Abstract

We investigated negative refraction and subwavelength imaging by a mechanically tunable photonic crystal (PC) slab. A honeycomb-structured PC composed of a silicon–polyimide membrane was used because it exhibits isotropic negative refraction within the second photonic band. Using the finite-difference time-domain (FDTD) method, we demonstrated focusing properties of the PC lenses at various frequencies and mechanical stresses. Analyses based on a ray optics model and equifrequency surface also confirmed the behavior observed by the FDTD simulations. These results suggested a mechanically tunable superlens, whose achievable frequency bandwidth was 12.9% of the center frequency for a mechanical stress of ±10%.

© 2006 Optical Society of America

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  1. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  2. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
    [CrossRef]
  4. A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell's law," Phys. Rev. Lett. 90, 137401 (2003).
    [CrossRef] [PubMed]
  5. N. C. Panoiu and R. M. Osgood, "Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials," Phys. Rev. E 68, 016611 (2003).
    [CrossRef]
  6. S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
    [CrossRef] [PubMed]
  7. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
    [CrossRef]
  8. P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
    [CrossRef] [PubMed]
  9. K. Bush and S. John, "Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
    [CrossRef]
  10. W. Park and C. J. Summers, "Optical properties of superlattice photonic crystal waveguides," Appl. Phys. Lett. 84, 2013-2015 (2004).
    [CrossRef]
  11. K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
    [CrossRef]
  12. N. C. Panoiu, M. Bahl, and R. M. Osgood, "Optically tunable superprism effect in nonlinear photonic crystals," Opt. Lett. 28, 2503-2505 (2003).
    [CrossRef] [PubMed]
  13. D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
    [CrossRef]
  14. W. Park and J. B. Lee, "Mechanically tunable photonic crystal structure," Appl. Phys. Lett. 85, 4845-4847 (2004).
    [CrossRef]
  15. Q. Wu and W. Park, "Broadband sub-wavelength imaging by mechanically tunable photonic crystal," J. Comput. Theor. Nanosci. 2, 202-206 (2005).
    [CrossRef]
  16. E. Schonbrun, M. Tinker, W. Park, and J. B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
    [CrossRef]
  17. X. Wang, Z. F. Ren, and K. Kempa, "Unrestricted superlensing in a triangular two-dimensional photonic crystal," Opt. Express 12, 2919-2924 (2004).
    [CrossRef] [PubMed]
  18. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-191 (2001).
    [CrossRef] [PubMed]
  19. M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
    [CrossRef]
  20. D. Felbacq and R. Smaâli, "Block modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals," Phys. Rev. Lett. 92, 193902 (2004).
    [CrossRef] [PubMed]
  21. 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]
  22. A. Martínez and J. Martí, "Negative refraction in two-dimensional photonic crystals: role of lattice orientation and interface termination," Phys. Rev. B 71, 235115 (2005).
    [CrossRef]
  23. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
    [CrossRef]

2005 (4)

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Q. Wu and W. Park, "Broadband sub-wavelength imaging by mechanically tunable photonic crystal," J. Comput. Theor. Nanosci. 2, 202-206 (2005).
[CrossRef]

E. Schonbrun, M. Tinker, W. Park, and J. B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

A. Martínez and J. Martí, "Negative refraction in two-dimensional photonic crystals: role of lattice orientation and interface termination," Phys. Rev. B 71, 235115 (2005).
[CrossRef]

2004 (4)

W. Park and J. B. Lee, "Mechanically tunable photonic crystal structure," Appl. Phys. Lett. 85, 4845-4847 (2004).
[CrossRef]

D. Felbacq and R. Smaâli, "Block modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals," Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef] [PubMed]

X. Wang, Z. F. Ren, and K. Kempa, "Unrestricted superlensing in a triangular two-dimensional photonic crystal," Opt. Express 12, 2919-2924 (2004).
[CrossRef] [PubMed]

W. Park and C. J. Summers, "Optical properties of superlattice photonic crystal waveguides," Appl. Phys. Lett. 84, 2013-2015 (2004).
[CrossRef]

2003 (5)

N. C. Panoiu, M. Bahl, and R. M. Osgood, "Optically tunable superprism effect in nonlinear photonic crystals," Opt. Lett. 28, 2503-2505 (2003).
[CrossRef] [PubMed]

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell's law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

N. C. Panoiu and R. M. Osgood, "Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials," Phys. Rev. E 68, 016611 (2003).
[CrossRef]

2002 (1)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
[CrossRef]

2001 (1)

2000 (3)

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
[CrossRef]

1999 (2)

K. Bush and S. John, "Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
[CrossRef]

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

1994 (1)

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ," Sov. Phys. Usp. 10, 509-514 (1968).
[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]

Bahl, M.

Berenger, J. P.

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Brock, J. B.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell's law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

Brueck, S. R. J.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Bush, K.

K. Bush and S. John, "Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
[CrossRef]

Chuang, I. L.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell's law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

Fan, W.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Felbacq, D.

D. Felbacq and R. Smaâli, "Block modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals," Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef] [PubMed]

Frauenglass, A.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Gopalan, V.

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

Houck, A. A.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell's law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-191 (2001).
[CrossRef] [PubMed]

John, S.

K. Bush and S. John, "Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-191 (2001).
[CrossRef] [PubMed]

Kawagishi, Y.

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

Kempa, K.

Kim, S.

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

Lee, J. B.

E. Schonbrun, M. Tinker, W. Park, and J. B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

W. Park and J. B. Lee, "Mechanically tunable photonic crystal structure," Appl. Phys. Lett. 85, 4845-4847 (2004).
[CrossRef]

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Malkova, N.

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

Malloy, K. J.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Martí, J.

A. Martínez and J. Martí, "Negative refraction in two-dimensional photonic crystals: role of lattice orientation and interface termination," Phys. Rev. B 71, 235115 (2005).
[CrossRef]

Martínez, A.

A. Martínez and J. Martí, "Negative refraction in two-dimensional photonic crystals: role of lattice orientation and interface termination," Phys. Rev. B 71, 235115 (2005).
[CrossRef]

Minhas, B. K.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Nakayama, K.

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

Notomi, M.

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

Osgood, R. M.

N. C. Panoiu, M. Bahl, and R. M. Osgood, "Optically tunable superprism effect in nonlinear photonic crystals," Opt. Lett. 28, 2503-2505 (2003).
[CrossRef] [PubMed]

N. C. Panoiu and R. M. Osgood, "Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials," Phys. Rev. E 68, 016611 (2003).
[CrossRef]

Ozaki, M.

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

Panoiu, N. C.

N. C. Panoiu and R. M. Osgood, "Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials," Phys. Rev. E 68, 016611 (2003).
[CrossRef]

N. C. Panoiu, M. Bahl, and R. M. Osgood, "Optically tunable superprism effect in nonlinear photonic crystals," Opt. Lett. 28, 2503-2505 (2003).
[CrossRef] [PubMed]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

Park, W.

E. Schonbrun, M. Tinker, W. Park, and J. B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

Q. Wu and W. Park, "Broadband sub-wavelength imaging by mechanically tunable photonic crystal," J. Comput. Theor. Nanosci. 2, 202-206 (2005).
[CrossRef]

W. Park and J. B. Lee, "Mechanically tunable photonic crystal structure," Appl. Phys. Lett. 85, 4845-4847 (2004).
[CrossRef]

W. Park and C. J. Summers, "Optical properties of superlattice photonic crystal waveguides," Appl. Phys. Lett. 84, 2013-2015 (2004).
[CrossRef]

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Ren, Z. F.

Schonbrun, E.

E. Schonbrun, M. Tinker, W. Park, and J. B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
[CrossRef]

Scrymgeour, D.

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
[CrossRef]

Shimoda, Y.

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

Smaâli, R.

D. Felbacq and R. Smaâli, "Block modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals," Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef] [PubMed]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
[CrossRef]

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

Summers, C. J.

W. Park and C. J. Summers, "Optical properties of superlattice photonic crystal waveguides," Appl. Phys. Lett. 84, 2013-2015 (2004).
[CrossRef]

Tinker, M.

E. Schonbrun, M. Tinker, W. Park, and J. B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

Wang, X.

Wu, Q.

Q. Wu and W. Park, "Broadband sub-wavelength imaging by mechanically tunable photonic crystal," J. Comput. Theor. Nanosci. 2, 202-206 (2005).
[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]

Yoshino, K.

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

Zhang, S.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (4)

W. Park and C. J. Summers, "Optical properties of superlattice photonic crystal waveguides," Appl. Phys. Lett. 84, 2013-2015 (2004).
[CrossRef]

K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayama, and M. Ozaki, "Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal," Appl. Phys. Lett. 75, 932-934 (1999).
[CrossRef]

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

W. Park and J. B. Lee, "Mechanically tunable photonic crystal structure," Appl. Phys. Lett. 85, 4845-4847 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

E. Schonbrun, M. Tinker, W. Park, and J. B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[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]

J. Comput. Phys. (1)

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

J. Comput. Theor. Nanosci. (1)

Q. Wu and W. Park, "Broadband sub-wavelength imaging by mechanically tunable photonic crystal," J. Comput. Theor. Nanosci. 2, 202-206 (2005).
[CrossRef]

Nature (1)

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (3)

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
[CrossRef]

A. Martínez and J. Martí, "Negative refraction in two-dimensional photonic crystals: role of lattice orientation and interface termination," Phys. Rev. B 71, 235115 (2005).
[CrossRef]

Phys. Rev. E (1)

N. C. Panoiu and R. M. Osgood, "Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials," Phys. Rev. E 68, 016611 (2003).
[CrossRef]

Phys. Rev. Lett. (5)

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

K. Bush and S. John, "Liquid-crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell's law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

D. Felbacq and R. Smaâli, "Block modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals," Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef] [PubMed]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2000).
[CrossRef]

Sov. Phys. Usp. (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(Color online) (a) Photonic band structure (TM mode) for a two-dimensional (2D) PC with a hexangular structure. The black dashed curve in (a) is the light dispersion curve in air. (b) E z field patterns for the second band of a triangular lattice of Si rods in polyimide and (c) the second (bottom) and sixth (top) bands of a honeycomb lattice. The hexagonal boundary defines the Wigner–Seitz unit cell.

Fig. 2
Fig. 2

(Color online) (a) Photonic band structure and (b) EFSs for a 2D PC with a honeycomb structure. Both of them are for TM modes. The black dashed curve in (a) is the light dispersion curve in air. The horizontal red dotted line represents a frequency of 0.309 where the light dispersion curve in air intersects with the second photonic band. (c) The schematic of the honeycomb structure composed of Si rods (with diameter as 0.8 a ) in polyimide. The lattice orientation Γ K and Γ M are also shown.

Fig. 3
Fig. 3

(Color online) Electric field distribution of point sources and their images across a 2D honeycomb PC slab, at source frequencies of (a) 0.295, (b) 0.300, (c) 0.305, (d) 0.309, (e) 0.315, and (f) 0.320. Red and blue colors are used to represent the positive and negative fields. The locations of the point sources are at a distance of 1.0 a 0 from the left edge of the slab. Images move away from the PC lenses as the frequency is increased.

Fig. 4
Fig. 4

(Color online) Electric field distribution of point sources and their images across a 2D honeycomb PC slab for various PC structures at a frequency of 0.305. The PCs are the (a) 5% compressed lattice, (b) 2% compressed lattice, (c) regular honeycomb lattice, (d) 2% stretched lattice, and (e) 5% stretched lattice. The positions of the sources are also at a distance of 1.0 a 0 from the left edge of the slabs.

Fig. 5
Fig. 5

(Color online) EFSs of various PC lattices at a frequency of 0.305. They are 5% (the outermost curve) and 2% (second from outside) compressed lattices, regular honeycomb lattice (middle curve), and 2% (second from inside) and 5% (the innermost curve) stretched lattices, which are the same structures we used to perform the FDTD simulation in Fig. 4.

Fig. 6
Fig. 6

(Color online) Focusing properties vary with PC slabs of different PC structures over a range of frequencies. Besides the regular honeycomb lattice, 2%, 5%, and 10% stretched and compressed lattices were examined as examples. PC structures are represented by curves with different colors and labels. The y axis is the distances between the imaging point and PC slab in the unit of lattice constant a 0 .

Equations (1)

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( d 1 + d 2 ) + ( t n eff ) ( cos θ inc cos θ PC ) = 0 .

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