Abstract

We propose a novel and simple approach for design sensitivity analysis using the beam propagation method (BPM). It exploits the adjoint variable technique to extract the response sensitivities with respect to all the design parameters, regardless of their number. The associated computational cost is less than that of an extra BPM simulation. The accuracy of the results are comparable to those obtained using the expensive central finite-difference approximations applied at the response level. Our approach is successfully illustrated through a number of examples.

© 2007 IEEE

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  1. N. K. Nikolova, R. Safian, E. A. Soliman, M. H. Bakr, J. W. Bandler, "Accelerated gradient based optimization using adjoint sensitivities," IEEE Trans. Antennas Propag. 52, 2147-2157 (2004).
  2. G. Veronis, R. W. Dutton, S. Fan, "Method for sensitivity analysis of photonic crystal devices," Opt. Lett. 29, 2288-2290 (2004).
  3. M. A. El Sabbagh, M. H. Bakr, J. W. Bandler, "Adjoint higher order sensitivities for fast full-wave optimization of microwave filters ," IEEE Trans. Microw. Theory Tech. 54, 3339-3351 (2006).
  4. M. H. Bakr, N. K. Nikolova, "An adjoint variable method for frequency domain TLM problems with conducting boundaries ," IEEE Microw. Wireless Compon. Lett. 13, 408-410 (2003).
  5. M. H. Bakr, N. K. Nikolova, "An adjoint variable method for time domain TLM with wideband Johns matrix boundaries ," IEEE Trans. Microw. Theory Tech. 52, 678-685 (2004).
  6. N. K. Nikolova, H. W. Tam, M. H. Bakr, "Sensitivity analysis with the FDTD method on structured grids," IEEE Trans. Microw. Theory Tech. 52, 1207-1216 (2004).
  7. M. A. Swillam, M. H. Bakr, N. K. Nikolova, X. Li, "Adjoint sensitivity analysis of dielectric discontinuities using FDTD," Electromagn 27, 123-140 (2007).
  8. H. Akel, J. P. Webb, "Design sensitivities for scattering-matrix calculation with tetrahedral edge elements ," IEEE Trans. Magn. 36, 1043-1046 (2000).
  9. M. A. Swillam, M. H. Bakr, X. Li, "Accurate sensitivity analysis of photonic devices exploiting the finite-difference time-domain central adjoint variable method," Appl. Opt. 46, 1492-1499 (2007).
  10. D. Yevick, B. Hermansson, "New formulation of the matrix beam propagation method: Application to rib waveguide ," IEEE J. Quantum Electron. 25, 221-229 (1989).
  11. W.-P. Huang, C. L. Xu, S. K. Chaudhuri, "A finite-difference vector beam propagation method for three-dimensional structures ," IEEE Photon. Technol. Lett. 4, 148-151 (1992).
  12. E. Kriezis, A. G. Papagiannakis, "A three-dimensional full vectorial beam propagation method for $z$-dependent structures," IEEE J. Quantum Electron. 33, 883-890 (1997).
  13. P. L. Ho, Y. Y. Lu, "A bidirectional beam propagation method for periodic waveguides," IEEE Photon. Technol. Lett. 14, 325-327 (2002).
  14. B. Saadany, D. A. Khalil, "Modeling of MOEMS components using HDL-A," IEEE J. Sel. Topics Quantum Electron. 8, 132-138 (2002).
  15. K. Zinoviev, C. Dominguez, J. A. Plaza, V. J. C. Busto, L. M. Lechuga, "A novel optical waveguide microcantilever sensor for the detection of nanomechanical forces ," J. Lightw. Technol. 24, 2132-2138 (2006).
  16. L. D. S. Alcantara, F. L. Teixeira, A. C. Cesar, B.-H. V. Borges, "A new full-vectorial FD-BPM scheme: Application to the analysis of magnetooptic and nonlinear saturable media," J. Lightw. Technol. 23, 2579-2585 (2005).
  17. M. D. Feit, J. A. Fleck, Jr."Light propagation in graded-index optical fibers," Appl. Opt. 17, 3990-3998 (1978).
  18. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  19. Y. Chung, N. Dagli, "An assessment of finite difference beam propagation method," IEEE J. Quantum Electron. 26, 1335-1339 (1990).
  20. K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000).
  21. G. R. Hadley, "Transparent boundary condition for the beam propagation method," IEEE J. Quantum Electron. 28, 363-370 (1992).
  22. D. Marcuse, Light Transmission Optics (Van Nostrand, 1972).
  23. L. B. Soldano, E. C. Pennings, "Optical multi-mode interference devices based on self-imaging: Principles and applications ," J. Lightw. Technol. 13, 615-627 (1995).

2007

M. A. Swillam, M. H. Bakr, N. K. Nikolova, X. Li, "Adjoint sensitivity analysis of dielectric discontinuities using FDTD," Electromagn 27, 123-140 (2007).

M. A. Swillam, M. H. Bakr, X. Li, "Accurate sensitivity analysis of photonic devices exploiting the finite-difference time-domain central adjoint variable method," Appl. Opt. 46, 1492-1499 (2007).

2006

K. Zinoviev, C. Dominguez, J. A. Plaza, V. J. C. Busto, L. M. Lechuga, "A novel optical waveguide microcantilever sensor for the detection of nanomechanical forces ," J. Lightw. Technol. 24, 2132-2138 (2006).

M. A. El Sabbagh, M. H. Bakr, J. W. Bandler, "Adjoint higher order sensitivities for fast full-wave optimization of microwave filters ," IEEE Trans. Microw. Theory Tech. 54, 3339-3351 (2006).

2005

L. D. S. Alcantara, F. L. Teixeira, A. C. Cesar, B.-H. V. Borges, "A new full-vectorial FD-BPM scheme: Application to the analysis of magnetooptic and nonlinear saturable media," J. Lightw. Technol. 23, 2579-2585 (2005).

2004

N. K. Nikolova, R. Safian, E. A. Soliman, M. H. Bakr, J. W. Bandler, "Accelerated gradient based optimization using adjoint sensitivities," IEEE Trans. Antennas Propag. 52, 2147-2157 (2004).

G. Veronis, R. W. Dutton, S. Fan, "Method for sensitivity analysis of photonic crystal devices," Opt. Lett. 29, 2288-2290 (2004).

M. H. Bakr, N. K. Nikolova, "An adjoint variable method for time domain TLM with wideband Johns matrix boundaries ," IEEE Trans. Microw. Theory Tech. 52, 678-685 (2004).

N. K. Nikolova, H. W. Tam, M. H. Bakr, "Sensitivity analysis with the FDTD method on structured grids," IEEE Trans. Microw. Theory Tech. 52, 1207-1216 (2004).

2003

M. H. Bakr, N. K. Nikolova, "An adjoint variable method for frequency domain TLM problems with conducting boundaries ," IEEE Microw. Wireless Compon. Lett. 13, 408-410 (2003).

2002

P. L. Ho, Y. Y. Lu, "A bidirectional beam propagation method for periodic waveguides," IEEE Photon. Technol. Lett. 14, 325-327 (2002).

B. Saadany, D. A. Khalil, "Modeling of MOEMS components using HDL-A," IEEE J. Sel. Topics Quantum Electron. 8, 132-138 (2002).

2000

H. Akel, J. P. Webb, "Design sensitivities for scattering-matrix calculation with tetrahedral edge elements ," IEEE Trans. Magn. 36, 1043-1046 (2000).

1997

E. Kriezis, A. G. Papagiannakis, "A three-dimensional full vectorial beam propagation method for $z$-dependent structures," IEEE J. Quantum Electron. 33, 883-890 (1997).

1995

L. B. Soldano, E. C. Pennings, "Optical multi-mode interference devices based on self-imaging: Principles and applications ," J. Lightw. Technol. 13, 615-627 (1995).

1992

G. R. Hadley, "Transparent boundary condition for the beam propagation method," IEEE J. Quantum Electron. 28, 363-370 (1992).

W.-P. Huang, C. L. Xu, S. K. Chaudhuri, "A finite-difference vector beam propagation method for three-dimensional structures ," IEEE Photon. Technol. Lett. 4, 148-151 (1992).

1990

Y. Chung, N. Dagli, "An assessment of finite difference beam propagation method," IEEE J. Quantum Electron. 26, 1335-1339 (1990).

1989

D. Yevick, B. Hermansson, "New formulation of the matrix beam propagation method: Application to rib waveguide ," IEEE J. Quantum Electron. 25, 221-229 (1989).

1978

Appl. Opt.

Electromagn

M. A. Swillam, M. H. Bakr, N. K. Nikolova, X. Li, "Adjoint sensitivity analysis of dielectric discontinuities using FDTD," Electromagn 27, 123-140 (2007).

IEEE J. Quantum Electron.

D. Yevick, B. Hermansson, "New formulation of the matrix beam propagation method: Application to rib waveguide ," IEEE J. Quantum Electron. 25, 221-229 (1989).

Y. Chung, N. Dagli, "An assessment of finite difference beam propagation method," IEEE J. Quantum Electron. 26, 1335-1339 (1990).

E. Kriezis, A. G. Papagiannakis, "A three-dimensional full vectorial beam propagation method for $z$-dependent structures," IEEE J. Quantum Electron. 33, 883-890 (1997).

G. R. Hadley, "Transparent boundary condition for the beam propagation method," IEEE J. Quantum Electron. 28, 363-370 (1992).

IEEE J. Sel. Topics Quantum Electron.

B. Saadany, D. A. Khalil, "Modeling of MOEMS components using HDL-A," IEEE J. Sel. Topics Quantum Electron. 8, 132-138 (2002).

IEEE Microw. Wireless Compon. Lett.

M. H. Bakr, N. K. Nikolova, "An adjoint variable method for frequency domain TLM problems with conducting boundaries ," IEEE Microw. Wireless Compon. Lett. 13, 408-410 (2003).

IEEE Photon. Technol. Lett.

W.-P. Huang, C. L. Xu, S. K. Chaudhuri, "A finite-difference vector beam propagation method for three-dimensional structures ," IEEE Photon. Technol. Lett. 4, 148-151 (1992).

P. L. Ho, Y. Y. Lu, "A bidirectional beam propagation method for periodic waveguides," IEEE Photon. Technol. Lett. 14, 325-327 (2002).

IEEE Trans. Antennas Propag.

N. K. Nikolova, R. Safian, E. A. Soliman, M. H. Bakr, J. W. Bandler, "Accelerated gradient based optimization using adjoint sensitivities," IEEE Trans. Antennas Propag. 52, 2147-2157 (2004).

IEEE Trans. Magn.

H. Akel, J. P. Webb, "Design sensitivities for scattering-matrix calculation with tetrahedral edge elements ," IEEE Trans. Magn. 36, 1043-1046 (2000).

IEEE Trans. Microw. Theory Tech.

M. H. Bakr, N. K. Nikolova, "An adjoint variable method for time domain TLM with wideband Johns matrix boundaries ," IEEE Trans. Microw. Theory Tech. 52, 678-685 (2004).

N. K. Nikolova, H. W. Tam, M. H. Bakr, "Sensitivity analysis with the FDTD method on structured grids," IEEE Trans. Microw. Theory Tech. 52, 1207-1216 (2004).

M. A. El Sabbagh, M. H. Bakr, J. W. Bandler, "Adjoint higher order sensitivities for fast full-wave optimization of microwave filters ," IEEE Trans. Microw. Theory Tech. 54, 3339-3351 (2006).

J. Lightw. Technol.

L. B. Soldano, E. C. Pennings, "Optical multi-mode interference devices based on self-imaging: Principles and applications ," J. Lightw. Technol. 13, 615-627 (1995).

K. Zinoviev, C. Dominguez, J. A. Plaza, V. J. C. Busto, L. M. Lechuga, "A novel optical waveguide microcantilever sensor for the detection of nanomechanical forces ," J. Lightw. Technol. 24, 2132-2138 (2006).

L. D. S. Alcantara, F. L. Teixeira, A. C. Cesar, B.-H. V. Borges, "A new full-vectorial FD-BPM scheme: Application to the analysis of magnetooptic and nonlinear saturable media," J. Lightw. Technol. 23, 2579-2585 (2005).

Opt. Lett.

Other

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

D. Marcuse, Light Transmission Optics (Van Nostrand, 1972).

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