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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 19 — Sep. 10, 2012
  • pp: 21558–21575

Robust optimization of adiabatic tapers for coupling to slow-light photonic-crystal waveguides

Ardavan Oskooi, Almir Mutapcic, Susumu Noda, J. D. Joannopoulos, Stephen P. Boyd, and Steven G. Johnson  »View Author Affiliations


Optics Express, Vol. 20, Issue 19, pp. 21558-21575 (2012)
http://dx.doi.org/10.1364/OE.20.021558


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Abstract

We investigate the design of taper structures for coupling to slow-light modes of various photonic-crystal waveguides while taking into account parameter uncertainties inherent in practical fabrication. Our short-length (11 periods) robust tapers designed for λ = 1.55μm and a slow-light group velocity of c/34 have a total loss of < 20dB even in the presence of nanometer-scale surface roughness, which outperform the corresponding non-robust designs by an order of magnitude. We discover a posteriori that the robust designs have smooth profiles that can be parameterized by a few-term (intrinsically smooth) sine series which helps the optimization to further boost the performance slightly. We ground these numerical results in an analytical foundation by deriving the scaling relationships between taper length, taper smoothness, and group velocity with the help of an exact equivalence with Fourier analysis.

© 2012 OSA

OCIS Codes
(130.0250) Integrated optics : Optoelectronics
(250.5300) Optoelectronics : Photonic integrated circuits
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(130.5296) Integrated optics : Photonic crystal waveguides

ToC Category:
Photonic Crystals

History
Original Manuscript: June 29, 2012
Revised Manuscript: August 24, 2012
Manuscript Accepted: August 25, 2012
Published: September 5, 2012

Citation
Ardavan Oskooi, Almir Mutapcic, Susumu Noda, J. D. Joannopoulos, Stephen P. Boyd, and Steven G. Johnson, "Robust optimization of adiabatic tapers for coupling to slow-light photonic-crystal waveguides," Opt. Express 20, 21558-21575 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-19-21558


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References

  1. S. Cox and D. Dobson, “Maximizing band gaps in two-dimensional photonic crystals,” SIAM J. Appl. Math 59, 2108–2120 (1999). [CrossRef]
  2. S. Cox and D. Dobson, “Band structure optimization of two-dimensional photonic crystals in H-polarization,” J. Comp. Physics 158, 214–224 (2000). [CrossRef]
  3. L. Frandsen, A. Harpoth, P. Borel, M. Kristensen, and J. Jensen, “Broadband photonic crystal waveguide 60° bend obtained utilizing topology optimization,” Opt. Express 12, 5916–5921 (2004). [CrossRef] [PubMed]
  4. P. Borel, A. Harpoth, L. Frandsen, M. Kristensen, P. Shi, J. Jensen, and O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996–2001 (2004). [CrossRef] [PubMed]
  5. D. Dobson and F. Santosa, “Optimal localization of eigenfunctions in an inhomogeneous medium,” SIAM J. Appl. Math 64, 762–774 (2004). [CrossRef]
  6. W. Frei, D. Tortorelli, and H. Johnson, “Topology optimization of a photonic crystal waveguide termination to maximize directional emission,” Appl. Phys. Letters 86(111114) (2005). [CrossRef]
  7. A. Håkansson, J. Sánchez-Dehesa, and L. Sanchis, “Inverse design of photonic crystal devices,” IEEE J. Selected Areas in Communications 23, 1365–1371 (2005). [CrossRef]
  8. C. Kao, S. Osher, and E. Yablonovitch, “Maximizing band gaps in two-dimensional photonic crystals,” Appl. Phys. B 81, 235–244 (2005). [CrossRef]
  9. N. Ikeda, Y. Sugimoto, Y. Watanabe, N. Ozaki, A. Mizutani, Y. Takata, J. Jensen, O. Sigmund, P. Borel, M. Kristensen, and K. Asakawa, “Topology optimised photonic crystal waveguide intersections with high-transmittance and low crosstalk,” Elec. Letters 42, 1031–1033 (2006). [CrossRef]
  10. W. Frei, D. Tortorelli, and H. Johnson, “Geometry projection method for optimizing photonic nanostructures,” Opt. Letters 32, 77–79 (2007). [CrossRef]
  11. L. He, C.-Y. Kao, and S. Osher, “Incorporating topological derivatives into shape derivatives based level set methods,” J. Comp. Physics 225, 891–909 (2007). [CrossRef]
  12. J. Riishede and O. Sigmund, “Inverse design of dispersion compensating optical fiber using topology optimization,” J. Opt. Soc. Am. B 25, 88–97 (2008). [CrossRef]
  13. O. Sigmund and K. Hougaard, “Geometric properties of optimal photonic crystals,” Phys. Rev. Letters 100(153904) (2008). [CrossRef]
  14. D. Dobson and L. Simeonova, “Optimization of periodic composite structures for sub-wavelength focusing,” Appl. Math. Optim. 60, 133–150 (2009). [CrossRef]
  15. R. Matze, J. Jensen, and O. Sigmund, “Systematic design of slow-light photonic waveguides,” J. Opt. Soc. Am. B 28, 2374–2382 (2011). [CrossRef]
  16. Y. Elesin, B. Lazarov, J. Jensen, and O. Sigmund, “Design of robust and efficient photonic switches using topology optimization,” Photon. and Nanostruc. 10, 153–165 (2012). [CrossRef]
  17. T. Happ, M. Kamp, and A. Forchel, “Photonic crystal tapers for ultracompact mode conversion,” Opt. Letters 26, 1102–1104 (2001). [CrossRef]
  18. A. Mekis and J. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightwave Tech. 19(6), 861–865 (2001). [CrossRef]
  19. M. Palamaru and P. Lalanne, “Photonic crystal waveguides: out of plane losses and adiabatic modal conversion,” Appl. Phys. Letters 78, 1466–1468 (2001). [CrossRef]
  20. P. Sanchis, J. Marti, J. Blasco, A. Martinez, and A. Garcia, “Mode matching technique for highly efficient coupling between dielectric waveguides and planar photonic crystal circuits,” Opt. Express 10, 1391–1397 (2002). [PubMed]
  21. A. Talneau, P. Lalanne, M. Agio, and C. Soukoulis, “Low-reflection photonic-crystal taper for efficient coupling between guide sections of arbitrary widths,” Opt. Letters 27, 1522–1524 (2002). [CrossRef]
  22. P. Bienstman, S. Assefa, S. Johnson, J. Joannopoulos, G. Petrich, and L. Kolodziejski, “Taper structures for coupling into photonic crystal slab waveguides,” J. Opt. Soc. Am. B 20, 1817–1821 (2003). [CrossRef]
  23. N. Moll and G.-L. Bona, “Comparison of three-dimensional photonic crystal slab waveguides with two-dimensional photonic crystal waveguides: efficient butt coupling into these photonic crystal waveguides,” J. Appl. Physics 93, 4986–4991 (2003). [CrossRef]
  24. P. Sanchis, J. Garcia, A. Martinez, F. Cuesta, A. Griol, and J. Marti, “Analysis of adiabatic coupling between photonic crystal single-line-defect and coupled-resonator optical waveguides,” Opt. Letters 28, 1903–1905 (2003). [CrossRef]
  25. E. Miyai and S. Noda, “Structural dependence of coupling between a two-dimensional photonic crystal waveguide and a wire waveguide,” J. Opt. Soc. Am. B 21, 67–72 (2004). [CrossRef]
  26. P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, “Analysis of butt coupling in photonic crystals,” IEEE J. Quant. Elec. 40, 541–550 (2004). [CrossRef]
  27. E. Khoo, A. Liu, and J. Wu, “Nonuniform photonic crystal taper for high-efficiency mode coupling,” Opt. Express 13, 7748–7759 (2005). [CrossRef] [PubMed]
  28. P. Sanchis, J. Marti, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Experimental results on adiabatic coupling into SOI photonic crystal coupled-cavity waveguides,” IEEE Photon. Tech. Letters 17, 1199–1201 (2005). [CrossRef]
  29. K. Dossou, L. Botten, C. de Sterke, R. McPhedran, A. Asatryan, S. Chen, and J. Brnovic, “Efficient couplers for photonic crystal waveguides,” Opt. Commun. 265, 207–219 (2006). [CrossRef]
  30. Y. Vlasov and S. McNab, “Coupling into the slow light mode in slab-type photonic crystal waveguides,” Opt. Letters 31, 50–52 (2006). [CrossRef]
  31. J. Hugonin, P. Lalanne, T. White, and T. Krauss, “Coupling into slow-mode photonic crystal waveguides,” Opt. Letters 32, 2638–2640 (2007). [CrossRef]
  32. P. Pottier, M. Gnan, and R. D. L. Rue, “Efficient coupling into slow-light photonic crystal channel guides using photonic crystal tapers,” Opt. Express 15, 6569–6575 (2007). [CrossRef] [PubMed]
  33. C. de Sterke, J. Walker, K. Dossou, and L. Botten, “Efficient slow light coupling into photonic crystals,” Opt. Express 15, 10984–10990 (2007). [CrossRef]
  34. P. Velha, J. Hugonin, and P. Lalanne, “Compact and efficient injection of light into band-edge slow-modes,” Opt. Express 15, 6102–6112 (2007). [CrossRef] [PubMed]
  35. J. Lu, S. Boyd, and J. Vuckovic, “Inverse design of a three-dimensional nanophotonic resonator,” Opt. Express 19, 10563–10570 (2011). [CrossRef]
  36. J. Lu and J. Vuckovic, “Objective-first design of high-efficiency, small-footprint couplers between arbitrary nanophotonic waveguide modes,” Opt. Express 20, 7221–7236 (2012). [CrossRef] [PubMed]
  37. M. Povinelli, S. Johnson, and J. Joannopoulos, “Slow-light, band-edge waveguides for tunable time delays,” Opt. Express 13(8), 7145–7159 (2005). [CrossRef] [PubMed]
  38. J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding The Flow Of Light, 2nd ed. (Princeton Univ. Press, 2008).
  39. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465–473 (2008). [CrossRef]
  40. S. Johnson, P. Bienstman, M. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66(066608) (2002). [CrossRef]
  41. G. Taguchi, R. Jugulum, and S. Taguchi, Computer-Based Robust Engineering: Essentials For DFSS (ASQ Quality Press, 2004).
  42. A. Bental, L. E. Ghaoui, and A. Nemirovski, Robust Optimization (Princeton University Press, 2009).
  43. A. Mutapcic, S. Boyd, A. Farjadpour, S. Johnson, and Y. Avniel, “Robust design of slow-light tapers in periodic waveguides,” Engineering Optimization 41, 365–384 (2009). [CrossRef]
  44. D. Bertsimas, O. Nohedani, and K. Teo, “Robust optimization for unconstrained simulation-based problems,” Oper. Research 58, 161–178 (2010). [CrossRef]
  45. F. Wang, J. Jensen, and O. Sigmund, “Robust topology optimization of photonic crystal waveguides with tailored dispersion properties,” J. Opt. Soc. Am. B 28, 387–397 (2011). [CrossRef]
  46. P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. and Quant. Electronics 33, 327–341 (2001). [CrossRef]
  47. T. White, L. Botten, C. de Sterke, K. Dossou, and R. McPhedran, “Efficient slow-light coupling in a photonic crystal waveguide without transition region,” Opt. Letters 33, 2644–2646 (2008). [CrossRef]
  48. A. Kurs, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Abrupt coupling between strongly dissimilar waveguides with 100% transmission,” Opt. Express 19, 13714–13721 (2011). [CrossRef]
  49. M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide,” Appl. Phys. Letters 85, 1466–1468 (2004). [CrossRef]
  50. J. Ma and M. Povinelli, “Effect of periodicity on optical forces between a one-dimensional periodic photonic crystal waveguide and an underlying substrate,” Appl. Phys. Letters 97(151102) (2010). [CrossRef]
  51. A. Oskooi, P. Favuzzi, Y. Kawakami, and S. Noda, “Tailoring repulsive optical forces in nanophotonic waveguides,” Opt. Letters 36, 4638–4640 (2011). [CrossRef]
  52. Y. Xu, R. Lee, and A. Yariv, “Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide,” JOSA-B 17(387–400) (2000). [CrossRef]
  53. M. Soljačić, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of non-linear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2059 (2002). [CrossRef]
  54. S. Anderson, A. Shroff, and P. Fauchet, “Slow light with photonic crystals for on-chip optical interconnects,” Adv. Opt. Technology 2008(293531) (2008).
  55. J. Hastings, M. Lim, J. Goodberlet, and H. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase- locked electron-beam lithography,” J. Vac. Sci. Tech. B 20, 2753–2757 (2002). [CrossRef]
  56. T. Segawa, S. Matsuo, Y. Ohiso, T. Ishii, and H. Suzuki, “Apodised sampled grating using InGaAsP/InP deep-ridge waveguide with vertical-groove surface grating,” Elec. Letters 40, 804–805 (2004). [CrossRef]
  57. M. Strain and M. Sorel, “Design and fabrication of integrated chirped bragg gratings for on-chip dispersion control,” IEEE J. Quant. Elec. 46, 774–782 (2010). [CrossRef]
  58. G. Strang, Computational Science and Engineering (Welleseley-Cambridge Press, Wellesley MA, 2007).
  59. S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, Cambridge, UK, 2004).
  60. M. Ghebrebrhan, P. Bermel, Y. Avniel, J. D. Joannopoulos, and S. G. Johnson, “Global optimization of silicon photovoltaic cell front coatings,” Opt. Express 17, 7505–7518 (2009). [CrossRef] [PubMed]
  61. P. Bermel, M. Ghebrebrhan, W. Chan, Y. X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljačić, J. D. Joannopoulos, S. G. Johnson, and I. Celanovic, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Opt. Express 18, A314–A334 (2010). [CrossRef] [PubMed]
  62. S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Physics 78, 1415–1418 (1995). [CrossRef]
  63. J. Foresi, P. Villeneuve, J. Ferrera, E. Thoen, G. Steinmeyer, S. Fan, J. Joannopoulos, L. Kimerling, H. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997). [CrossRef]
  64. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001). [CrossRef] [PubMed]
  65. J. E. Avron and A. Elgart, “Adiabatic theorem without a gap condition,” Commun. Math. Physics 203, 445–463 (1999). [CrossRef]
  66. K. O. Mead and L. M. Delves, “On the convergence rate of generalized Fourier expansions,” IMA J. Appl. Math. 12(3), 247–259 (1973). [CrossRef]
  67. J. P. Boyd, Chebyshev And Fourier Spectral Methods, 2nd ed. (Springer, 1989). [CrossRef]
  68. A. Oskooi, L. Zhang, Y. Avniel, and S. Johnson, “The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers,” Opt. Express 16(15), 11376–11392 (2008). [CrossRef]
  69. S. G. Johnson, M. L. Povinelli, P. Bienstman, M. Skorobogatiy, M. Soljačić, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Coupling, scattering and perturbation theory: semi-analytical analyses of photonic-crystal waveguides,” in Proc. 2003 5th Intl. Conf. on Transparent Optical Networks and 2nd European Symp. on Photonic Crystals, vol. 1, pp. 103–109 (2003). [CrossRef]
  70. P. Bienstman, “CAMFR: CAvity Modeling FRamework,” Software at http://camfr.sourceforge.net .
  71. M. L. Povinelli, S. G. Johnson, E. Lidorikis, J. D. Joannopoulos, and M. Soljačić, “Effect of a photonic band gap on scattering from waveguide disorder,” Appl. Phys. Letters 84, 3639–3641 (2004). [CrossRef]
  72. 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 1.5μm light in photonic crystals based on dielectric rods,” Appl. Phys. Letters 85, 6110–6112 (2004). [CrossRef]
  73. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech, Norwood, MA, 2005).
  74. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Communications 181, 687–702 (2010). [CrossRef]
  75. J. Nocedal and S. Wright, Numerical Optimization (Springer, New York, 1999). [CrossRef]
  76. A. Conn, N. Gould, and P. Toint, Trust Region Methods (SIAM, Philadelphia, PA, 2000). [CrossRef]

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