OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 30, Iss. 1 — Jan. 1, 2013
  • pp: 40–50

Comparisons of the transmission and resonant tunneling between the superlattice composed of two alternating photonic crystals and its effective structure

Ting-Hang Pei and Yang-Tung Huang  »View Author Affiliations

JOSA B, Vol. 30, Issue 1, pp. 40-50 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (797 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

OCIS Codes
(050.2065) Diffraction and gratings : Effective medium theory
(260.2065) Physical optics : Effective medium theory
(350.4238) Other areas of optics : Nanophotonics and photonic crystals

ToC Category:
Diffraction and Gratings

Original Manuscript: August 7, 2012
Revised Manuscript: October 26, 2012
Manuscript Accepted: October 26, 2012
Published: December 6, 2012

Ting-Hang Pei and Yang-Tung Huang, "Comparisons of the transmission and resonant tunneling between the superlattice composed of two alternating photonic crystals and its effective structure," J. Opt. Soc. Am. B 30, 40-50 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. C. Maxwell-Garnett, “Colors in metal glasses and in metallic films,” Philos. Trans. R. Soc. A 203, 385–420 (1904). [CrossRef]
  2. D. A. G. Bruggman, “Dielectric constant and conductivity of mixtures of isotropic materials,” Ann. Phys. (Leipzig) 24, 636 (1935).
  3. D. J. Bergrnan, “Rigorous bounds for the complex dielectric constant of a two-component composite,” Ann. Phys. (N.Y.) 138, 78 (1982). [CrossRef]
  4. D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982). [CrossRef]
  5. J. M. dos Santos and L. M. Bernardo, “Antireflection structures with use of multilevel subwavelength zero-order gratings,” Appl. Opt. 36, 8935–8938 (1997). [CrossRef]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. W. Stork, N. Streibl, H. Haidner, and P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett. 16, 1921–1923 (1991). [CrossRef]
  11. C. W. Haggans, L. Li, and R. K. Kostuk, “Effective-medium theory of zeroth-order lamellar gratings in conical mountings,” J. Opt. Soc. Am. A 10, 2217–2225 (1993). [CrossRef]
  12. D. H. Raguin and G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993). [CrossRef]
  13. E. B. Grann, M. G. Moharam, and D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. A 11, 2695–2703 (1994). [CrossRef]
  14. H. Kikuta, Y. Ohira, H. Kubo, and K. Iwata, “Effective medium theory of two-dimensional subwavelength gratings in the non-quasi-static limit,” J. Opt. Soc. Am. A 15, 1577–1585 (1998). [CrossRef]
  15. P. Lalanne and J.-P. Hugonin, “High-order effective-medium theory of subwavelength gratings in classical mounting: application to volume holograms,” J. Opt. Soc. Am. A 15, 1843–1851 (1998). [CrossRef]
  16. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981). [CrossRef]
  17. 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]
  18. 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]
  19. 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]
  20. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).
  21. K. M. Leung and Y. F. Liu, “Photon band structures: the plane-wave method,” Phys. Rev. B 41, 10188–10190 (1990). [CrossRef]
  22. 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]
  23. 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]
  24. 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]
  25. S.-Y. Lin, V. M. Hietala, L. Wang, and E. D. Jones, “Highly dispersive photonic band-gap prism,” Opt. Lett. 21, 1771–1773 (1996). [CrossRef]
  26. 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]
  27. 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]
  28. 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]
  29. 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]
  30. 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]
  31. 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]
  32. 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]
  33. 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]
  34. 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]
  35. 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]
  36. 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]
  37. 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]
  38. P. Yeh, “Resonant tunneling of electromagnetic radiation in superlattice structures,” J. Opt. Soc. Am. A 2, 568–571 (1985). [CrossRef]
  39. P. Yeh, Optical Waves in Layered Media (Wiley, 1991).
  40. K. Sakoda, “Optical transmittance of a two-dimensional triangular photonic lattice,” Phys. Rev. B 51, 4672–4675 (1995). [CrossRef]
  41. K. Sakoda, “Transmittance and Bragg reflectivity of two-dimensional photonic lattices,” Phys. Rev. B 52, 8992–9002 (1995). [CrossRef]
  42. K. Sakoda, Optical Properties of Photonic Crystals, 2nd ed. (Springer, 2005).
  43. 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]
  44. 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]
  45. 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]
  46. 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]
  47. 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]
  48. 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]
  49. 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]
  50. J. G. Shawn-Yu Lin and J. G. Fleming, “A three-dimensional optical photonic crystal,” J. Lightwave Technol. 17, 1944–1947 (1999). [CrossRef]
  51. 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]
  52. 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]
  53. 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]
  54. 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]
  55. P. Lalanne, “Effective medium theory applied to photonic crystals composed of cubic or square cylinders,” Appl. Opt. 35, 5369–5380 (1996). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited