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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. 25, Iss. 12 — Dec. 1, 2008
  • pp: C65–C74

Slow-light dispersion in coupled periodic waveguides

Andrey A. Sukhorukov, Andrei V. Lavrinenko, Dmitry N. Chigrin, Dmitry E. Pelinovsky, and Yuri S. Kivshar  »View Author Affiliations


JOSA B, Vol. 25, Issue 12, pp. C65-C74 (2008)
http://dx.doi.org/10.1364/JOSAB.25.000C65


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Abstract

Periodic waveguides bring a new twist to the typical waveguiding problems of the intermediate case between photonic crystal waveguides and photonic wires or ridge waveguides. We develop an asymptotic theory applicable for a broad class of coupled periodic waveguide structures and use the analytical expressions to identify the generic types of dispersion in the vicinity of a photonic band edge, where the group velocity of light is reduced. We show that the dispersion can be controlled by the longitudinal shift between the waveguides. We also demonstrate through finite-difference time-domain simulations examples of spatial and temporal pulse dynamics in association with different types of slow-light dispersion.

© 2008 Optical Society of America

OCIS Codes
(230.7370) Optical devices : Waveguides
(250.5300) Optoelectronics : Photonic integrated circuits
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Slow Light in Coupled Resonators and Waveguides

History
Original Manuscript: April 17, 2008
Revised Manuscript: July 24, 2008
Manuscript Accepted: July 25, 2008
Published: September 18, 2008

Citation
Andrey A. Sukhorukov, Andrei V. Lavrinenko, Dmitry N. Chigrin, Dmitry E. Pelinovsky, and Yuri S. Kivshar, "Slow-light dispersion in coupled periodic waveguides," J. Opt. Soc. Am. B 25, C65-C74 (2008)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-25-12-C65


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References

  1. X. Letartre, C. Seassal, C. Grillet, P. Rojo Romeo, P. Viktorovitch, M. L. d'Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a singleline photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79, 2312-2314 (2001). [CrossRef]
  2. Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65-69 (2005). [CrossRef]
  3. 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]
  4. R. S. Jacobsen, A. V. Lavrinenko, L. H. Frandsen, C. Peucheret, B. Zsigri, G. Moulin, J. Fage Pedersen, and P. I. Borel, “Direct experimental and numerical determination of extremely high group indices in photonic crystal waveguides,” Opt. Express 13, 7861-7871 (2005). [CrossRef]
  5. J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nat. Phys. 2, 775-780 (2006).
  6. M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15, 219-226 (2007). [CrossRef]
  7. S. C. Huang, M. Kato, E. Kuramochi, C. P. Lee, and M. Notomi, “Time-domain and spectral-domain investigation of inflection-point slow-light modes in photonic crystal coupled waveguides,” Opt. Express 15, 3543-3549 (2007). [CrossRef]
  8. R. J. P. Engelen, Y. Sugimoto, Y. Watanabe, J. P. Korterik, N. Ikeda, and N. F. van Hulst, K. Asakawa, and L. Kuipers, “The effect of higher-order dispersion on slow light propagation in photonic crystal waveguides,” Opt. Express 14, 1658-1672 (2006). [CrossRef]
  9. A. Figotin and I. Vitebskiy, “Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers,” Phys. Rev. E 72, 036619 (2005). [CrossRef]
  10. M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92, 063903 (2004). [CrossRef]
  11. A. A. Sukhorukov, C. J. Handmer, C. M. de Sterke, and M. J. Steel, “Slow light with flat or offset band edges in few-mode fiber with two gratings,” Opt. Express 15, 17954-17959 (2007). [CrossRef]
  12. S. Ha, A. A. Sukhorukov, K. B. Dossou, L. C. Botten, A. V. Lavrinenko, D. N. Chigrin, and Yu. S. Kivshar, “Dispersionless tunneling of slow light in antisymmetric photonic crystal couplers,” Opt. Express 16, 1104-1114 (2008). [CrossRef]
  13. R. Marz and H. P. Nolting, “Spectral properties of asymmetrical optical directional-couplers with periodic structures,” Opt. Quantum Electron. 19, 273-287 (1987). [CrossRef]
  14. G. Perrone, M. Laurenzano, and I. Montrosset, “Design and feasibility analysis of an innovative integrated grating-assisted add-drop multiplexer,” J. Lightwave Technol. 19, 1943-1948 (2001). [CrossRef]
  15. M. Aslund, J. Canning, L. Poladian, C. M. de Sterke, and A. Judge, “Antisymmetric grating coupler: experimental results,” Appl. Opt. 42, 6578-6583 (2003).
  16. J. M. Castro, D. F. Geraghty, S. Honkanen, C. M. Greiner, D. Iazikov, and T. W. Mossberg, “Demonstration of mode conversion using anti-symmetric waveguide Bragg gratings,” Opt. Express 13, 4180-4184 (2005). [CrossRef]
  17. S. Ha, A. A. Sukhorukov, and Yu. S. Kivshar, “Slow-light switching in nonlinear Bragg-grating couplers,” Opt. Lett. 32, 1429-1431 (2007). [CrossRef]
  18. H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys. 79, 7483-7492 (1996). [CrossRef]
  19. D. N. Chigrin, A. V. Lavrinenko, and C. M. S. Torres, “Nanopillars photonic crystal waveguides,” Opt. Express 12, 617-622 (2004). [CrossRef]
  20. D. N. Chigrin, A. V. Lavrinenko, and C. M. S. Torres, “Numerical characterization of nanopillar photonic crystal waveguides and directional couplers,” Opt. Quantum Electron. 37, 331-341 (2005). [CrossRef]
  21. D. N. Chigrin, S. V. Zhukovsky, A. V. Lavrinenko, and J. Kroha, “Coupled nanopillar waveguides optical properties and applications,” Phys. Status Solidi A 204, 3647-3661 (2007). [CrossRef]
  22. Y. G. Boucher, A. V. Lavrinenko, and D. N. Chigrin, “Out-of-phase coupled periodic waveguides: a 'couplonic' approach,” Opt. Quantum Electron. 39, 837-847 (2007). [CrossRef]
  23. J. T. Mok, M. Ibsen, C. M. de Sterke, and B. J. Eggleton, “Dispersionless slow light with 5-pulse-width delay in fibre Bragg grating,” Electron. Lett. 43, 1418-1419 (2007). [CrossRef]
  24. M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3, 211-219 (2004). [CrossRef]
  25. R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441, 199-202 (2006). [CrossRef]
  26. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).
  27. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).
  28. P. St. J. Russell, T. A. Birks, and F. D. Lloyd Lucas, “Photonic Bloch waves and photonic band gaps,” in Confined Electrons and Photons, E.Burstein and C.Weisbuch, eds. (Plenum, 1995), pp. 585-633.
  29. M. Tokushima, H. Yamada, and Y. Arakawa, “1.5-μm-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab,” Appl. Phys. Lett. 84, 4298-4300 (2004). [CrossRef]
  30. S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, “Guiding 1.5 μm light in photonic crystals based on dielectric rods,” Appl. Phys. Lett. 85, 6110-6112 (2004). [CrossRef]
  31. X. Y. Ao, L. Liu, L. Wosinski, and S. L. He, “Polarization beam splitter based on a two-dimensional photonic crystal of pillar type,” Appl. Phys. Lett. 89, 171115 (2006). [CrossRef]
  32. J. She, E. Forsberg, X. Y. Ao, and S. L. He, “High-efficiency polarization beam splitters based on a two-dimensional polymer photonic crystal,” J. Opt. A, Pure Appl. Opt. 8, 345-349 (2006). [CrossRef]
  33. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis,” Opt. Express 8, 173-190 (2001).
  34. S. M. Jensen, “The nonlinear coherent coupler,” IEEE Trans. Microwave Theory Tech. MTT-30, 1568-1571 (1982). [CrossRef]
  35. A. A. Maier, “Optical transistors and bistable elements on the basis of non-linear transmission of light by the systems with unidirectional coupled waves,” Kvantovaya Elektron. (Moscow) 9, 2296-2302 (1982) (in Russian) A. A. Maier,[Quantum Electron. 12, 1490-1494 (1982)].
  36. S. R. Friberg, Y. Silberberg, M. K. Oliver, M. J. Andrejco, M. A. Saifi, and P. W. Smith, “Ultrafast all-optical switching in a dual-core fiber nonlinear coupler,” Appl. Phys. Lett. 51, 1135-1137 (1987). [CrossRef]
  37. D. Goldring, U. Levy, and D. Mendlovic, “Highly dispersive micro-ring resonator based on one dimensional photonic crystal waveguide design and analysis,” Opt. Express 15, 3156-3168 (2007). [CrossRef]
  38. D. Goldring, U. Levy, I. E. Dotan, A. Tsukernik, M. Oksman, I. Rubin, Y. David, and D. Mendlovic, “Experimental measurement of quality factor enhancement using slow light modes in one dimensional photonic crystal,” Opt. Express 16, 5585-5595 (2008). [CrossRef]
  39. N. K. Efremidis and D. N. Christodoulides, “Discrete solitons in nonlinear zigzag optical waveguide arrays with tailored diffraction properties,” Phys. Rev. E 65, 056607 (2002). [CrossRef]

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