Abstract

Using terahertz spectroscopy, we measure the normal-incidence transmission coefficient of photonic crystals consisting of a periodic lattice of air holes in a silicon slab. Sharp resonant features are observed in the transmission spectra due to coupling of the leaky photonic crystal modes, called guided resonances, to the continuum of free-space modes. The resonances show considerable sensitivity to the structural parameters of the slab, including the slab thickness. By varying each crystal parameter systematically, we study the dependence of the resonances on the geometry of the photonic crystal slabs. Even small changes in a parameter such as the slab thickness, for example, can lead to dramatic changes in the optical spectrum. We also compare the transmission spectrum of a photonic crystal slab with a hexagonal lattice to that of a slab with a square lattice. In most cases, the experimental results match very well with numerical simulations based on the finite element method.

© 2008 Optical Society of America

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  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).
  2. K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001).
  3. S. G. Johnson and J. D. Joannopoulos, Photonic Crystals: The Road from Theory to Practice (Springer, 2002).
  4. E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983-986 (2000).
    [CrossRef] [PubMed]
  5. A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787-3790 (1996).
    [CrossRef] [PubMed]
  6. S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751-5758 (1999).
    [CrossRef]
  7. S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212-8222 (2000).
    [CrossRef]
  8. R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, G. T. K. Guven, E. Ozbay, and C. M. Soukoulis, “Negative refraction and superlens behavior in a two-dimensional photonic crystal,” Phys. Rev. B 71, 085106 (2005).
    [CrossRef]
  9. S. N. Tandon, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2D-periodic photonic crystal slabs,” Photon. Nanostruct. Fundam. Appl. 3, 10-18 (2005).
    [CrossRef]
  10. P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5, 93-96 (2006).
    [CrossRef] [PubMed]
  11. T. Matsumoto, T. Asatsuma, and T. Baba, “Experimental demonstration of a wavelength demultiplexer based on negative-refractive photonic-crystal components,” Appl. Phys. Lett. 91, 091117 (2007).
    [CrossRef]
  12. M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438-1440 (1997).
    [CrossRef]
  13. V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De la Rue, “Resonant coupling of near-infrared radiation to photonic band structure waveguides,” J. Lightwave Technol. 17, 2050-2057 (1999).
    [CrossRef]
  14. S. H. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
    [CrossRef]
  15. S. H. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569-572 (2003).
    [CrossRef]
  16. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866-1878 (1961).
    [CrossRef]
  17. A. R. P. Rau, “Perspectives on the Fano resonance formula,” Phys. Scr. 69, C10-C13 (2004).
    [CrossRef]
  18. A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563-565 (2001).
    [CrossRef]
  19. H. Y. Ryu, Y. H. Lee, R. L. Sellin, and D. Bimberg, “Over 30-fold enhancement of light extraction from free-standing photonic crystal slabs with InGaAs quantum dots at low temperature,” Appl. Phys. Lett. 79, 3573-3575 (2001).
    [CrossRef]
  20. M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308, 1296-1298 (2005).
    [CrossRef] [PubMed]
  21. V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. H. Fan, “Angular and polarization properties of a photonic crystal slab mirror,” Opt. Express 12, 1575-1582 (2004).
    [CrossRef] [PubMed]
  22. A. E. Miroshnichenko and Y. S. Kivshar, “Sharp bends in photonic crystal waveguides as nonlinear Fano resonators,” Opt. Express 13, 3969-3976 (2005).
    [CrossRef] [PubMed]
  23. W. Suh, M. F. Yanik, O. Solgaard, and S. H. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82, 1999-2001 (2003).
    [CrossRef]
  24. W. Suh and S. H. Fan, “Mechanically switchable photonic crystal filter with either all-pass transmission or flat-top reflection characteristics,” Opt. Lett. 28, 1763-1765 (2003).
    [CrossRef] [PubMed]
  25. Y. Kanamori, T. Kitani, and K. Hane, “Control of guided resonance in a photonic crystal slab using microelectromechanical actuators,” Appl. Phys. Lett. 90, 031911 (2007).
    [CrossRef]
  26. A. Rosenberg, M. W. Carter, J. A. Casey, M. Kim, R. T. Holm, R. L. Henry, C. R. Eddy, V. A. Shamamian, K. Bussmann, S. Shi, and D. W. Prather, “Guided resonances in asymmetrical GaN photonic crystal slabs observed in the visible spectrum,” Opt. Express 13, 6564-6571 (2005).
    [CrossRef] [PubMed]
  27. O. Kilic, S. Kim, W. Suh, Y. A. Peter, A. S. Sudbo, M. F. Yanik, S. H. Fan, and O. Solgaard, “Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders,” Opt. Lett. 29, 2782-2784 (2004).
    [CrossRef] [PubMed]
  28. T. Prasad, V. L. Colvin, and D. M. Mittleman, “The effect of structural disorder on guided resonances in photonic crystal slabs studied with terahertz time-domain spectroscopy, Opt. Express 15, 16954-16965 (2007).
    [CrossRef] [PubMed]
  29. V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young, and S. R. Johnson, “Photonic band structure of dielectric membranes periodically textured in two dimensions,” Phys. Rev. B 62, 4204-4207 (2000).
    [CrossRef]
  30. K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. H. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
    [CrossRef]
  31. Z. P. Jian and D. M. Mittleman, “Characterization of guided resonances in photonic crystal slabs using terahertz time-domain spectroscopy,” J. Appl. Phys. 100, 123113 (2006).
    [CrossRef]
  32. J. F. Song, R. P. Zaccaria, M. B. Yu, and X. W. Sun, “Tunable Fano resonance in photonic crystal slabs,” Opt. Express 14, 8812-8826 (2006).
    [CrossRef] [PubMed]
  33. C. Grillet, D. Freeman, B. Luther-Davies, S. Madden, R. McPhedran, D. J. Moss, M. J. Steel, and B. J. Eggleton, “Characterization and modeling of Fano resonances in chalcogenide photonic crystal membranes,” Opt. Express 14, 369-376 (2006).
    [CrossRef] [PubMed]
  34. M. van Exter and D. R. Grischkowsky, “Characterization of an optoelectronic terahertz beam system,” IEEE Trans. Microwave Theory Tech. 38, 1684-1691 (1990).
    [CrossRef]
  35. Z. P. Jian, J. Pearce, and D. M. Mittleman, “Two-dimensional photonic crystal slabs in parallel-plate metal waveguides studied with terahertz time-domain spectroscopy,” Semicond. Sci. Technol. 20, S300-S306 (2005).
    [CrossRef]
  36. T. Prasad, V. L. Colvin, Z. Jian, and D. M. Mittleman, “Superprism effect in a metal-clad terahertz photonic crystal slab,” Opt. Lett. 32, 683-685 (2007).
    [CrossRef] [PubMed]
  37. N. Jukam and M. S. Sherwin, “Two-dimensional terahertz photonic crystals fabricated by deep reactive ion etching in Si,” Appl. Phys. Lett. 83, 21-23 (2003).
    [CrossRef]
  38. C. Yee, N. Jukam, and M. Sherwin, “Transmission of single mode ultrathin terahertz photonic crystal slabs,” Appl. Phys. Lett. 91, 194104 (2007).
    [CrossRef]
  39. D. Grischkowsky, S. Keiding, M. Vanexter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7, 2006-2015 (1990).
    [CrossRef]
  40. W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials: I. Scalar case,” J. Comp. Physiol. 150, 468-481 (1999).
  41. W. R. Frei and H. T. Johnson, “Finite-element analysis of disorder effects in photonic crystals,” Phys. Rev. B 70, 165116 (2004).
    [CrossRef]
  42. J. A. Deibel, N. Berndsen, K. Wang, and D. M. Mittleman, “Frequency-dependent radiation patterns emitted by THz plasmons on finite length cylindrical metal wires,” Opt. Express 14, 8772-8778 (2006).
    [CrossRef] [PubMed]
  43. J. Deibel, M. Escarra, N. Berndsen, K. Wang, and D. M. Mittleman, “Finite element method simulations of guided wave phenomena at terahertz frequencies,” Proc. IEEE 95, 1624-1640 (2007).
    [CrossRef]
  44. W. Suh, O. Solgaard, and S. Fan, “Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs,” J. Appl. Phys. 98, 033102 (2005).
    [CrossRef]
  45. T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
    [CrossRef]
  46. Z. Jian and D. M. Mittleman, “Out-of-plane dispersion and homogenization in photonic crystal slabs,” Appl. Phys. Lett. 87, 191113 (2005).
    [CrossRef]
  47. V. Lousse and J. P. Vigneron, “Use of Fano resonances for bistable optical transfer through photonic crystal films,” Phys. Rev. B 69, 155106 (2004).
    [CrossRef]
  48. G.Kozlov and A.Volkov, “Coherent source submillimeter wave spectroscopy,” in Millimeter and Submillimeter Wave Spectroscopy of Solids, G.Grüner, ed. (Springer-Verlag, 1998).
    [CrossRef]
  49. B. Gorshunov, A. Volkov, I. Spektor, A. Prokhorov, A. Mukhin, M. Dressel, S. Uchida, and A. Loidl, “Terahertz BWO spectroscopy,” Int. J. Infrared Millim. Waves 26, 1217-1240 (2005).
    [CrossRef]
  50. T. W. Crowe, D. W. Porterfield, J. L. Hesler, W. L. Bishop, D. S. Kurtz, and K. Hui, “Terahertz technology for imaging and spectroscopy,” Proc. SPIE 6212, 62120V (2006).
    [CrossRef]

2007 (6)

T. Matsumoto, T. Asatsuma, and T. Baba, “Experimental demonstration of a wavelength demultiplexer based on negative-refractive photonic-crystal components,” Appl. Phys. Lett. 91, 091117 (2007).
[CrossRef]

Y. Kanamori, T. Kitani, and K. Hane, “Control of guided resonance in a photonic crystal slab using microelectromechanical actuators,” Appl. Phys. Lett. 90, 031911 (2007).
[CrossRef]

T. Prasad, V. L. Colvin, and D. M. Mittleman, “The effect of structural disorder on guided resonances in photonic crystal slabs studied with terahertz time-domain spectroscopy, Opt. Express 15, 16954-16965 (2007).
[CrossRef] [PubMed]

T. Prasad, V. L. Colvin, Z. Jian, and D. M. Mittleman, “Superprism effect in a metal-clad terahertz photonic crystal slab,” Opt. Lett. 32, 683-685 (2007).
[CrossRef] [PubMed]

C. Yee, N. Jukam, and M. Sherwin, “Transmission of single mode ultrathin terahertz photonic crystal slabs,” Appl. Phys. Lett. 91, 194104 (2007).
[CrossRef]

J. Deibel, M. Escarra, N. Berndsen, K. Wang, and D. M. Mittleman, “Finite element method simulations of guided wave phenomena at terahertz frequencies,” Proc. IEEE 95, 1624-1640 (2007).
[CrossRef]

2006 (7)

J. A. Deibel, N. Berndsen, K. Wang, and D. M. Mittleman, “Frequency-dependent radiation patterns emitted by THz plasmons on finite length cylindrical metal wires,” Opt. Express 14, 8772-8778 (2006).
[CrossRef] [PubMed]

T. W. Crowe, D. W. Porterfield, J. L. Hesler, W. L. Bishop, D. S. Kurtz, and K. Hui, “Terahertz technology for imaging and spectroscopy,” Proc. SPIE 6212, 62120V (2006).
[CrossRef]

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. H. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[CrossRef]

Z. P. Jian and D. M. Mittleman, “Characterization of guided resonances in photonic crystal slabs using terahertz time-domain spectroscopy,” J. Appl. Phys. 100, 123113 (2006).
[CrossRef]

J. F. Song, R. P. Zaccaria, M. B. Yu, and X. W. Sun, “Tunable Fano resonance in photonic crystal slabs,” Opt. Express 14, 8812-8826 (2006).
[CrossRef] [PubMed]

C. Grillet, D. Freeman, B. Luther-Davies, S. Madden, R. McPhedran, D. J. Moss, M. J. Steel, and B. J. Eggleton, “Characterization and modeling of Fano resonances in chalcogenide photonic crystal membranes,” Opt. Express 14, 369-376 (2006).
[CrossRef] [PubMed]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5, 93-96 (2006).
[CrossRef] [PubMed]

2005 (9)

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308, 1296-1298 (2005).
[CrossRef] [PubMed]

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, G. T. K. Guven, E. Ozbay, and C. M. Soukoulis, “Negative refraction and superlens behavior in a two-dimensional photonic crystal,” Phys. Rev. B 71, 085106 (2005).
[CrossRef]

S. N. Tandon, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2D-periodic photonic crystal slabs,” Photon. Nanostruct. Fundam. Appl. 3, 10-18 (2005).
[CrossRef]

A. Rosenberg, M. W. Carter, J. A. Casey, M. Kim, R. T. Holm, R. L. Henry, C. R. Eddy, V. A. Shamamian, K. Bussmann, S. Shi, and D. W. Prather, “Guided resonances in asymmetrical GaN photonic crystal slabs observed in the visible spectrum,” Opt. Express 13, 6564-6571 (2005).
[CrossRef] [PubMed]

A. E. Miroshnichenko and Y. S. Kivshar, “Sharp bends in photonic crystal waveguides as nonlinear Fano resonators,” Opt. Express 13, 3969-3976 (2005).
[CrossRef] [PubMed]

Z. P. Jian, J. Pearce, and D. M. Mittleman, “Two-dimensional photonic crystal slabs in parallel-plate metal waveguides studied with terahertz time-domain spectroscopy,” Semicond. Sci. Technol. 20, S300-S306 (2005).
[CrossRef]

B. Gorshunov, A. Volkov, I. Spektor, A. Prokhorov, A. Mukhin, M. Dressel, S. Uchida, and A. Loidl, “Terahertz BWO spectroscopy,” Int. J. Infrared Millim. Waves 26, 1217-1240 (2005).
[CrossRef]

Z. Jian and D. M. Mittleman, “Out-of-plane dispersion and homogenization in photonic crystal slabs,” Appl. Phys. Lett. 87, 191113 (2005).
[CrossRef]

W. Suh, O. Solgaard, and S. Fan, “Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs,” J. Appl. Phys. 98, 033102 (2005).
[CrossRef]

2004 (5)

W. R. Frei and H. T. Johnson, “Finite-element analysis of disorder effects in photonic crystals,” Phys. Rev. B 70, 165116 (2004).
[CrossRef]

V. Lousse and J. P. Vigneron, “Use of Fano resonances for bistable optical transfer through photonic crystal films,” Phys. Rev. B 69, 155106 (2004).
[CrossRef]

O. Kilic, S. Kim, W. Suh, Y. A. Peter, A. S. Sudbo, M. F. Yanik, S. H. Fan, and O. Solgaard, “Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders,” Opt. Lett. 29, 2782-2784 (2004).
[CrossRef] [PubMed]

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. H. Fan, “Angular and polarization properties of a photonic crystal slab mirror,” Opt. Express 12, 1575-1582 (2004).
[CrossRef] [PubMed]

A. R. P. Rau, “Perspectives on the Fano resonance formula,” Phys. Scr. 69, C10-C13 (2004).
[CrossRef]

2003 (4)

S. H. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569-572 (2003).
[CrossRef]

W. Suh, M. F. Yanik, O. Solgaard, and S. H. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82, 1999-2001 (2003).
[CrossRef]

W. Suh and S. H. Fan, “Mechanically switchable photonic crystal filter with either all-pass transmission or flat-top reflection characteristics,” Opt. Lett. 28, 1763-1765 (2003).
[CrossRef] [PubMed]

N. Jukam and M. S. Sherwin, “Two-dimensional terahertz photonic crystals fabricated by deep reactive ion etching in Si,” Appl. Phys. Lett. 83, 21-23 (2003).
[CrossRef]

2002 (1)

S. H. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[CrossRef]

2001 (3)

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

H. Y. Ryu, Y. H. Lee, R. L. Sellin, and D. Bimberg, “Over 30-fold enhancement of light extraction from free-standing photonic crystal slabs with InGaAs quantum dots at low temperature,” Appl. Phys. Lett. 79, 3573-3575 (2001).
[CrossRef]

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[CrossRef]

2000 (3)

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983-986 (2000).
[CrossRef] [PubMed]

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young, and S. R. Johnson, “Photonic band structure of dielectric membranes periodically textured in two dimensions,” Phys. Rev. B 62, 4204-4207 (2000).
[CrossRef]

1999 (3)

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De la Rue, “Resonant coupling of near-infrared radiation to photonic band structure waveguides,” J. Lightwave Technol. 17, 2050-2057 (1999).
[CrossRef]

W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials: I. Scalar case,” J. Comp. Physiol. 150, 468-481 (1999).

1997 (1)

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438-1440 (1997).
[CrossRef]

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

1990 (2)

D. Grischkowsky, S. Keiding, M. Vanexter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7, 2006-2015 (1990).
[CrossRef]

M. van Exter and D. R. Grischkowsky, “Characterization of an optoelectronic terahertz beam system,” IEEE Trans. Microwave Theory Tech. 38, 1684-1691 (1990).
[CrossRef]

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866-1878 (1961).
[CrossRef]

Appl. Phys. Lett. (9)

T. Matsumoto, T. Asatsuma, and T. Baba, “Experimental demonstration of a wavelength demultiplexer based on negative-refractive photonic-crystal components,” Appl. Phys. Lett. 91, 091117 (2007).
[CrossRef]

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438-1440 (1997).
[CrossRef]

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

H. Y. Ryu, Y. H. Lee, R. L. Sellin, and D. Bimberg, “Over 30-fold enhancement of light extraction from free-standing photonic crystal slabs with InGaAs quantum dots at low temperature,” Appl. Phys. Lett. 79, 3573-3575 (2001).
[CrossRef]

W. Suh, M. F. Yanik, O. Solgaard, and S. H. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82, 1999-2001 (2003).
[CrossRef]

Y. Kanamori, T. Kitani, and K. Hane, “Control of guided resonance in a photonic crystal slab using microelectromechanical actuators,” Appl. Phys. Lett. 90, 031911 (2007).
[CrossRef]

N. Jukam and M. S. Sherwin, “Two-dimensional terahertz photonic crystals fabricated by deep reactive ion etching in Si,” Appl. Phys. Lett. 83, 21-23 (2003).
[CrossRef]

C. Yee, N. Jukam, and M. Sherwin, “Transmission of single mode ultrathin terahertz photonic crystal slabs,” Appl. Phys. Lett. 91, 194104 (2007).
[CrossRef]

Z. Jian and D. M. Mittleman, “Out-of-plane dispersion and homogenization in photonic crystal slabs,” Appl. Phys. Lett. 87, 191113 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

M. van Exter and D. R. Grischkowsky, “Characterization of an optoelectronic terahertz beam system,” IEEE Trans. Microwave Theory Tech. 38, 1684-1691 (1990).
[CrossRef]

Int. J. Infrared Millim. Waves (1)

B. Gorshunov, A. Volkov, I. Spektor, A. Prokhorov, A. Mukhin, M. Dressel, S. Uchida, and A. Loidl, “Terahertz BWO spectroscopy,” Int. J. Infrared Millim. Waves 26, 1217-1240 (2005).
[CrossRef]

J. Appl. Phys. (2)

W. Suh, O. Solgaard, and S. Fan, “Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs,” J. Appl. Phys. 98, 033102 (2005).
[CrossRef]

Z. P. Jian and D. M. Mittleman, “Characterization of guided resonances in photonic crystal slabs using terahertz time-domain spectroscopy,” J. Appl. Phys. 100, 123113 (2006).
[CrossRef]

J. Comp. Physiol. (1)

W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials: I. Scalar case,” J. Comp. Physiol. 150, 468-481 (1999).

J. Lightwave Technol. (1)

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

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

Nat. Mater. (1)

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5, 93-96 (2006).
[CrossRef] [PubMed]

Nature (1)

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983-986 (2000).
[CrossRef] [PubMed]

Opt. Express (7)

J. F. Song, R. P. Zaccaria, M. B. Yu, and X. W. Sun, “Tunable Fano resonance in photonic crystal slabs,” Opt. Express 14, 8812-8826 (2006).
[CrossRef] [PubMed]

C. Grillet, D. Freeman, B. Luther-Davies, S. Madden, R. McPhedran, D. J. Moss, M. J. Steel, and B. J. Eggleton, “Characterization and modeling of Fano resonances in chalcogenide photonic crystal membranes,” Opt. Express 14, 369-376 (2006).
[CrossRef] [PubMed]

A. Rosenberg, M. W. Carter, J. A. Casey, M. Kim, R. T. Holm, R. L. Henry, C. R. Eddy, V. A. Shamamian, K. Bussmann, S. Shi, and D. W. Prather, “Guided resonances in asymmetrical GaN photonic crystal slabs observed in the visible spectrum,” Opt. Express 13, 6564-6571 (2005).
[CrossRef] [PubMed]

T. Prasad, V. L. Colvin, and D. M. Mittleman, “The effect of structural disorder on guided resonances in photonic crystal slabs studied with terahertz time-domain spectroscopy, Opt. Express 15, 16954-16965 (2007).
[CrossRef] [PubMed]

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. H. Fan, “Angular and polarization properties of a photonic crystal slab mirror,” Opt. Express 12, 1575-1582 (2004).
[CrossRef] [PubMed]

A. E. Miroshnichenko and Y. S. Kivshar, “Sharp bends in photonic crystal waveguides as nonlinear Fano resonators,” Opt. Express 13, 3969-3976 (2005).
[CrossRef] [PubMed]

J. A. Deibel, N. Berndsen, K. Wang, and D. M. Mittleman, “Frequency-dependent radiation patterns emitted by THz plasmons on finite length cylindrical metal wires,” Opt. Express 14, 8772-8778 (2006).
[CrossRef] [PubMed]

Opt. Lett. (3)

Photon. Nanostruct. Fundam. Appl. (1)

S. N. Tandon, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2D-periodic photonic crystal slabs,” Photon. Nanostruct. Fundam. Appl. 3, 10-18 (2005).
[CrossRef]

Phys. Rev. (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866-1878 (1961).
[CrossRef]

Phys. Rev. B (9)

S. H. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[CrossRef]

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, G. T. K. Guven, E. Ozbay, and C. M. Soukoulis, “Negative refraction and superlens behavior in a two-dimensional photonic crystal,” Phys. Rev. B 71, 085106 (2005).
[CrossRef]

V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young, and S. R. Johnson, “Photonic band structure of dielectric membranes periodically textured in two dimensions,” Phys. Rev. B 62, 4204-4207 (2000).
[CrossRef]

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. H. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[CrossRef]

W. R. Frei and H. T. Johnson, “Finite-element analysis of disorder effects in photonic crystals,” Phys. Rev. B 70, 165116 (2004).
[CrossRef]

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[CrossRef]

V. Lousse and J. P. Vigneron, “Use of Fano resonances for bistable optical transfer through photonic crystal films,” Phys. Rev. B 69, 155106 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Phys. Scr. (1)

A. R. P. Rau, “Perspectives on the Fano resonance formula,” Phys. Scr. 69, C10-C13 (2004).
[CrossRef]

Proc. IEEE (1)

J. Deibel, M. Escarra, N. Berndsen, K. Wang, and D. M. Mittleman, “Finite element method simulations of guided wave phenomena at terahertz frequencies,” Proc. IEEE 95, 1624-1640 (2007).
[CrossRef]

Proc. SPIE (1)

T. W. Crowe, D. W. Porterfield, J. L. Hesler, W. L. Bishop, D. S. Kurtz, and K. Hui, “Terahertz technology for imaging and spectroscopy,” Proc. SPIE 6212, 62120V (2006).
[CrossRef]

Science (1)

M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous inhibition and redistribution of spontaneous light emission in photonic crystals,” Science 308, 1296-1298 (2005).
[CrossRef] [PubMed]

Semicond. Sci. Technol. (1)

Z. P. Jian, J. Pearce, and D. M. Mittleman, “Two-dimensional photonic crystal slabs in parallel-plate metal waveguides studied with terahertz time-domain spectroscopy,” Semicond. Sci. Technol. 20, S300-S306 (2005).
[CrossRef]

Other (4)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2001).

S. G. Johnson and J. D. Joannopoulos, Photonic Crystals: The Road from Theory to Practice (Springer, 2002).

G.Kozlov and A.Volkov, “Coherent source submillimeter wave spectroscopy,” in Millimeter and Submillimeter Wave Spectroscopy of Solids, G.Grüner, ed. (Springer-Verlag, 1998).
[CrossRef]

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Figures (17)

Fig. 1
Fig. 1

Schematic of the experimental setup. The terahertz radiation propagates in the direction perpendicular to the plane of the photonic crystal slab. The terahertz beam spot size is 8 mm .

Fig. 2
Fig. 2

(a) Top view of the photonic crystal slab with a hexagonal lattice of air holes. The crystal parameters are r = 150 , a = 400 , and t = 300 μ m . The scale bar is 300 μ m . (b) Normal-incidence transmission spectrum of the photonic crystal slab shown in (a). The open circles are experimental results while the solid curve is obtained from simulations based on the FEM.

Fig. 3
Fig. 3

Top, FEM model for the hexagonal lattice photonic crystal. The electromagnetic radiation propagates in the direction indicated by the arrow; t is the slab thickness. Bottom, hexagonal lattice with high-symmetry directions marked. The dashed rectangle is a cross section of the smallest unit cell used in the FEM simulations.

Fig. 4
Fig. 4

Same as Fig. 2b except that the solid curve is obtained from an analytical expression [Eq. (4)], using the parameters given in Table 1.

Fig. 5
Fig. 5

Variation of guided resonances with the hole radii r. Normal-incidence transmission spectra of photonic crystal slabs with (a) r = 180 , (b) r = 150 , and (c) r = 125 μ m . The lattice parameter and slab thickness are identical for all the samples, a = 400 and t = 300 μ m . The open black circles are experimental results while the solid curves are results of FEM simulations. The theoretical spectrum in (c) matches well with the experimental spectrum when t = 296 μ m is used in the simulation.

Fig. 6
Fig. 6

Variation of guided resonances with the lattice parameter a. Normal-incidence transmission spectra of photonic crystal slabs with (a) a = 575 , (b) a = 480 , and (c) a = 400 μ m . The hole radius and slab thickness are identical for all the samples, r = 150 μ m and t = 300 μ m . The open circles are experimental results while the solid curves are results of FEM simulations.

Fig. 7
Fig. 7

(a) Shifts in the positions of the first three resonances as a function of r a (extracted from Figs. 5, 6). (b) (left) Variation of the filling fraction of the air holes and (right) the average refractive index of the photonic crystal slab as a function of the r a value of the hexagonal lattice. The dashed vertical lines depict the r a values of the samples whose transmission spectra are shown in Figs. 5, 6.

Fig. 8
Fig. 8

Normal-incidence transmission spectra of photonic crystal slabs with (a) r = 125 , a = 400 μ m and (b) r = 150 , a = 480 μ m . These are the same as Figs. 5c, 6b, respectively. The r a value and the slab thickness are identical for the two samples, r a = 0.3125 and t = 300 μ m . The open circles are experimental results while the solid curves are results of FEM simulations.

Fig. 9
Fig. 9

Variation of guided resonances with the slab thickness t. Normal-incidence transmission spectra of photonic crystal slabs with (a) t = 300 , (b) t = 275 , and (c) t = 250 μ m . The hole radius and lattice parameter are identical for all the samples, r = 150 and a = 400 μ m . The open circles are experimental results while the solid curves are results of FEM simulations.

Fig. 10
Fig. 10

Shift in the position of the first seven resonances as a function of the slab thickness t (extracted from Fig. 9).

Fig. 11
Fig. 11

Same as Fig. 9 but for samples with r = 150 and a = 480 μ m . Slab thicknesses are (a) t = 300 , (b) t = 275 , and (c) t = 250 μ m .

Fig. 12
Fig. 12

(Color) Electric field distributions in the planes along half the slab thickness for the three crystals (with r = 150 and a = 480 μ m ) whose transmission spectra are shown in Fig. 11. (a) At 0.375 THz for t = 300 μ m , (b) at 0.382 THz for t = 275 μ m , and (c) at 0.392 THz for t = 250 μ m . The solid black curves depict the hole boundaries, and the arrows denote directions of the in-plane field.

Fig. 13
Fig. 13

Same as Fig. 9 but for samples with r = 150 and a = 575 μ m . Slab thicknesses are (a) t = 300 , (b) t = 275 , and (c) t = 250 μ m .

Fig. 14
Fig. 14

Portion of the relative phase spectrum for the three crystals (with r = 150 and a = 575 μ m ) whose transmission spectra are shown in Fig. 14. The symbols are experimental results, while the solid curves are the corresponding FEM simulations. The results for t = 300 and t = 275 μ m are vertically offset for clarity.

Fig. 15
Fig. 15

(a) High-resolution calculation of the line shape of the lowest-frequency resonance for three different values of the slab thickness for a photonic crystal slab with r = 150 and a = 400 μ m (as in Fig. 10). A frequency resolution of 0.1 GHz is used in the FEM simulations. For the 250 μ m thick slab, the resonance is quite narrow ( 380 MHz ) with a Q-factor in excess of 1100. (b) Measured transmission spectra for two samples corresponding to two of the curves in (a). These measurements were performed using a BWO source with a spectral resolution below 1 GHz .

Fig. 16
Fig. 16

Same as Fig. 3 but for a square lattice.

Fig. 17
Fig. 17

Normal-incidence transmission spectra of photonic crystal slabs with (a) hexagonal and (b) square lattices. The crystal parameters are identical for the two samples, r = 180 , a = 400 , and t = 300 μ m . The open circles are experimental results while the solid curves are results of FEM simulations.

Tables (2)

Tables Icon

Table 1 Resonant Frequencies ( ω j ) and the Corresponding Linewidths ( γ j ) of the First Seven Guided Resonances Shown in Fig. 2b a

Tables Icon

Table 2 Shifts in the Positions of the First Three Resonances for a 2% Change in the r a Ratio, the Hole Radius, and the Lattice Parameter a

Equations (6)

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

t GR j ( ω ) = ρ τ Ω j ( ω ) 1 + i Ω j ( ω ) ,
Ω j ( ω ) = ω ω j γ j ,
t ( ω ) = t FP ( ω ) + t GR 1 ( ω ) + t GR 2 ( ω ) + t GR 3 ( ω ) + ,
t ( ω ) = t FP + j = 1 N ρ τ Ω j ( ω ) 1 + i Ω j ( ω ) .
ϕ h = 2 π 3 ( r a ) 2 ,
n ̃ = ( ε S i × ϕ S i ) + ( ε h × ϕ h ) ,

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