Abstract

Photonic crystals and optical bandgap structures, which facilitate high-precision control of electromagnetic-field propagation, are gaining ever-increasing attention in both scientific and commercial applications. One common photonic device is the distributed Bragg reflector (DBR), which exhibits high reflectivity at certain frequencies. Analysis of the transient interaction of an electromagnetic pulse with such a device can be formulated in terms of the time-domain volume integral equation and, in turn, solved numerically with the method of moments. Owing to the frequency-dependent reflectivity of such devices, the extent of field penetration into deep layers of the device will be different depending on the frequency content of the impinging pulse. We show how this phenomenon can be exploited to reduce the number of basis functions needed for the solution. To this end, we use spatiotemporal wavelet basis functions, which possess the multiresolution property in both spatial and temporal domains. To select the dominant functions in the solution, we use an iterative impedance matrix compression (IMC) procedure, which gradually constructs and solves a compressed version of the matrix equation until the desired degree of accuracy has been achieved. Results show that when the electromagnetic pulse is reflected, the transient IMC omits basis functions defined over the last layers of the DBR, as anticipated.

© 2004 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  27. Y. Shifman, Y. Leviatan, “On the use of spatiotemporal multiresolution analysis in method of moments solutions for the time-domain integral equation,” IEEE Trans. Antennas Propag. 49, 1123–1129 (2001).
    [CrossRef]
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    [CrossRef]
  36. S. J. Dodson, S. P. Walker, M. J. Bluck, “Implicitness and stability of time domain integral equation scattering analysis,” J. Appl. Comput. Electromag. Soc. 13, 291–301 (1998).
  37. Z. Baharav, Y. Leviatan, “Impedance matrix compression (IMC) using iteratively selected wavelet-basis,” IEEE Trans. Antennas Propag. 46, 226–233 (1998).
    [CrossRef]
  38. Z. Baharav, Y. Leviatan, “Wavelets in electromagnetics: the impedance matrix compression (IMC) method,” Int. J. Num. Model. 11, 69–84 (1998).
    [CrossRef]

2002 (5)

L. Shen, S. He, “Analysis for the convergence problem of the plane-wave expansion method for photonic crystals,” J. Opt. Soc. Am. A 19, 1021–1024 (2002).
[CrossRef]

O. Vanbesien, T. Akalin, J. Danglot, D. Lippens, “A highly directive dipole antenna embedded in a Fabry–Perot type cavity,” IEEE Microw. Wire. Compon. Lett. 12, 48–50 (2002).
[CrossRef]

A. Yariv, “Coupled-wave formalism for optical waveguiding by transverse Bragg reflection,” Opt. Lett. 27, 936–938 (2002).
[CrossRef]

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 286 modelling task,” Opt. Quantum Electron. 34, 445–470 (2002).
[CrossRef]

Y. Shifman, Y. Leviatan, “Analysis of transient interaction of electromagnetic pulse with an air layer in a dielectric medium using wavelet-based implicit tdie formulation,” IEEE Trans. Microwave Theory Tech. 50, 2018–2022 (2002).
[CrossRef]

2001 (1)

Y. Shifman, Y. Leviatan, “On the use of spatiotemporal multiresolution analysis in method of moments solutions for the time-domain integral equation,” IEEE Trans. Antennas Propag. 49, 1123–1129 (2001).
[CrossRef]

2000 (1)

B. Shanker, A. A. Ergin, K. Aygun, E. Michielssen, “Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time-domain algorithm,” IEEE Trans. Antennas Propag. 48, 510–523 (2000).
[CrossRef]

1999 (2)

A. A. Ergin, B. Shanker, E. Michielssen, “The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena,” IEEE Antennas Propag. Mag.August1999, pp. 39–52.

S. M. Rao, D. A. Vechinski, T. K. Sarkar, “Transient scattering by conducting cylinders—implicit solution for the transverse electric case,” Microwave Opt. Technol. Lett. 21, 129–134 (1999).
[CrossRef]

1998 (6)

S. M. Rao, T. K. Sarkar, “Transient analysis of electromagnetic scattering from wire structures utilizing an implicit time-domain integral-equation technique,” Microwave Opt. Technol. Lett. 17, 66–69 (1998).
[CrossRef]

M. D. Pocock, M. J. Bluck, S. P. Walker, “Electromagnetic scattering from 3-D curved dielectric bodies using time-domain integral equations,” IEEE Trans. Antennas Propag. 46, 1212–1219 (1998).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “Fast evaluation of three-dimensional transient wave fields using diagonal translation operators,” J. Comput. Phys. 146, 157–180 (1998).
[CrossRef]

S. J. Dodson, S. P. Walker, M. J. Bluck, “Implicitness and stability of time domain integral equation scattering analysis,” J. Appl. Comput. Electromag. Soc. 13, 291–301 (1998).

Z. Baharav, Y. Leviatan, “Impedance matrix compression (IMC) using iteratively selected wavelet-basis,” IEEE Trans. Antennas Propag. 46, 226–233 (1998).
[CrossRef]

Z. Baharav, Y. Leviatan, “Wavelets in electromagnetics: the impedance matrix compression (IMC) method,” Int. J. Num. Model. 11, 69–84 (1998).
[CrossRef]

1997 (1)

S. M. Rao, T. K. Sarkar, “Time-domain modeling of two-dimensional conducting cylinders utilizing an implicit scheme—TM incident,” Microwave Opt. Technol. Lett. 15, 342–347 (1997).
[CrossRef]

1996 (4)

P. J. Davies, “On the stability of time-marching schemes for the general surface electric-field integral equation,” IEEE Trans. Antennas Propag. 44, 1467–1473 (1996).
[CrossRef]

Z. Baharav, Y. Leviatan, “Impedance matrix compression with the use of wavelet expansions,” Microwave Opt. Technol. Lett. 12, 268–272 (1996).
[CrossRef]

Z. Baharav, Y. Leviatan, “Impedance matrix compression using adaptively-constructed basis functions,” IEEE Trans. Antennas Propag. 44, 1231–1238 (1996).
[CrossRef]

Z. Baharav, Y. Leviatan, “Impedance matrix compression (IMC) using iteratively selected wavelet basis for MFIE formulations,” Microwave Opt. Technol. Lett. 12, 145–150 (1996).
[CrossRef]

1994 (1)

E. K. Miller, “Time domain modeling in electromagnetics,” J. Electron. Waves Appl. 8, 1125–1172 (1994).
[CrossRef]

1992 (1)

D. A. Vechinski, S. M. Rao, “Transient scattering from two-dimensional dielectric cylinders and arbitrary shape,” IEEE Trans. Antennas Propag. 40, 1054–1060 (1992).
[CrossRef]

1986 (1)

S. M. Rao, T. K. Sarkar, S. A. Dianat, “A novel technique to the solution of transient electromagnetic scattering from thin wires,” IEEE Trans. Antennas Propag. AP-34, 630–634 (1986).
[CrossRef]

1984 (1)

S. M. Rao, T. K. Sarkar, S. A. Dianat, “The application of the conjugate gradient method to solution of transient electromagnetic scattering from thin wires,” Radio Sci. 19, 1319–1326 (1984).
[CrossRef]

Akalin, T.

O. Vanbesien, T. Akalin, J. Danglot, D. Lippens, “A highly directive dipole antenna embedded in a Fabry–Perot type cavity,” IEEE Microw. Wire. Compon. Lett. 12, 48–50 (2002).
[CrossRef]

Aygun, K.

B. Shanker, A. A. Ergin, K. Aygun, E. Michielssen, “Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time-domain algorithm,” IEEE Trans. Antennas Propag. 48, 510–523 (2000).
[CrossRef]

Baets, R.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 286 modelling task,” Opt. Quantum Electron. 34, 445–470 (2002).
[CrossRef]

Baharav, Z.

Z. Baharav, Y. Leviatan, “Impedance matrix compression (IMC) using iteratively selected wavelet-basis,” IEEE Trans. Antennas Propag. 46, 226–233 (1998).
[CrossRef]

Z. Baharav, Y. Leviatan, “Wavelets in electromagnetics: the impedance matrix compression (IMC) method,” Int. J. Num. Model. 11, 69–84 (1998).
[CrossRef]

Z. Baharav, Y. Leviatan, “Impedance matrix compression with the use of wavelet expansions,” Microwave Opt. Technol. Lett. 12, 268–272 (1996).
[CrossRef]

Z. Baharav, Y. Leviatan, “Impedance matrix compression using adaptively-constructed basis functions,” IEEE Trans. Antennas Propag. 44, 1231–1238 (1996).
[CrossRef]

Z. Baharav, Y. Leviatan, “Impedance matrix compression (IMC) using iteratively selected wavelet basis for MFIE formulations,” Microwave Opt. Technol. Lett. 12, 145–150 (1996).
[CrossRef]

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, 1989).

Bienstman, P.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 286 modelling task,” Opt. Quantum Electron. 34, 445–470 (2002).
[CrossRef]

Bluck, M. J.

M. D. Pocock, M. J. Bluck, S. P. Walker, “Electromagnetic scattering from 3-D curved dielectric bodies using time-domain integral equations,” IEEE Trans. Antennas Propag. 46, 1212–1219 (1998).
[CrossRef]

S. J. Dodson, S. P. Walker, M. J. Bluck, “Implicitness and stability of time domain integral equation scattering analysis,” J. Appl. Comput. Electromag. Soc. 13, 291–301 (1998).

Cangellaris, A.

W. Pinello, A. Ruehli, A. Cangellaris, “Stabilization of time domain solutions of EFIE based on partial element equivalent circuit models,” in Digest of IEEE–APS International Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 2, pp. 966–969.

Collin, R. E.

R. E. Collin, Foundations for Microwave Engineering, 2nd ed. (McGraw-Hill, New York, 1996).

Ctyroky, J.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 286 modelling task,” Opt. Quantum Electron. 34, 445–470 (2002).
[CrossRef]

Danglot, J.

O. Vanbesien, T. Akalin, J. Danglot, D. Lippens, “A highly directive dipole antenna embedded in a Fabry–Perot type cavity,” IEEE Microw. Wire. Compon. Lett. 12, 48–50 (2002).
[CrossRef]

Daubechies, I.

I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1992).

Davies, P. J.

P. J. Davies, “On the stability of time-marching schemes for the general surface electric-field integral equation,” IEEE Trans. Antennas Propag. 44, 1467–1473 (1996).
[CrossRef]

De La Rue, R. M.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 286 modelling task,” Opt. Quantum Electron. 34, 445–470 (2002).
[CrossRef]

De Ridder, R.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 286 modelling task,” Opt. Quantum Electron. 34, 445–470 (2002).
[CrossRef]

Dianat, S. A.

S. M. Rao, T. K. Sarkar, S. A. Dianat, “A novel technique to the solution of transient electromagnetic scattering from thin wires,” IEEE Trans. Antennas Propag. AP-34, 630–634 (1986).
[CrossRef]

S. M. Rao, T. K. Sarkar, S. A. Dianat, “The application of the conjugate gradient method to solution of transient electromagnetic scattering from thin wires,” Radio Sci. 19, 1319–1326 (1984).
[CrossRef]

Dodson, S. J.

S. J. Dodson, S. P. Walker, M. J. Bluck, “Implicitness and stability of time domain integral equation scattering analysis,” J. Appl. Comput. Electromag. Soc. 13, 291–301 (1998).

Ergin, A. A.

B. Shanker, A. A. Ergin, K. Aygun, E. Michielssen, “Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time-domain algorithm,” IEEE Trans. Antennas Propag. 48, 510–523 (2000).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena,” IEEE Antennas Propag. Mag.August1999, pp. 39–52.

A. A. Ergin, B. Shanker, E. Michielssen, “Fast evaluation of three-dimensional transient wave fields using diagonal translation operators,” J. Comput. Phys. 146, 157–180 (1998).
[CrossRef]

E. Michielssen, A. A. Ergin, B. Shanker, “Computational complexity and implementation of two-level plane wave time domain algorithm for scalar wave equation,” in Digest of IEEE-APS International Symposium (Institute of Electrical and Electronics Engineers, New York, 1998), pp. 944–947.

Garrett, J.

J. Garrett, A. Ruehli, C. Paul, “Stability improvements of integral equations,” in Digest of IEEE-APS International Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 3, pp. 1810–1813.

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

He, S.

Heiss, W.

G. Springholz, T. Schwarzl, W. Heiss, H. Seyringer, S. Lanzerstorfer, H. Krenn, “Fabrication of highly efficient mid-infrared Bragg mirrors from IV–VI semiconductors,” in Proceedings of Current Developments of Microelectronics (Society for Microelectronics, Bad Hofgastein, Austria, 1999), pp. 71–74.

Helfert, S.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 286 modelling task,” Opt. Quantum Electron. 34, 445–470 (2002).
[CrossRef]

Hugonin, J. P.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 286 modelling task,” Opt. Quantum Electron. 34, 445–470 (2002).
[CrossRef]

Klaasse, G.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 286 modelling task,” Opt. Quantum Electron. 34, 445–470 (2002).
[CrossRef]

Krenn, H.

G. Springholz, T. Schwarzl, W. Heiss, H. Seyringer, S. Lanzerstorfer, H. Krenn, “Fabrication of highly efficient mid-infrared Bragg mirrors from IV–VI semiconductors,” in Proceedings of Current Developments of Microelectronics (Society for Microelectronics, Bad Hofgastein, Austria, 1999), pp. 71–74.

Lalanne, P.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 286 modelling task,” Opt. Quantum Electron. 34, 445–470 (2002).
[CrossRef]

Lanzerstorfer, S.

G. Springholz, T. Schwarzl, W. Heiss, H. Seyringer, S. Lanzerstorfer, H. Krenn, “Fabrication of highly efficient mid-infrared Bragg mirrors from IV–VI semiconductors,” in Proceedings of Current Developments of Microelectronics (Society for Microelectronics, Bad Hofgastein, Austria, 1999), pp. 71–74.

Leviatan, Y.

Y. Shifman, Y. Leviatan, “Analysis of transient interaction of electromagnetic pulse with an air layer in a dielectric medium using wavelet-based implicit tdie formulation,” IEEE Trans. Microwave Theory Tech. 50, 2018–2022 (2002).
[CrossRef]

Y. Shifman, Y. Leviatan, “On the use of spatiotemporal multiresolution analysis in method of moments solutions for the time-domain integral equation,” IEEE Trans. Antennas Propag. 49, 1123–1129 (2001).
[CrossRef]

Z. Baharav, Y. Leviatan, “Impedance matrix compression (IMC) using iteratively selected wavelet-basis,” IEEE Trans. Antennas Propag. 46, 226–233 (1998).
[CrossRef]

Z. Baharav, Y. Leviatan, “Wavelets in electromagnetics: the impedance matrix compression (IMC) method,” Int. J. Num. Model. 11, 69–84 (1998).
[CrossRef]

Z. Baharav, Y. Leviatan, “Impedance matrix compression (IMC) using iteratively selected wavelet basis for MFIE formulations,” Microwave Opt. Technol. Lett. 12, 145–150 (1996).
[CrossRef]

Z. Baharav, Y. Leviatan, “Impedance matrix compression using adaptively-constructed basis functions,” IEEE Trans. Antennas Propag. 44, 1231–1238 (1996).
[CrossRef]

Z. Baharav, Y. Leviatan, “Impedance matrix compression with the use of wavelet expansions,” Microwave Opt. Technol. Lett. 12, 268–272 (1996).
[CrossRef]

Lippens, D.

O. Vanbesien, T. Akalin, J. Danglot, D. Lippens, “A highly directive dipole antenna embedded in a Fabry–Perot type cavity,” IEEE Microw. Wire. Compon. Lett. 12, 48–50 (2002).
[CrossRef]

Lu, M.

M. Lu, E. Michielssen, “Closed form evaluation of time domain fields due to rao-wilton-glisson sources for use in marching-on-in-time based EFIE solvers,” in Proceedings of 2002 IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 74–77.

Michielssen, E.

B. Shanker, A. A. Ergin, K. Aygun, E. Michielssen, “Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time-domain algorithm,” IEEE Trans. Antennas Propag. 48, 510–523 (2000).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena,” IEEE Antennas Propag. Mag.August1999, pp. 39–52.

A. A. Ergin, B. Shanker, E. Michielssen, “Fast evaluation of three-dimensional transient wave fields using diagonal translation operators,” J. Comput. Phys. 146, 157–180 (1998).
[CrossRef]

D. S. Weile, B. Shanker, E. Michielssen, “An accurate scheme for the numerical solution of the time domain electric field integral equation,” in Proceedings of 2001 IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 2001), Vol. 4, pp. 516–519.

M. Lu, E. Michielssen, “Closed form evaluation of time domain fields due to rao-wilton-glisson sources for use in marching-on-in-time based EFIE solvers,” in Proceedings of 2002 IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 74–77.

D. S. Weile, C. Nan-Wei, B. Shanker, E. Michielssen, “An accurate time-marching solution method for the electric field integral equation using a bandlimited extrapolator,” in Proceedings of 2002 IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 162–165.

E. Michielssen, A. A. Ergin, B. Shanker, “Computational complexity and implementation of two-level plane wave time domain algorithm for scalar wave equation,” in Digest of IEEE-APS International Symposium (Institute of Electrical and Electronics Engineers, New York, 1998), pp. 944–947.

Miller, E. K.

E. K. Miller, “Time domain modeling in electromagnetics,” J. Electron. Waves Appl. 8, 1125–1172 (1994).
[CrossRef]

Mittra, R.

R. Mittra, “Integral equation methods for transient scattering,” in Transient Electromagnetic Fields, Vol. 10 of Topics in Applied Physics, L. B. Felsen, ed. (Springer-Verlag, Berlin, 1976), pp. 73–128.
[CrossRef]

Nan-Wei, C.

D. S. Weile, C. Nan-Wei, B. Shanker, E. Michielssen, “An accurate time-marching solution method for the electric field integral equation using a bandlimited extrapolator,” in Proceedings of 2002 IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 162–165.

Nguyen, T.

G. Strang, T. Nguyen, Wavelets and Filter Banks (Wellesley–Cambridge Press, Wellesley, Mass., 1996).

Paul, C.

J. Garrett, A. Ruehli, C. Paul, “Stability improvements of integral equations,” in Digest of IEEE-APS International Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 3, pp. 1810–1813.

Petracek, J.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 286 modelling task,” Opt. Quantum Electron. 34, 445–470 (2002).
[CrossRef]

Pinello, W.

W. Pinello, A. Ruehli, A. Cangellaris, “Stabilization of time domain solutions of EFIE based on partial element equivalent circuit models,” in Digest of IEEE–APS International Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 2, pp. 966–969.

Pocock, M. D.

M. D. Pocock, M. J. Bluck, S. P. Walker, “Electromagnetic scattering from 3-D curved dielectric bodies using time-domain integral equations,” IEEE Trans. Antennas Propag. 46, 1212–1219 (1998).
[CrossRef]

Pregla, R.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 286 modelling task,” Opt. Quantum Electron. 34, 445–470 (2002).
[CrossRef]

Rao, S. M.

S. M. Rao, D. A. Vechinski, T. K. Sarkar, “Transient scattering by conducting cylinders—implicit solution for the transverse electric case,” Microwave Opt. Technol. Lett. 21, 129–134 (1999).
[CrossRef]

S. M. Rao, T. K. Sarkar, “Transient analysis of electromagnetic scattering from wire structures utilizing an implicit time-domain integral-equation technique,” Microwave Opt. Technol. Lett. 17, 66–69 (1998).
[CrossRef]

S. M. Rao, T. K. Sarkar, “Time-domain modeling of two-dimensional conducting cylinders utilizing an implicit scheme—TM incident,” Microwave Opt. Technol. Lett. 15, 342–347 (1997).
[CrossRef]

D. A. Vechinski, S. M. Rao, “Transient scattering from two-dimensional dielectric cylinders and arbitrary shape,” IEEE Trans. Antennas Propag. 40, 1054–1060 (1992).
[CrossRef]

S. M. Rao, T. K. Sarkar, S. A. Dianat, “A novel technique to the solution of transient electromagnetic scattering from thin wires,” IEEE Trans. Antennas Propag. AP-34, 630–634 (1986).
[CrossRef]

S. M. Rao, T. K. Sarkar, S. A. Dianat, “The application of the conjugate gradient method to solution of transient electromagnetic scattering from thin wires,” Radio Sci. 19, 1319–1326 (1984).
[CrossRef]

Ruehli, A.

W. Pinello, A. Ruehli, A. Cangellaris, “Stabilization of time domain solutions of EFIE based on partial element equivalent circuit models,” in Digest of IEEE–APS International Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 2, pp. 966–969.

J. Garrett, A. Ruehli, C. Paul, “Stability improvements of integral equations,” in Digest of IEEE-APS International Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 3, pp. 1810–1813.

Sarkar, T. K.

S. M. Rao, D. A. Vechinski, T. K. Sarkar, “Transient scattering by conducting cylinders—implicit solution for the transverse electric case,” Microwave Opt. Technol. Lett. 21, 129–134 (1999).
[CrossRef]

S. M. Rao, T. K. Sarkar, “Transient analysis of electromagnetic scattering from wire structures utilizing an implicit time-domain integral-equation technique,” Microwave Opt. Technol. Lett. 17, 66–69 (1998).
[CrossRef]

S. M. Rao, T. K. Sarkar, “Time-domain modeling of two-dimensional conducting cylinders utilizing an implicit scheme—TM incident,” Microwave Opt. Technol. Lett. 15, 342–347 (1997).
[CrossRef]

S. M. Rao, T. K. Sarkar, S. A. Dianat, “A novel technique to the solution of transient electromagnetic scattering from thin wires,” IEEE Trans. Antennas Propag. AP-34, 630–634 (1986).
[CrossRef]

S. M. Rao, T. K. Sarkar, S. A. Dianat, “The application of the conjugate gradient method to solution of transient electromagnetic scattering from thin wires,” Radio Sci. 19, 1319–1326 (1984).
[CrossRef]

Schwarzl, T.

G. Springholz, T. Schwarzl, W. Heiss, H. Seyringer, S. Lanzerstorfer, H. Krenn, “Fabrication of highly efficient mid-infrared Bragg mirrors from IV–VI semiconductors,” in Proceedings of Current Developments of Microelectronics (Society for Microelectronics, Bad Hofgastein, Austria, 1999), pp. 71–74.

Seyringer, H.

G. Springholz, T. Schwarzl, W. Heiss, H. Seyringer, S. Lanzerstorfer, H. Krenn, “Fabrication of highly efficient mid-infrared Bragg mirrors from IV–VI semiconductors,” in Proceedings of Current Developments of Microelectronics (Society for Microelectronics, Bad Hofgastein, Austria, 1999), pp. 71–74.

Shanker, B.

B. Shanker, A. A. Ergin, K. Aygun, E. Michielssen, “Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time-domain algorithm,” IEEE Trans. Antennas Propag. 48, 510–523 (2000).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena,” IEEE Antennas Propag. Mag.August1999, pp. 39–52.

A. A. Ergin, B. Shanker, E. Michielssen, “Fast evaluation of three-dimensional transient wave fields using diagonal translation operators,” J. Comput. Phys. 146, 157–180 (1998).
[CrossRef]

E. Michielssen, A. A. Ergin, B. Shanker, “Computational complexity and implementation of two-level plane wave time domain algorithm for scalar wave equation,” in Digest of IEEE-APS International Symposium (Institute of Electrical and Electronics Engineers, New York, 1998), pp. 944–947.

D. S. Weile, B. Shanker, E. Michielssen, “An accurate scheme for the numerical solution of the time domain electric field integral equation,” in Proceedings of 2001 IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 2001), Vol. 4, pp. 516–519.

D. S. Weile, C. Nan-Wei, B. Shanker, E. Michielssen, “An accurate time-marching solution method for the electric field integral equation using a bandlimited extrapolator,” in Proceedings of 2002 IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 162–165.

Shen, L.

Shifman, Y.

Y. Shifman, Y. Leviatan, “Analysis of transient interaction of electromagnetic pulse with an air layer in a dielectric medium using wavelet-based implicit tdie formulation,” IEEE Trans. Microwave Theory Tech. 50, 2018–2022 (2002).
[CrossRef]

Y. Shifman, Y. Leviatan, “On the use of spatiotemporal multiresolution analysis in method of moments solutions for the time-domain integral equation,” IEEE Trans. Antennas Propag. 49, 1123–1129 (2001).
[CrossRef]

Y. Shifman, “Spatio-temporal multiresolution analysis for efficient method of moments solutions of transient electro-magnetic wave scattering,” Ph.D. thesis (Technion–Israel Institute of Technology, Haifa, Israel, 2002).

Springholz, G.

G. Springholz, T. Schwarzl, W. Heiss, H. Seyringer, S. Lanzerstorfer, H. Krenn, “Fabrication of highly efficient mid-infrared Bragg mirrors from IV–VI semiconductors,” in Proceedings of Current Developments of Microelectronics (Society for Microelectronics, Bad Hofgastein, Austria, 1999), pp. 71–74.

Stoffer, R.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 286 modelling task,” Opt. Quantum Electron. 34, 445–470 (2002).
[CrossRef]

Strang, G.

G. Strang, T. Nguyen, Wavelets and Filter Banks (Wellesley–Cambridge Press, Wellesley, Mass., 1996).

Vanbesien, O.

O. Vanbesien, T. Akalin, J. Danglot, D. Lippens, “A highly directive dipole antenna embedded in a Fabry–Perot type cavity,” IEEE Microw. Wire. Compon. Lett. 12, 48–50 (2002).
[CrossRef]

Vechinski, D. A.

S. M. Rao, D. A. Vechinski, T. K. Sarkar, “Transient scattering by conducting cylinders—implicit solution for the transverse electric case,” Microwave Opt. Technol. Lett. 21, 129–134 (1999).
[CrossRef]

D. A. Vechinski, S. M. Rao, “Transient scattering from two-dimensional dielectric cylinders and arbitrary shape,” IEEE Trans. Antennas Propag. 40, 1054–1060 (1992).
[CrossRef]

Walker, S. P.

M. D. Pocock, M. J. Bluck, S. P. Walker, “Electromagnetic scattering from 3-D curved dielectric bodies using time-domain integral equations,” IEEE Trans. Antennas Propag. 46, 1212–1219 (1998).
[CrossRef]

S. J. Dodson, S. P. Walker, M. J. Bluck, “Implicitness and stability of time domain integral equation scattering analysis,” J. Appl. Comput. Electromag. Soc. 13, 291–301 (1998).

Weile, D. S.

D. S. Weile, C. Nan-Wei, B. Shanker, E. Michielssen, “An accurate time-marching solution method for the electric field integral equation using a bandlimited extrapolator,” in Proceedings of 2002 IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 162–165.

D. S. Weile, B. Shanker, E. Michielssen, “An accurate scheme for the numerical solution of the time domain electric field integral equation,” in Proceedings of 2001 IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 2001), Vol. 4, pp. 516–519.

Yariv, A.

IEEE Antennas Propag. Mag. (1)

A. A. Ergin, B. Shanker, E. Michielssen, “The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena,” IEEE Antennas Propag. Mag.August1999, pp. 39–52.

IEEE Microw. Wire. Compon. Lett. (1)

O. Vanbesien, T. Akalin, J. Danglot, D. Lippens, “A highly directive dipole antenna embedded in a Fabry–Perot type cavity,” IEEE Microw. Wire. Compon. Lett. 12, 48–50 (2002).
[CrossRef]

IEEE Trans. Antennas Propag. (8)

B. Shanker, A. A. Ergin, K. Aygun, E. Michielssen, “Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time-domain algorithm,” IEEE Trans. Antennas Propag. 48, 510–523 (2000).
[CrossRef]

D. A. Vechinski, S. M. Rao, “Transient scattering from two-dimensional dielectric cylinders and arbitrary shape,” IEEE Trans. Antennas Propag. 40, 1054–1060 (1992).
[CrossRef]

P. J. Davies, “On the stability of time-marching schemes for the general surface electric-field integral equation,” IEEE Trans. Antennas Propag. 44, 1467–1473 (1996).
[CrossRef]

M. D. Pocock, M. J. Bluck, S. P. Walker, “Electromagnetic scattering from 3-D curved dielectric bodies using time-domain integral equations,” IEEE Trans. Antennas Propag. 46, 1212–1219 (1998).
[CrossRef]

S. M. Rao, T. K. Sarkar, S. A. Dianat, “A novel technique to the solution of transient electromagnetic scattering from thin wires,” IEEE Trans. Antennas Propag. AP-34, 630–634 (1986).
[CrossRef]

Z. Baharav, Y. Leviatan, “Impedance matrix compression using adaptively-constructed basis functions,” IEEE Trans. Antennas Propag. 44, 1231–1238 (1996).
[CrossRef]

Y. Shifman, Y. Leviatan, “On the use of spatiotemporal multiresolution analysis in method of moments solutions for the time-domain integral equation,” IEEE Trans. Antennas Propag. 49, 1123–1129 (2001).
[CrossRef]

Z. Baharav, Y. Leviatan, “Impedance matrix compression (IMC) using iteratively selected wavelet-basis,” IEEE Trans. Antennas Propag. 46, 226–233 (1998).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

Y. Shifman, Y. Leviatan, “Analysis of transient interaction of electromagnetic pulse with an air layer in a dielectric medium using wavelet-based implicit tdie formulation,” IEEE Trans. Microwave Theory Tech. 50, 2018–2022 (2002).
[CrossRef]

Int. J. Num. Model. (1)

Z. Baharav, Y. Leviatan, “Wavelets in electromagnetics: the impedance matrix compression (IMC) method,” Int. J. Num. Model. 11, 69–84 (1998).
[CrossRef]

J. Appl. Comput. Electromag. Soc. (1)

S. J. Dodson, S. P. Walker, M. J. Bluck, “Implicitness and stability of time domain integral equation scattering analysis,” J. Appl. Comput. Electromag. Soc. 13, 291–301 (1998).

J. Comput. Phys. (1)

A. A. Ergin, B. Shanker, E. Michielssen, “Fast evaluation of three-dimensional transient wave fields using diagonal translation operators,” J. Comput. Phys. 146, 157–180 (1998).
[CrossRef]

J. Electron. Waves Appl. (1)

E. K. Miller, “Time domain modeling in electromagnetics,” J. Electron. Waves Appl. 8, 1125–1172 (1994).
[CrossRef]

J. Opt. Soc. Am. A (1)

Microwave Opt. Technol. Lett. (5)

S. M. Rao, T. K. Sarkar, “Time-domain modeling of two-dimensional conducting cylinders utilizing an implicit scheme—TM incident,” Microwave Opt. Technol. Lett. 15, 342–347 (1997).
[CrossRef]

Z. Baharav, Y. Leviatan, “Impedance matrix compression with the use of wavelet expansions,” Microwave Opt. Technol. Lett. 12, 268–272 (1996).
[CrossRef]

Z. Baharav, Y. Leviatan, “Impedance matrix compression (IMC) using iteratively selected wavelet basis for MFIE formulations,” Microwave Opt. Technol. Lett. 12, 145–150 (1996).
[CrossRef]

S. M. Rao, T. K. Sarkar, “Transient analysis of electromagnetic scattering from wire structures utilizing an implicit time-domain integral-equation technique,” Microwave Opt. Technol. Lett. 17, 66–69 (1998).
[CrossRef]

S. M. Rao, D. A. Vechinski, T. K. Sarkar, “Transient scattering by conducting cylinders—implicit solution for the transverse electric case,” Microwave Opt. Technol. Lett. 21, 129–134 (1999).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets, R. De Ridder, R. Stoffer, G. Klaasse, J. Petracek, P. Lalanne, J. P. Hugonin, R. M. De La Rue, “Bragg waveguide grating as 1D photonic band gap structure: COST 286 modelling task,” Opt. Quantum Electron. 34, 445–470 (2002).
[CrossRef]

Radio Sci. (1)

S. M. Rao, T. K. Sarkar, S. A. Dianat, “The application of the conjugate gradient method to solution of transient electromagnetic scattering from thin wires,” Radio Sci. 19, 1319–1326 (1984).
[CrossRef]

Other (14)

G. Springholz, T. Schwarzl, W. Heiss, H. Seyringer, S. Lanzerstorfer, H. Krenn, “Fabrication of highly efficient mid-infrared Bragg mirrors from IV–VI semiconductors,” in Proceedings of Current Developments of Microelectronics (Society for Microelectronics, Bad Hofgastein, Austria, 1999), pp. 71–74.

J. Garrett, A. Ruehli, C. Paul, “Stability improvements of integral equations,” in Digest of IEEE-APS International Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 3, pp. 1810–1813.

W. Pinello, A. Ruehli, A. Cangellaris, “Stabilization of time domain solutions of EFIE based on partial element equivalent circuit models,” in Digest of IEEE–APS International Symposium (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 2, pp. 966–969.

E. Michielssen, A. A. Ergin, B. Shanker, “Computational complexity and implementation of two-level plane wave time domain algorithm for scalar wave equation,” in Digest of IEEE-APS International Symposium (Institute of Electrical and Electronics Engineers, New York, 1998), pp. 944–947.

D. S. Weile, B. Shanker, E. Michielssen, “An accurate scheme for the numerical solution of the time domain electric field integral equation,” in Proceedings of 2001 IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 2001), Vol. 4, pp. 516–519.

D. S. Weile, C. Nan-Wei, B. Shanker, E. Michielssen, “An accurate time-marching solution method for the electric field integral equation using a bandlimited extrapolator,” in Proceedings of 2002 IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 162–165.

M. Lu, E. Michielssen, “Closed form evaluation of time domain fields due to rao-wilton-glisson sources for use in marching-on-in-time based EFIE solvers,” in Proceedings of 2002 IEEE Antennas and Propagation Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 74–77.

I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1992).

G. Strang, T. Nguyen, Wavelets and Filter Banks (Wellesley–Cambridge Press, Wellesley, Mass., 1996).

Y. Shifman, “Spatio-temporal multiresolution analysis for efficient method of moments solutions of transient electro-magnetic wave scattering,” Ph.D. thesis (Technion–Israel Institute of Technology, Haifa, Israel, 2002).

R. E. Collin, Foundations for Microwave Engineering, 2nd ed. (McGraw-Hill, New York, 1996).

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, 1989).

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

R. Mittra, “Integral equation methods for transient scattering,” in Transient Electromagnetic Fields, Vol. 10 of Topics in Applied Physics, L. B. Felsen, ed. (Springer-Verlag, Berlin, 1976), pp. 73–128.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Scattering of an electromagnetic plane wave by a DBR.

Fig. 2
Fig. 2

Transient interaction of a Gaussian electromagnetic pulse with a DBR at various time instances. The dashed curves represent the field obtained after three IMC iterations, and the solid curves represent the reference solution.

Fig. 3
Fig. 3

Transient interaction of a Gaussian electromagnetic pulse with a DBR at various time instances. The dashed curves represent the field obtained after three IMC iterations, and the solid curves represent the reference solution.

Fig. 4
Fig. 4

Transient interaction of a Gaussian electromagnetic pulse with a DBR at various time instances. The dashed curves represent the field obtained after six IMC iterations, and the solid curves represent the reference solution.

Fig. 5
Fig. 5

Transient interaction of a Gaussian electromagnetic pulse with a DBR at various time instances. The dashed curves represent the field obtained after six IMC iterations, and the solid curves represent the reference solution.

Fig. 6
Fig. 6

Haar spatiotemporal basis functions selected with the iterative IMC procedure to span the field in the dielectric sections of the DBR after (a) three and (b) six iterations.

Fig. 7
Fig. 7

Normalized error versus compression ratio.

Fig. 8
Fig. 8

Compression ratio as a function of maximum number of possible unknowns. Compression ratios were computed at the indicated normalized error levels.

Fig. 9
Fig. 9

Normalized error in the solution of the DBR problem as a function of time of execution, as obtained with the iterative IMC (solid curve), and the CG procedure (dashed curve).

Equations (20)

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

Einc(z, t)=xˆExinc(z, t)=xˆE0incexp-τΔT2cos(ω0τ),
τ=t-td-z/c,
Jxe(z, t)=(ε-ε0)tExd(z, t),    zD,    t,
D={z|(dd+da)×(j-1)z(dd+da)(j-1)+dd}j=1Nel.
LVIE{Exd(z, t)}=Exinc(z, t),    zD,    t,
LVIE{Ψ(z, t)}Ψ(z, t)+μ0c0(ε-ε0)2×zDdzτΨ(z, τ)|τ=t-|z-z|/c0,zD,    t.
Exd(z, t)=n=1NSp=1NTanpUn(z)Tp(t),    zD,    t,
{WmU(z)}m=1MS,    MSNS,
{WqT(t)}q=1MT,    MTNT,
ZM×NIN×1=VM×1,
M=MT×MS,
N=NT×NS,
Zij=WmU(z), WqT(t), LVIE{Un(z)Tp(t)},i=m+(q-1)×MS,j=n+(p-1)×NS,
Ij=anp,    j=n+(p-1)×NS,
Vi=WmU(z), WqT(t), Exinc(z, t),i=m+(q-1)×MS.
Exa(z, t)=Exinc(z, t)-μ0c0(ε-ε0)2×zDdzτExd(z, τ)|τ=t-|z-z|/c0,
Ex(z, t)=Exa(z, t)zDExd(z, t)zD,    t.
compression ratio=1-M(l)×N(l)M×N,
ΔEx(l)=Ex(l)(z, t)-ExREF(z, t)2ExREF(z, t)2,
Ψ(z, t)2=z0z1dztstarttenddt|Ψ(z, t)|2(z1-z0)×(tend-tstart)1/2,

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