D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).

E. Centeno, D. Cassagne, J.-P. Albert, "Mirage and superbending effect in two-dimensional graded photonic crystals," Phys. Rev. B 73, 235119-1-235119-5 (2006).

2005 (2)

T. Matsumoto, S. Fujita, T. Baba, "Wavelength demultiplexer consisting of photonic crystal superprism and superlens," Opt. Exp. 13, 10768-10776 (2005).

E. Centeno, D. Cassagne, "Graded photonic crystals," Opt. Lett. 30, 2278-2280 (2005).

2004 (2)

Jiao, S. Fan, D. A. B. Miller, "Designing for beam propagation in periodic and nonperiodic nanostructures: Extended Hamiltonian method," Phys. Rev. E 70, 036612-1-036612-9 (2004).

A. Lupu, E. Cassan, S. Laval, L. El Melhaoui, P. Lyan, J. Fedeli, "Experimental evidence for superprism phenomena in SOI photonic crystals," Opt. Exp. 12, 5690-5696 (2004).

2002 (1)

S. Kawakami, "Analytically solvable model of photonic crystal structures and novel phenomena," J. Lightw. Technol. 20, 1644-1650 (2002).

1999 (1)

P. S. J. Russell, T. A. Birks, "Hamiltonian approach of non-uniform photonic crystals," J. Lightw. Technol. 17, 1982-1988 (1999).

1991 (1)

P. S. J. Russell, "Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures," J. Modern. Optics 38, 1599-1619 (1991).

Appl. Phys. Lett. (1)

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, J.-M. Lourtioz, "Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect," Appl. Phys. Lett. 92, 133501-1-133501-3 (2008).

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, "MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method," Comput. Phys. Commun. 181, 687-702 (2009).

J. Lightw. Technol. (2)

S. Kawakami, "Analytically solvable model of photonic crystal structures and novel phenomena," J. Lightw. Technol. 20, 1644-1650 (2002).

P. S. J. Russell, T. A. Birks, "Hamiltonian approach of non-uniform photonic crystals," J. Lightw. Technol. 17, 1982-1988 (1999).

J. Modern. Optics (1)

P. S. J. Russell, "Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures," J. Modern. Optics 38, 1599-1619 (1991).

Nature Mater. (1)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, X. Zhang, "An optical cloak made of dielectrics," Nature Mater. 8, 568-571 (2009).

Nature Photon. (Lett.) (1)

L. H. Gabrielli, J. Cardenas, C. B. Poitras, M. Lipson, "Silicon nanostructure cloak operating at optical frequencies," Nature Photon. (Lett.) 3, 1-3 (2009).

Opt. Exp. (4)

A. Lupu, E. Cassan, S. Laval, L. El Melhaoui, P. Lyan, J. Fedeli, "Experimental evidence for superprism phenomena in SOI photonic crystals," Opt. Exp. 12, 5690-5696 (2004).

T. Matsumoto, S. Fujita, T. Baba, "Wavelength demultiplexer consisting of photonic crystal superprism and superlens," Opt. Exp. 13, 10768-10776 (2005).

D. Bernier, X. Le Roux, A. Lupu, D. Marris-Morini, L. Vivien, E. Cassan, "Compact, low cross-talk CWDM demultiplexer using photonic crystal superprism," Opt. Exp. 16, 17209-17214 (2008).

N. I. Landry, W. J. Padilla, "Guiding light with conformal transformations," Opt. Exp. 17, 14872-14879 (2009).

Opt. Lett. (1)

Phys. Rev. B (1)

E. Centeno, D. Cassagne, J.-P. Albert, "Mirage and superbending effect in two-dimensional graded photonic crystals," Phys. Rev. B 73, 235119-1-235119-5 (2006).

Phys. Rev. E (2)

Jiao, S. Fan, D. A. B. Miller, "Designing for beam propagation in periodic and nonperiodic nanostructures: Extended Hamiltonian method," Phys. Rev. E 70, 036612-1-036612-9 (2004).

S. A. Cummer, B.-I. Popa, D. Schuring, D. R. Smith, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621-1-036621-5 (2006).

Phys. Rev. Lett. (2)

J. Li, J. B. Pendry, "Hiding under the carpet: A new strategy for cloaking," Phys. Rev. Lett. 101, 203901-1-203901-3 (2008).

N. Fabre, L. Lalouat, B. Cluzel, X. Mélique, D. Lippens, F. de Fornel, O. Vanbésien, "Optical near-field microscopy of light focusing through a photonic crystal flat lens," Phys. Rev. Lett. 101, 073901-1-073901-4 (2008).

Science (2)

J. B. Pendry, D. Schurig, D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).

U. Leonhardt, T. Tyc, "Broadband invisibility by non-euclidean cloaking," Science 323, 110-112 (2009).

Other (1)

http://ab-initio.mit.edu/wiki/index.php/MIT_Photonic_Bands.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.