• Photonics Research
  • Vol. 4, Issue 2, 0093 (2016)
Yufei Xing1, Domenico Spina2, Ang Li1, Tom Dhaene2, and Wim Bogaerts1、3、*
Author Affiliations
  • 1Photonics Research Group, Department of Information Technology, Center for Nano and Biophotonics, Ghent University imec, Ghent B-9000, Belgium
  • 2Department of Information Technology, Internet Based Communication Networks and Services (IBCN), Ghent University iMinds, Gaston Crommenlaan 8 Bus 201, B-9050 Gent, Belgium
  • 3Luceda Photonics, 9200 Dendermonde, Belgium
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    DOI: 10.1364/prj.4.000093 Cite this Article Set citation alerts
    Yufei Xing, Domenico Spina, Ang Li, Tom Dhaene, Wim Bogaerts. Stochastic collocation for device-level variability analysis in integrated photonics[J]. Photonics Research, 2016, 4(2): 0093 Copy Citation Text show less
    References

    [1] M. Streshinsky, R. Ding, Y. Liu, A. Novack, C. Galland, A.-J. Lim, G. Q. Lo, T. Baehr-Jones, M. Hochberg. The road to affordable, large-scale silicon photonics. Opt. Photon. News, 24, 32-39(2013).

    [2] W. Bogaerts, M. Fiers, P. Dumon. Design challenges in silicon photonics. IEEE J. Sel. Top. Quantum Electron., 20, 1-8(2014).

    [3] L. Chrostowski, X. Wang, J. Flueckiger, Y. Wu, Y. Wang, S. T. Fard. Impact of fabrication non-uniformity on chip-scale silicon photonic integrated circuits. Optical Fiber Communication Conference, Th2A.37(2014).

    [4] S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, R. Baets. Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology. IEEE J. Sel. Top. Quantum Electron., 16, 316-324(2010).

    [5] G. S. Fishman. Monte Carlo: Concepts, Algorithms, and Applications(1996).

    [6] D. Spina, F. Ferranti, G. Antonini, T. Dhaene, L. Knockaert. Efficient variability analysis of electromagnetic systems via polynomial chaos and model order reduction. IEEE Trans. Compon. Packag. Manuf. Technol., 4, 1038-1051(2014).

    [7] P. R. Johnston. Defibrillation thresholds: a generalised polynomial chaos study. Conference in Computing in Cardiology(2014).

    [8] K.-K. K. Kim, R. D. Braatz. Generalized polynomial chaos expansion approaches to approximate stochastic receding horizon control with applications to probabilistic collision checking and avoidance. IEEE International Conference on Control Applications(2012).

    [9] D. Cassano, F. Morichetti, A. Melloni. Statistical analysis of photonic integrated circuits via polynomial-chaos expansion. Advanced Photonics, JT3A.8(2013).

    [10] T. Weng, Z. Zhang, Z. Su, Y. Marzouk, A. Melloni, L. Daniel. Uncertainty quantification of silicon photonic devices with correlated and non-Gaussian random parameters. Opt. Express, 23, 4242-4254(2015).

    [11] M. S. Eldred. Recent advance in non-intrusive polynomial-chaos and stochastic collocation methods for uncertainty analysis and design. Proceedings of 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference(2009).

    [12] N. Agarwal, N. R. Aluru. Weighted Smolyak algorithm for solution of stochastic differential equations on non-uniform probability measures. Int. J. Numer. Meth. Eng., 85, 1365-1389(2011).

    [13] N. Agarwal, N. R. Aluru. Stochastic analysis of electrostatic mems subjected to parameter variations. J. Microelectromech. Syst., 18, 1454-1468(2009).

    [14] D. Xiu. Fast numerical methods for stochastic computations: a review. Commun. Comput. Phys., 5, 242-272(2009).

    [15] W. A. Weiser, S. E. Zarantonello. A note on piecewise linear and multilinear table interpolation in many dimensions. Math. Comput., 50, 189-196(1988).

    [16] B. Ganapathysubramanian, N. Zabaras. Sparse grid collocation schemes for stochastic natural convection problems. J. Comput. Phys., 225, 652-685(2007).

    [17] V. Barthelmann, E. Novak, K. Ritter. High dimensional polynomial interpolation on sparse grid. Adv. Comput. Math., 12, 273-288(2000).

    [18] E. Novak, K. Ritter. High dimensional integration of smooth functions over cubes. Numer. Math., 75, 79-97(1996).

    [19] E. Novak, K. Ritter. Simple cubature formulas with high polynomial exactness. Constr. Approx., 15, 499-522(1999).

    [20] A. Der Kiureghian, P. L. Liu. Structural reliability under incomplete probability information. J. Eng. Mech., 112, 85-104(1986).

    [21] M. Loeve. Probability Theory(1977).

    [22] W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, S. Beckx. Basic structures for photonic integrated circuits in silicon-on-insulator. Opt. Express, 12, 1583-1591(2004).

    [23] L. Chrostowski, M. Hochberg. Silicon Photonics Design: From Devices to Systems(2015).

    Yufei Xing, Domenico Spina, Ang Li, Tom Dhaene, Wim Bogaerts. Stochastic collocation for device-level variability analysis in integrated photonics[J]. Photonics Research, 2016, 4(2): 0093
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