Abstract

The present contribution is concerned with applying beam-type expansion to a planar aperture time-dependent (TD) electromagnetic field in which the propagating elements, the electromagnetic pulsed-beams, are a priori decomposed into transverse electric (TE) and transverse magnetic (TM) field polarizations. The propagating field is described as a discrete superposition of tilted, shifted, and delayed TE and TM electromagnetic pulsed-beam propagators over the frame spectral lattice. These waveobjects are evaluated by using TD plane-wave spectral representations. Explicit asymptotic expressions for electromagnetic isodiffracting pulsed-quadratic beam propagators are presented, as well as a numerical example.

© 2012 Optical Society of America

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  1. B. Steinberg, E. Heyman, and L. Felsen, “Phase space beam summation for time-harmonic radiation from large apertures,” J. Opt. Soc. Am. A 8, 41–59 (1991).
    [CrossRef]
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    [CrossRef]
  3. A. Shlivinski, E. Heyman, A. Boag, and C. Letrou, “A phase-space beam summation formulation for ultra wideband radiation,” IEEE Trans. Antennas Propag. 52, 2042–2056 (2004).
    [CrossRef]
  4. A. Shlivinski, E. Heyman, and A. Boag, “A phase-space beam summation formulation for ultrawide-band radiation—Part II: A multiband scheme,” IEEE Trans. Antennas Propag. 53, 948–957 (2005).
    [CrossRef]
  5. M. Katsav and E. Heyman, “Phase space Gaussian beam summation analysis of half plane diffraction,” IEEE Trans. Antennas Propag. 55, 1535–1545 (2007).
    [CrossRef]
  6. B. Steinberg, E. Heyman, and L. Felsen, “Phase space beam summation for time dependent radiation from large apertures: continuous parametrization,” J. Opt. Soc. Am. A 8, 943–958 (1991).
    [CrossRef]
  7. T. Melamed, “Phase-space beam summation: a local spectrum analysis for time-dependent radiation,” J. Electromagn. Waves Appl. 11, 739–773 (1997).
    [CrossRef]
  8. A. Shlivinski, E. Heyman, and A. Boag, “A pulsed beam summation formulation for short pulse radiation based on windowed Radon transform (WRT) frames,” IEEE Trans. Antennas Propag. 53, 3030–3048 (2005).
    [CrossRef]
  9. A. Shlivinski and E. Heyman, “Windowed Radon transform frames,” Appl. Comput. Harmon. Anal. 26, 322–343 (2009).
    [CrossRef]
  10. Y. Gluk and E. Heyman, “Pulsed beams expansion algorithms for time-dependent point-source radiation. A basic algorithm and a standard-pulsed-beams algorithm,” IEEE Trans. Antennas Propag. 59, 1356–1371 (2011).
    [CrossRef]
  11. Y. Hadad and T. Melamed, “Non-orthogonal domain parabolic equation and its Gaussian beam solutions,” IEEE Trans. Antennas Propag. 58, 1164–1172 (2010).
    [CrossRef]
  12. Y. Hadad and T. Melamed, “Parameterization of the tilted Gaussian beam waveobjects,” Prog. Electromagn. Res. 102, 65–80 (2010).
    [CrossRef]
  13. Y. Hadad and T. Melamed, “Time-dependent tilted pulsed-beams and their properties,” IEEE Trans. Antennas Propag. 59, 3855–3862 (2011).
    [CrossRef]
  14. S. Shin and L. Felsen, “Gaussian beams in anisotropic media,” Appl. Phys. 5, 239–250 (1974).
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  17. I. Tinkelman and T. Melamed, “Local spectrum analysis of field propagation in anisotropic media. Part I—Time-harmonic fields,” J. Opt. Soc. Am. A 22, 1200–1207 (2005).
    [CrossRef]
  18. I. Tinkelman and T. Melamed, “Local spectrum analysis of field propagation in anisotropic media. Part II—Time-dependent fields,” J. Opt. Soc. Am. A 22, 1208–1215 (2005).
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  19. T. Melamed and L. Felsen, “Pulsed beam propagation in lossless dispersive media. Part I: Theory,” J. Opt. Soc. Am. A 15, 1268–1276 (1998).
    [CrossRef]
  20. T. Melamed and L. Felsen, “Pulsed beam propagation in lossless dispersive media. Part II: A numerical example,” J. Opt. Soc. Am. A 15, 1277–1284 (1998).
    [CrossRef]
  21. T. Melamed and L. B. Felsen, “Pulsed beam propagation in dispersive media via pulsed plane wave spectral decomposition,” IEEE Trans. Antennas Propag. 48, 901–908 (2000).
    [CrossRef]
  22. V. Ĉerveny, M. M. Popov, and I. Pŝenĉik, “Computation of wave fields in inhomogeneous media—Gaussian beam approach,” Geophys. J. Roy. Astron. Soc 70, 109–128 (1982).
    [CrossRef]
  23. B. W. A. N. Norris and J. Schrieffer, “Gaussian wave packets in inhomogeneous media with curved interfaces,” Proc. R. Soc. Lond. 412, 93–123 (1987).
    [CrossRef]
  24. E. Heyman, “Pulsed beam propagation in an inhomogeneous medium,” IEEE Trans. Antennas Propag. 42, 311–319 (1994).
    [CrossRef]
  25. F. Bass and L. Resnick, “Wave beam propagation in layered media,” Prog. Electromagn. Res. 38, 111–123 (2002).
    [CrossRef]
  26. T. Melamed, “Phase-space Green’s functions for modeling time-harmonic scattering from smooth inhomogeneous objects,” J. Math. Phys. 45, 2232–2246 (2004).
    [CrossRef]
  27. T. Melamed, “Time-domain phase-space Green’s functions for inhomogeneous media,” in Ultrawideband/Short Pulse Electromagnetics 6, E. L. Mokole, M. Kragalott, K. R. Gerlach, M. Kragalott, and K. R. Gerlach, eds. (Springer-Verlag, 2007), pp. 56–63.
  28. Y. Hadad and T. Melamed, “Tilted Gaussian beam propagation in inhomogeneous media,” J. Opt. Soc. Am. A 27, 1840–1850 (2010).
    [CrossRef]
  29. H. Chou, P. Pathak, and R. Burkholder, “Application of Gaussian-ray basis functions for the rapid analysis of electromagnetic radiation from reflector antennas,” IEE Proc. Microw. Antennas Propag. 150, 177–183 (2003).
    [CrossRef]
  30. H. Chou, P. Pathak, and R. Burkholder, “Novel Gaussian beam method for the rapid analysis of large reflector antennas,” IEEE Trans. Antennas Propag. 49, 880–893 (2001).
    [CrossRef]
  31. H.-T. Chou and P. Pathak, “Fast Gaussian beam based synthesis of shaped reflector antennas for contoured beam applications,” IEE Proc. Microw. Antennas Propag. 151, 13–20 (2004).
    [CrossRef]
  32. R. Collin, “Scattering of an incident Gaussian beam by a perfectly conducting rough surface,” IEEE Trans. Antennas Propag. 42, 70–74 (1994).
    [CrossRef]
  33. O. Kilic and R. Lang, “Scattering of a pulsed beam by a random medium over ground,” J. Electromagn. Waves Appl. 15, 481–516 (2001).
    [CrossRef]
  34. G. Gordon, E. Heyman, and R. Mazar, “A phase-space Gaussian beam summation representation of rough surface scattering,” J. Acoust. Soc. Am. 117, 1911–1921 (2005).
    [CrossRef]
  35. G. Gordon, E. Heyman, and R. Mazar, “Phase space beam summation analysis of rough surface waveguide,” J. Acoust. Soc. Am. 117, 1922–1932 (2005).
    [CrossRef]
  36. T. Melamed, E. Heyman, and L. Felsen, “Local spectral analysis of short-pulse-excited scattering from weakly inhomogenous media: Part I–forward scattering,” IEEE Trans. Antennas Propag. 47, 1208–1217 (1999).
    [CrossRef]
  37. T. Melamed, E. Heyman, and L. Felsen, “Local spectral analysis of short-pulse-excited scattering from weakly inhomogeneous media: Part II–inverse scattering,” IEEE Trans. Antennas Propag. 47, 1218–1227 (1999).
    [CrossRef]
  38. V. Galdi, H. Feng, D. Castanon, W. Karl, and L. Felsen, “Moderately rough surface underground imaging via short-pulse quasi-ray Gaussian beams,” IEEE Trans. Antennas Propag. 51, 2304–2318 (2003).
    [CrossRef]
  39. T. Melamed, “On localization aspects of frequency-domain cattering from low-contrast objects,” IEEE Antennas Wireless Propag. Lett. 2, 40–42 (2003).
    [CrossRef]
  40. R. Nowack, S. Dasgupta, G. Schuster, and J.-M. Sheng, “Correlation migration using Gaussian beams of scattered teleseismic body waves,” Bull. Seismol. Soc. Am. 96, 1–10(2006).
    [CrossRef]
  41. M. Popov, N. Semtchenok, P. Popov, and A. Verdel, “Depth migration by the Gaussian beam summation method,” Geophysics 75, S81–S93 (2010).
    [CrossRef]
  42. N. Bleistein and S. Gray, “Amplitude calculations for 3D Gaussian beam migration using complex-valued traveltimes,” Inverse Probl. 26, 085017 (2010).
    [CrossRef]
  43. T. Melamed, “TE and TM beam decomposition of time-harmonic electromagnetic waves,” J. Opt. Soc. Am. A 28, 401–409(2011).
    [CrossRef]
  44. E. Heyman and T. Melamed, “Certain considerations in aperture synthesis of ultrawideband/short-pulse radiation,” IEEE Trans. Antennas Propag. 42, 518–525 (1994).
    [CrossRef]
  45. T. Melamed, “Exact Gaussian beam expansion of time-harmonic electromagnetic waves,” J. Electromagn. Waves Appl. 23, 975–986 (2009).
    [CrossRef]
  46. T. Melamed, “Pulsed beam expansion of electromagnetic aperture fields,” Prog. Electromagn. Res. 114, 317–332(2011).
    [CrossRef]
  47. E. Heyman and T. Melamed, Space-Time Representation of Ultra Wideband Signals (Elsevier, 1998), pp. 1–63.
  48. C. Chapman, “A new method for computing synthetic seismograms,” Geophys. J. Roy. Astron. Soc. 54, 481–518 (1978).
    [CrossRef]
  49. R. Martínez-Herrero, P. Mejías, S. Bosch, and A. Carnicer, “Vectorial structure of nonparaxial electromagnetic beams,” J. Opt. Soc. Am. A 18, 1678–1680 (2001).
    [CrossRef]
  50. E. Heyman and L. Felsen, “Complex source pulsed beam fields,” J. Opt. Soc. Am. A 6, 806–817 (1989).
    [CrossRef]

2011 (4)

Y. Gluk and E. Heyman, “Pulsed beams expansion algorithms for time-dependent point-source radiation. A basic algorithm and a standard-pulsed-beams algorithm,” IEEE Trans. Antennas Propag. 59, 1356–1371 (2011).
[CrossRef]

Y. Hadad and T. Melamed, “Time-dependent tilted pulsed-beams and their properties,” IEEE Trans. Antennas Propag. 59, 3855–3862 (2011).
[CrossRef]

T. Melamed, “TE and TM beam decomposition of time-harmonic electromagnetic waves,” J. Opt. Soc. Am. A 28, 401–409(2011).
[CrossRef]

T. Melamed, “Pulsed beam expansion of electromagnetic aperture fields,” Prog. Electromagn. Res. 114, 317–332(2011).
[CrossRef]

2010 (5)

M. Popov, N. Semtchenok, P. Popov, and A. Verdel, “Depth migration by the Gaussian beam summation method,” Geophysics 75, S81–S93 (2010).
[CrossRef]

N. Bleistein and S. Gray, “Amplitude calculations for 3D Gaussian beam migration using complex-valued traveltimes,” Inverse Probl. 26, 085017 (2010).
[CrossRef]

Y. Hadad and T. Melamed, “Non-orthogonal domain parabolic equation and its Gaussian beam solutions,” IEEE Trans. Antennas Propag. 58, 1164–1172 (2010).
[CrossRef]

Y. Hadad and T. Melamed, “Parameterization of the tilted Gaussian beam waveobjects,” Prog. Electromagn. Res. 102, 65–80 (2010).
[CrossRef]

Y. Hadad and T. Melamed, “Tilted Gaussian beam propagation in inhomogeneous media,” J. Opt. Soc. Am. A 27, 1840–1850 (2010).
[CrossRef]

2009 (2)

A. Shlivinski and E. Heyman, “Windowed Radon transform frames,” Appl. Comput. Harmon. Anal. 26, 322–343 (2009).
[CrossRef]

T. Melamed, “Exact Gaussian beam expansion of time-harmonic electromagnetic waves,” J. Electromagn. Waves Appl. 23, 975–986 (2009).
[CrossRef]

2007 (1)

M. Katsav and E. Heyman, “Phase space Gaussian beam summation analysis of half plane diffraction,” IEEE Trans. Antennas Propag. 55, 1535–1545 (2007).
[CrossRef]

2006 (1)

R. Nowack, S. Dasgupta, G. Schuster, and J.-M. Sheng, “Correlation migration using Gaussian beams of scattered teleseismic body waves,” Bull. Seismol. Soc. Am. 96, 1–10(2006).
[CrossRef]

2005 (6)

A. Shlivinski, E. Heyman, and A. Boag, “A pulsed beam summation formulation for short pulse radiation based on windowed Radon transform (WRT) frames,” IEEE Trans. Antennas Propag. 53, 3030–3048 (2005).
[CrossRef]

A. Shlivinski, E. Heyman, and A. Boag, “A phase-space beam summation formulation for ultrawide-band radiation—Part II: A multiband scheme,” IEEE Trans. Antennas Propag. 53, 948–957 (2005).
[CrossRef]

I. Tinkelman and T. Melamed, “Local spectrum analysis of field propagation in anisotropic media. Part I—Time-harmonic fields,” J. Opt. Soc. Am. A 22, 1200–1207 (2005).
[CrossRef]

I. Tinkelman and T. Melamed, “Local spectrum analysis of field propagation in anisotropic media. Part II—Time-dependent fields,” J. Opt. Soc. Am. A 22, 1208–1215 (2005).
[CrossRef]

G. Gordon, E. Heyman, and R. Mazar, “A phase-space Gaussian beam summation representation of rough surface scattering,” J. Acoust. Soc. Am. 117, 1911–1921 (2005).
[CrossRef]

G. Gordon, E. Heyman, and R. Mazar, “Phase space beam summation analysis of rough surface waveguide,” J. Acoust. Soc. Am. 117, 1922–1932 (2005).
[CrossRef]

2004 (3)

H.-T. Chou and P. Pathak, “Fast Gaussian beam based synthesis of shaped reflector antennas for contoured beam applications,” IEE Proc. Microw. Antennas Propag. 151, 13–20 (2004).
[CrossRef]

A. Shlivinski, E. Heyman, A. Boag, and C. Letrou, “A phase-space beam summation formulation for ultra wideband radiation,” IEEE Trans. Antennas Propag. 52, 2042–2056 (2004).
[CrossRef]

T. Melamed, “Phase-space Green’s functions for modeling time-harmonic scattering from smooth inhomogeneous objects,” J. Math. Phys. 45, 2232–2246 (2004).
[CrossRef]

2003 (4)

V. Galdi, H. Feng, D. Castanon, W. Karl, and L. Felsen, “Moderately rough surface underground imaging via short-pulse quasi-ray Gaussian beams,” IEEE Trans. Antennas Propag. 51, 2304–2318 (2003).
[CrossRef]

T. Melamed, “On localization aspects of frequency-domain cattering from low-contrast objects,” IEEE Antennas Wireless Propag. Lett. 2, 40–42 (2003).
[CrossRef]

H. Chou, P. Pathak, and R. Burkholder, “Application of Gaussian-ray basis functions for the rapid analysis of electromagnetic radiation from reflector antennas,” IEE Proc. Microw. Antennas Propag. 150, 177–183 (2003).
[CrossRef]

I. Tinkelman and T. Melamed, “Gaussian beam propagation in generic anisotropic wavenumber profiles,” Opt. Lett. 28, 1081–1083 (2003).
[CrossRef]

2002 (2)

F. Bass and L. Resnick, “Wave beam propagation in layered media,” Prog. Electromagn. Res. 38, 111–123 (2002).
[CrossRef]

J. Arnold, “Rays, beams and diffraction in a discrete phase space: Wilson bases,” Opt. Express 10, 716–727 (2002).
[CrossRef]

2001 (3)

H. Chou, P. Pathak, and R. Burkholder, “Novel Gaussian beam method for the rapid analysis of large reflector antennas,” IEEE Trans. Antennas Propag. 49, 880–893 (2001).
[CrossRef]

O. Kilic and R. Lang, “Scattering of a pulsed beam by a random medium over ground,” J. Electromagn. Waves Appl. 15, 481–516 (2001).
[CrossRef]

R. Martínez-Herrero, P. Mejías, S. Bosch, and A. Carnicer, “Vectorial structure of nonparaxial electromagnetic beams,” J. Opt. Soc. Am. A 18, 1678–1680 (2001).
[CrossRef]

2000 (1)

T. Melamed and L. B. Felsen, “Pulsed beam propagation in dispersive media via pulsed plane wave spectral decomposition,” IEEE Trans. Antennas Propag. 48, 901–908 (2000).
[CrossRef]

1999 (2)

T. Melamed, E. Heyman, and L. Felsen, “Local spectral analysis of short-pulse-excited scattering from weakly inhomogenous media: Part I–forward scattering,” IEEE Trans. Antennas Propag. 47, 1208–1217 (1999).
[CrossRef]

T. Melamed, E. Heyman, and L. Felsen, “Local spectral analysis of short-pulse-excited scattering from weakly inhomogeneous media: Part II–inverse scattering,” IEEE Trans. Antennas Propag. 47, 1218–1227 (1999).
[CrossRef]

1998 (3)

1997 (1)

T. Melamed, “Phase-space beam summation: a local spectrum analysis for time-dependent radiation,” J. Electromagn. Waves Appl. 11, 739–773 (1997).
[CrossRef]

1994 (3)

E. Heyman, “Pulsed beam propagation in an inhomogeneous medium,” IEEE Trans. Antennas Propag. 42, 311–319 (1994).
[CrossRef]

R. Collin, “Scattering of an incident Gaussian beam by a perfectly conducting rough surface,” IEEE Trans. Antennas Propag. 42, 70–74 (1994).
[CrossRef]

E. Heyman and T. Melamed, “Certain considerations in aperture synthesis of ultrawideband/short-pulse radiation,” IEEE Trans. Antennas Propag. 42, 518–525 (1994).
[CrossRef]

1991 (2)

1989 (1)

1987 (1)

B. W. A. N. Norris and J. Schrieffer, “Gaussian wave packets in inhomogeneous media with curved interfaces,” Proc. R. Soc. Lond. 412, 93–123 (1987).
[CrossRef]

1982 (1)

V. Ĉerveny, M. M. Popov, and I. Pŝenĉik, “Computation of wave fields in inhomogeneous media—Gaussian beam approach,” Geophys. J. Roy. Astron. Soc 70, 109–128 (1982).
[CrossRef]

1978 (1)

C. Chapman, “A new method for computing synthetic seismograms,” Geophys. J. Roy. Astron. Soc. 54, 481–518 (1978).
[CrossRef]

1974 (1)

S. Shin and L. Felsen, “Gaussian beams in anisotropic media,” Appl. Phys. 5, 239–250 (1974).
[CrossRef]

Arnold, J.

Bass, F.

F. Bass and L. Resnick, “Wave beam propagation in layered media,” Prog. Electromagn. Res. 38, 111–123 (2002).
[CrossRef]

Bleistein, N.

N. Bleistein and S. Gray, “Amplitude calculations for 3D Gaussian beam migration using complex-valued traveltimes,” Inverse Probl. 26, 085017 (2010).
[CrossRef]

Boag, A.

A. Shlivinski, E. Heyman, and A. Boag, “A pulsed beam summation formulation for short pulse radiation based on windowed Radon transform (WRT) frames,” IEEE Trans. Antennas Propag. 53, 3030–3048 (2005).
[CrossRef]

A. Shlivinski, E. Heyman, and A. Boag, “A phase-space beam summation formulation for ultrawide-band radiation—Part II: A multiband scheme,” IEEE Trans. Antennas Propag. 53, 948–957 (2005).
[CrossRef]

A. Shlivinski, E. Heyman, A. Boag, and C. Letrou, “A phase-space beam summation formulation for ultra wideband radiation,” IEEE Trans. Antennas Propag. 52, 2042–2056 (2004).
[CrossRef]

Bosch, S.

Burkholder, R.

H. Chou, P. Pathak, and R. Burkholder, “Application of Gaussian-ray basis functions for the rapid analysis of electromagnetic radiation from reflector antennas,” IEE Proc. Microw. Antennas Propag. 150, 177–183 (2003).
[CrossRef]

H. Chou, P. Pathak, and R. Burkholder, “Novel Gaussian beam method for the rapid analysis of large reflector antennas,” IEEE Trans. Antennas Propag. 49, 880–893 (2001).
[CrossRef]

Carnicer, A.

Castanon, D.

V. Galdi, H. Feng, D. Castanon, W. Karl, and L. Felsen, “Moderately rough surface underground imaging via short-pulse quasi-ray Gaussian beams,” IEEE Trans. Antennas Propag. 51, 2304–2318 (2003).
[CrossRef]

Cerveny, V.

V. Ĉerveny, M. M. Popov, and I. Pŝenĉik, “Computation of wave fields in inhomogeneous media—Gaussian beam approach,” Geophys. J. Roy. Astron. Soc 70, 109–128 (1982).
[CrossRef]

Chapman, C.

C. Chapman, “A new method for computing synthetic seismograms,” Geophys. J. Roy. Astron. Soc. 54, 481–518 (1978).
[CrossRef]

Chou, H.

H. Chou, P. Pathak, and R. Burkholder, “Application of Gaussian-ray basis functions for the rapid analysis of electromagnetic radiation from reflector antennas,” IEE Proc. Microw. Antennas Propag. 150, 177–183 (2003).
[CrossRef]

H. Chou, P. Pathak, and R. Burkholder, “Novel Gaussian beam method for the rapid analysis of large reflector antennas,” IEEE Trans. Antennas Propag. 49, 880–893 (2001).
[CrossRef]

Chou, H.-T.

H.-T. Chou and P. Pathak, “Fast Gaussian beam based synthesis of shaped reflector antennas for contoured beam applications,” IEE Proc. Microw. Antennas Propag. 151, 13–20 (2004).
[CrossRef]

Collin, R.

R. Collin, “Scattering of an incident Gaussian beam by a perfectly conducting rough surface,” IEEE Trans. Antennas Propag. 42, 70–74 (1994).
[CrossRef]

Dasgupta, S.

R. Nowack, S. Dasgupta, G. Schuster, and J.-M. Sheng, “Correlation migration using Gaussian beams of scattered teleseismic body waves,” Bull. Seismol. Soc. Am. 96, 1–10(2006).
[CrossRef]

Felsen, L.

V. Galdi, H. Feng, D. Castanon, W. Karl, and L. Felsen, “Moderately rough surface underground imaging via short-pulse quasi-ray Gaussian beams,” IEEE Trans. Antennas Propag. 51, 2304–2318 (2003).
[CrossRef]

T. Melamed, E. Heyman, and L. Felsen, “Local spectral analysis of short-pulse-excited scattering from weakly inhomogeneous media: Part II–inverse scattering,” IEEE Trans. Antennas Propag. 47, 1218–1227 (1999).
[CrossRef]

T. Melamed, E. Heyman, and L. Felsen, “Local spectral analysis of short-pulse-excited scattering from weakly inhomogenous media: Part I–forward scattering,” IEEE Trans. Antennas Propag. 47, 1208–1217 (1999).
[CrossRef]

T. Melamed and L. Felsen, “Pulsed beam propagation in lossless dispersive media. Part I: Theory,” J. Opt. Soc. Am. A 15, 1268–1276 (1998).
[CrossRef]

T. Melamed and L. Felsen, “Pulsed beam propagation in lossless dispersive media. Part II: A numerical example,” J. Opt. Soc. Am. A 15, 1277–1284 (1998).
[CrossRef]

B. Steinberg, E. Heyman, and L. Felsen, “Phase space beam summation for time-harmonic radiation from large apertures,” J. Opt. Soc. Am. A 8, 41–59 (1991).
[CrossRef]

B. Steinberg, E. Heyman, and L. Felsen, “Phase space beam summation for time dependent radiation from large apertures: continuous parametrization,” J. Opt. Soc. Am. A 8, 943–958 (1991).
[CrossRef]

E. Heyman and L. Felsen, “Complex source pulsed beam fields,” J. Opt. Soc. Am. A 6, 806–817 (1989).
[CrossRef]

S. Shin and L. Felsen, “Gaussian beams in anisotropic media,” Appl. Phys. 5, 239–250 (1974).
[CrossRef]

Felsen, L. B.

T. Melamed and L. B. Felsen, “Pulsed beam propagation in dispersive media via pulsed plane wave spectral decomposition,” IEEE Trans. Antennas Propag. 48, 901–908 (2000).
[CrossRef]

Feng, H.

V. Galdi, H. Feng, D. Castanon, W. Karl, and L. Felsen, “Moderately rough surface underground imaging via short-pulse quasi-ray Gaussian beams,” IEEE Trans. Antennas Propag. 51, 2304–2318 (2003).
[CrossRef]

Galdi, V.

V. Galdi, H. Feng, D. Castanon, W. Karl, and L. Felsen, “Moderately rough surface underground imaging via short-pulse quasi-ray Gaussian beams,” IEEE Trans. Antennas Propag. 51, 2304–2318 (2003).
[CrossRef]

Gluk, Y.

Y. Gluk and E. Heyman, “Pulsed beams expansion algorithms for time-dependent point-source radiation. A basic algorithm and a standard-pulsed-beams algorithm,” IEEE Trans. Antennas Propag. 59, 1356–1371 (2011).
[CrossRef]

Gordon, G.

G. Gordon, E. Heyman, and R. Mazar, “A phase-space Gaussian beam summation representation of rough surface scattering,” J. Acoust. Soc. Am. 117, 1911–1921 (2005).
[CrossRef]

G. Gordon, E. Heyman, and R. Mazar, “Phase space beam summation analysis of rough surface waveguide,” J. Acoust. Soc. Am. 117, 1922–1932 (2005).
[CrossRef]

Gray, S.

N. Bleistein and S. Gray, “Amplitude calculations for 3D Gaussian beam migration using complex-valued traveltimes,” Inverse Probl. 26, 085017 (2010).
[CrossRef]

Hadad, Y.

Y. Hadad and T. Melamed, “Time-dependent tilted pulsed-beams and their properties,” IEEE Trans. Antennas Propag. 59, 3855–3862 (2011).
[CrossRef]

Y. Hadad and T. Melamed, “Non-orthogonal domain parabolic equation and its Gaussian beam solutions,” IEEE Trans. Antennas Propag. 58, 1164–1172 (2010).
[CrossRef]

Y. Hadad and T. Melamed, “Parameterization of the tilted Gaussian beam waveobjects,” Prog. Electromagn. Res. 102, 65–80 (2010).
[CrossRef]

Y. Hadad and T. Melamed, “Tilted Gaussian beam propagation in inhomogeneous media,” J. Opt. Soc. Am. A 27, 1840–1850 (2010).
[CrossRef]

Heyman, E.

Y. Gluk and E. Heyman, “Pulsed beams expansion algorithms for time-dependent point-source radiation. A basic algorithm and a standard-pulsed-beams algorithm,” IEEE Trans. Antennas Propag. 59, 1356–1371 (2011).
[CrossRef]

A. Shlivinski and E. Heyman, “Windowed Radon transform frames,” Appl. Comput. Harmon. Anal. 26, 322–343 (2009).
[CrossRef]

M. Katsav and E. Heyman, “Phase space Gaussian beam summation analysis of half plane diffraction,” IEEE Trans. Antennas Propag. 55, 1535–1545 (2007).
[CrossRef]

G. Gordon, E. Heyman, and R. Mazar, “Phase space beam summation analysis of rough surface waveguide,” J. Acoust. Soc. Am. 117, 1922–1932 (2005).
[CrossRef]

A. Shlivinski, E. Heyman, and A. Boag, “A pulsed beam summation formulation for short pulse radiation based on windowed Radon transform (WRT) frames,” IEEE Trans. Antennas Propag. 53, 3030–3048 (2005).
[CrossRef]

G. Gordon, E. Heyman, and R. Mazar, “A phase-space Gaussian beam summation representation of rough surface scattering,” J. Acoust. Soc. Am. 117, 1911–1921 (2005).
[CrossRef]

A. Shlivinski, E. Heyman, and A. Boag, “A phase-space beam summation formulation for ultrawide-band radiation—Part II: A multiband scheme,” IEEE Trans. Antennas Propag. 53, 948–957 (2005).
[CrossRef]

A. Shlivinski, E. Heyman, A. Boag, and C. Letrou, “A phase-space beam summation formulation for ultra wideband radiation,” IEEE Trans. Antennas Propag. 52, 2042–2056 (2004).
[CrossRef]

T. Melamed, E. Heyman, and L. Felsen, “Local spectral analysis of short-pulse-excited scattering from weakly inhomogenous media: Part I–forward scattering,” IEEE Trans. Antennas Propag. 47, 1208–1217 (1999).
[CrossRef]

T. Melamed, E. Heyman, and L. Felsen, “Local spectral analysis of short-pulse-excited scattering from weakly inhomogeneous media: Part II–inverse scattering,” IEEE Trans. Antennas Propag. 47, 1218–1227 (1999).
[CrossRef]

E. Heyman, “Pulsed beam propagation in an inhomogeneous medium,” IEEE Trans. Antennas Propag. 42, 311–319 (1994).
[CrossRef]

E. Heyman and T. Melamed, “Certain considerations in aperture synthesis of ultrawideband/short-pulse radiation,” IEEE Trans. Antennas Propag. 42, 518–525 (1994).
[CrossRef]

B. Steinberg, E. Heyman, and L. Felsen, “Phase space beam summation for time-harmonic radiation from large apertures,” J. Opt. Soc. Am. A 8, 41–59 (1991).
[CrossRef]

B. Steinberg, E. Heyman, and L. Felsen, “Phase space beam summation for time dependent radiation from large apertures: continuous parametrization,” J. Opt. Soc. Am. A 8, 943–958 (1991).
[CrossRef]

E. Heyman and L. Felsen, “Complex source pulsed beam fields,” J. Opt. Soc. Am. A 6, 806–817 (1989).
[CrossRef]

E. Heyman and T. Melamed, Space-Time Representation of Ultra Wideband Signals (Elsevier, 1998), pp. 1–63.

Karl, W.

V. Galdi, H. Feng, D. Castanon, W. Karl, and L. Felsen, “Moderately rough surface underground imaging via short-pulse quasi-ray Gaussian beams,” IEEE Trans. Antennas Propag. 51, 2304–2318 (2003).
[CrossRef]

Katsav, M.

M. Katsav and E. Heyman, “Phase space Gaussian beam summation analysis of half plane diffraction,” IEEE Trans. Antennas Propag. 55, 1535–1545 (2007).
[CrossRef]

Kilic, O.

O. Kilic and R. Lang, “Scattering of a pulsed beam by a random medium over ground,” J. Electromagn. Waves Appl. 15, 481–516 (2001).
[CrossRef]

Lang, R.

O. Kilic and R. Lang, “Scattering of a pulsed beam by a random medium over ground,” J. Electromagn. Waves Appl. 15, 481–516 (2001).
[CrossRef]

Letrou, C.

A. Shlivinski, E. Heyman, A. Boag, and C. Letrou, “A phase-space beam summation formulation for ultra wideband radiation,” IEEE Trans. Antennas Propag. 52, 2042–2056 (2004).
[CrossRef]

Martínez-Herrero, R.

Mazar, R.

G. Gordon, E. Heyman, and R. Mazar, “A phase-space Gaussian beam summation representation of rough surface scattering,” J. Acoust. Soc. Am. 117, 1911–1921 (2005).
[CrossRef]

G. Gordon, E. Heyman, and R. Mazar, “Phase space beam summation analysis of rough surface waveguide,” J. Acoust. Soc. Am. 117, 1922–1932 (2005).
[CrossRef]

Mejías, P.

Melamed, T.

T. Melamed, “Pulsed beam expansion of electromagnetic aperture fields,” Prog. Electromagn. Res. 114, 317–332(2011).
[CrossRef]

T. Melamed, “TE and TM beam decomposition of time-harmonic electromagnetic waves,” J. Opt. Soc. Am. A 28, 401–409(2011).
[CrossRef]

Y. Hadad and T. Melamed, “Time-dependent tilted pulsed-beams and their properties,” IEEE Trans. Antennas Propag. 59, 3855–3862 (2011).
[CrossRef]

Y. Hadad and T. Melamed, “Parameterization of the tilted Gaussian beam waveobjects,” Prog. Electromagn. Res. 102, 65–80 (2010).
[CrossRef]

Y. Hadad and T. Melamed, “Non-orthogonal domain parabolic equation and its Gaussian beam solutions,” IEEE Trans. Antennas Propag. 58, 1164–1172 (2010).
[CrossRef]

Y. Hadad and T. Melamed, “Tilted Gaussian beam propagation in inhomogeneous media,” J. Opt. Soc. Am. A 27, 1840–1850 (2010).
[CrossRef]

T. Melamed, “Exact Gaussian beam expansion of time-harmonic electromagnetic waves,” J. Electromagn. Waves Appl. 23, 975–986 (2009).
[CrossRef]

I. Tinkelman and T. Melamed, “Local spectrum analysis of field propagation in anisotropic media. Part I—Time-harmonic fields,” J. Opt. Soc. Am. A 22, 1200–1207 (2005).
[CrossRef]

I. Tinkelman and T. Melamed, “Local spectrum analysis of field propagation in anisotropic media. Part II—Time-dependent fields,” J. Opt. Soc. Am. A 22, 1208–1215 (2005).
[CrossRef]

T. Melamed, “Phase-space Green’s functions for modeling time-harmonic scattering from smooth inhomogeneous objects,” J. Math. Phys. 45, 2232–2246 (2004).
[CrossRef]

I. Tinkelman and T. Melamed, “Gaussian beam propagation in generic anisotropic wavenumber profiles,” Opt. Lett. 28, 1081–1083 (2003).
[CrossRef]

T. Melamed, “On localization aspects of frequency-domain cattering from low-contrast objects,” IEEE Antennas Wireless Propag. Lett. 2, 40–42 (2003).
[CrossRef]

T. Melamed and L. B. Felsen, “Pulsed beam propagation in dispersive media via pulsed plane wave spectral decomposition,” IEEE Trans. Antennas Propag. 48, 901–908 (2000).
[CrossRef]

T. Melamed, E. Heyman, and L. Felsen, “Local spectral analysis of short-pulse-excited scattering from weakly inhomogenous media: Part I–forward scattering,” IEEE Trans. Antennas Propag. 47, 1208–1217 (1999).
[CrossRef]

T. Melamed, E. Heyman, and L. Felsen, “Local spectral analysis of short-pulse-excited scattering from weakly inhomogeneous media: Part II–inverse scattering,” IEEE Trans. Antennas Propag. 47, 1218–1227 (1999).
[CrossRef]

T. Melamed and L. Felsen, “Pulsed beam propagation in lossless dispersive media. Part II: A numerical example,” J. Opt. Soc. Am. A 15, 1277–1284 (1998).
[CrossRef]

T. Melamed and L. Felsen, “Pulsed beam propagation in lossless dispersive media. Part I: Theory,” J. Opt. Soc. Am. A 15, 1268–1276 (1998).
[CrossRef]

T. Melamed, “Phase-space beam summation: a local spectrum analysis for time-dependent radiation,” J. Electromagn. Waves Appl. 11, 739–773 (1997).
[CrossRef]

E. Heyman and T. Melamed, “Certain considerations in aperture synthesis of ultrawideband/short-pulse radiation,” IEEE Trans. Antennas Propag. 42, 518–525 (1994).
[CrossRef]

T. Melamed, “Time-domain phase-space Green’s functions for inhomogeneous media,” in Ultrawideband/Short Pulse Electromagnetics 6, E. L. Mokole, M. Kragalott, K. R. Gerlach, M. Kragalott, and K. R. Gerlach, eds. (Springer-Verlag, 2007), pp. 56–63.

E. Heyman and T. Melamed, Space-Time Representation of Ultra Wideband Signals (Elsevier, 1998), pp. 1–63.

Mukunda, N.

Norris, B. W. A. N.

B. W. A. N. Norris and J. Schrieffer, “Gaussian wave packets in inhomogeneous media with curved interfaces,” Proc. R. Soc. Lond. 412, 93–123 (1987).
[CrossRef]

Nowack, R.

R. Nowack, S. Dasgupta, G. Schuster, and J.-M. Sheng, “Correlation migration using Gaussian beams of scattered teleseismic body waves,” Bull. Seismol. Soc. Am. 96, 1–10(2006).
[CrossRef]

Pathak, P.

H.-T. Chou and P. Pathak, “Fast Gaussian beam based synthesis of shaped reflector antennas for contoured beam applications,” IEE Proc. Microw. Antennas Propag. 151, 13–20 (2004).
[CrossRef]

H. Chou, P. Pathak, and R. Burkholder, “Application of Gaussian-ray basis functions for the rapid analysis of electromagnetic radiation from reflector antennas,” IEE Proc. Microw. Antennas Propag. 150, 177–183 (2003).
[CrossRef]

H. Chou, P. Pathak, and R. Burkholder, “Novel Gaussian beam method for the rapid analysis of large reflector antennas,” IEEE Trans. Antennas Propag. 49, 880–893 (2001).
[CrossRef]

Popov, M.

M. Popov, N. Semtchenok, P. Popov, and A. Verdel, “Depth migration by the Gaussian beam summation method,” Geophysics 75, S81–S93 (2010).
[CrossRef]

Popov, M. M.

V. Ĉerveny, M. M. Popov, and I. Pŝenĉik, “Computation of wave fields in inhomogeneous media—Gaussian beam approach,” Geophys. J. Roy. Astron. Soc 70, 109–128 (1982).
[CrossRef]

Popov, P.

M. Popov, N. Semtchenok, P. Popov, and A. Verdel, “Depth migration by the Gaussian beam summation method,” Geophysics 75, S81–S93 (2010).
[CrossRef]

Psencik, I.

V. Ĉerveny, M. M. Popov, and I. Pŝenĉik, “Computation of wave fields in inhomogeneous media—Gaussian beam approach,” Geophys. J. Roy. Astron. Soc 70, 109–128 (1982).
[CrossRef]

Resnick, L.

F. Bass and L. Resnick, “Wave beam propagation in layered media,” Prog. Electromagn. Res. 38, 111–123 (2002).
[CrossRef]

Schrieffer, J.

B. W. A. N. Norris and J. Schrieffer, “Gaussian wave packets in inhomogeneous media with curved interfaces,” Proc. R. Soc. Lond. 412, 93–123 (1987).
[CrossRef]

Schuster, G.

R. Nowack, S. Dasgupta, G. Schuster, and J.-M. Sheng, “Correlation migration using Gaussian beams of scattered teleseismic body waves,” Bull. Seismol. Soc. Am. 96, 1–10(2006).
[CrossRef]

Semtchenok, N.

M. Popov, N. Semtchenok, P. Popov, and A. Verdel, “Depth migration by the Gaussian beam summation method,” Geophysics 75, S81–S93 (2010).
[CrossRef]

Sheng, J.-M.

R. Nowack, S. Dasgupta, G. Schuster, and J.-M. Sheng, “Correlation migration using Gaussian beams of scattered teleseismic body waves,” Bull. Seismol. Soc. Am. 96, 1–10(2006).
[CrossRef]

Shin, S.

S. Shin and L. Felsen, “Gaussian beams in anisotropic media,” Appl. Phys. 5, 239–250 (1974).
[CrossRef]

Shlivinski, A.

A. Shlivinski and E. Heyman, “Windowed Radon transform frames,” Appl. Comput. Harmon. Anal. 26, 322–343 (2009).
[CrossRef]

A. Shlivinski, E. Heyman, and A. Boag, “A pulsed beam summation formulation for short pulse radiation based on windowed Radon transform (WRT) frames,” IEEE Trans. Antennas Propag. 53, 3030–3048 (2005).
[CrossRef]

A. Shlivinski, E. Heyman, and A. Boag, “A phase-space beam summation formulation for ultrawide-band radiation—Part II: A multiband scheme,” IEEE Trans. Antennas Propag. 53, 948–957 (2005).
[CrossRef]

A. Shlivinski, E. Heyman, A. Boag, and C. Letrou, “A phase-space beam summation formulation for ultra wideband radiation,” IEEE Trans. Antennas Propag. 52, 2042–2056 (2004).
[CrossRef]

Simon, R.

Steinberg, B.

Tinkelman, I.

Verdel, A.

M. Popov, N. Semtchenok, P. Popov, and A. Verdel, “Depth migration by the Gaussian beam summation method,” Geophysics 75, S81–S93 (2010).
[CrossRef]

Appl. Comput. Harmon. Anal. (1)

A. Shlivinski and E. Heyman, “Windowed Radon transform frames,” Appl. Comput. Harmon. Anal. 26, 322–343 (2009).
[CrossRef]

Appl. Phys. (1)

S. Shin and L. Felsen, “Gaussian beams in anisotropic media,” Appl. Phys. 5, 239–250 (1974).
[CrossRef]

Bull. Seismol. Soc. Am. (1)

R. Nowack, S. Dasgupta, G. Schuster, and J.-M. Sheng, “Correlation migration using Gaussian beams of scattered teleseismic body waves,” Bull. Seismol. Soc. Am. 96, 1–10(2006).
[CrossRef]

Geophys. J. Roy. Astron. Soc (1)

V. Ĉerveny, M. M. Popov, and I. Pŝenĉik, “Computation of wave fields in inhomogeneous media—Gaussian beam approach,” Geophys. J. Roy. Astron. Soc 70, 109–128 (1982).
[CrossRef]

Geophys. J. Roy. Astron. Soc. (1)

C. Chapman, “A new method for computing synthetic seismograms,” Geophys. J. Roy. Astron. Soc. 54, 481–518 (1978).
[CrossRef]

Geophysics (1)

M. Popov, N. Semtchenok, P. Popov, and A. Verdel, “Depth migration by the Gaussian beam summation method,” Geophysics 75, S81–S93 (2010).
[CrossRef]

IEE Proc. Microw. Antennas Propag. (2)

H. Chou, P. Pathak, and R. Burkholder, “Application of Gaussian-ray basis functions for the rapid analysis of electromagnetic radiation from reflector antennas,” IEE Proc. Microw. Antennas Propag. 150, 177–183 (2003).
[CrossRef]

H.-T. Chou and P. Pathak, “Fast Gaussian beam based synthesis of shaped reflector antennas for contoured beam applications,” IEE Proc. Microw. Antennas Propag. 151, 13–20 (2004).
[CrossRef]

IEEE Antennas Wireless Propag. Lett. (1)

T. Melamed, “On localization aspects of frequency-domain cattering from low-contrast objects,” IEEE Antennas Wireless Propag. Lett. 2, 40–42 (2003).
[CrossRef]

IEEE Trans. Antennas Propag. (15)

T. Melamed, E. Heyman, and L. Felsen, “Local spectral analysis of short-pulse-excited scattering from weakly inhomogenous media: Part I–forward scattering,” IEEE Trans. Antennas Propag. 47, 1208–1217 (1999).
[CrossRef]

T. Melamed, E. Heyman, and L. Felsen, “Local spectral analysis of short-pulse-excited scattering from weakly inhomogeneous media: Part II–inverse scattering,” IEEE Trans. Antennas Propag. 47, 1218–1227 (1999).
[CrossRef]

V. Galdi, H. Feng, D. Castanon, W. Karl, and L. Felsen, “Moderately rough surface underground imaging via short-pulse quasi-ray Gaussian beams,” IEEE Trans. Antennas Propag. 51, 2304–2318 (2003).
[CrossRef]

E. Heyman and T. Melamed, “Certain considerations in aperture synthesis of ultrawideband/short-pulse radiation,” IEEE Trans. Antennas Propag. 42, 518–525 (1994).
[CrossRef]

R. Collin, “Scattering of an incident Gaussian beam by a perfectly conducting rough surface,” IEEE Trans. Antennas Propag. 42, 70–74 (1994).
[CrossRef]

H. Chou, P. Pathak, and R. Burkholder, “Novel Gaussian beam method for the rapid analysis of large reflector antennas,” IEEE Trans. Antennas Propag. 49, 880–893 (2001).
[CrossRef]

E. Heyman, “Pulsed beam propagation in an inhomogeneous medium,” IEEE Trans. Antennas Propag. 42, 311–319 (1994).
[CrossRef]

Y. Hadad and T. Melamed, “Time-dependent tilted pulsed-beams and their properties,” IEEE Trans. Antennas Propag. 59, 3855–3862 (2011).
[CrossRef]

T. Melamed and L. B. Felsen, “Pulsed beam propagation in dispersive media via pulsed plane wave spectral decomposition,” IEEE Trans. Antennas Propag. 48, 901–908 (2000).
[CrossRef]

Y. Gluk and E. Heyman, “Pulsed beams expansion algorithms for time-dependent point-source radiation. A basic algorithm and a standard-pulsed-beams algorithm,” IEEE Trans. Antennas Propag. 59, 1356–1371 (2011).
[CrossRef]

Y. Hadad and T. Melamed, “Non-orthogonal domain parabolic equation and its Gaussian beam solutions,” IEEE Trans. Antennas Propag. 58, 1164–1172 (2010).
[CrossRef]

A. Shlivinski, E. Heyman, A. Boag, and C. Letrou, “A phase-space beam summation formulation for ultra wideband radiation,” IEEE Trans. Antennas Propag. 52, 2042–2056 (2004).
[CrossRef]

A. Shlivinski, E. Heyman, and A. Boag, “A phase-space beam summation formulation for ultrawide-band radiation—Part II: A multiband scheme,” IEEE Trans. Antennas Propag. 53, 948–957 (2005).
[CrossRef]

M. Katsav and E. Heyman, “Phase space Gaussian beam summation analysis of half plane diffraction,” IEEE Trans. Antennas Propag. 55, 1535–1545 (2007).
[CrossRef]

A. Shlivinski, E. Heyman, and A. Boag, “A pulsed beam summation formulation for short pulse radiation based on windowed Radon transform (WRT) frames,” IEEE Trans. Antennas Propag. 53, 3030–3048 (2005).
[CrossRef]

Inverse Probl. (1)

N. Bleistein and S. Gray, “Amplitude calculations for 3D Gaussian beam migration using complex-valued traveltimes,” Inverse Probl. 26, 085017 (2010).
[CrossRef]

J. Acoust. Soc. Am. (2)

G. Gordon, E. Heyman, and R. Mazar, “A phase-space Gaussian beam summation representation of rough surface scattering,” J. Acoust. Soc. Am. 117, 1911–1921 (2005).
[CrossRef]

G. Gordon, E. Heyman, and R. Mazar, “Phase space beam summation analysis of rough surface waveguide,” J. Acoust. Soc. Am. 117, 1922–1932 (2005).
[CrossRef]

J. Electromagn. Waves Appl. (3)

O. Kilic and R. Lang, “Scattering of a pulsed beam by a random medium over ground,” J. Electromagn. Waves Appl. 15, 481–516 (2001).
[CrossRef]

T. Melamed, “Phase-space beam summation: a local spectrum analysis for time-dependent radiation,” J. Electromagn. Waves Appl. 11, 739–773 (1997).
[CrossRef]

T. Melamed, “Exact Gaussian beam expansion of time-harmonic electromagnetic waves,” J. Electromagn. Waves Appl. 23, 975–986 (2009).
[CrossRef]

J. Math. Phys. (1)

T. Melamed, “Phase-space Green’s functions for modeling time-harmonic scattering from smooth inhomogeneous objects,” J. Math. Phys. 45, 2232–2246 (2004).
[CrossRef]

J. Opt. Soc. Am. A (11)

R. Simon and N. Mukunda, “Shape-invariant anisotropic Gaussian Schell-model beams: a complete characterization,” J. Opt. Soc. Am. A 15, 1361–1370 (1998).
[CrossRef]

B. Steinberg, E. Heyman, and L. Felsen, “Phase space beam summation for time-harmonic radiation from large apertures,” J. Opt. Soc. Am. A 8, 41–59 (1991).
[CrossRef]

B. Steinberg, E. Heyman, and L. Felsen, “Phase space beam summation for time dependent radiation from large apertures: continuous parametrization,” J. Opt. Soc. Am. A 8, 943–958 (1991).
[CrossRef]

I. Tinkelman and T. Melamed, “Local spectrum analysis of field propagation in anisotropic media. Part I—Time-harmonic fields,” J. Opt. Soc. Am. A 22, 1200–1207 (2005).
[CrossRef]

I. Tinkelman and T. Melamed, “Local spectrum analysis of field propagation in anisotropic media. Part II—Time-dependent fields,” J. Opt. Soc. Am. A 22, 1208–1215 (2005).
[CrossRef]

T. Melamed and L. Felsen, “Pulsed beam propagation in lossless dispersive media. Part I: Theory,” J. Opt. Soc. Am. A 15, 1268–1276 (1998).
[CrossRef]

T. Melamed and L. Felsen, “Pulsed beam propagation in lossless dispersive media. Part II: A numerical example,” J. Opt. Soc. Am. A 15, 1277–1284 (1998).
[CrossRef]

R. Martínez-Herrero, P. Mejías, S. Bosch, and A. Carnicer, “Vectorial structure of nonparaxial electromagnetic beams,” J. Opt. Soc. Am. A 18, 1678–1680 (2001).
[CrossRef]

E. Heyman and L. Felsen, “Complex source pulsed beam fields,” J. Opt. Soc. Am. A 6, 806–817 (1989).
[CrossRef]

T. Melamed, “TE and TM beam decomposition of time-harmonic electromagnetic waves,” J. Opt. Soc. Am. A 28, 401–409(2011).
[CrossRef]

Y. Hadad and T. Melamed, “Tilted Gaussian beam propagation in inhomogeneous media,” J. Opt. Soc. Am. A 27, 1840–1850 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. R. Soc. Lond. (1)

B. W. A. N. Norris and J. Schrieffer, “Gaussian wave packets in inhomogeneous media with curved interfaces,” Proc. R. Soc. Lond. 412, 93–123 (1987).
[CrossRef]

Prog. Electromagn. Res. (3)

F. Bass and L. Resnick, “Wave beam propagation in layered media,” Prog. Electromagn. Res. 38, 111–123 (2002).
[CrossRef]

Y. Hadad and T. Melamed, “Parameterization of the tilted Gaussian beam waveobjects,” Prog. Electromagn. Res. 102, 65–80 (2010).
[CrossRef]

T. Melamed, “Pulsed beam expansion of electromagnetic aperture fields,” Prog. Electromagn. Res. 114, 317–332(2011).
[CrossRef]

Other (2)

E. Heyman and T. Melamed, Space-Time Representation of Ultra Wideband Signals (Elsevier, 1998), pp. 1–63.

T. Melamed, “Time-domain phase-space Green’s functions for inhomogeneous media,” in Ultrawideband/Short Pulse Electromagnetics 6, E. L. Mokole, M. Kragalott, K. R. Gerlach, M. Kragalott, and K. R. Gerlach, eds. (Springer-Verlag, 2007), pp. 56–63.

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Figures (6)

Fig. 1.
Fig. 1.

Discrete frame spectral lattice. The fields in z 0 are evaluated by superposition of tilted, shifted, and delayed PBs, which are emanating from the aperture distribution plane over the discrete frame spatial-directional-temporal lattice in Eq. (19). Each beam propagator emanates from a lattice point ( x ¯ , y ¯ ) , in a direction of ( ϑ ¯ x , ϑ ¯ y ) = cos 1 [ ( κ ¯ x , κ ¯ y ) ] with respect to the corresponding axis and in delay time of τ ¯ .

Fig. 2.
Fig. 2.

Aperture electric field E x in Eq. (56) over z = 0 plane at t = 0 .

Fig. 3.
Fig. 3.

TE and TM spectral distributions of the aperture field. E ˜ TE ( κ t , τ ) distribution in (a)  ( κ x , τ ) plane for κ y = 0 , (b)  ( κ y , τ ) plane for κ x = 0 , and (c)  ( κ x , κ y ) plane for τ = 0 . (d)–(f) are the same as (a)–(c) for the E ˜ TM distribution.

Fig. 4.
Fig. 4.

TE expansion coefficients a N TE in various planes: (a) in ( x ¯ , κ ¯ y ) plane for y ¯ = κ ¯ x = τ ¯ = 0 and (b) in ( κ ¯ x , κ ¯ y ) plane for x ¯ = y ¯ = τ ¯ = 0 .

Fig. 5.
Fig. 5.

TM expansion coefficients a N TM in various planes: (a) in ( x ¯ , κ ¯ x ) plane for y ¯ = κ ¯ y = τ ¯ = 0 and (b) in ( κ ¯ x , κ ¯ y ) plane for x ¯ = y ¯ = τ ¯ = 0 .

Fig. 6.
Fig. 6.

Propagating field E x ( r , t ) for z = 2 c T and t = 2 T . (a) Reference field in Eq. (56). (b) Synthesized field. (c) Error in the reconstruction.

Equations (59)

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E t ( r t , t ) = E x ( r t , t ) x ^ + E y ( r t , t ) y ^ ,
Ĕ ( r , t ) = 1 π j d t E ( r , t ) t t , Im t 0.
Ĕ ( r , t ) = E ( r , t ) j H t E ( r , t ) , t real ,
E ( r , t ) = Re Ĕ ( r , t ) .
E ˜ ˘ t ( κ t , τ ) = E ˜ ˘ x ( κ t , τ ) x ^ + E ˜ ˘ y ( κ t , τ ) y ^ ,
E ˜ ˘ t ( κ t , τ ) = d 2 r t Ĕ t ( r t , τ + c 1 κ t · r t ) ,
Ĕ t ( r t , t ) = 1 ( 2 π c ) 2 d 2 κ t t 2 E ˜ ˘ t ( κ t , t c 1 κ t · r t ) ,
E ˜ ˘ z ( κ t , τ ) = ( κ x E ˜ ˘ x + κ y E ˜ ˘ y ) / κ z ,
κ z = 1 κ x 2 κ y 2 ,
Ĕ ( r , t ) = 1 ( 2 π c ) 2 d 2 κ t t 2 E ˜ ˘ ( κ t , t c 1 κ ^ · r ) ,
E ˜ ˘ ( κ t , τ ) = E ˜ ˘ t ( κ t , τ ) + z ^ E ˜ ˘ z ( κ t , τ ) ,
κ ^ = ( κ x , κ y , κ z ) .
n ^ ( κ t ) = κ t 1 ( κ y x ^ κ x y ^ ) , t ^ ( κ t ) = κ z κ t 1 ( κ x x ^ + κ y y ^ ) κ t z ^ ,
E ˜ ˘ ( κ t , τ ) = E ˜ ˘ TE ( κ t , τ ) n ^ ( κ t ) + E ˜ ˘ TM ( κ t , τ ) t ^ ( κ t ) ,
E ˜ ˘ TE ( κ t , τ ) = κ t 1 ( κ y E ˜ ˘ x κ x E ˜ ˘ y ) , E ˜ ˘ TM ( κ t , τ ) = ( κ z κ t ) 1 ( κ x E ˜ ˘ x + κ y E ˜ ˘ y ) .
E ( r , t ) = E TE ( r , t ) + E TM ( r , t ) ,
E TE ( r , t ) = Re [ 1 ( 2 π c ) 2 d 2 κ t n ^ ( κ t ) t 2 E ˜ ˘ TE ( κ t , t c 1 κ ^ · r ) ] , E TM ( r , t ) = Re [ 1 ( 2 π c ) 2 d 2 κ t t ^ ( κ t ) t 2 E ˜ ˘ TM ( κ t , t c 1 κ ^ · r ) ] .
Ω = ( ω min , ω max ) .
( x ¯ , y ¯ , κ ¯ x , κ ¯ y , τ ¯ ) = ( N x Δ x ¯ , N y Δ y ¯ , N κ x Δ κ ¯ x , N κ y Δ κ ¯ y , N τ Δ τ ¯ ) ,
ω ¯ Δ κ ¯ Δ r ¯ t = 2 π c ν ,
Δ τ ¯ < 2 π / ( ω max + ω h ) ,
ψ N ( r t , t ) = ψ [ r t r ¯ t , t τ ¯ c 1 κ ¯ t · ( r t r ¯ t ) ] ,
φ N ( r t , t ) = φ [ r t r ¯ t , t τ ¯ c 1 κ ¯ t · ( r t r ¯ t ) ] .
u 0 ( r t , t ) = N a N ψ N ( r t , t ) ,
a N = d t d 2 r t u 0 ( r t , t ) φ N ( r t , t ) .
u 0 ( r t , t ) = 1 ( 2 π c ) 2 d 2 κ t t 2 u ˜ 0 ( κ t , t c 1 κ t · r t ) .
a N = 1 ( 2 π c ) 2 d τ d 2 κ t τ 2 u ˜ 0 ( κ t , τ ) φ ˜ N ( κ t , τ ) ,
φ ˜ N ( κ t , τ ) = τ ¯ φ ˜ ( κ t κ ¯ t , τ τ ¯ + c 1 κ t · r ¯ t ) .
u ( r , t ) = N a N P N ( r , t ) ,
[ 2 c 2 t 2 ] P N ( r , t ) = 0 ,
P N ( r , t ) = d 2 r t z 2 π R 2 ( R 1 + c 1 t ) ψ N ( r t , t R / c ) ,
P ˘ N ( r , t ) = 1 ( 2 π c ) 2 d 2 κ t t 2 ψ ˜ ˘ N ( κ t , t c 1 κ ^ · r ) ,
ψ ˜ ˘ N ( κ t , τ ) = d 2 r t ψ̆ N ( r t , τ + c 1 κ t · r t ) .
ψ ˜ ˘ N ( κ t , τ ) = ψ ˜ ˘ ( κ t κ ¯ t , τ τ ¯ + c 1 κ t · r ¯ t ) .
κ ¯ ^ = ( κ ¯ t , κ ¯ z ) , κ ¯ z = 1 κ ¯ t 2 ,
u ˜ ˘ 0 ( κ t , τ ) = N a N ψ ˜ ˘ N ( κ t , τ ) ,
ψ ( r t , t ) = Re [ ğ ( t j r t 2 / 2 b c ) ] , ψ ˜ ( κ t , τ ) = 2 π b c Im [ ğ ( τ j b κ t 2 / 2 c ) ] ,
φ ( r t , t ) 2 ω ¯ 3 Δ r ¯ t 2 Im [ ğ ( t j r t 2 / 2 b c ) ] , φ ˜ ( κ t , τ ) 4 π b c ω ¯ 3 Δ r ¯ t 2 Re [ ğ ( τ j b κ t 2 / 2 c ) ] .
g ˘ ( t ) = { 1 π j t [ sinc ( Δ L t ) e j ( ω L Δ L ) t sinc ( Δ H t ) e j ( ω H + Δ H ) t ] } ,
( x b N y b N z b N ) = ( cos ϑ ¯ N cos φ ¯ N cos ϑ ¯ N sin φ ¯ N sin ϑ ¯ N sin φ ¯ N cos φ ¯ N 0 sin ϑ ¯ N cos φ ¯ N sin ϑ ¯ N sin φ ¯ N cos ϑ ¯ N ) ( x x ¯ y y ¯ z ) ,
cos ϑ ¯ N = κ ¯ z , cos φ ¯ N = κ ¯ x / κ ¯ t , sin φ ¯ N = κ ¯ y / κ ¯ t .
r t r ¯ t = z tan ϑ ¯ N ( cos φ ¯ N x ^ + sin φ ¯ N y ^ ) ,
P N ( r , t ) Re [ j F N 1 z b N j F N 1 j F N 2 z b N j F N 2 × g ˘ ( t τ ¯ z b N c x b N 2 / 2 c z b N j F N 1 y b N 2 / 2 c z b N j F N 2 ) ] .
F N 1 = b cos 2 ϑ ¯ N , F N 2 = b ,
a N TE / TM = d t d 2 r t E TE / TM ( r t , t ) φ N ( r t , t ) ,
E TE / TM ( r t , t ) = 1 ( 2 π c ) 2 d 2 κ t t 2 E ˜ TE / TM ( κ t , t c 1 κ t · r t ) .
a N TE / TM = 1 ( 2 π c ) 2 d τ d 2 κ t τ 2 E ˜ TE / TM ( κ t , τ ) φ ˜ N ( κ t , τ ) ,
E ˜ ˘ TE / TM ( κ t , τ ) = N a N TE / TM ψ ˜ ˘ N ( κ t , τ ) ,
E TE / TM ( r , t ) = N a N TE / TM E N TE / TM ( r , t ) ,
Ĕ N TE ( r , t ) = 1 ( 2 π c ) 2 d 2 κ t t 2 n ^ ( κ t ) ψ ˜ ˘ N ( κ t , t c 1 κ ^ · r ) , Ĕ N TM ( r , t ) = 1 ( 2 π c ) 2 d 2 κ t t 2 t ^ ( κ t ) ψ ˜ ˘ N ( κ t , t c 1 κ ^ · r ) ,
E N TE ( r , t ) n ^ ( κ ¯ t ) P N ( r , t ) , E N TM ( r , t ) t ^ ( κ ¯ t ) P N ( r , t ) ,
H ( r , t ) = H TE ( r , t ) + H TM ( r , t ) ,
H TE / TM ( r , t ) = N a N TE / TM H N TE / TM ( r , t ) ,
N TE ( r , t ) = 1 η 0 1 ( 2 π c ) 2 d 2 κ t t ^ ( κ t ) t 2 ψ ˜ ˘ N ( κ t , t c 1 κ ^ · r ) , N TM ( r , t ) = 1 η 0 1 ( 2 π c ) 2 d 2 κ t n ^ ( κ t ) t 2 ψ ˜ ˘ N ( κ t , t c 1 κ ^ · r ) ,
H N TE ( r , t ) η 0 1 t ^ ( κ ¯ t ) P N ( r , t ) , H N TM ( r , t ) η 0 1 n ^ ( κ ¯ t ) P N ( r , t ) ,
E ( r , t ) = Re V 0 f ˘ ( t d ) 4 π R x ^ , R = [ x 2 + y 2 + ( z z j b z ) 2 ] 1 2 , t d = t t R / c ,
f ˘ ( t ) = e j ω c t [ 2 sinc ( 2 π t T ) + sinc ( 2 π ( t T / 2 ) T ) + sinc ( 2 π ( t + T / 2 ) T ) ] ,
E ˜ x ( κ t , τ ) = d t d 2 r t E x ( r t , t ) δ ( t τ c 1 κ t · r t ) .
δ w ( t ) = 1 π T w / 2 t 2 + ( T w / 2 ) 2 ,

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