Abstract

Transmissions and resonant tunneling of superlattices composed of two alternating triangular photonic crystals (PhCs) and their corresponding effective one-dimensional (1D) superlattices are discussed. In the first case, below 0.40 (c/a), the transmissions of effective 1D superlattices calculated by the effective medium theory (EMT) match those of two-alternating-PhC superlattices calculated by the internal-field expansion method. No matter whether the propagating direction is along the symmetric (along ΓK or ΓM directions) or nonsymmetric axes (incident angle θ=45°), the results hold very well. In the second case, resonant-tunneling phenomena and transmissions of the two-period superlattice composed of two alternating PhCs (the resonant-tunneling superlattice) can also be predicted by EMT below 0.20 (c/a). However, due to the evanescent waves at oblique incidence, the interface effect between two PhCs becomes explicit in the higher-frequency region and results in the deviations of resonant-tunneling frequencies in EMT calculations. By modifying the effective refractive indices of both PhCs, deviations are corrected and EMT calculations can exhibit resonant tunneling at right frequencies. Furthermore, the resonant-tunneling superlattice with larger background dielectric constant displays fewer modifications on the effective refractive indices.

© 2012 Optical Society of America

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2012 (3)

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108, 037401 (2012).
[CrossRef]

T.-H. Pei and Y.-T. Huang, “Analyzing the propagating waves in the two-dimensional photonic crystal by the decoupled internal-field expansion method,” AIP Advances 2, 0120188 (2012).
[CrossRef]

R. Ozaki and T. Yamasaki, “Propagation characteristics of dielectric waveguides with arbitrary inhomogeneous media along the middle layer,” IEICE Trans. Electron. e95-c, 53–62 (2012).
[CrossRef]

2011 (4)

T.-H. Pei and Y.-T. Huang, “The high-transmission photonic crystal heterostructure Y-branch waveguide operating at photonic band region,” J. Appl. Phys. 109, 034504 (2011).
[CrossRef]

T.-H. Pei and Y.-T. Huang, “The equivalent structure and some optical properties of the periodic-defect photonic crystal,” J. Appl. Phys. 109, 073104 (2011).
[CrossRef]

S. Kocaman, M. S. Aras, P. Hsieh, J. F. Mcmillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5,1–7 (2011).
[CrossRef]

T.-H. Pei, S. Thiyagu, and Z. Pei, “Ultra high-density silicon nanowires for extremely low reflection in visible regime,” Appl. Phys. Lett. 99, 153108 (2011).
[CrossRef]

2010 (2)

P. Han, Y. W. Chen, and X.-C. Zhang, “Application of silicon micropyramid structures for antireflection of terahertz waves,” IEEE J. Sel. Topics Quantum Electron. 16, 338–343 (2010).
[CrossRef]

Y. W. Chen, P. Han, X.-C. Zhang, M.-L. Kuo, and S.-Y. Lin, “Three-dimensional inverted photonic grating with engineerable refractive indices for broadband antireflection of terahertz waves,” Opt. Lett. 35, 3159–3161 (2010).
[CrossRef]

2009 (3)

V. Sivakov, G. Andrä, A. Gawlik, A. Berger, J. Plentz, F. Falk, and S. H. Christiansen, “Silicon nanowire-based solar cells on glass: Synthesis, optical properties, and cell parameters,” Nano Lett. 9, 1549–1554 (2009).
[CrossRef]

V. Mocella, S. Cabrini, A. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902–133905 (2009).
[CrossRef]

S. Kocaman, R. Chatterjee, N. Panoiu, J. Mcmillan, M. Yu, R. Osgood, D. Kwong, and C. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102, 203905 (2009).
[CrossRef]

2008 (1)

Y.-J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, and J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8, 1501–1505 (2008).
[CrossRef]

2007 (1)

R. Irawan, D. Zhang, S. Chuan Tjin, and X. Yuan, “Biosensor based on two-dimensional photonic lattice,” Microwave Opt. Technol. Lett. 49, 1171–1175 (2007).
[CrossRef]

2006 (3)

A. E. Serebryannikov, T. Magath, and K. Schuenemann, “Bragg transmittance of s-polarized waves through finite-thickness photonic crystals with a periodically corrugated interface,” Phys. Rev. E 74, 066607 (2006).
[CrossRef]

D. G. Stavenga, S. Foletti, G. Palasantzas, and K. Arikawa, “Light on the moth-eye corneal nipple array of butterflies,” Proc. R. Soc. B 273, 661–667 (2006).
[CrossRef]

Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. Au Kong, “Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials,” Opt. Express 14, 2220–2227 (2006).
[CrossRef]

2005 (2)

I. De Leon and F. S. Roux, “Fourier analysis of reflection and refraction in two-dimensional photonic crystals,” Phys. Rev. B 71, 235105 (2005).
[CrossRef]

W. Jiang, R. T. Chen, and X. Lu, “Theory of light refraction at the surface of a photonic crystal,” Phys. Rev. B 71, 245115 (2005).
[CrossRef]

2004 (1)

D. Felbacq and R. Smaâli, “Bloch modes dressed by evanescent waves and the generalized Goos–Hänchen effect in photonic crystals,” Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef]

2003 (3)

S. A. Darmanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003).
[CrossRef]

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

L. Escoubas, J. J. Simon, M. Loli, G. Berginc, F. Flory, and H. Giovannini, “An antireflective silicon grating working in the resonance domain for the near infrared spectral region,” Opt. Commun. 226, 81–88 (2003).
[CrossRef]

2001 (1)

S. Foteinopoulou, A. Rosenberg, M. M. Sigalas, and C. M. Soukoulis, “In- and out-of-plane propagation of electromagnetic waves in low index contrast two dimensional photonic crystals,” J. Appl. Phys. 89, 824–830 (2001).
[CrossRef]

2000 (1)

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(2000).
[CrossRef]

1999 (6)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

P. Halevi, A. A. Krokhin, and J. Arriaga, “Photonic crystal optics and homogenization of 2D periodic composites,” Phys. Rev. Lett. 82, 719–722 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdre, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045–1052 (1999).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. de la Rue, R. Houdre, U. Oesterle, and C. Jouanin, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, C. J. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional photonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
[CrossRef]

J. G. Shawn-Yu Lin and J. G. Fleming, “A three-dimensional optical photonic crystal,” J. Lightwave Technol. 17, 1944–1947 (1999).
[CrossRef]

1998 (3)

1997 (1)

1996 (2)

1995 (2)

K. Sakoda, “Optical transmittance of a two-dimensional triangular photonic lattice,” Phys. Rev. B 51, 4672–4675 (1995).
[CrossRef]

K. Sakoda, “Transmittance and Bragg reflectivity of two-dimensional photonic lattices,” Phys. Rev. B 52, 8992–9002 (1995).
[CrossRef]

1994 (1)

1993 (3)

1992 (1)

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[CrossRef]

1991 (1)

1990 (1)

K. M. Leung and Y. F. Liu, “Photon band structures: the plane-wave method,” Phys. Rev. B 41, 10188–10190 (1990).
[CrossRef]

1985 (1)

1982 (2)

D. J. Bergrnan, “Rigorous bounds for the complex dielectric constant of a two-component composite,” Ann. Phys. (N.Y.) 138, 78 (1982).
[CrossRef]

D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

1981 (1)

1935 (1)

D. A. G. Bruggman, “Dielectric constant and conductivity of mixtures of isotropic materials,” Ann. Phys. (Leipzig) 24, 636 (1935).

1904 (1)

J. C. Maxwell-Garnett, “Colors in metal glasses and in metallic films,” Philos. Trans. R. Soc. A 203, 385–420 (1904).
[CrossRef]

Andrä, G.

V. Sivakov, G. Andrä, A. Gawlik, A. Berger, J. Plentz, F. Falk, and S. H. Christiansen, “Silicon nanowire-based solar cells on glass: Synthesis, optical properties, and cell parameters,” Nano Lett. 9, 1549–1554 (2009).
[CrossRef]

Aras, M. S.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. Mcmillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5,1–7 (2011).
[CrossRef]

Arikawa, K.

D. G. Stavenga, S. Foletti, G. Palasantzas, and K. Arikawa, “Light on the moth-eye corneal nipple array of butterflies,” Proc. R. Soc. B 273, 661–667 (2006).
[CrossRef]

Arlandis, J.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108, 037401 (2012).
[CrossRef]

Arriaga, J.

P. Halevi, A. A. Krokhin, and J. Arriaga, “Photonic crystal optics and homogenization of 2D periodic composites,” Phys. Rev. Lett. 82, 719–722 (1999).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

Bardinal, V.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdre, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045–1052 (1999).
[CrossRef]

Benisty, H.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. de la Rue, R. Houdre, U. Oesterle, and C. Jouanin, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, C. J. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional photonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdre, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045–1052 (1999).
[CrossRef]

Berger, A.

V. Sivakov, G. Andrä, A. Gawlik, A. Berger, J. Plentz, F. Falk, and S. H. Christiansen, “Silicon nanowire-based solar cells on glass: Synthesis, optical properties, and cell parameters,” Nano Lett. 9, 1549–1554 (2009).
[CrossRef]

Berginc, G.

L. Escoubas, J. J. Simon, M. Loli, G. Berginc, F. Flory, and H. Giovannini, “An antireflective silicon grating working in the resonance domain for the near infrared spectral region,” Opt. Commun. 226, 81–88 (2003).
[CrossRef]

Bergrnan, D. J.

D. J. Bergrnan, “Rigorous bounds for the complex dielectric constant of a two-component composite,” Ann. Phys. (N.Y.) 138, 78 (1982).
[CrossRef]

Bernardo, L. M.

Biris, C. G.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. Mcmillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5,1–7 (2011).
[CrossRef]

Bruggman, D. A. G.

D. A. G. Bruggman, “Dielectric constant and conductivity of mixtures of isotropic materials,” Ann. Phys. (Leipzig) 24, 636 (1935).

Cabrini, S.

V. Mocella, S. Cabrini, A. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902–133905 (2009).
[CrossRef]

Campos, J.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108, 037401 (2012).
[CrossRef]

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[CrossRef]

Plentz, J.

V. Sivakov, G. Andrä, A. Gawlik, A. Berger, J. Plentz, F. Falk, and S. H. Christiansen, “Silicon nanowire-based solar cells on glass: Synthesis, optical properties, and cell parameters,” Nano Lett. 9, 1549–1554 (2009).
[CrossRef]

Pollès, R.

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108, 037401 (2012).
[CrossRef]

Pommet, D. A.

Raguin, D. H.

Ran, L.

Rattier, M.

Rendina, I.

V. Mocella, S. Cabrini, A. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902–133905 (2009).
[CrossRef]

Rosenberg, A.

S. Foteinopoulou, A. Rosenberg, M. M. Sigalas, and C. M. Soukoulis, “In- and out-of-plane propagation of electromagnetic waves in low index contrast two dimensional photonic crystals,” J. Appl. Phys. 89, 824–830 (2001).
[CrossRef]

Roux, F. S.

I. De Leon and F. S. Roux, “Fourier analysis of reflection and refraction in two-dimensional photonic crystals,” Phys. Rev. B 71, 235105 (2005).
[CrossRef]

Ruby, D. S.

Y.-J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, and J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8, 1501–1505 (2008).
[CrossRef]

Sakoda, K.

K. Sakoda, “Optical transmittance of a two-dimensional triangular photonic lattice,” Phys. Rev. B 51, 4672–4675 (1995).
[CrossRef]

K. Sakoda, “Transmittance and Bragg reflectivity of two-dimensional photonic lattices,” Phys. Rev. B 52, 8992–9002 (1995).
[CrossRef]

Schuenemann, K.

A. E. Serebryannikov, T. Magath, and K. Schuenemann, “Bragg transmittance of s-polarized waves through finite-thickness photonic crystals with a periodically corrugated interface,” Phys. Rev. E 74, 066607 (2006).
[CrossRef]

Serebryannikov, A. E.

A. E. Serebryannikov, T. Magath, and K. Schuenemann, “Bragg transmittance of s-polarized waves through finite-thickness photonic crystals with a periodically corrugated interface,” Phys. Rev. E 74, 066607 (2006).
[CrossRef]

Shen, L.

Sheng, P.

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

Sigalas, M. M.

S. Foteinopoulou, A. Rosenberg, M. M. Sigalas, and C. M. Soukoulis, “In- and out-of-plane propagation of electromagnetic waves in low index contrast two dimensional photonic crystals,” J. Appl. Phys. 89, 824–830 (2001).
[CrossRef]

Simon, J. J.

L. Escoubas, J. J. Simon, M. Loli, G. Berginc, F. Flory, and H. Giovannini, “An antireflective silicon grating working in the resonance domain for the near infrared spectral region,” Opt. Commun. 226, 81–88 (2003).
[CrossRef]

Sivakov, V.

V. Sivakov, G. Andrä, A. Gawlik, A. Berger, J. Plentz, F. Falk, and S. H. Christiansen, “Silicon nanowire-based solar cells on glass: Synthesis, optical properties, and cell parameters,” Nano Lett. 9, 1549–1554 (2009).
[CrossRef]

Smaâli, R.

D. Felbacq and R. Smaâli, “Bloch modes dressed by evanescent waves and the generalized Goos–Hänchen effect in photonic crystals,” Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef]

Smith, C. J.

D. Labilloy, H. Benisty, C. Weisbuch, C. J. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional photonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
[CrossRef]

Smith, C. J. M.

Soukoulis, C. M.

S. Foteinopoulou, A. Rosenberg, M. M. Sigalas, and C. M. Soukoulis, “In- and out-of-plane propagation of electromagnetic waves in low index contrast two dimensional photonic crystals,” J. Appl. Phys. 89, 824–830 (2001).
[CrossRef]

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B 48, 14936–14943 (1993).
[CrossRef]

Sözüer, H. S.

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[CrossRef]

Stavenga, D. G.

D. G. Stavenga, S. Foletti, G. Palasantzas, and K. Arikawa, “Light on the moth-eye corneal nipple array of butterflies,” Proc. R. Soc. B 273, 661–667 (2006).
[CrossRef]

Stein, A.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. Mcmillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5,1–7 (2011).
[CrossRef]

Stork, W.

Streibl, N.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).

Thiyagu, S.

T.-H. Pei, S. Thiyagu, and Z. Pei, “Ultra high-density silicon nanowires for extremely low reflection in visible regime,” Appl. Phys. Lett. 99, 153108 (2011).
[CrossRef]

Tjin, S. Chuan

R. Irawan, D. Zhang, S. Chuan Tjin, and X. Yuan, “Biosensor based on two-dimensional photonic lattice,” Microwave Opt. Technol. Lett. 49, 1171–1175 (2007).
[CrossRef]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960–963 (1998).
[CrossRef]

Wang, L.

Weisbuch, C.

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. de la Rue, R. Houdre, U. Oesterle, and C. Jouanin, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, C. J. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional photonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdre, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045–1052 (1999).
[CrossRef]

Wong, C.

S. Kocaman, R. Chatterjee, N. Panoiu, J. Mcmillan, M. Yu, R. Osgood, D. Kwong, and C. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102, 203905 (2009).
[CrossRef]

Wong, C. W.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. Mcmillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5,1–7 (2011).
[CrossRef]

Yamasaki, T.

R. Ozaki and T. Yamasaki, “Propagation characteristics of dielectric waveguides with arbitrary inhomogeneous media along the middle layer,” IEICE Trans. Electron. e95-c, 53–62 (2012).
[CrossRef]

Yeh, P.

Yu, M.

S. Kocaman, R. Chatterjee, N. Panoiu, J. Mcmillan, M. Yu, R. Osgood, D. Kwong, and C. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102, 203905 (2009).
[CrossRef]

Yu, M. B.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. Mcmillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5,1–7 (2011).
[CrossRef]

Yuan, X.

R. Irawan, D. Zhang, S. Chuan Tjin, and X. Yuan, “Biosensor based on two-dimensional photonic lattice,” Microwave Opt. Technol. Lett. 49, 1171–1175 (2007).
[CrossRef]

Yuan, Y.

Zayats, A. V.

S. A. Darmanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003).
[CrossRef]

Zhang, D.

R. Irawan, D. Zhang, S. Chuan Tjin, and X. Yuan, “Biosensor based on two-dimensional photonic lattice,” Microwave Opt. Technol. Lett. 49, 1171–1175 (2007).
[CrossRef]

Zhang, X.-C.

Y. W. Chen, P. Han, X.-C. Zhang, M.-L. Kuo, and S.-Y. Lin, “Three-dimensional inverted photonic grating with engineerable refractive indices for broadband antireflection of terahertz waves,” Opt. Lett. 35, 3159–3161 (2010).
[CrossRef]

P. Han, Y. W. Chen, and X.-C. Zhang, “Application of silicon micropyramid structures for antireflection of terahertz waves,” IEEE J. Sel. Topics Quantum Electron. 16, 338–343 (2010).
[CrossRef]

Zhou, L.

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

AIP Advances (1)

T.-H. Pei and Y.-T. Huang, “Analyzing the propagating waves in the two-dimensional photonic crystal by the decoupled internal-field expansion method,” AIP Advances 2, 0120188 (2012).
[CrossRef]

Am. J. Phys. (1)

D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

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D. A. G. Bruggman, “Dielectric constant and conductivity of mixtures of isotropic materials,” Ann. Phys. (Leipzig) 24, 636 (1935).

Ann. Phys. (N.Y.) (1)

D. J. Bergrnan, “Rigorous bounds for the complex dielectric constant of a two-component composite,” Ann. Phys. (N.Y.) 138, 78 (1982).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

T.-H. Pei, S. Thiyagu, and Z. Pei, “Ultra high-density silicon nanowires for extremely low reflection in visible regime,” Appl. Phys. Lett. 99, 153108 (2011).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdre, U. Oesterle, and V. Bardinal, “Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices,” IEEE J. Quantum Electron. 35, 1045–1052 (1999).
[CrossRef]

IEEE J. Sel. Topics Quantum Electron. (1)

P. Han, Y. W. Chen, and X.-C. Zhang, “Application of silicon micropyramid structures for antireflection of terahertz waves,” IEEE J. Sel. Topics Quantum Electron. 16, 338–343 (2010).
[CrossRef]

IEICE Trans. Electron. (1)

R. Ozaki and T. Yamasaki, “Propagation characteristics of dielectric waveguides with arbitrary inhomogeneous media along the middle layer,” IEICE Trans. Electron. e95-c, 53–62 (2012).
[CrossRef]

J. Appl. Phys. (3)

S. Foteinopoulou, A. Rosenberg, M. M. Sigalas, and C. M. Soukoulis, “In- and out-of-plane propagation of electromagnetic waves in low index contrast two dimensional photonic crystals,” J. Appl. Phys. 89, 824–830 (2001).
[CrossRef]

T.-H. Pei and Y.-T. Huang, “The high-transmission photonic crystal heterostructure Y-branch waveguide operating at photonic band region,” J. Appl. Phys. 109, 034504 (2011).
[CrossRef]

T.-H. Pei and Y.-T. Huang, “The equivalent structure and some optical properties of the periodic-defect photonic crystal,” J. Appl. Phys. 109, 073104 (2011).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (5)

Microwave Opt. Technol. Lett. (1)

R. Irawan, D. Zhang, S. Chuan Tjin, and X. Yuan, “Biosensor based on two-dimensional photonic lattice,” Microwave Opt. Technol. Lett. 49, 1171–1175 (2007).
[CrossRef]

Nano Lett. (2)

Y.-J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, and J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8, 1501–1505 (2008).
[CrossRef]

V. Sivakov, G. Andrä, A. Gawlik, A. Berger, J. Plentz, F. Falk, and S. H. Christiansen, “Silicon nanowire-based solar cells on glass: Synthesis, optical properties, and cell parameters,” Nano Lett. 9, 1549–1554 (2009).
[CrossRef]

Nat. Photonics (1)

S. Kocaman, M. S. Aras, P. Hsieh, J. F. Mcmillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics 5,1–7 (2011).
[CrossRef]

Opt. Commun. (1)

L. Escoubas, J. J. Simon, M. Loli, G. Berginc, F. Flory, and H. Giovannini, “An antireflective silicon grating working in the resonance domain for the near infrared spectral region,” Opt. Commun. 226, 81–88 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Philos. Trans. R. Soc. A (1)

J. C. Maxwell-Garnett, “Colors in metal glasses and in metallic films,” Philos. Trans. R. Soc. A 203, 385–420 (1904).
[CrossRef]

Phys. Rev. B (11)

K. M. Leung and Y. F. Liu, “Photon band structures: the plane-wave method,” Phys. Rev. B 41, 10188–10190 (1990).
[CrossRef]

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[CrossRef]

S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B 48, 14936–14943 (1993).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

S. A. Darmanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, C. J. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, “Finely resolved transmission spectra and band structure of two-dimensional photonic crystals using emission from InAs quantum dots,” Phys. Rev. B 59, 1649–1652 (1999).
[CrossRef]

K. Sakoda, “Optical transmittance of a two-dimensional triangular photonic lattice,” Phys. Rev. B 51, 4672–4675 (1995).
[CrossRef]

K. Sakoda, “Transmittance and Bragg reflectivity of two-dimensional photonic lattices,” Phys. Rev. B 52, 8992–9002 (1995).
[CrossRef]

I. De Leon and F. S. Roux, “Fourier analysis of reflection and refraction in two-dimensional photonic crystals,” Phys. Rev. B 71, 235105 (2005).
[CrossRef]

W. Jiang, R. T. Chen, and X. Lu, “Theory of light refraction at the surface of a photonic crystal,” Phys. Rev. B 71, 245115 (2005).
[CrossRef]

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(2000).
[CrossRef]

Phys. Rev. E (1)

A. E. Serebryannikov, T. Magath, and K. Schuenemann, “Bragg transmittance of s-polarized waves through finite-thickness photonic crystals with a periodically corrugated interface,” Phys. Rev. E 74, 066607 (2006).
[CrossRef]

Phys. Rev. Lett. (7)

D. Felbacq and R. Smaâli, “Bloch modes dressed by evanescent waves and the generalized Goos–Hänchen effect in photonic crystals,” Phys. Rev. Lett. 92, 193902 (2004).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960–963 (1998).
[CrossRef]

V. Mocella, S. Cabrini, A. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett. 102, 133902–133905 (2009).
[CrossRef]

S. Kocaman, R. Chatterjee, N. Panoiu, J. Mcmillan, M. Yu, R. Osgood, D. Kwong, and C. Wong, “Observation of zeroth-order band gaps in negative-refraction photonic crystal superlattices at near-infrared frequencies,” Phys. Rev. Lett. 102, 203905 (2009).
[CrossRef]

J. Arlandis, E. Centeno, R. Pollès, A. Moreau, J. Campos, O. Gauthier-Lafaye, and A. Monmayrant, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108, 037401 (2012).
[CrossRef]

P. Halevi, A. A. Krokhin, and J. Arriaga, “Photonic crystal optics and homogenization of 2D periodic composites,” Phys. Rev. Lett. 82, 719–722 (1999).
[CrossRef]

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

Proc. R. Soc. B (1)

D. G. Stavenga, S. Foletti, G. Palasantzas, and K. Arikawa, “Light on the moth-eye corneal nipple array of butterflies,” Proc. R. Soc. B 273, 661–667 (2006).
[CrossRef]

Other (3)

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).

K. Sakoda, Optical Properties of Photonic Crystals, 2nd ed. (Springer, 2005).

P. Yeh, Optical Waves in Layered Media (Wiley, 1991).

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Figures (9)

Fig. 1.
Fig. 1.

Geometry of the superlattice composed of two alternating PhCs.

Fig. 2.
Fig. 2.

(a) and (b) denote two possible interfaces used in the case in which the propagation direction is along ΓK.

Fig. 3.
Fig. 3.

(a) Resonant-tunneling superlattice composed of two triangular PhCs with a number of periods L=2 and ta=tb=3a. (b) Effective resonant-tunneling superlattice.

Fig. 4.
Fig. 4.

Case in which the y axis is along the ΓK direction with θ=0° (dashed curve, IFEM; solid curve, EMT).

Fig. 5.
Fig. 5.

Case in which the y axis is along the ΓM direction with θ=0° (dashed curve, IFEM; solid curve, EMT).

Fig. 6.
Fig. 6.

Case in which the y axis is along the ΓK direction with θ=45° (dashed curve, IFEM; solid curve, EMT).

Fig. 7.
Fig. 7.

Case in which the y axis is along the ΓM direction with θ=45° (dashed curve, IFEM; solid curve, EMT).

Fig. 8.
Fig. 8.

Case of light propagating along the ΓM direction where θ=60°, ta=tb=23a, εa=2.25, r1=0.12a and r2=0.42a.

Fig. 9.
Fig. 9.

Case of light propagating along the ΓK direction where θ=30°, ta=tb=23a,εa=6.25, r1=0.10a, and r2=0.45a.

Equations (5)

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

p=[(neff1ωc)2β2]1/2,
q=[β2(neff2ωc)2]1/2.
M=(M11M12M21M22)=Dincident1[j=1NDjPjDj1]Dtran,
Dj=(11nicosθinicosθi).
neff,i=neff,i02+π23(aλ)2f2(1f)2(εa1.0),(i=1,2),

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