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Volumn 41, Issue 4, 2009, Pages 365-384

Robust design of slow-light tapers in periodic waveguides

Author keywords

Coupling taper; PDE constrained optimization; Periodic waveguide; Photonics; Robust optimization; Shape optimization; Slow light

Indexed keywords

COUPLING POWER; FAST METHODS; HIGH YIELD; OPTIMIZATION METHOD; PARAMETER VARIATION; PDE-CONSTRAINED OPTIMIZATION; PERIODIC WAVEGUIDE; PERIODIC WAVEGUIDES; REFLECTION COEFFICIENTS; ROBUST DESIGNS; ROBUST OPTIMIZATION; ROBUST PERFORMANCE; SLOW-LIGHT; SUCCESSIVE REFINEMENT; UNCERTAIN PARAMETERS;

EID: 66849135843     PISSN: 0305215X     EISSN: 10290273     Source Type: Journal    
DOI: 10.1080/03052150802576797     Document Type: Article
Times cited : (43)

References (85)
  • 2
    • 1942454397 scopus 로고    scopus 로고
    • Efficient input and output fiber coupling to a photonic crystal waveguide
    • Barclay, P., et al., 2004. Efficient input and output fiber coupling to a photonic crystal waveguide. Optics Letters, 29 (7), 697-699.
    • (2004) Optics Letters , vol.29 , Issue.7 , pp. 697-699
    • Barclay, P.1
  • 4
    • 0141712989 scopus 로고    scopus 로고
    • Robust optimization: Methodology and applications
    • Ben-Tal, A. and Nemirovski, A., 2002. Robust optimization: methodology and applications. Mathematical Programming Series B, 92 (3), 453-480.
    • (2002) Mathematical Programming Series B , vol.92 , Issue.3 , pp. 453-480
    • Ben-Tal, A.1    Nemirovski, A.2
  • 5
    • 28044459877 scopus 로고
    • A perfectly matched layer for the absorption of electromagnetic waves
    • Bérenger, J.-P., 1994. A perfectly matched layer for the absorption of electromagnetic waves. Journal of Computational Physics, 114 (1), 185-200.
    • (1994) Journal of Computational Physics , vol.114 , Issue.1 , pp. 185-200
    • Bérenger, J.-P.1
  • 6
    • 33644689113 scopus 로고    scopus 로고
    • Tractable approximations to robust conic optimization problems
    • Bertsimas, D. and Sim, M., 2006. Tractable approximations to robust conic optimization problems. Mathematical Programming, 107 (1-2), 5-36.
    • (2006) Mathematical Programming , vol.107 , Issue.1-2 , pp. 5-36
    • Bertsimas, D.1    Sim, M.2
  • 9
    • 70449575955 scopus 로고    scopus 로고
    • [online]. Department of Information Technology (INTEC), Ghent University, Ghent, Belgium. Available from: camfr.sourceforge.net. [Accessed 1 October 2006]
    • Bienstman, P., 2006. CAMFR: cavity modelling framework software [online]. Department of Information Technology (INTEC), Ghent University, Ghent, Belgium. Available from: camfr.sourceforge.net. [Accessed 1 October 2006].
    • (2006) CAMFR: Cavity Modelling Framework Software
    • Bienstman, P.1
  • 14
    • 12344268988 scopus 로고    scopus 로고
    • Uncertain convex programs: Randomized solutions and confidence levels
    • Calafiore, G. and Campi, M., 2005. Uncertain convex programs: randomized solutions and confidence levels. Mathematical Programming, 102 (1), 25-46.
    • (2005) Mathematical Programming , vol.102 , Issue.1 , pp. 25-46
    • Calafiore, G.1    Campi, M.2
  • 17
    • 0038070188 scopus 로고    scopus 로고
    • Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution
    • Cao, Y., et al., 2003. Adjoint sensitivity analysis for differential-algebraic equations: the adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing, 24 (3), 1076-1089.
    • (2003) SIAM Journal on Scientific Computing , vol.24 , Issue.3 , pp. 1076-1089
    • Cao, Y.1
  • 19
    • 0032340223 scopus 로고    scopus 로고
    • Parameter estimation in the presence of bounded data uncertainties
    • Chandrasekaran, S., et al., 1998. Parameter estimation in the presence of bounded data uncertainties. SIAM Journal on Matrix Analysis and Applications, 19 (1), 235-252.
    • (1998) SIAM Journal on Matrix Analysis and Applications , vol.19 , Issue.1 , pp. 235-252
    • Chandrasekaran, S.1
  • 20
    • 3042680283 scopus 로고    scopus 로고
    • Numerical design for efficiently coupling conventional and photonic-crystal waveguides
    • Chietera, G., et al., 2004. Numerical design for efficiently coupling conventional and photonic-crystal waveguides. Microwave and Optical Technology Letters, 42 (3), 196-199.
    • (2004) Microwave and Optical Technology Letters , vol.42 , Issue.3 , pp. 196-199
    • Chietera, G.1
  • 24
    • 5544258192 scopus 로고    scopus 로고
    • On constraint sampling in the linear programming approach to approximate dynamic programming
    • de Farias, D. and Roy, B.V., 2004. On constraint sampling in the linear programming approach to approximate dynamic programming. Mathematics of Operations Research, 29 (3), 462-478.
    • (2004) Mathematics of Operations Research , vol.29 , Issue.3 , pp. 462-478
    • De Farias, D.1    Roy, B.V.2
  • 26
    • 33747144241 scopus 로고    scopus 로고
    • Efficient couplers for photonic crystal waveguides
    • Dossou, K., et al., 2006. Efficient couplers for photonic crystal waveguides. Optics Communications, 265 (1), 207-219.
    • (2006) Optics Communications , vol.265 , Issue.1 , pp. 207-219
    • Dossou, K.1
  • 27
  • 28
    • 4344618310 scopus 로고    scopus 로고
    • Worst-case value-at-risk and robust portfolio optimization: A conic programming approach
    • El Ghaoui, L., Oks, M., and Oustry, F., 2003. Worst-case value-at-risk and robust portfolio optimization: a conic programming approach. Operations Research, 51 (4), 543-556.
    • (2003) Operations Research , vol.51 , Issue.4 , pp. 543-556
    • El Ghaoui, L.1    Oks, M.2    Oustry, F.3
  • 29
    • 0032252302 scopus 로고    scopus 로고
    • Robust solutions to uncertain semidefinite programs
    • El Ghaoui, L., Oustry, F., and Lebret, H., 1998. Robust solutions to uncertain semidefinite programs. SIAM Journal on Optimization, 9 (1), 33-52.
    • (1998) SIAM Journal on Optimization , vol.9 , Issue.1 , pp. 33-52
    • El Ghaoui, L.1    Oustry, F.2    Lebret, H.3
  • 33
    • 0035420436 scopus 로고    scopus 로고
    • On shape optimization of optical waveguides using inverse problem techniques
    • Felici, T. and Engl, H., 2001. On shape optimization of optical waveguides using inverse problem techniques. Inverse Problems, 17 (4), 1141-1162.
    • (2001) Inverse Problems , vol.17 , Issue.4 , pp. 1141-1162
    • Felici, T.1    Engl, H.2
  • 34
    • 17444372724 scopus 로고    scopus 로고
    • SNOPT: An SQP algorithm for large-scale constrained optimization
    • Gill, P., Murray,W., and Saunders, M., 2005. SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM Review, 47 (1), 99-131.
    • (2005) SIAM Review , vol.47 , Issue.1 , pp. 99-131
    • Murrayw., G.P.1    Saunders, M.2
  • 35
    • 33744798398 scopus 로고    scopus 로고
    • Robust convex quadratically constrained programming
    • Goldfarb, D. and Iyengar, G., 2003. Robust convex quadratically constrained programming. Mathematical Programming, 97 (3), 495-515.
    • (2003) Mathematical Programming , vol.97 , Issue.3 , pp. 495-515
    • Goldfarb, D.1    Iyengar, G.2
  • 36
    • 34250655441 scopus 로고    scopus 로고
    • [online]. Information Systems Laboratory, Department of Electrical Engineering, Stanford University, Stanford, CA.Available from: [Accessed 10 December 2007]
    • Grant, M., Boyd, S., andYe,Y., 2006. CVX: matlab software for disciplined convex programming, version 1.0RC [online]. Information Systems Laboratory, Department of Electrical Engineering, Stanford University, Stanford, CA.Available from: www.stanford.edu/boyd/cvx/. [Accessed 10 December 2007].
    • (2006) CVX: Matlab Software for Disciplined Convex Programming, Version 1.0RC
    • Grant, M.1    Boyd, S.2    Ye, Y.3
  • 38
    • 30344454686 scopus 로고    scopus 로고
    • High-efficiency defect-based photonic-crystal tapers designed by a genetic algorithm
    • Hakansson, A., et al., 2005. High-efficiency defect-based photonic-crystal tapers designed by a genetic algorithm. Journal of Lightwave Technology, 23 (11), 3881-3888.
    • (2005) Journal of Lightwave Technology , vol.23 , Issue.11 , pp. 3881-3888
    • Hakansson, A.1
  • 39
    • 0001165272 scopus 로고    scopus 로고
    • Photonic crystal tapers for ultracompact mode conversion
    • Happ, T., Kamp, M., and Forchel, A., 2001. Photonic crystal tapers for ultracompact mode conversion. Optics Letters, 26 (14), 1102-1104.
    • (2001) Optics Letters , vol.26 , Issue.14 , pp. 1102-1104
    • Happ, T.1    Kamp, M.2    Forchel, A.3
  • 40
    • 0027657329 scopus 로고
    • Semi-infinite programming: Theory, methods, and applications
    • Hettich, R. and Kortanek, K., 1993. Semi-infinite programming: theory, methods, and applications. SIAM Review, 35 (3), 380-429.
    • (1993) SIAM Review , vol.35 , Issue.3 , pp. 380-429
    • Hettich, R.1    Kortanek, K.2
  • 41
    • 0345445979 scopus 로고    scopus 로고
    • Parallel microgenetic algorithm design for photonic crystal and waveguide structures
    • Jiang, J., et al., 2003. Parallel microgenetic algorithm design for photonic crystal and waveguide structures. Optics Letters, 28 (23), 2381-2383.
    • (2003) Optics Letters , vol.28 , Issue.23 , pp. 2381-2383
    • Jiang, J.1
  • 43
    • 41349100489 scopus 로고    scopus 로고
    • Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals
    • Johnson, S.G., et al., 2002. Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 66 (2), 066608.1-066608.15.
    • (2002) Physical Review E: Statistical, Nonlinear, and Soft Matter Physics , vol.66 , Issue.2 , pp. 0666081-06660815
    • Johnson, S.G.1
  • 45
    • 0000278298 scopus 로고    scopus 로고
    • Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis
    • Johnson, S.G. and Joannopoulos, J.D. (2001b). Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis. Optics Express, 8 (3), 173-190.
    • (2001) Optics Express , vol.8 , Issue.3 , pp. 173-190
    • Johnson, S.G.1    Joannopoulos, J.D.2
  • 46
    • 34249771252 scopus 로고
    • Corrected sequential linear programming for sparse minimax optimization
    • Jonasson, K. and Madsen, K., 1994. Corrected sequential linear programming for sparse minimax optimization. BIT Numerical Mathematics, 34 (3), 372-387.
    • (1994) BIT Numerical Mathematics , vol.34 , Issue.3 , pp. 372-387
    • Jonasson, K.1    Madsen, K.2
  • 47
    • 30144441183 scopus 로고    scopus 로고
    • Nonuniform photonic crystal taper for high-efficiency mode coupling
    • Khoo, E., Liu, A., andWu, J., 2005. Nonuniform photonic crystal taper for high-efficiency mode coupling. Optics Express, 13 (20), 7748-7759.
    • (2005) Optics Express , vol.13 , Issue.20 , pp. 7748-7759
    • Khoo, E.1    Liu, A.2    Wu, J.3
  • 48
    • 0242667172 scopus 로고    scopus 로고
    • Optimization by direct search: Newperspectives on some classical and modern methods
    • Kolda, T., Lewis, R., and Torczon,V., 2003. Optimization by direct search: Newperspectives on some classical and modern methods. SIAM Review, 45 (3), 385-482.
    • (2003) SIAM Review , vol.45 , Issue.3 , pp. 385-482
    • Kolda, T.1    Lewis, R.2    Torczon, V.3
  • 49
    • 0037106749 scopus 로고    scopus 로고
    • Grating-assisted coupling of optical fibers and photonic crystal waveguides
    • Kuang, W., et al., 2002. Grating-assisted coupling of optical fibers and photonic crystal waveguides. Optics Letters, 27 (18), 1604-1606.
    • (2002) Optics Letters , vol.27 , Issue.18 , pp. 1604-1606
    • Kuang, W.1
  • 50
    • 0042967740 scopus 로고    scopus 로고
    • A robust minimax approach to classiflcation
    • Lanckriet, G., et al., 2003. A robust minimax approach to classiflcation. Journal of Machine Learning Research, 3 (3), 555-582.
    • (2003) Journal of Machine Learning Research , vol.3 , Issue.3 , pp. 555-582
    • Lanckriet, G.1
  • 52
    • 24744432463 scopus 로고    scopus 로고
    • Efficient nonadiabatic planar waveguide tapers
    • Luyssaert, B., et al., 2005. Efficient nonadiabatic planar waveguide tapers. Journal of Lightwave Technology, 23 (8), 2462-2468.
    • (2005) Journal of Lightwave Technology , vol.23 , Issue.8 , pp. 2462-2468
    • Luyssaert, B.1
  • 55
    • 0035365299 scopus 로고    scopus 로고
    • Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides
    • Mekis, A. and Joannopoulos, J., 2001. Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides. Journal of Lightwave Technology, 19 (6), 861-865.
    • (2001) Journal of Lightwave Technology , vol.19 , Issue.6 , pp. 861-865
    • Mekis, A.1    Joannopoulos, J.2
  • 57
    • 0000238336 scopus 로고
    • A simplex method for function minimization
    • Nelder, J.A. and Mead, R., 1965. A simplex method for function minimization. The Computer Journal, 7 (4), 308-313.
    • (1965) The Computer Journal , vol.7 , Issue.4 , pp. 308-313
    • Nelder, J.A.1    Mead, R.2
  • 59
    • 0035848247 scopus 로고    scopus 로고
    • Photonic crystal waveguides: Out-of-plane losses and adiabatic modal conversion
    • DOI 10.1063/1.1354666
    • Palamaru, M. and Lalanne, P., 2001. Photonic crystal waveguides: out-of-plane losses and adiabatic modal conversion. Applied Physics Letters, 78 (11), 1466-1468. (Pubitemid 33616921)
    • (2001) Applied Physics Letters , vol.78 , Issue.11 , pp. 1466-1468
    • Palamaru, M.1    Lalanne, Ph.2
  • 61
    • 0042631392 scopus 로고    scopus 로고
    • Photonic crystal continuous taper for low-loss direct coupling into 2D photonic crystal channel waveguides and further device functionality
    • Pottier, P., Ntakis, I., and La, R.D., 2003. Photonic crystal continuous taper for low-loss direct coupling into 2D photonic crystal channel waveguides and further device functionality. Optics Communications, 223 (4), 339-347.
    • (2003) Optics Communications , vol.223 , Issue.4 , pp. 339-347
    • Pottier, P.1    Ntakis, I.2    La, R.D.3
  • 62
    • 24944444778 scopus 로고    scopus 로고
    • Slow-light, band-edge waveguides for tunable time delays
    • Povinelli, M.L., Johnson, S.G., and Joannopoulos, J.D., 2005. Slow-light, band-edge waveguides for tunable time delays. Optics Express, 13, 7145-7159.
    • (2005) Optics Express , vol.13 , pp. 7145-7159
    • Povinelli, M.L.1    Johnson, S.G.2    Joannopoulos, J.D.3
  • 63
    • 0037106696 scopus 로고    scopus 로고
    • High-efficiency coupling structure for a single-line-defect photonic-crystal waveguide
    • Prather, D., et al., 2002. High-efficiency coupling structure for a single-line-defect photonic-crystal waveguide. Optics Letters, 27 (18), 1601-1603.
    • (2002) Optics Letters , vol.27 , Issue.18 , pp. 1601-1603
    • Prather, D.1
  • 64
    • 0003410675 scopus 로고
    • London, UK: Kluwer Academic Publishers
    • Prekopa, A., 1995. Stochastic programming. London, UK: Kluwer Academic Publishers.
    • (1995) Stochastic Programming
    • Prekopa, A.1
  • 65
    • 0000514655 scopus 로고
    • Scenarios and policy aggregation in optimization under uncertainty
    • Rockafellar, R.T. andWets, R.J.-B., 1991. Scenarios and policy aggregation in optimization under uncertainty. Mathematics of Operations Research, 16 (1), 119-147.
    • (1991) Mathematics of Operations Research , vol.16 , Issue.1 , pp. 119-147
    • Rockafellar, R.T.1    Wets, R.J.-B.2
  • 68
    • 2442673143 scopus 로고    scopus 로고
    • Analysis of butt coupling in photonic crystals
    • Sanchis, P., et al., 2004. Analysis of butt coupling in photonic crystals. IEEE Journal of Quantum Electronics, 40 (5), 541-550.
    • (2004) IEEE Journal of Quantum Electronics , vol.40 , Issue.5 , pp. 541-550
    • Sanchis, P.1
  • 71
    • 0010680207 scopus 로고
    • Convex programming with set-inclusive constraints and applications to inexact linear programming
    • Soyster, A., 1973. Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations Research, 21, 1154-1157.
    • (1973) Operations Research , vol.21 , pp. 1154-1157
    • Soyster, A.1
  • 72
    • 0032164713 scopus 로고    scopus 로고
    • A very short planar silica spot-size converter using a nonperiodic segmented waveguide
    • Spühler, M.M., et al., 1998. A very short planar silica spot-size converter using a nonperiodic segmented waveguide. Journal of Lightwave Technology, 16 (9), 1680-1685.
    • (1998) Journal of Lightwave Technology , vol.16 , Issue.9 , pp. 1680-1685
    • Spühler, M.M.1
  • 73
    • 0033296299 scopus 로고    scopus 로고
    • Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
    • Software available from: sedumi.mcmaster.ca
    • Sturm, J., 1999. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, 11, 625-653. Software available from: sedumi.mcmaster.ca.
    • (1999) Optimization Methods and Software , vol.11 , pp. 625-653
    • Sturm, J.1
  • 75
    • 0036725561 scopus 로고    scopus 로고
    • Low-reflection photonic-crystal taper for efficient coupling between guide sections of arbitrary widths
    • Talneau, A., et al., 2002. Low-reflection photonic-crystal taper for efficient coupling between guide sections of arbitrary widths. Optics Letters, 27 (17), 1522-1524.
    • (2002) Optics Letters , vol.27 , Issue.17 , pp. 1522-1524
    • Talneau, A.1
  • 76
    • 24344442679 scopus 로고
    • An overview of Taguchi method and newly developed statistical methods for robust design
    • Tsui, K.-L., 1992. An overview of Taguchi method and newly developed statistical methods for robust design. IIE Transactions, 24 (5), 44-57.
    • (1992) IIE Transactions , vol.24 , Issue.5 , pp. 44-57
    • Tsui, K.-L.1
  • 77
    • 0037304809 scopus 로고    scopus 로고
    • Robust adaptive beamforming using worst-case performance optimization: A solution to the signal mismatch problem
    • Vorobyov, S., Gershman, A., and Luo, Z.-Q., 2003. Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem. IEEE Transactions on Signal Processing, 51 (2), 313-324.
    • (2003) IEEE Transactions on Signal Processing , vol.51 , Issue.2 , pp. 313-324
    • Vorobyov, S.1    Gershman, A.2    Luo, Z.-Q.3
  • 78
    • 0031145395 scopus 로고    scopus 로고
    • Integrated optical elliptic couplers: Modeling, design, and applications
    • Wei, C., et al., 1997. Integrated optical elliptic couplers: modeling, design, and applications. Journal of Lightwave Technology, 15 (5), 906-912.
    • (1997) Journal of Lightwave Technology , vol.15 , Issue.5 , pp. 906-912
    • Wei, C.1
  • 80
    • 0001242027 scopus 로고    scopus 로고
    • Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry
    • Xu,Y., Lee, R.K., andYariv, A. (2000a). Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry. Optics Letters, 25 (10), 755-757.
    • (2000) Optics Letters , vol.25 , Issue.10 , pp. 755-757
    • Xu, Y.1    Lee, R.K.2    Yariv, A.3
  • 81
    • 0034389924 scopus 로고    scopus 로고
    • Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide
    • Xu, Y., Lee, R.K., and Yariv, A., (2000b). Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide. Journal of the Optical Society of America - Part B, Optical Physics, 17 (3), 387-400.
    • (2000) Journal of the Optical Society of America - Part B, Optical Physics , vol.17 , Issue.3 , pp. 387-400
    • Xu, Y.1    Lee, R.K.2    Yariv, A.3
  • 84
    • 33646374429 scopus 로고    scopus 로고
    • Horn waveguide couplers for interfacing between two-dimensional photonic crystal and single mode planar dielectric waveguides
    • Zhang, B., 2006. Horn waveguide couplers for interfacing between two-dimensional photonic crystal and single mode planar dielectric waveguides. Acta Physica Sinica, 55 (4), 1857-1861.
    • (2006) Acta Physica Sinica , vol.55 , Issue.4 , pp. 1857-1861
    • Zhang, B.1


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