Abstract

In this paper, we propose a theory for wideband adjoint sensitivity analysis of problems with nonlinear media. We show that the sensitivities of the desired response with respect to all shape and material parameters are obtained through one extra adjoint simulation. Unlike linear problems, the system matrices of this adjoint simulation are time varying. Their values are determined during the original simulation. The proposed theory exploits the time-domain transmission line modeling (TLM) and provides an efficient AVM approach for sensitivity analysis of general time domain objective functions. The theory has been illustrated through a number of examples.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. A. Maas, Nonlinear microwave circuits. (IEEE, 1997).
  2. A. E. Schmitz, R. H. Walden, L. E. Larson, S. E. Rosenbaum, R. A. Metzger, J. R. Behnke, P. A. Macdonald, “A deep-submicrometer microwave/digital CMOS/SOS technology,” IEEE Electron Device Lett. 12(1), 16–17 (1991).
    [CrossRef]
  3. N. Camilleri, J. Costa, D. Lovelace, and D. Ngo, “Silicon MOSFETs, the microwave device technology for the 1990s,” in Microwave Symposium Digest, IEEE MTT-S International, (1993), pp. 545–548.
    [CrossRef]
  4. P. Russer, N. Fichtner, “Nanoelectronics in radio-frequency technology,” IEEE Microw. Mag. 11(3), 119–135 (2010).
    [CrossRef]
  5. S. A. Sørngård, S. I. Simonsen, J. P. Hansen, “High-order harmonic generation from graphene: Strong attosecond pulses with arbitrary polarization,” Phys. Rev. A 87(5), 053803 (2013).
    [CrossRef]
  6. M. A. Foster, A. C. Turner, M. Lipson, A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16(2), 1300–1320 (2008).
    [CrossRef] [PubMed]
  7. C. Koos, L. Jacome, C. Poulton, J. Leuthold, W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express 15(10), 5976–5990 (2007).
    [CrossRef] [PubMed]
  8. N. G. R. Broderick, T. M. Monro, P. J. Bennett, D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24(20), 1395–1397 (1999).
    [CrossRef] [PubMed]
  9. P. L. Kelley, “Self-Focusing of Optical Beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965).
    [CrossRef]
  10. J. M. Dudley, J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fibre,” Nat. Photonics 3(2), 85–90 (2009).
    [CrossRef]
  11. T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4(12), 822–832 (2010).
    [CrossRef]
  12. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Efficient visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” in Summaries of Papers Presented at the Conference on Lasers and Electro-Optics, CLEO ’99 (1999), CPD8/1–CPD8/2.
    [CrossRef]
  13. J. K. Ranka, R. S. Windeler, A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25(1), 25–27 (2000).
    [CrossRef] [PubMed]
  14. Y. Gontier, M. Trahin, “Frequency conversion involving Raman-like processes above the ionization threshold,” IEEE J. Quantum Electron. 18(7), 1137–1145 (1982).
    [CrossRef]
  15. R. Claps, V. Raghunathan, D. Dimitropoulos, B. Jalali, “Influence of nonlinear absorption on Raman amplification in Silicon waveguides,” Opt. Express 12(12), 2774–2780 (2004).
    [CrossRef] [PubMed]
  16. R. Dekker, N. Usechak, M. Först, A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), R249–R271 (2007).
    [CrossRef]
  17. T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
    [CrossRef]
  18. S. Kawanishi, O. Kamatani, “All-optical time division multiplexing using four-wave mixing,” Electron. Lett. 30(20), 1697–1698 (1994).
    [CrossRef]
  19. A. M. Darwish, E. P. Ippen, H. Q. Le, J. P. Donnelly, S. H. Groves, “Optimization of four‐wave mixing conversion efficiency in the presence of nonlinear loss,” Appl. Phys. Lett. 69(6), 737–739 (1996).
    [CrossRef]
  20. Ö. Boyraz, P. Koonath, V. Raghunathan, B. Jalali, “All optical switching and continuum generation in silicon waveguides,” Opt. Express 12(17), 4094–4102 (2004).
    [CrossRef] [PubMed]
  21. C. Koos, L. Jacome, C. Poulton, J. Leuthold, W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express 15(10), 5976–5990 (2007).
    [CrossRef] [PubMed]
  22. V. Rizzoli, A. Costanzo, D. Masotti, A. Lipparini, F. Mastri, “Computer-aided optimization of nonlinear microwave circuits with the aid of electromagnetic simulation,” IEEE Trans. Microw. Theory Tech. 52(1), 362–377 (2004).
    [CrossRef]
  23. R. M. Joseph, A. Taflove, “FDTD Maxwell’s equations models for nonlinear electrodynamics and optics,” IEEE Trans. Antenn. Propag. 45(3), 364–374 (1997).
    [CrossRef]
  24. P. Russer, P. P. M. So, W. J. R. Hoefer, “Modeling of nonlinear active regions in TLM (distributed circuits),” IEEE Microw. Guided Wave Letts. 1(1), 10–13 (1991).
    [CrossRef]
  25. M. Nakhla, J. Vlach, “A piecewise harmonic balance technique for determination of periodic response of nonlinear systems,” IEEE Trans. Circ. Syst. 23(2), 85–91 (1976).
    [CrossRef]
  26. J. E. Rayas-Sanchez, “EM-based optimization of microwave circuits using artificial neural networks: the state-of-the-art,” IEEE Trans. Microw. Theory Tech. 52(1), 420–435 (2004).
    [CrossRef]
  27. J. S. Jensen, “Topology optimization of nonlinear optical devices,” Struct. Multidisc. Optim. 43(6), 731–743 (2011).
    [CrossRef]
  28. M. Gao, C. Jiang, W. Hu, J. Wang, “Optimized design of two-pump fiber optical parametric amplifier with two-section nonlinear fibers using genetic algorithm,” Opt. Express 12(23), 5603–5613 (2004).
    [CrossRef] [PubMed]
  29. M. H. Bakr, J. W. Bandler, K. Madsen, J. E. Rayas-Sanchez, J. Sondergaard, “Space-mapping optimization of microwave circuits exploiting surrogate models,” IEEE Trans. Microw. Theory Tech. 48(12), 2297–2306 (2000).
    [CrossRef]
  30. L. Zhang, J. Xu, M. C. E. Yagoub, R. Ding, Q.-J. Zhang, “Efficient analytical formulation and sensitivity analysis of neuro-space mapping for nonlinear microwave device modeling,” IEEE Trans. Microw. Theory Tech. 53(9), 2752–2767 (2005).
    [CrossRef]
  31. H. Igarashi, K. Watanabe, “Complex adjoint variable method for finite-element analysis of eddy current problems,” IEEE Trans. Magn. 46(8), 2739–2742 (2010).
    [CrossRef]
  32. I.-H. Park, B.-T. Lee, S.-Y. Hahn, “Design sensitivity analysis for nonlinear magnetostatic problems using finite element method,” IEEE Trans. Magn. 28(2), 1533–1536 (1992).
    [CrossRef]
  33. B. Lojek, “Sensitivity analysis of nonlinear circuits,” Electronic Circuits and Systems, IEE Proceedings 129(3), 85–88 (1982).
    [CrossRef]
  34. Y. Chung, C. Cheon, I. Park, S. Hahn, “Optimal shape design of microwave device using FDTD and design sensitivity analysis,” IEEE Trans. Microw. Theory Tech. 48(12), 2289–2296 (2000).
    [CrossRef]
  35. Y. Chung, J. Ryu, C. Cheon, I. Park, S. Hahn, “Optimal design method for microwave device using time domain method and design sensitivity analysis—Part I: FETD case,” IEEE Trans. Magn. 37(5), 3289–3293 (2001).
    [CrossRef]
  36. Y. Chung, C. Cheon, I. Park, S. Hahn, “Optimal design method for microwave device using time domain method and design sensitivity analysis—Part II: FDTD case,” IEEE Trans. Magn. 37(5), 3255–3259 (2001).
    [CrossRef]
  37. J. P. Webb, “Design sensitivity of frequency response in 3-D finite-element analysis of microwave devices,” IEEE Trans. Magn. 38(2), 1109–1112 (2002).
    [CrossRef]
  38. M. H. Bakr, N. K. Nikolova, “An adjoint variable method for time-domain transmission line modeling with fixed structured grids,” IEEE Trans. Microw. Theory Tech. 52(2), 554–559 (2004).
    [CrossRef]
  39. M. H. Bakr, P. Zhao, N. K. Nikolova, “Adjoint first order sensitivities of transient responses and their applications in the solution of inverse problems,” IEEE Trans. Antenn. Propag. 57(7), 2137–2146 (2009).
    [CrossRef]
  40. M. H. Bakr, N. K. Nikolova, P. A. W. Basl, “Self-Adjoint S-Parameter Sensitivities for Lossless Homogeneous TLM Problems,” International Journal of Numerical Modeling: Electronic Networks, Devices and Fields 18(6), 441–455 (2005).
    [CrossRef]
  41. P. A. W. Basl, M. H. Bakr, N. K. Nikolova, “Theory of self-adjoint S-parameter sensitivities for lossless nonhomogeneous transmission-line modeling problems,” IET Microwave Antennas Propag. 2(3), 211–220 (2008).
    [CrossRef]
  42. O. S. Ahmed, M. H. Bakr, X. Li, T. Nomura, “A Time-Domain Adjoint Variable Method for Materials With Dispersive Constitutive Parameters,” IEEE Trans. Microw. Theory Tech. 60(10), 2959–2971 (2012).
    [CrossRef]
  43. Optimetrics: parametrics and optimization using Ansoft HFSS,” Microwave Journal, (1999). [Online]. Available: http://www.microwavejournal.com/articles/2779-parametrics-and-optimization-using-ansoft-hfss . [Accessed 18 Nov. 2013].
  44. Press Release, “Sensitivity analysis and adapted optimization strategies for CST MICROWAVE STUDIO transient solver,” May 2010. [Online]. Available: www.cst.com/Content/News/Documents/2010_5_Timedomain2011_web.pdf . [Accessed 23 Oct. 2013].
  45. A. S. Saini, M. S. Nakhla, R. Achar, “Generalized time-domain adjoint sensitivity analysis of distributed MTL networks,” IEEE Trans. Microw. Theory Tech. 60(11), 3359–3368 (2012).
    [CrossRef]
  46. S. Lum, M. Nakhla, Q.-J. Zhang, “Sensitivity analysis of lossy coupled transmission lines with nonlinear terminations,” IEEE Trans. Microw. Theory Tech. 42(4), 607–615 (1994).
    [CrossRef]
  47. O. S. Ahmed, M. H. Bakr, X. Li, “A memory-efficient implementation of TLM- based adjoint sensitivity analysis,” IEEE Trans. Antenn. Propag. 60(4), 2122–2125 (2012).
    [CrossRef]
  48. O. S. Ahmed, M. H. Bakr, X. Li, “An impulse sampling approach for efficient 3D TLM-based adjoint sensitivity analysis,” Prog. Electromagnetics Res. 142, 485–503 (2013).
    [CrossRef]

2013 (2)

S. A. Sørngård, S. I. Simonsen, J. P. Hansen, “High-order harmonic generation from graphene: Strong attosecond pulses with arbitrary polarization,” Phys. Rev. A 87(5), 053803 (2013).
[CrossRef]

O. S. Ahmed, M. H. Bakr, X. Li, “An impulse sampling approach for efficient 3D TLM-based adjoint sensitivity analysis,” Prog. Electromagnetics Res. 142, 485–503 (2013).
[CrossRef]

2012 (4)

O. S. Ahmed, M. H. Bakr, X. Li, “A memory-efficient implementation of TLM- based adjoint sensitivity analysis,” IEEE Trans. Antenn. Propag. 60(4), 2122–2125 (2012).
[CrossRef]

O. S. Ahmed, M. H. Bakr, X. Li, T. Nomura, “A Time-Domain Adjoint Variable Method for Materials With Dispersive Constitutive Parameters,” IEEE Trans. Microw. Theory Tech. 60(10), 2959–2971 (2012).
[CrossRef]

A. S. Saini, M. S. Nakhla, R. Achar, “Generalized time-domain adjoint sensitivity analysis of distributed MTL networks,” IEEE Trans. Microw. Theory Tech. 60(11), 3359–3368 (2012).
[CrossRef]

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[CrossRef]

2011 (1)

J. S. Jensen, “Topology optimization of nonlinear optical devices,” Struct. Multidisc. Optim. 43(6), 731–743 (2011).
[CrossRef]

2010 (3)

H. Igarashi, K. Watanabe, “Complex adjoint variable method for finite-element analysis of eddy current problems,” IEEE Trans. Magn. 46(8), 2739–2742 (2010).
[CrossRef]

P. Russer, N. Fichtner, “Nanoelectronics in radio-frequency technology,” IEEE Microw. Mag. 11(3), 119–135 (2010).
[CrossRef]

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4(12), 822–832 (2010).
[CrossRef]

2009 (2)

J. M. Dudley, J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fibre,” Nat. Photonics 3(2), 85–90 (2009).
[CrossRef]

M. H. Bakr, P. Zhao, N. K. Nikolova, “Adjoint first order sensitivities of transient responses and their applications in the solution of inverse problems,” IEEE Trans. Antenn. Propag. 57(7), 2137–2146 (2009).
[CrossRef]

2008 (2)

P. A. W. Basl, M. H. Bakr, N. K. Nikolova, “Theory of self-adjoint S-parameter sensitivities for lossless nonhomogeneous transmission-line modeling problems,” IET Microwave Antennas Propag. 2(3), 211–220 (2008).
[CrossRef]

M. A. Foster, A. C. Turner, M. Lipson, A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16(2), 1300–1320 (2008).
[CrossRef] [PubMed]

2007 (3)

2005 (2)

L. Zhang, J. Xu, M. C. E. Yagoub, R. Ding, Q.-J. Zhang, “Efficient analytical formulation and sensitivity analysis of neuro-space mapping for nonlinear microwave device modeling,” IEEE Trans. Microw. Theory Tech. 53(9), 2752–2767 (2005).
[CrossRef]

M. H. Bakr, N. K. Nikolova, P. A. W. Basl, “Self-Adjoint S-Parameter Sensitivities for Lossless Homogeneous TLM Problems,” International Journal of Numerical Modeling: Electronic Networks, Devices and Fields 18(6), 441–455 (2005).
[CrossRef]

2004 (6)

M. H. Bakr, N. K. Nikolova, “An adjoint variable method for time-domain transmission line modeling with fixed structured grids,” IEEE Trans. Microw. Theory Tech. 52(2), 554–559 (2004).
[CrossRef]

V. Rizzoli, A. Costanzo, D. Masotti, A. Lipparini, F. Mastri, “Computer-aided optimization of nonlinear microwave circuits with the aid of electromagnetic simulation,” IEEE Trans. Microw. Theory Tech. 52(1), 362–377 (2004).
[CrossRef]

R. Claps, V. Raghunathan, D. Dimitropoulos, B. Jalali, “Influence of nonlinear absorption on Raman amplification in Silicon waveguides,” Opt. Express 12(12), 2774–2780 (2004).
[CrossRef] [PubMed]

Ö. Boyraz, P. Koonath, V. Raghunathan, B. Jalali, “All optical switching and continuum generation in silicon waveguides,” Opt. Express 12(17), 4094–4102 (2004).
[CrossRef] [PubMed]

M. Gao, C. Jiang, W. Hu, J. Wang, “Optimized design of two-pump fiber optical parametric amplifier with two-section nonlinear fibers using genetic algorithm,” Opt. Express 12(23), 5603–5613 (2004).
[CrossRef] [PubMed]

J. E. Rayas-Sanchez, “EM-based optimization of microwave circuits using artificial neural networks: the state-of-the-art,” IEEE Trans. Microw. Theory Tech. 52(1), 420–435 (2004).
[CrossRef]

2002 (1)

J. P. Webb, “Design sensitivity of frequency response in 3-D finite-element analysis of microwave devices,” IEEE Trans. Magn. 38(2), 1109–1112 (2002).
[CrossRef]

2001 (2)

Y. Chung, J. Ryu, C. Cheon, I. Park, S. Hahn, “Optimal design method for microwave device using time domain method and design sensitivity analysis—Part I: FETD case,” IEEE Trans. Magn. 37(5), 3289–3293 (2001).
[CrossRef]

Y. Chung, C. Cheon, I. Park, S. Hahn, “Optimal design method for microwave device using time domain method and design sensitivity analysis—Part II: FDTD case,” IEEE Trans. Magn. 37(5), 3255–3259 (2001).
[CrossRef]

2000 (3)

J. K. Ranka, R. S. Windeler, A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25(1), 25–27 (2000).
[CrossRef] [PubMed]

Y. Chung, C. Cheon, I. Park, S. Hahn, “Optimal shape design of microwave device using FDTD and design sensitivity analysis,” IEEE Trans. Microw. Theory Tech. 48(12), 2289–2296 (2000).
[CrossRef]

M. H. Bakr, J. W. Bandler, K. Madsen, J. E. Rayas-Sanchez, J. Sondergaard, “Space-mapping optimization of microwave circuits exploiting surrogate models,” IEEE Trans. Microw. Theory Tech. 48(12), 2297–2306 (2000).
[CrossRef]

1999 (1)

1997 (1)

R. M. Joseph, A. Taflove, “FDTD Maxwell’s equations models for nonlinear electrodynamics and optics,” IEEE Trans. Antenn. Propag. 45(3), 364–374 (1997).
[CrossRef]

1996 (1)

A. M. Darwish, E. P. Ippen, H. Q. Le, J. P. Donnelly, S. H. Groves, “Optimization of four‐wave mixing conversion efficiency in the presence of nonlinear loss,” Appl. Phys. Lett. 69(6), 737–739 (1996).
[CrossRef]

1994 (2)

S. Kawanishi, O. Kamatani, “All-optical time division multiplexing using four-wave mixing,” Electron. Lett. 30(20), 1697–1698 (1994).
[CrossRef]

S. Lum, M. Nakhla, Q.-J. Zhang, “Sensitivity analysis of lossy coupled transmission lines with nonlinear terminations,” IEEE Trans. Microw. Theory Tech. 42(4), 607–615 (1994).
[CrossRef]

1992 (1)

I.-H. Park, B.-T. Lee, S.-Y. Hahn, “Design sensitivity analysis for nonlinear magnetostatic problems using finite element method,” IEEE Trans. Magn. 28(2), 1533–1536 (1992).
[CrossRef]

1991 (2)

A. E. Schmitz, R. H. Walden, L. E. Larson, S. E. Rosenbaum, R. A. Metzger, J. R. Behnke, P. A. Macdonald, “A deep-submicrometer microwave/digital CMOS/SOS technology,” IEEE Electron Device Lett. 12(1), 16–17 (1991).
[CrossRef]

P. Russer, P. P. M. So, W. J. R. Hoefer, “Modeling of nonlinear active regions in TLM (distributed circuits),” IEEE Microw. Guided Wave Letts. 1(1), 10–13 (1991).
[CrossRef]

1982 (2)

Y. Gontier, M. Trahin, “Frequency conversion involving Raman-like processes above the ionization threshold,” IEEE J. Quantum Electron. 18(7), 1137–1145 (1982).
[CrossRef]

B. Lojek, “Sensitivity analysis of nonlinear circuits,” Electronic Circuits and Systems, IEE Proceedings 129(3), 85–88 (1982).
[CrossRef]

1976 (1)

M. Nakhla, J. Vlach, “A piecewise harmonic balance technique for determination of periodic response of nonlinear systems,” IEEE Trans. Circ. Syst. 23(2), 85–91 (1976).
[CrossRef]

1965 (1)

P. L. Kelley, “Self-Focusing of Optical Beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965).
[CrossRef]

Achar, R.

A. S. Saini, M. S. Nakhla, R. Achar, “Generalized time-domain adjoint sensitivity analysis of distributed MTL networks,” IEEE Trans. Microw. Theory Tech. 60(11), 3359–3368 (2012).
[CrossRef]

Ahmed, O. S.

O. S. Ahmed, M. H. Bakr, X. Li, “An impulse sampling approach for efficient 3D TLM-based adjoint sensitivity analysis,” Prog. Electromagnetics Res. 142, 485–503 (2013).
[CrossRef]

O. S. Ahmed, M. H. Bakr, X. Li, T. Nomura, “A Time-Domain Adjoint Variable Method for Materials With Dispersive Constitutive Parameters,” IEEE Trans. Microw. Theory Tech. 60(10), 2959–2971 (2012).
[CrossRef]

O. S. Ahmed, M. H. Bakr, X. Li, “A memory-efficient implementation of TLM- based adjoint sensitivity analysis,” IEEE Trans. Antenn. Propag. 60(4), 2122–2125 (2012).
[CrossRef]

Arpin, P.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4(12), 822–832 (2010).
[CrossRef]

Badolato, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[CrossRef]

Bakr, M. H.

O. S. Ahmed, M. H. Bakr, X. Li, “An impulse sampling approach for efficient 3D TLM-based adjoint sensitivity analysis,” Prog. Electromagnetics Res. 142, 485–503 (2013).
[CrossRef]

O. S. Ahmed, M. H. Bakr, X. Li, T. Nomura, “A Time-Domain Adjoint Variable Method for Materials With Dispersive Constitutive Parameters,” IEEE Trans. Microw. Theory Tech. 60(10), 2959–2971 (2012).
[CrossRef]

O. S. Ahmed, M. H. Bakr, X. Li, “A memory-efficient implementation of TLM- based adjoint sensitivity analysis,” IEEE Trans. Antenn. Propag. 60(4), 2122–2125 (2012).
[CrossRef]

M. H. Bakr, P. Zhao, N. K. Nikolova, “Adjoint first order sensitivities of transient responses and their applications in the solution of inverse problems,” IEEE Trans. Antenn. Propag. 57(7), 2137–2146 (2009).
[CrossRef]

P. A. W. Basl, M. H. Bakr, N. K. Nikolova, “Theory of self-adjoint S-parameter sensitivities for lossless nonhomogeneous transmission-line modeling problems,” IET Microwave Antennas Propag. 2(3), 211–220 (2008).
[CrossRef]

M. H. Bakr, N. K. Nikolova, P. A. W. Basl, “Self-Adjoint S-Parameter Sensitivities for Lossless Homogeneous TLM Problems,” International Journal of Numerical Modeling: Electronic Networks, Devices and Fields 18(6), 441–455 (2005).
[CrossRef]

M. H. Bakr, N. K. Nikolova, “An adjoint variable method for time-domain transmission line modeling with fixed structured grids,” IEEE Trans. Microw. Theory Tech. 52(2), 554–559 (2004).
[CrossRef]

M. H. Bakr, J. W. Bandler, K. Madsen, J. E. Rayas-Sanchez, J. Sondergaard, “Space-mapping optimization of microwave circuits exploiting surrogate models,” IEEE Trans. Microw. Theory Tech. 48(12), 2297–2306 (2000).
[CrossRef]

Bandler, J. W.

M. H. Bakr, J. W. Bandler, K. Madsen, J. E. Rayas-Sanchez, J. Sondergaard, “Space-mapping optimization of microwave circuits exploiting surrogate models,” IEEE Trans. Microw. Theory Tech. 48(12), 2297–2306 (2000).
[CrossRef]

Basl, P. A. W.

P. A. W. Basl, M. H. Bakr, N. K. Nikolova, “Theory of self-adjoint S-parameter sensitivities for lossless nonhomogeneous transmission-line modeling problems,” IET Microwave Antennas Propag. 2(3), 211–220 (2008).
[CrossRef]

M. H. Bakr, N. K. Nikolova, P. A. W. Basl, “Self-Adjoint S-Parameter Sensitivities for Lossless Homogeneous TLM Problems,” International Journal of Numerical Modeling: Electronic Networks, Devices and Fields 18(6), 441–455 (2005).
[CrossRef]

Behnke, J. R.

A. E. Schmitz, R. H. Walden, L. E. Larson, S. E. Rosenbaum, R. A. Metzger, J. R. Behnke, P. A. Macdonald, “A deep-submicrometer microwave/digital CMOS/SOS technology,” IEEE Electron Device Lett. 12(1), 16–17 (1991).
[CrossRef]

Bennett, P. J.

Boyraz, Ö.

Broderick, N. G. R.

Chen, M.-C.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4(12), 822–832 (2010).
[CrossRef]

Cheon, C.

Y. Chung, J. Ryu, C. Cheon, I. Park, S. Hahn, “Optimal design method for microwave device using time domain method and design sensitivity analysis—Part I: FETD case,” IEEE Trans. Magn. 37(5), 3289–3293 (2001).
[CrossRef]

Y. Chung, C. Cheon, I. Park, S. Hahn, “Optimal design method for microwave device using time domain method and design sensitivity analysis—Part II: FDTD case,” IEEE Trans. Magn. 37(5), 3255–3259 (2001).
[CrossRef]

Y. Chung, C. Cheon, I. Park, S. Hahn, “Optimal shape design of microwave device using FDTD and design sensitivity analysis,” IEEE Trans. Microw. Theory Tech. 48(12), 2289–2296 (2000).
[CrossRef]

Chung, Y.

Y. Chung, C. Cheon, I. Park, S. Hahn, “Optimal design method for microwave device using time domain method and design sensitivity analysis—Part II: FDTD case,” IEEE Trans. Magn. 37(5), 3255–3259 (2001).
[CrossRef]

Y. Chung, J. Ryu, C. Cheon, I. Park, S. Hahn, “Optimal design method for microwave device using time domain method and design sensitivity analysis—Part I: FETD case,” IEEE Trans. Magn. 37(5), 3289–3293 (2001).
[CrossRef]

Y. Chung, C. Cheon, I. Park, S. Hahn, “Optimal shape design of microwave device using FDTD and design sensitivity analysis,” IEEE Trans. Microw. Theory Tech. 48(12), 2289–2296 (2000).
[CrossRef]

Claps, R.

Costanzo, A.

V. Rizzoli, A. Costanzo, D. Masotti, A. Lipparini, F. Mastri, “Computer-aided optimization of nonlinear microwave circuits with the aid of electromagnetic simulation,” IEEE Trans. Microw. Theory Tech. 52(1), 362–377 (2004).
[CrossRef]

Darwish, A. M.

A. M. Darwish, E. P. Ippen, H. Q. Le, J. P. Donnelly, S. H. Groves, “Optimization of four‐wave mixing conversion efficiency in the presence of nonlinear loss,” Appl. Phys. Lett. 69(6), 737–739 (1996).
[CrossRef]

Dekker, R.

R. Dekker, N. Usechak, M. Först, A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), R249–R271 (2007).
[CrossRef]

Dimitropoulos, D.

Ding, R.

L. Zhang, J. Xu, M. C. E. Yagoub, R. Ding, Q.-J. Zhang, “Efficient analytical formulation and sensitivity analysis of neuro-space mapping for nonlinear microwave device modeling,” IEEE Trans. Microw. Theory Tech. 53(9), 2752–2767 (2005).
[CrossRef]

Donnelly, J. P.

A. M. Darwish, E. P. Ippen, H. Q. Le, J. P. Donnelly, S. H. Groves, “Optimization of four‐wave mixing conversion efficiency in the presence of nonlinear loss,” Appl. Phys. Lett. 69(6), 737–739 (1996).
[CrossRef]

Driessen, A.

R. Dekker, N. Usechak, M. Först, A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), R249–R271 (2007).
[CrossRef]

Dudley, J. M.

J. M. Dudley, J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fibre,” Nat. Photonics 3(2), 85–90 (2009).
[CrossRef]

Fichtner, N.

P. Russer, N. Fichtner, “Nanoelectronics in radio-frequency technology,” IEEE Microw. Mag. 11(3), 119–135 (2010).
[CrossRef]

Först, M.

R. Dekker, N. Usechak, M. Först, A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), R249–R271 (2007).
[CrossRef]

Foster, M. A.

Freude, W.

Gaeta, A. L.

Gao, M.

Gontier, Y.

Y. Gontier, M. Trahin, “Frequency conversion involving Raman-like processes above the ionization threshold,” IEEE J. Quantum Electron. 18(7), 1137–1145 (1982).
[CrossRef]

Groves, S. H.

A. M. Darwish, E. P. Ippen, H. Q. Le, J. P. Donnelly, S. H. Groves, “Optimization of four‐wave mixing conversion efficiency in the presence of nonlinear loss,” Appl. Phys. Lett. 69(6), 737–739 (1996).
[CrossRef]

Hahn, S.

Y. Chung, J. Ryu, C. Cheon, I. Park, S. Hahn, “Optimal design method for microwave device using time domain method and design sensitivity analysis—Part I: FETD case,” IEEE Trans. Magn. 37(5), 3289–3293 (2001).
[CrossRef]

Y. Chung, C. Cheon, I. Park, S. Hahn, “Optimal design method for microwave device using time domain method and design sensitivity analysis—Part II: FDTD case,” IEEE Trans. Magn. 37(5), 3255–3259 (2001).
[CrossRef]

Y. Chung, C. Cheon, I. Park, S. Hahn, “Optimal shape design of microwave device using FDTD and design sensitivity analysis,” IEEE Trans. Microw. Theory Tech. 48(12), 2289–2296 (2000).
[CrossRef]

Hahn, S.-Y.

I.-H. Park, B.-T. Lee, S.-Y. Hahn, “Design sensitivity analysis for nonlinear magnetostatic problems using finite element method,” IEEE Trans. Magn. 28(2), 1533–1536 (1992).
[CrossRef]

Hansen, J. P.

S. A. Sørngård, S. I. Simonsen, J. P. Hansen, “High-order harmonic generation from graphene: Strong attosecond pulses with arbitrary polarization,” Phys. Rev. A 87(5), 053803 (2013).
[CrossRef]

Hennessy, K. J.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[CrossRef]

Hoefer, W. J. R.

P. Russer, P. P. M. So, W. J. R. Hoefer, “Modeling of nonlinear active regions in TLM (distributed circuits),” IEEE Microw. Guided Wave Letts. 1(1), 10–13 (1991).
[CrossRef]

Hu, E. L.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[CrossRef]

Hu, W.

Igarashi, H.

H. Igarashi, K. Watanabe, “Complex adjoint variable method for finite-element analysis of eddy current problems,” IEEE Trans. Magn. 46(8), 2739–2742 (2010).
[CrossRef]

Imamoglu, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[CrossRef]

Ippen, E. P.

A. M. Darwish, E. P. Ippen, H. Q. Le, J. P. Donnelly, S. H. Groves, “Optimization of four‐wave mixing conversion efficiency in the presence of nonlinear loss,” Appl. Phys. Lett. 69(6), 737–739 (1996).
[CrossRef]

Jacome, L.

Jalali, B.

Jensen, J. S.

J. S. Jensen, “Topology optimization of nonlinear optical devices,” Struct. Multidisc. Optim. 43(6), 731–743 (2011).
[CrossRef]

Jiang, C.

Joseph, R. M.

R. M. Joseph, A. Taflove, “FDTD Maxwell’s equations models for nonlinear electrodynamics and optics,” IEEE Trans. Antenn. Propag. 45(3), 364–374 (1997).
[CrossRef]

Kamatani, O.

S. Kawanishi, O. Kamatani, “All-optical time division multiplexing using four-wave mixing,” Electron. Lett. 30(20), 1697–1698 (1994).
[CrossRef]

Kapteyn, H. C.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4(12), 822–832 (2010).
[CrossRef]

Kawanishi, S.

S. Kawanishi, O. Kamatani, “All-optical time division multiplexing using four-wave mixing,” Electron. Lett. 30(20), 1697–1698 (1994).
[CrossRef]

Kelley, P. L.

P. L. Kelley, “Self-Focusing of Optical Beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965).
[CrossRef]

Koonath, P.

Koos, C.

Larson, L. E.

A. E. Schmitz, R. H. Walden, L. E. Larson, S. E. Rosenbaum, R. A. Metzger, J. R. Behnke, P. A. Macdonald, “A deep-submicrometer microwave/digital CMOS/SOS technology,” IEEE Electron Device Lett. 12(1), 16–17 (1991).
[CrossRef]

Le, H. Q.

A. M. Darwish, E. P. Ippen, H. Q. Le, J. P. Donnelly, S. H. Groves, “Optimization of four‐wave mixing conversion efficiency in the presence of nonlinear loss,” Appl. Phys. Lett. 69(6), 737–739 (1996).
[CrossRef]

Lee, B.-T.

I.-H. Park, B.-T. Lee, S.-Y. Hahn, “Design sensitivity analysis for nonlinear magnetostatic problems using finite element method,” IEEE Trans. Magn. 28(2), 1533–1536 (1992).
[CrossRef]

Leuthold, J.

Li, X.

O. S. Ahmed, M. H. Bakr, X. Li, “An impulse sampling approach for efficient 3D TLM-based adjoint sensitivity analysis,” Prog. Electromagnetics Res. 142, 485–503 (2013).
[CrossRef]

O. S. Ahmed, M. H. Bakr, X. Li, T. Nomura, “A Time-Domain Adjoint Variable Method for Materials With Dispersive Constitutive Parameters,” IEEE Trans. Microw. Theory Tech. 60(10), 2959–2971 (2012).
[CrossRef]

O. S. Ahmed, M. H. Bakr, X. Li, “A memory-efficient implementation of TLM- based adjoint sensitivity analysis,” IEEE Trans. Antenn. Propag. 60(4), 2122–2125 (2012).
[CrossRef]

Lipparini, A.

V. Rizzoli, A. Costanzo, D. Masotti, A. Lipparini, F. Mastri, “Computer-aided optimization of nonlinear microwave circuits with the aid of electromagnetic simulation,” IEEE Trans. Microw. Theory Tech. 52(1), 362–377 (2004).
[CrossRef]

Lipson, M.

Lojek, B.

B. Lojek, “Sensitivity analysis of nonlinear circuits,” Electronic Circuits and Systems, IEE Proceedings 129(3), 85–88 (1982).
[CrossRef]

Lum, S.

S. Lum, M. Nakhla, Q.-J. Zhang, “Sensitivity analysis of lossy coupled transmission lines with nonlinear terminations,” IEEE Trans. Microw. Theory Tech. 42(4), 607–615 (1994).
[CrossRef]

Macdonald, P. A.

A. E. Schmitz, R. H. Walden, L. E. Larson, S. E. Rosenbaum, R. A. Metzger, J. R. Behnke, P. A. Macdonald, “A deep-submicrometer microwave/digital CMOS/SOS technology,” IEEE Electron Device Lett. 12(1), 16–17 (1991).
[CrossRef]

Madsen, K.

M. H. Bakr, J. W. Bandler, K. Madsen, J. E. Rayas-Sanchez, J. Sondergaard, “Space-mapping optimization of microwave circuits exploiting surrogate models,” IEEE Trans. Microw. Theory Tech. 48(12), 2297–2306 (2000).
[CrossRef]

Masotti, D.

V. Rizzoli, A. Costanzo, D. Masotti, A. Lipparini, F. Mastri, “Computer-aided optimization of nonlinear microwave circuits with the aid of electromagnetic simulation,” IEEE Trans. Microw. Theory Tech. 52(1), 362–377 (2004).
[CrossRef]

Mastri, F.

V. Rizzoli, A. Costanzo, D. Masotti, A. Lipparini, F. Mastri, “Computer-aided optimization of nonlinear microwave circuits with the aid of electromagnetic simulation,” IEEE Trans. Microw. Theory Tech. 52(1), 362–377 (2004).
[CrossRef]

Metzger, R. A.

A. E. Schmitz, R. H. Walden, L. E. Larson, S. E. Rosenbaum, R. A. Metzger, J. R. Behnke, P. A. Macdonald, “A deep-submicrometer microwave/digital CMOS/SOS technology,” IEEE Electron Device Lett. 12(1), 16–17 (1991).
[CrossRef]

Monro, T. M.

Murnane, M. M.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4(12), 822–832 (2010).
[CrossRef]

Nakhla, M.

S. Lum, M. Nakhla, Q.-J. Zhang, “Sensitivity analysis of lossy coupled transmission lines with nonlinear terminations,” IEEE Trans. Microw. Theory Tech. 42(4), 607–615 (1994).
[CrossRef]

M. Nakhla, J. Vlach, “A piecewise harmonic balance technique for determination of periodic response of nonlinear systems,” IEEE Trans. Circ. Syst. 23(2), 85–91 (1976).
[CrossRef]

Nakhla, M. S.

A. S. Saini, M. S. Nakhla, R. Achar, “Generalized time-domain adjoint sensitivity analysis of distributed MTL networks,” IEEE Trans. Microw. Theory Tech. 60(11), 3359–3368 (2012).
[CrossRef]

Nikolova, N. K.

M. H. Bakr, P. Zhao, N. K. Nikolova, “Adjoint first order sensitivities of transient responses and their applications in the solution of inverse problems,” IEEE Trans. Antenn. Propag. 57(7), 2137–2146 (2009).
[CrossRef]

P. A. W. Basl, M. H. Bakr, N. K. Nikolova, “Theory of self-adjoint S-parameter sensitivities for lossless nonhomogeneous transmission-line modeling problems,” IET Microwave Antennas Propag. 2(3), 211–220 (2008).
[CrossRef]

M. H. Bakr, N. K. Nikolova, P. A. W. Basl, “Self-Adjoint S-Parameter Sensitivities for Lossless Homogeneous TLM Problems,” International Journal of Numerical Modeling: Electronic Networks, Devices and Fields 18(6), 441–455 (2005).
[CrossRef]

M. H. Bakr, N. K. Nikolova, “An adjoint variable method for time-domain transmission line modeling with fixed structured grids,” IEEE Trans. Microw. Theory Tech. 52(2), 554–559 (2004).
[CrossRef]

Nomura, T.

O. S. Ahmed, M. H. Bakr, X. Li, T. Nomura, “A Time-Domain Adjoint Variable Method for Materials With Dispersive Constitutive Parameters,” IEEE Trans. Microw. Theory Tech. 60(10), 2959–2971 (2012).
[CrossRef]

Park, I.

Y. Chung, C. Cheon, I. Park, S. Hahn, “Optimal design method for microwave device using time domain method and design sensitivity analysis—Part II: FDTD case,” IEEE Trans. Magn. 37(5), 3255–3259 (2001).
[CrossRef]

Y. Chung, J. Ryu, C. Cheon, I. Park, S. Hahn, “Optimal design method for microwave device using time domain method and design sensitivity analysis—Part I: FETD case,” IEEE Trans. Magn. 37(5), 3289–3293 (2001).
[CrossRef]

Y. Chung, C. Cheon, I. Park, S. Hahn, “Optimal shape design of microwave device using FDTD and design sensitivity analysis,” IEEE Trans. Microw. Theory Tech. 48(12), 2289–2296 (2000).
[CrossRef]

Park, I.-H.

I.-H. Park, B.-T. Lee, S.-Y. Hahn, “Design sensitivity analysis for nonlinear magnetostatic problems using finite element method,” IEEE Trans. Magn. 28(2), 1533–1536 (1992).
[CrossRef]

Popmintchev, T.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4(12), 822–832 (2010).
[CrossRef]

Poulton, C.

Raghunathan, V.

Ranka, J. K.

Rayas-Sanchez, J. E.

J. E. Rayas-Sanchez, “EM-based optimization of microwave circuits using artificial neural networks: the state-of-the-art,” IEEE Trans. Microw. Theory Tech. 52(1), 420–435 (2004).
[CrossRef]

M. H. Bakr, J. W. Bandler, K. Madsen, J. E. Rayas-Sanchez, J. Sondergaard, “Space-mapping optimization of microwave circuits exploiting surrogate models,” IEEE Trans. Microw. Theory Tech. 48(12), 2297–2306 (2000).
[CrossRef]

Reinhard, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[CrossRef]

Richardson, D. J.

Rizzoli, V.

V. Rizzoli, A. Costanzo, D. Masotti, A. Lipparini, F. Mastri, “Computer-aided optimization of nonlinear microwave circuits with the aid of electromagnetic simulation,” IEEE Trans. Microw. Theory Tech. 52(1), 362–377 (2004).
[CrossRef]

Rosenbaum, S. E.

A. E. Schmitz, R. H. Walden, L. E. Larson, S. E. Rosenbaum, R. A. Metzger, J. R. Behnke, P. A. Macdonald, “A deep-submicrometer microwave/digital CMOS/SOS technology,” IEEE Electron Device Lett. 12(1), 16–17 (1991).
[CrossRef]

Russer, P.

P. Russer, N. Fichtner, “Nanoelectronics in radio-frequency technology,” IEEE Microw. Mag. 11(3), 119–135 (2010).
[CrossRef]

P. Russer, P. P. M. So, W. J. R. Hoefer, “Modeling of nonlinear active regions in TLM (distributed circuits),” IEEE Microw. Guided Wave Letts. 1(1), 10–13 (1991).
[CrossRef]

Ryu, J.

Y. Chung, J. Ryu, C. Cheon, I. Park, S. Hahn, “Optimal design method for microwave device using time domain method and design sensitivity analysis—Part I: FETD case,” IEEE Trans. Magn. 37(5), 3289–3293 (2001).
[CrossRef]

Saini, A. S.

A. S. Saini, M. S. Nakhla, R. Achar, “Generalized time-domain adjoint sensitivity analysis of distributed MTL networks,” IEEE Trans. Microw. Theory Tech. 60(11), 3359–3368 (2012).
[CrossRef]

Schmitz, A. E.

A. E. Schmitz, R. H. Walden, L. E. Larson, S. E. Rosenbaum, R. A. Metzger, J. R. Behnke, P. A. Macdonald, “A deep-submicrometer microwave/digital CMOS/SOS technology,” IEEE Electron Device Lett. 12(1), 16–17 (1991).
[CrossRef]

Simonsen, S. I.

S. A. Sørngård, S. I. Simonsen, J. P. Hansen, “High-order harmonic generation from graphene: Strong attosecond pulses with arbitrary polarization,” Phys. Rev. A 87(5), 053803 (2013).
[CrossRef]

So, P. P. M.

P. Russer, P. P. M. So, W. J. R. Hoefer, “Modeling of nonlinear active regions in TLM (distributed circuits),” IEEE Microw. Guided Wave Letts. 1(1), 10–13 (1991).
[CrossRef]

Sondergaard, J.

M. H. Bakr, J. W. Bandler, K. Madsen, J. E. Rayas-Sanchez, J. Sondergaard, “Space-mapping optimization of microwave circuits exploiting surrogate models,” IEEE Trans. Microw. Theory Tech. 48(12), 2297–2306 (2000).
[CrossRef]

Sørngård, S. A.

S. A. Sørngård, S. I. Simonsen, J. P. Hansen, “High-order harmonic generation from graphene: Strong attosecond pulses with arbitrary polarization,” Phys. Rev. A 87(5), 053803 (2013).
[CrossRef]

Stentz, A. J.

Taflove, A.

R. M. Joseph, A. Taflove, “FDTD Maxwell’s equations models for nonlinear electrodynamics and optics,” IEEE Trans. Antenn. Propag. 45(3), 364–374 (1997).
[CrossRef]

Taylor, J. R.

J. M. Dudley, J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fibre,” Nat. Photonics 3(2), 85–90 (2009).
[CrossRef]

Trahin, M.

Y. Gontier, M. Trahin, “Frequency conversion involving Raman-like processes above the ionization threshold,” IEEE J. Quantum Electron. 18(7), 1137–1145 (1982).
[CrossRef]

Turner, A. C.

Usechak, N.

R. Dekker, N. Usechak, M. Först, A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), R249–R271 (2007).
[CrossRef]

Vlach, J.

M. Nakhla, J. Vlach, “A piecewise harmonic balance technique for determination of periodic response of nonlinear systems,” IEEE Trans. Circ. Syst. 23(2), 85–91 (1976).
[CrossRef]

Volz, T.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[CrossRef]

Walden, R. H.

A. E. Schmitz, R. H. Walden, L. E. Larson, S. E. Rosenbaum, R. A. Metzger, J. R. Behnke, P. A. Macdonald, “A deep-submicrometer microwave/digital CMOS/SOS technology,” IEEE Electron Device Lett. 12(1), 16–17 (1991).
[CrossRef]

Wang, J.

Watanabe, K.

H. Igarashi, K. Watanabe, “Complex adjoint variable method for finite-element analysis of eddy current problems,” IEEE Trans. Magn. 46(8), 2739–2742 (2010).
[CrossRef]

Webb, J. P.

J. P. Webb, “Design sensitivity of frequency response in 3-D finite-element analysis of microwave devices,” IEEE Trans. Magn. 38(2), 1109–1112 (2002).
[CrossRef]

Windeler, R. S.

Winger, M.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[CrossRef]

Xu, J.

L. Zhang, J. Xu, M. C. E. Yagoub, R. Ding, Q.-J. Zhang, “Efficient analytical formulation and sensitivity analysis of neuro-space mapping for nonlinear microwave device modeling,” IEEE Trans. Microw. Theory Tech. 53(9), 2752–2767 (2005).
[CrossRef]

Yagoub, M. C. E.

L. Zhang, J. Xu, M. C. E. Yagoub, R. Ding, Q.-J. Zhang, “Efficient analytical formulation and sensitivity analysis of neuro-space mapping for nonlinear microwave device modeling,” IEEE Trans. Microw. Theory Tech. 53(9), 2752–2767 (2005).
[CrossRef]

Zhang, L.

L. Zhang, J. Xu, M. C. E. Yagoub, R. Ding, Q.-J. Zhang, “Efficient analytical formulation and sensitivity analysis of neuro-space mapping for nonlinear microwave device modeling,” IEEE Trans. Microw. Theory Tech. 53(9), 2752–2767 (2005).
[CrossRef]

Zhang, Q.-J.

L. Zhang, J. Xu, M. C. E. Yagoub, R. Ding, Q.-J. Zhang, “Efficient analytical formulation and sensitivity analysis of neuro-space mapping for nonlinear microwave device modeling,” IEEE Trans. Microw. Theory Tech. 53(9), 2752–2767 (2005).
[CrossRef]

S. Lum, M. Nakhla, Q.-J. Zhang, “Sensitivity analysis of lossy coupled transmission lines with nonlinear terminations,” IEEE Trans. Microw. Theory Tech. 42(4), 607–615 (1994).
[CrossRef]

Zhao, P.

M. H. Bakr, P. Zhao, N. K. Nikolova, “Adjoint first order sensitivities of transient responses and their applications in the solution of inverse problems,” IEEE Trans. Antenn. Propag. 57(7), 2137–2146 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

A. M. Darwish, E. P. Ippen, H. Q. Le, J. P. Donnelly, S. H. Groves, “Optimization of four‐wave mixing conversion efficiency in the presence of nonlinear loss,” Appl. Phys. Lett. 69(6), 737–739 (1996).
[CrossRef]

Electron. Lett. (1)

S. Kawanishi, O. Kamatani, “All-optical time division multiplexing using four-wave mixing,” Electron. Lett. 30(20), 1697–1698 (1994).
[CrossRef]

Electronic Circuits and Systems, IEE Proceedings (1)

B. Lojek, “Sensitivity analysis of nonlinear circuits,” Electronic Circuits and Systems, IEE Proceedings 129(3), 85–88 (1982).
[CrossRef]

IEEE Electron Device Lett. (1)

A. E. Schmitz, R. H. Walden, L. E. Larson, S. E. Rosenbaum, R. A. Metzger, J. R. Behnke, P. A. Macdonald, “A deep-submicrometer microwave/digital CMOS/SOS technology,” IEEE Electron Device Lett. 12(1), 16–17 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. Gontier, M. Trahin, “Frequency conversion involving Raman-like processes above the ionization threshold,” IEEE J. Quantum Electron. 18(7), 1137–1145 (1982).
[CrossRef]

IEEE Microw. Guided Wave Letts. (1)

P. Russer, P. P. M. So, W. J. R. Hoefer, “Modeling of nonlinear active regions in TLM (distributed circuits),” IEEE Microw. Guided Wave Letts. 1(1), 10–13 (1991).
[CrossRef]

IEEE Microw. Mag. (1)

P. Russer, N. Fichtner, “Nanoelectronics in radio-frequency technology,” IEEE Microw. Mag. 11(3), 119–135 (2010).
[CrossRef]

IEEE Trans. Antenn. Propag. (3)

O. S. Ahmed, M. H. Bakr, X. Li, “A memory-efficient implementation of TLM- based adjoint sensitivity analysis,” IEEE Trans. Antenn. Propag. 60(4), 2122–2125 (2012).
[CrossRef]

M. H. Bakr, P. Zhao, N. K. Nikolova, “Adjoint first order sensitivities of transient responses and their applications in the solution of inverse problems,” IEEE Trans. Antenn. Propag. 57(7), 2137–2146 (2009).
[CrossRef]

R. M. Joseph, A. Taflove, “FDTD Maxwell’s equations models for nonlinear electrodynamics and optics,” IEEE Trans. Antenn. Propag. 45(3), 364–374 (1997).
[CrossRef]

IEEE Trans. Circ. Syst. (1)

M. Nakhla, J. Vlach, “A piecewise harmonic balance technique for determination of periodic response of nonlinear systems,” IEEE Trans. Circ. Syst. 23(2), 85–91 (1976).
[CrossRef]

IEEE Trans. Magn. (5)

Y. Chung, J. Ryu, C. Cheon, I. Park, S. Hahn, “Optimal design method for microwave device using time domain method and design sensitivity analysis—Part I: FETD case,” IEEE Trans. Magn. 37(5), 3289–3293 (2001).
[CrossRef]

Y. Chung, C. Cheon, I. Park, S. Hahn, “Optimal design method for microwave device using time domain method and design sensitivity analysis—Part II: FDTD case,” IEEE Trans. Magn. 37(5), 3255–3259 (2001).
[CrossRef]

J. P. Webb, “Design sensitivity of frequency response in 3-D finite-element analysis of microwave devices,” IEEE Trans. Magn. 38(2), 1109–1112 (2002).
[CrossRef]

H. Igarashi, K. Watanabe, “Complex adjoint variable method for finite-element analysis of eddy current problems,” IEEE Trans. Magn. 46(8), 2739–2742 (2010).
[CrossRef]

I.-H. Park, B.-T. Lee, S.-Y. Hahn, “Design sensitivity analysis for nonlinear magnetostatic problems using finite element method,” IEEE Trans. Magn. 28(2), 1533–1536 (1992).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (9)

Y. Chung, C. Cheon, I. Park, S. Hahn, “Optimal shape design of microwave device using FDTD and design sensitivity analysis,” IEEE Trans. Microw. Theory Tech. 48(12), 2289–2296 (2000).
[CrossRef]

M. H. Bakr, J. W. Bandler, K. Madsen, J. E. Rayas-Sanchez, J. Sondergaard, “Space-mapping optimization of microwave circuits exploiting surrogate models,” IEEE Trans. Microw. Theory Tech. 48(12), 2297–2306 (2000).
[CrossRef]

L. Zhang, J. Xu, M. C. E. Yagoub, R. Ding, Q.-J. Zhang, “Efficient analytical formulation and sensitivity analysis of neuro-space mapping for nonlinear microwave device modeling,” IEEE Trans. Microw. Theory Tech. 53(9), 2752–2767 (2005).
[CrossRef]

M. H. Bakr, N. K. Nikolova, “An adjoint variable method for time-domain transmission line modeling with fixed structured grids,” IEEE Trans. Microw. Theory Tech. 52(2), 554–559 (2004).
[CrossRef]

O. S. Ahmed, M. H. Bakr, X. Li, T. Nomura, “A Time-Domain Adjoint Variable Method for Materials With Dispersive Constitutive Parameters,” IEEE Trans. Microw. Theory Tech. 60(10), 2959–2971 (2012).
[CrossRef]

J. E. Rayas-Sanchez, “EM-based optimization of microwave circuits using artificial neural networks: the state-of-the-art,” IEEE Trans. Microw. Theory Tech. 52(1), 420–435 (2004).
[CrossRef]

A. S. Saini, M. S. Nakhla, R. Achar, “Generalized time-domain adjoint sensitivity analysis of distributed MTL networks,” IEEE Trans. Microw. Theory Tech. 60(11), 3359–3368 (2012).
[CrossRef]

S. Lum, M. Nakhla, Q.-J. Zhang, “Sensitivity analysis of lossy coupled transmission lines with nonlinear terminations,” IEEE Trans. Microw. Theory Tech. 42(4), 607–615 (1994).
[CrossRef]

V. Rizzoli, A. Costanzo, D. Masotti, A. Lipparini, F. Mastri, “Computer-aided optimization of nonlinear microwave circuits with the aid of electromagnetic simulation,” IEEE Trans. Microw. Theory Tech. 52(1), 362–377 (2004).
[CrossRef]

IET Microwave Antennas Propag. (1)

P. A. W. Basl, M. H. Bakr, N. K. Nikolova, “Theory of self-adjoint S-parameter sensitivities for lossless nonhomogeneous transmission-line modeling problems,” IET Microwave Antennas Propag. 2(3), 211–220 (2008).
[CrossRef]

International Journal of Numerical Modeling: Electronic Networks, Devices and Fields (1)

M. H. Bakr, N. K. Nikolova, P. A. W. Basl, “Self-Adjoint S-Parameter Sensitivities for Lossless Homogeneous TLM Problems,” International Journal of Numerical Modeling: Electronic Networks, Devices and Fields 18(6), 441–455 (2005).
[CrossRef]

J. Phys. D Appl. Phys. (1)

R. Dekker, N. Usechak, M. Först, A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), R249–R271 (2007).
[CrossRef]

Nat. Photonics (3)

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, A. Imamoğlu, “Ultrafast all-optical switching by single photons,” Nat. Photonics 6(9), 607–609 (2012).
[CrossRef]

J. M. Dudley, J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fibre,” Nat. Photonics 3(2), 85–90 (2009).
[CrossRef]

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4(12), 822–832 (2010).
[CrossRef]

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. A (1)

S. A. Sørngård, S. I. Simonsen, J. P. Hansen, “High-order harmonic generation from graphene: Strong attosecond pulses with arbitrary polarization,” Phys. Rev. A 87(5), 053803 (2013).
[CrossRef]

Phys. Rev. Lett. (1)

P. L. Kelley, “Self-Focusing of Optical Beams,” Phys. Rev. Lett. 15(26), 1005–1008 (1965).
[CrossRef]

Prog. Electromagnetics Res. (1)

O. S. Ahmed, M. H. Bakr, X. Li, “An impulse sampling approach for efficient 3D TLM-based adjoint sensitivity analysis,” Prog. Electromagnetics Res. 142, 485–503 (2013).
[CrossRef]

Struct. Multidisc. Optim. (1)

J. S. Jensen, “Topology optimization of nonlinear optical devices,” Struct. Multidisc. Optim. 43(6), 731–743 (2011).
[CrossRef]

Other (5)

Optimetrics: parametrics and optimization using Ansoft HFSS,” Microwave Journal, (1999). [Online]. Available: http://www.microwavejournal.com/articles/2779-parametrics-and-optimization-using-ansoft-hfss . [Accessed 18 Nov. 2013].

Press Release, “Sensitivity analysis and adapted optimization strategies for CST MICROWAVE STUDIO transient solver,” May 2010. [Online]. Available: www.cst.com/Content/News/Documents/2010_5_Timedomain2011_web.pdf . [Accessed 23 Oct. 2013].

N. Camilleri, J. Costa, D. Lovelace, and D. Ngo, “Silicon MOSFETs, the microwave device technology for the 1990s,” in Microwave Symposium Digest, IEEE MTT-S International, (1993), pp. 545–548.
[CrossRef]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Efficient visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” in Summaries of Papers Presented at the Conference on Lasers and Electro-Optics, CLEO ’99 (1999), CPD8/1–CPD8/2.
[CrossRef]

S. A. Maas, Nonlinear microwave circuits. (IEEE, 1997).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

The RC circuit of example 1.

Fig. 2
Fig. 2

The original and adjoint responses of the circuit in Fig. 1 for the set of values R1 = 1000.0 Ω, R2 = 1000.0 Ω, and C = 60.0 µF.

Fig. 3
Fig. 3

The sensitivities of the objective function (21) with respect to the nonlinear coefficients of the resistor R2 (p0 and p2) for a sweep of the coefficient po with R1 = 1000.0 Ω, C = 10.0 µF, and p2 = 50.0 shown in (a) and (b) respectively; the sensitivities estimated using AVM ( + ) and sensitivities obtained using the central finite difference method (CFD) (o).

Fig. 4
Fig. 4

The sensitivities of the objective function (21) with respect to the circuit parameters C and R1 for a sweep of the parameter po with R1 = 1000.0 Ω, C = 10.0 µF, and p2 = 50.0 shown in (a) and (b) respectively; the sensitivities estimated using AVM ( + ) and sensitivities obtained using the central finite difference method (CFD) (o).

Fig. 5
Fig. 5

A nonlinear region in a parallel plate waveguide.

Fig. 6
Fig. 6

The adjoint sensitivities ( + ) as compared to the central finite difference (o) for a sweep of the parameter po for the microwave example.

Fig. 7
Fig. 7

The structure of the optical example.

Fig. 8
Fig. 8

The modal profile of the excitation used in the photonic example.

Fig. 9
Fig. 9

The adjoint sensitivities ( + ) as compared to the central finite difference (CFD) (o) for a sweep of the parameter p 0 ε for the photonic example.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

F= 0 T m Ω g(x,V)  dΩ dt= 0 T m G(x,V)   dt,
F x i = 0 T m e G x i dt+   0 T m ( G V ) T V x i  dt,
V k+1 =CS V k + V k s ,
λ k1 = S T C T λ k + V k s,λ ,  λ N T =0,
F x i e F x i  -Δt k λ k T Δ A i Δ x i V k , i=1,2,, n,
ε r = p 0 + p 1 E+ p 2 E 2 + p 3 E 3 ,
V k + ( V  t ) k ΔtCS V k + V k s .
V t = 1 Δt (CSI)V+ V s Δt .
2 V t x i = 1 Δt (C[ (S V ¯ ) p T p x i + (S V ¯ ) V T V x i +S V x i ] V x i ),
0 T m λ T [ 2 V t x i 1 Δt C[ (S V ¯ ) p T p x i + (S V ¯ ) V T V x i +S V x i ]+ 1 Δt V x i ]  dt=0.
0 T m ( λ T t +λ T [ 1 Δt C (S V ¯ ) V T + 1 Δt CS 1 Δt I ] ) V x i  dt=  0 T m λ T Δt C (S V ¯ ) p T p x i dt.
( λ T t +λ T [ 1 Δt C (S V ¯ ) V T + 1 Δt CS 1 Δt I ] )= G V T .
λ k1 = ( (S V ¯ ) V T +S ) T C T λ k Δt G V .
F x i = 0 T m e G x i dt 0 T m λ T C (S V ¯ ) p T p x i dt,  i=1,2,, n.
S n = ( (S V ¯ ) V T +S ) .
S n (j) = ( ( S (j) V ¯ (j) ) V (j)T + S (j) ), j=1,2,...,N.
J (j) = ( S (j) V ¯ (j) ) p (j)T
λ ˜ k = C T λ k
V c t = V S R 1 C ( R 1 + R 2 R 1 R 2 C ) V c .
R 2 = p o + p 2 V c 2 .
F= 0 T m ( V s (t) V c (t)) 2 dt = 0 T m ψ(t)dt .
λ t = λ S R 1 C [ ( R 1 + R 2 R 1 R 2 C )+ 1 C d d V c ( V ¯ c R 2 ) ]λ,
ε r = p o + p 1 E y + p 2 E y 2 ,
F= 0 T m Ω E y 2  dΩdt,
ε r = p 0 ε + p 1 ε E y + p 2 ε E y 2 ,
σ = p 2 σ E y 2 ,

Metrics