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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry M. Van Driel
  • Vol. 24, Iss. 12 — Dec. 1, 2007
  • pp: 2964–2971

Exploring light propagating in photonic crystals with Fourier optics

Nicolas Le Thomas, Romuald Houdré, Maria V. Kotlyar, David O'Brien, and Thomas F. Krauss  »View Author Affiliations


JOSA B, Vol. 24, Issue 12, pp. 2964-2971 (2007)
http://dx.doi.org/10.1364/JOSAB.24.002964


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Abstract

Photonic crystals (PhCs) act on light in two different ways: confinement and modification of propagation. Both phenomena rely on the complex interplay between multiply scattered waves that can form what is known as a Bloch mode. Here, we present a technique that allows direct imaging of Bloch modes, both in real space and in k-space. The technique gives access to the location of the field maxima inside the PhC, the dispersion relation, equifrequency surfaces, as well as reflection and transmission coefficients. Our key advance is that we retrieve the desired information comprehensively, without postprocessing or cumbersome near-field scanning techniques, even for modes that are nominally lossless, i.e., below the light line. To highlight the potential of the technique, we extract the dispersion curve of a coupled cavity waveguide consisting of as many as 100 cavities, as well as the equifrequency surfaces and polarization properties of a PhC beam splitter.

© 2007 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(130.0130) Integrated optics : Integrated optics
(130.2790) Integrated optics : Guided waves
(130.5990) Integrated optics : Semiconductors

ToC Category:
Photonic Crystals

History
Original Manuscript: August 3, 2007
Manuscript Accepted: September 26, 2007
Published: November 14, 2007

Citation
Nicolas Le Thomas, Romuald Houdré, Maria V. Kotlyar, David O'Brien, and Thomas F. Krauss, "Exploring light propagating in photonic crystals with Fourier optics," J. Opt. Soc. Am. B 24, 2964-2971 (2007)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-12-2964


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References

  1. T. F. Krauss, R. M. De La Rue, and S. Brand, "Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths," Nature 383, 699-702 (1996). [CrossRef]
  2. X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d'Yerville, D. Cassagne, and C. Jouanin, "Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes," Appl. Phys. Lett. 79, 2312-2314 (2001). [CrossRef]
  3. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001). [CrossRef] [PubMed]
  4. T. Baba and T. Matsumoto, "Resolution of photonic crystal superprism," Appl. Phys. Lett. 81, 2325-2327 (2002). [CrossRef]
  5. M. J. Steel, R. Zoli, C. Grillet, R. C. McPhedran, C. Martijn de Sterke, A. Norton, P. Bassi, and B. J. Eggleton, "Analytic properties of photonic crystal superprism parameters," Phys. Rev. E 71, 056608 (2005). [CrossRef]
  6. H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94, 123901 (2005). [CrossRef] [PubMed]
  7. H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005). [CrossRef] [PubMed]
  8. R. Wüest, D. Erni, P. Strasser, F. Robin, H. Jäckel, B. C. Buchler, A. F. Koenderink, V. Sandoghdar, and R. Harbers, "A standing-wave meter to measure dispersion and loss of photonic-crystal waveguides," Appl. Phys. Lett. 87, 261110 (2005). [CrossRef]
  9. P. Kramper, M. Kafesaki, C. M. Soukoulis, A. Birner, F. Mller, U. Gsele, R. B. Wehrspohn, J. Mlynek, and V. Sandoghdar, "Near-field visualization of light confinement in a photonic crystal microresonator," Opt. Lett. 29, 174-176 (2004). [CrossRef] [PubMed]
  10. N. Louvion, D. Gérard, J. Mouette, F. de Fornel, C. Seassal, X. Letartre, A. Rahmani, and S. Callard, "Local observation and spectroscopy of optical modes in an active photonic-crystal microcavity," Phys. Rev. Lett. 94, 113907 (2005). [CrossRef] [PubMed]
  11. R. Zengerle, "Light propagation in singly and doubly periodic planar waveguides," J. Mod. Opt. 34, 1589-1617 (1987). [CrossRef]
  12. M. Galli, D. Bajoni, M. Patrini, G. Guizzetti, D. Gerace, L. C. Andreani, M. Belotti, and Y. Chen, Phys. Rev. B 72, 125322 (2005). [CrossRef]
  13. M. Loncar, D. Nedeljkovic, T. P. Pearsall, J. Vuckovic, A. Scherer, S. Kuchinsky, and D. C. Allan, "Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides," Appl. Phys. Lett. 80, 1689-1691 (2002). [CrossRef]
  14. G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005). [CrossRef] [PubMed]
  15. P. St. J. Russell, "Optics of Floquet-Bloch waves in dielectric gratings," Appl. Phys. B 39, 231-246 (1986). [CrossRef]
  16. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopuolou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature 423, 604-605 (2003). [CrossRef] [PubMed]
  17. 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]
  18. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, 10096-10099 (1998). [CrossRef]
  19. S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, "Focusing of sound in a 3D phononic crystal," Phys. Rev. Lett. 93, 024301 (2004). [CrossRef] [PubMed]
  20. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999). [CrossRef]
  21. 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 centimeter-scale supercollimation in a large-area two-dimensional photonic crystal," Nat. Mater. 5, 93-96 (2006). [CrossRef] [PubMed]
  22. R. Ferrini, A. Berrier, L. A. Dunbar, R. Houdré, M. Mulot, S. Anand, S. de Rossi, and A. Talneau, "Minimization of out-of-plane losses in planar photonic crystals by optimizing the vertical waveguide," Appl. Phys. Lett. 85, 3998-4000 (2004). [CrossRef]
  23. Note that here the PhC structure is excited in the second band of the dispersion diagram. As a result the group velocity in the first Brillouin zone is positive for "negative" wave vectors value, hence the image of the FW propagating wave in the Fourier space is located at −kx.
  24. N. Le Thomas, R. Houdré, L. H. Frandsen, J. Fage-Pedersen, A. V. Lavrinenko, and P. I. Borel, "Grating-assisted superresolution of slow waves in Fourier space," Phys. Rev. B 76, 035103 (2007). [CrossRef]
  25. M. I. Kobolov and C. Fabre, "Quantum limits on optical resolution," Phys. Rev. Lett. 85, 3789-3792 (2000). [CrossRef]
  26. C. K. Rushforth and R. W. Harris, "Restoration, resolution, and noise," J. Opt. Soc. Am. 58, 539-545 (1968). [CrossRef]
  27. N. Stefanou and A. Modinos, "Impurity bands in photonic insulator," Phys. Rev. B 57, 12127-12133 (1998). [CrossRef]
  28. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett. 24, 711-713 (1999). [CrossRef]
  29. M. F. Yanik, W. Suh, Z. Wang, and S. Fan, "Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency," Phys. Rev. Lett. 93, 233903 (2004). [CrossRef] [PubMed]
  30. M. F. Yanik and S. Fan, "Stopping light all-optically," Phys. Rev. Lett. 92, 083901 (2004). [CrossRef] [PubMed]
  31. B.-S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Astrophys. J., Suppl. Ser. 4, 93-96 (2005).
  32. M. L. Povinelli and S. Fan, "Radiation loss of coupled-resonator waveguides in photonic-crystal slabs," Appl. Phys. Lett. 89, 191114 (2006). [CrossRef]
  33. R. Mitra, Computer Techniques for Electromagnetics (Pergamon, 1973), Chap 2.
  34. E. E. Orlova, J. N. Hovenier, T. O. Klaassen, I. Kasalynas, A. J. L. Adam, J. R. Gao, T. M. Klapwijk, B. S. Williams, S. Kumar, Q. Hu, and J. L. Reno, "Antenna model for wire lasers," Phys. Rev. Lett. 96, 173904 (2006). [CrossRef] [PubMed]
  35. B. Lombardet, L. A. Dunbar, R. Ferrini, and R. Houdré, "Fourier analysis of Bloch wave propagation in photonic crystals," J. Opt. Soc. Am. B 22, 1179-1190 (2005). [CrossRef]

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