volume | PIER Journals

Abstract

This paper studies the surface modes at the interface of finite size Electromagnetic Band Gap (EBG) woodpile structures. The impact of different types of woodpile terminations on the properties of these surface modes is analyzed. For all the studied terminations there exist surface modes which must be taken into account when designing components based on this EBG structure.

1. Joannopoulos, J. D., R. D. Meade, and J. N. Finn, Photonic Crystals: Molding the Flow of Light, Princeton University Press, 1995.

2. Lourtioz, J. M., V. Berger, J. M. Gerard, and H. Benisty, "Photonic Crystals: Towards Nanoscale Photonic Devices," Springer, 2005. Google Scholar

3. Ho, K. M., C. T. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: New layer-by-layer periodic structure," Solid State Comm., Vol. 89, 413-416, 1994.
doi:10.1016/0038-1098(94)90202-X Google Scholar

4. Sozuer, H. S. and J. P. Dowling, "Photonic band calculations for woodpile structure," J. Mod. Opt., Vol. 43, 231-234, 1994.
doi:10.1080/09500349414550291 Google Scholar

5. Martinez, B., I. Ederra, R. Gonzalo, B. Alderman, L. Azcona, P. G. Huggard, B. de Hon, A. Hussain, S. R. Andrews, L. Marchand, and P. de Maagt, "Manufacturing tolerance analysis, fabrication and characterisation of 3D submillimetre wave electromagnetic bandgap crystals," IEEE Trans. Microw. Theory Tech., Vol. 55, No. 4, 672-681, 2007.
doi:10.1109/TMTT.2007.892803 Google Scholar

6. Ozbay, E., "Layer-by-layer photonic crystals from microwave to far-infrared frequencies," J. Opt. Soc. Amer. B, Vol. 13, No. 9, 1945-1955, 1996.
doi:10.1364/JOSAB.13.001945 Google Scholar

7. Gonzalo, R., B. Martinez, C. M. Mann, H. Pellemans, P. H. Bolivar, and P. de Maagt, "A low cost fabrication technique for symmetrical and asymmetrical layer by layer photonic crystal at submillimeter wave frequencies," IEEE Trans. Microw. Theory Tech., Vol. 50, No. 10, 2384-2393, 2002.
doi:10.1109/TMTT.2002.803446 Google Scholar

8. Noda, S., K. Tomoda, N. Yamamoto, and A. Chutinan, "Full Three-dimensional photonic bandgap crystal at near-infrared wavelengths," Science, Vol. 289, No. 5479, 604-606, 2000.
doi:10.1126/science.289.5479.604 Google Scholar

9. Lin, S. Y., J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature, Vol. 394, No. 6690, 251-252, 1998.
doi:10.1038/28343 Google Scholar

10. Lin, S. Y. and J. G. Fleming, "A three dimensional optical photonic crystal," J. Lightwave Technol., Vol. 17, No. 11, 1944-1947, 1999.
doi:10.1109/50.802977 Google Scholar

11. Gonzalo, R., I. Ederra, C. M. Mann, and P. de Maagt, "Radiation properties of terahertz dipole antenna mounted on photonic crystal," Electron. Lett., Vol. 37, No. 10, 613-614, 2001.
doi:10.1049/el:20010435 Google Scholar

12. Ederra, I., R. Gonzalo, B. E. J. Alderman, P. G. Huggard, B. P. de Hon, M. C. van Beurden, A. Murk, L. Marchand, and P. Maagt, "Electromagnetic bandgap based planar imaging array for 500 GHz ," IEEE Trans. Microw. Theory Tech., Vol. 56, No. 11, 2256-2265, 2008.
doi:10.1109/TMTT.2008.2005926 Google Scholar

13. Weily, A. R., K. P. Esselle, and B. C. Sanders, "Photonic crystal horn and array antennas," Phys. Rev. E, Vol. 68, No. 1, 016609-1-016609-6, 2003.
doi:10.1103/PhysRevE.68.016609 Google Scholar

14. Ederra, I., L. Azcona, B. E. J. Alderman, A. Laisne, R. Gonzalo, C. M. Mann, D. N. Matheson, and P. de Maagt, "A 250 GHz sub-harmonic mixer design using EBG technology," IEEE Trans. Antennas Propagat., Vol. 55, No. 11, 2974-2982, 2007.
doi:10.1109/TAP.2007.908367 Google Scholar

15. Bayindir, M., E. Ozbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, "Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides," Phys. Rev. B, Condens. Matter, Vol. 63, No. 8, 081107, 2001.
doi:10.1103/PhysRevB.63.081107 Google Scholar

16. Weily, A. R., T. S. Bird, K. P. Esselle, and B. C. Sanders, "Woodpile EBG phase shifter," Elec. Lett., Vol. 42, No. 25, 1463-1464, 2006.
doi:10.1049/el:20062820 Google Scholar

17. Kawashima, S., K. Ishizaki, and S. Noda, "Light propagation in three-dimensional photonic crystals," Opt. Express, Vol. 18, No. 1, 386-392, 2010.
doi:10.1364/OE.18.000386 Google Scholar

18. Sell, C., C. Christensen, J. Muehlmeier, G. Tuttle, Z. Y. Li, and K. M. Ho, "Waveguide networks in three-dimensional layer-by-layer photonic crystals," Appl. Phys. Lett., Vol. 84, No. 23, 4605-4607, 2004.
doi:10.1063/1.1751212 Google Scholar

19. Kohli, P., C. Christensen, J. Muehlmeier, R. Biswas, G. Tuttle, and K.-M. Ho, "Add-drop filters in three-dimensional layer-by-layer photonic crystals using waveguides and resonant cavities," Appl. Phys. Lett., Vol. 89, No. 23, 231103, 2006.
doi:10.1063/1.2400398 Google Scholar

20. Ederra, I., B. Martinez, A. B. Labajos, J. Teniente, R. Gonzalo, and P. de Maagt, "Experimental verification of the reduction of coupling between dipole antennas by using a woodpile substrate," IEEE Trans. Antennas Propagat., Vol. 54, No. 7, 2105-2111, 2006.
doi:10.1109/TAP.2006.877192 Google Scholar

21. Meade, R. D., K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B, Vol. 44, No. 19, 1991.
doi:10.1103/PhysRevB.44.10961 Google Scholar

22. Feng, S., H.-Y. Sang, Z.-Y. Li, B.-Y. Cheng, and D.-Z. Zhang, "Sensitivity of surface states to the stack sequence of one-dimensional photonic crystals," J. Opt. A: Pure Appl. Opt., Vol. 7, No. 8, 374-381, 2005.
doi:10.1088/1464-4258/7/8/004 Google Scholar

23. Zhang, X., L. M. Li, Z. Q. Zhang, and C. T. Chan, "Surface states in two-dimensional metallodielectric photonic crystals studied by a multiple-scattering method ," Phys. Rev. B, Vol. 63, No. 12, 125114, 2001.
doi:10.1103/PhysRevB.63.125114 Google Scholar

24. Vlasov, Y. A., N. Moll, and S. J. McNab, "Observation of surface states in a truncated photonic crystal slab," Opt. Lett., Vol. 29, No. 18, 2175-2177, 2004.
doi:10.1364/OL.29.002175 Google Scholar

25. Robertson, W. M. and M. S. May, "Surface electromagnetic wave excitation on one-dimensional photonic band-gap arrays," Appl. Phys. Lett., Vol. 74, No. 13, 1800-1802, 1999.
doi:10.1063/1.123090 Google Scholar

26. Ramos-Mendieta, F. and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: Effect of the position of the surface plane ," Phys. Rev. B, Vol. 59, No. 23, 15112-15120, 1999.
doi:10.1103/PhysRevB.59.15112 Google Scholar

27. Qiu, M. and S. He, "Surface modes in two-dimensional dielectric and metallic photonic band gap structures: A FDTD study," Phys. Lett. A, Vol. 282, 85-91, 2001.
doi:10.1016/S0375-9601(01)00156-6 Google Scholar

28. Ishizaki, K. and S. Noda, "Manipulation of photons at the surface of three-dimensional photonic crystals," Nature, Vol. 460, 367-371, 2009.
doi:10.1038/nature08190 Google Scholar

29. Eyni, Z., S. Roshan Entezar, A. Namdar, and H. Tajalli, "Tamm states of a nonlinear slab sandwiched between a uniform medium and a one-dimensional photonic crystal," Progress In Electromagnetics Research Letters, Vol. 18, 115-124, 2010.
doi:10.2528/PIERL10072105 Google Scholar

30. Gaspar-Armentaa, J. A., F. Villa, and T. Lpez-Ros, "Surface waves in finite one-dimensional photonic crystals: mode coupling," Opt. Commun., Vol. 216, 379-384, 2003.
doi:10.1016/S0030-4018(02)02361-1 Google Scholar

31. Ramos-Mendieta, F. and P. Halevi, "Electromagnetic surface modes of a dielectric superlattice: The supercell method," J. Opt. Soc. Am. B, Vol. 14, No. 2, 370-381, 1997.
doi:10.1364/JOSAB.14.000370 Google Scholar

32. Ozbay, E., A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, "Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods," Phys. Rev. B, Vol. 50, No. 3, 1945-1948, 1994.
doi:10.1103/PhysRevB.50.1945 Google Scholar

33. Gonzalo, R., B. Martinez, and P. de Maagt, "The effect of dielectric permittivity on the properties of photonic bandgap devices ," Microw. Opt. Technol. Lett., Vol. 23, No. 2, 92-95, 1999.
doi:10.1002/(SICI)1098-2760(19991020)23:2<92::AID-MOP9>3.0.CO;2-J Google Scholar

34. Johnson, S. G. and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis ," Opt. Express, Vol. 8, No. 3, 173-190, 2001.
doi:10.1364/OE.8.000173 Google Scholar

35. Reynolds, A. L., H. M. H. Chong, I. G. Thayne, J. M. Arnold, and P. de Maagt, "Analysis of membrane support structures for integrated antenna usage on two-dimensional photonic-bandgap structures," IEEE Trans. Microw. Theory and Tech., Vol. 49, No. 7, 1254-1261, 2001.
doi:10.1109/22.932244 Google Scholar

Dr. Inigo Ederra

Dr. Juan Carlos Iriarte

Prof. Ramon Gonzalo

Dr. Peter de Maagt