Abstract

Paraxial Gaussian beams (GB’s) are collimated wave objects that have found wide application in optical system analysis and design. A GB propagates in physical space according to well-established quasi-geometric-optical rules that can accommodate weakly inhomogeneous media as well as reflection from and transmission through curved interfaces and thin-lens configurations. We examine the GB concept from a broad perspective in the frequency domain (FD) and the short-pulse time domain (TD) and within as well as arbitrarily beyond the paraxial constraint. For the formal analysis, which is followed by physics-matched high-frequency asymptotics, we use a (space–time)–(wavenumber–frequency) phase-space format to discuss the exact complex-source-point method and the associated asymptotic beam tracking by means of complex rays, the TD pulsed-beam (PB) ultrawideband wave-packet counterpart of the FD GB, GB’s and PB’s as basis functions for representing arbitrary fields, GB and PB diffraction, and FD–TD radiation from extended continuous aperture distributions in which the GB and the PB bases, installed through windowed transforms, yield numerically compact physics-matched a priori localization in the plane-wave-based nonwindowed spectral representations.

© 2001 Optical Society of America

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2000 (2)

E. Heyman, V. Lomakin, G. Kaiser, “Physical source realization of complex source pulsed beams,” J. Acoust. Soc. Am. 107, 1880–1891 (2000).
[CrossRef] [PubMed]

M. A. Porras, R. Borghi, M. Santarsiero, “Few-optical-cycles Bessel–Gauss pulsed beams in free space,” Phys. Rev. E 62, 5729–5737 (2000).
[CrossRef]

1999 (7)

H. D. Cheung, E. V. Jull, “Scattering of antenna beams by local cylinders,” J. Electromagn. Waves Appl. 13, 1315–1331 (1999).
[CrossRef]

A. A. Ergin, B. Shanker, E. Michielssen, “The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena,” IEEE Trans Antennas Propag. 41, 39–52 (1999).
[CrossRef]

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

T. Melamed, E. Heyman, L. B. 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]

B. Rao, L. Carin, “Beam-tracing-based inverse scattering for general aperture antennas,” J. Opt. Soc. Am. A 16, 2219–2231 (1999).
[CrossRef]

S. Feng, H. G. Winful, “Spatiotemporal transformations of isodiffracting ultrashort pulses by nondispersive quadratic phase media,” J. Opt. Soc. Am. A 16, 2500–2509 (1999).
[CrossRef]

M. A. Porras, “Nonsinusoidal few-cycle pulsed light beams in free space,” J. Opt. Soc. Am. B 16, 1468–1474 (1999).
[CrossRef]

1998 (9)

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]

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

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

T. J. Cloutier, A. Safaeincili, D. E. Chimenti, S. Zeroug, L. B. Felsen, “Ultrasonic beam reflection from fluid-loaded cylindrical shells,” J. Appl. Phys. 83, 2408–2419 (1998).
[CrossRef]

B. Rao, L. Carin, “Hybrid (parabolic equation) (Gaussian beam) algorithm for wave propagation through large inhomogeneous regions,” IEEE Trans. Antennas Propag. 46, 700–709 (1998).
[CrossRef]

D. Lugara, C. Letrou, “Alternative to Gabor’s representation of plane aperture radiation,” Electron. Lett. 34, 2286–2287 (1998).
[CrossRef]

K. Oughstun, “The angular spectrum representation and the Sherman expansion of pulsed EM fields in dispersive attenuative media,” Pure Appl. Opt. 7, 1059–1078 (1998).
[CrossRef]

J. Oz, E. Heyman, “Modal theory for the two-frequency mutual coherence function in random media. Beam waves,” Waves Random Media 8, 159–174 (1998).
[CrossRef]

M. A. Porras, “Ultrashort pulsed Gaussian light beams,” Phys. Rev. E 58, 1086–1093 (1998).
[CrossRef]

1997 (4)

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

A. N. Norris, T. B. Hansen, “Exact complex source representations of time-harmonic radiation,” Wave Motion 25, 127–141 (1997).
[CrossRef]

T. Melamed, E. Heyman, “Spectral analysis of time-domain diffraction tomography,” Radio Sci. 32, 593–604 (1997).
[CrossRef]

T. B. Hansen, A. N. Norris, “Exact complex source representations of transient radiation,” Wave Motion 26, 101–115 (1997).
[CrossRef]

1996 (3)

J. Gozani, “Pulsed beam propagation through random media,” Opt. Lett. 21, 1712–1714 (1996).
[CrossRef] [PubMed]

E. Heyman, “Transient plane wave spectrum representation for radiation from volume source distribution,” J. Math. Phys. 37, 658–681 (1996).
[CrossRef]

S. Zeroug, F. E. Stanke, R. Burridge, “A complex-transducer-point model for finite emitting and receiving ultrasonic transducers,” Wave Motion 24, 21–40 (1996).
[CrossRef]

1995 (3)

E. Heyman, R. Ianconescu, “Pulsed beam diffraction by a perfectly conducting wedge. Part II: local scattering models,” IEEE Trans. Antennas Propag. 43, 519–528 (1995).
[CrossRef]

Y. Dezhong, “Complex source representation of time harmonic radiation from a plane aperture,” IEEE Trans. Antennas Propag. 43, 720–723 (1995).
[CrossRef]

A. M. Shaarawi, I. M. Besieris, R. W. Ziolkowski, S. M. Sedky, “Generation of approximate focus-wave-mode pulses from wide-band dynamic Gaussian apertures,” J. Opt. Soc. Am. A 12, 1954–1964 (1995).
[CrossRef]

1994 (6)

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

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

R. Ianconescu, E. Heyman, “Pulsed beam diffraction by a perfectly conducting wedge. Part I: exact solution,” IEEE Trans. Antennas Propag. 42, 1377–1385 (1994).
[CrossRef]

T. B. Hansen, A. D. Yaghjian, “Planar near field scanning in the time domain. Part I: formulation,” IEEE Trans. Antennas Propag. 42, 1280–1291 (1994).
[CrossRef]

T. B. Hansen, A. D. Yaghjian, “Planar near field scanning in the time domain. Part II: sampling theorem and computation schemes,” IEEE Trans. Antennas Propag. 42, 1292–1300 (1994).
[CrossRef]

S. Zeroug, L. B. Felsen, “Nonspecular reflection of two- and three-dimensional acoustic beams from fluid-immersed plane-layered elastic structures,” J. Acoust. Soc. Am. 95, 3075–3089 (1994).
[CrossRef]

1993 (2)

E. Heyman, R. Strachielevitz, D. Koslof, “Pulsed beam reflection and transmission at a planar interface: exact solutions and approximate local models,” Wave Motion 18, 315–343 (1993).
[CrossRef]

B. Z. Steinberg, E. Heyman, “The local Radon transform and variable scale resolution with application to time-dependent radiation,” SIAM J. Appl. Math 53, 381–400 (1993).
[CrossRef]

1992 (4)

A. Wünsche, “Transition from the paraxial approximation to exact solutions of the wave equation and application to Gaussian beams,” J. Opt. Soc. Am. A 9, 765–774 (1992).
[CrossRef]

E. Heyman, I. Beracha, “Complex multipole pulsed beams and Hermite pulsed beams: a novel expansion scheme for transient radiation from well-collimated apertures,” J. Opt. Soc. Am. A 9, 1779–1793 (1992).
[CrossRef]

J.-Y. Lu, J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free space scalar wave equations and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19–31 (1992).
[CrossRef]

S. Zeroug, L. B. Felsen, “Nonspecular reflection of beams forms liquid–solid interfaces,” J. Nondestruct. Eval. 11, 263–278 (1992).
[CrossRef]

1991 (6)

G. A. Suedan, E. V. Jull, “3-dimensional scalar beam diffraction by a half plane,” Comput. Phys. Commun. 68, 346–352 (1991).
[CrossRef]

G. A. Suedan, E. V. Jull, “Beam diffraction by planar and parabolic reflectors,” IEEE Trans. Antennas Propag. 39, 521–527 (1991).
[CrossRef]

R. J. Burkholder, P. H. Pathak, “Analysis of EM penetration into and scattering by electrically large open waveguide cavities using Gaussian beam shooting,” Proc. IEEE 79, 1401–1412 (1991).
[CrossRef]

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

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

B. Z. Steinberg, E. Heyman, “Phase-space beam summation for time-dependent radiation from large apertures: discretized parameterization,” J. Opt. Soc. Am. A 8, 959–966 (1991).
[CrossRef]

1990 (4)

H. E. Moses, R. T. Prosser, “Acoustic and electromagnetic bullets. New exact solutions of the acoustic and Maxwell’s equation,” SIAM J. Appl. Math. 50, 1325–1340 (1990).
[CrossRef]

E. Heyman, B. Z. Steinberg, R. Ianconescu, “Electromagnetic complex source pulsed beam fields,” IEEE Trans. Antennas Propag. 38, 957–963 (1990).
[CrossRef]

J. J. Maciel, L. B. Felsen, “Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers: I—plane layer,” IEEE Trans. Antennas Propag. 38, 1607–1617 (1990).
[CrossRef]

J. J. Maciel, L. B. Felsen, “Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers: II—circular layer,” IEEE Trans. Antennas Propag. 38, 1618–1624 (1990).
[CrossRef]

1989 (4)

J. J. Maciel, L. B. Felsen, “Systematic study of fields due to extended apertures by Gaussian beam discretization,” IEEE Trans. Antennas Propag. 37, 884–892 (1989).
[CrossRef]

E. Heyman, “Complex source pulsed beam expansion of transient radiation,” Wave Motion 11, 337–349 (1989).
[CrossRef]

E. Heyman, “The focus wave mode: a dilemma with causality,” IEEE Trans. Antennas Propag. 37, 1604–1608 (1989).
[CrossRef]

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

1988 (1)

1987 (10)

E. Heyman, B. Z. Steinberg, “A spectral analysis of complex-source pulsed beams,” J. Opt. Soc. Am. A 4, 473–480 (1987).
[CrossRef]

E. Heyman, B. Z. Steinberg, L. B. Felsen, “Spectral analysis of focus wave modes,” J. Opt. Soc. Am. A 4, 2081–2091 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction free beam,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

I. T. Lu, L. B. Felsen, Y. Z. Ruan, “Spectral aspects of the Gaussian beam method: reflection from homogeneous half space,” Geophys. J. R. Astron. Soc. 89, 915–922 (1987).
[CrossRef]

E. Heyman, L. B. Felsen, “Weakly dispersive spectral theory of transients (STT). Part I: formulation and interpretation,” IEEE Trans. Antennas Propag. 35, 80–86 (1987).
[CrossRef]

E. Heyman, L. B. Felsen, “Weakly dispersive spectral theory of transients (STT). Part II: evaluation of the spectral integral,” IEEE Trans. Antennas Propag. 35, 574–580 (1987).
[CrossRef]

E. Heyman, “Weakly dispersive spectral theory of transients (STT). Part III: applications,” IEEE Trans. Antennas Propag. 35, 1258–1266 (1987).
[CrossRef]

E. Heyman, L. B. Felsen, “Real and complex spectra—an alternative view of WKBJ seismograms,” Geophys. J. R. Astron. Soc. 91, 1087–1126 (1987).
[CrossRef]

B. S. White, A. Noris, A. Bayliss, R. Burridge, “Some remarks on the Gaussian beam summation method,” Geophys. J. R. Astron. Soc. 89, 579–636 (1987).
[CrossRef]

1986 (9)

A. J. Bogush, R. E. Elkins, “Gaussian beam expansions for large aperture antennas,” IEEE Trans. Antennas Propag. 34, 228–243 (1986).
[CrossRef]

E. Heyman, L. B. Felsen, “Propagating pulsed beam solution by complex source parameter substitution,” IEEE Trans. Antennas Propag. 34, 1062–1065 (1986).
[CrossRef]

H. E. Moses, R. T. Prosser, “Initial conditions, sources, and currents for prescribed time-dependent acoustic and electromagnetic fields in three dimensions. Part I: the inverse initial value problem. Acoustic and electromagnetic ‘bullets,’ expanding waves, and implodidng waves,” IEEE Trans. Antennas Propag. 34, 188–196 (1986).
[CrossRef]

J. M. Arnold, “Spectral synthesis of uniform wave functions,” Wave Motion 8, 135–150 (1986).
[CrossRef]

E. Zauderer, “Complex argument Hermite–Gaussian and Laguerre–Gaussian beams,” J. Opt. Soc. Am. A 3, 465–469 (1986).
[CrossRef]

L. B. Felsen, “Real spectra, complex spectra, compact spectra,” J. Opt. Soc. Am. A 3, 486–496 (1986).
[CrossRef]

P. D. Einziger, S. Raz, M. Shapira, “Gabor representation and aperture theory,” J. Opt. Soc. Am. A 3, 508–522 (1986).
[CrossRef]

Y. Z. Ruan, L. B. Felsen, “Reflection and transmission of beams at a curved interface,” J. Opt. Soc. Am. A 3, 566–579 (1986).
[CrossRef]

A. N. Norris, “Complex point-source representation of real sources and the Gaussian beam summation method,” J. Opt. Soc. Am. A 3, 2005–2010 (1986).
[CrossRef]

1985 (5)

T. Takenaka, M. Yokota, O. Fukumitsu, “Propagation of light beams beyond the paraxial approximation,” J. Opt. Soc. Am. A 2, 826–829 (1985).
[CrossRef]

C. J. Thompson, C. H. Chapman, “An introduction to Maslov’s asymptotic method,” Geophys. J. R. Astron. Soc. 83, 143–168 (1985).
[CrossRef]

R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,” J. Math. Phys. 26, 861–863 (1985).
[CrossRef]

X. J. Gao, L. B. Felsen, “Complex ray analysis of beam transmission through two-dimensional radomes,” IEEE Trans. Antennas Propag. 33, 963–975 (1985).
[CrossRef]

V. C̆ervený, “Gaussian beam synthetic seismograms,” J. Geophys. Res. 58, 44–72 (1985).

1984 (2)

G. Ghione, I. Montrosset, L. B. Felsen, “Complex ray analysis of radiation from large apertures with tapered illumination,” IEEE Trans. Antennas Propag. 32, 689–693 (1984).
[CrossRef]

R. W. Ziolkowski, G. A. Deschamps, “The asymptotic evaluation of high-frequency fields near a caustic: an introduction to Maslov’s method,” Radio Sci. 19, 1001–1025 (1984).
[CrossRef]

1983 (2)

G. P. Agrawal, M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983).
[CrossRef]

J. N. Brittingham, “Focus wave modes in homogeneous Maxwell’s equations: transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
[CrossRef]

1982 (4)

P. D. Einziger, L. B. Felsen, “Evanescent waves and complex rays,” IEEE Trans. Antennas Propag. 30, 594–604 (1982).
[CrossRef]

M. M. Popov, “A new method of computation of wave fields using Gaussian beams,” Wave Motion 4, 85–95 (1982).
[CrossRef]

V. C̆ervený, M. M. Popov, I. Ps̆enc̆hik, “Computation of wave films in inhomogeneous media—Gaussian beam approach,” Geophys. J. R. Astron. Soc. 70, 109–128 (1982).
[CrossRef]

J. V. Hasselmann, L. B. Felsen, “Asymptotic analysis of parabolic reflector antennas,” IEEE Trans. Antennas Propag. 30, 677–685 (1982).
[CrossRef]

1981 (1)

M. Couture, P. A. Bélanger, “From Gaussian beam tocomplex-source-point spherical wave,” Phys. Rev. A 24, 355–359 (1981).
[CrossRef]

1980 (3)

J. M. Arnold, L. B. Felsen, “Rigorous asymptotic theory of evanescent waves for guided propagation,” J. Acoust. Soc. Am. 67, 757–763 (1980).
[CrossRef]

J. M. Arnold, L. B. Felsen, “Rigorous evanescent wave theory for guided modes in graded index optical fibers,” IEEE Trans. Microwave Theory Tech. 28, 996–999 (1980).
[CrossRef]

M. J. Bastiaans, “The expansion of an optical signal into a discrete set of Gaussian beams,” Optik 57, 95–102 (1980).

1979 (2)

A. L. Cullen, P. K. Yu, “Complex source-point theory of the electromagnetic open resonator,” Proc. R. Soc. London, Ser. A 366, 155–171 (1979).
[CrossRef]

A. C. Green, H. L. Bertoni, L. B. Felsen, “Properties of the shadow cast by a half-screen when illuminated by a Gaussian beam,” J. Opt. Soc. Am. 69, 1503–1508 (1979).
[CrossRef]

1977 (3)

S. Y. Shin, L. B. Felsen, “Gaussian beam modes by multipoles with complex source points,” J. Opt. Soc. Am. 67, 699–700 (1977).
[CrossRef]

L. B. Felsen, “Rays, modes, and beams in optical fiber waveguides,” Opt. Quantum Electron. 9, 189–195 (1977).
[CrossRef]

S. Y. Shin, L. B. Felsen, “Lateral shifts of totally reflected Gaussian beams,” Radio Sci. 12, 551–564 (1977).
[CrossRef]

1976 (1)

1975 (1)

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

1974 (3)

S. Choudhary, L. B. Felsen, “Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking,” Proc. IEEE 62, 1530–1541 (1974).
[CrossRef]

W. D. Wang, G. A. Deschamps, “Application of complex ray tracing to scattering problems,” Proc. IEEE 62, 1541–1551 (1974).
[CrossRef]

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

1973 (3)

J. W. Ra, H. Bertoni, L. B. Felsen, “Reflection and transmission of beams at dielectric interfaces,” SIAM J. Appl. Math. 24, 396–412 (1973).
[CrossRef]

S. Choudhary, L. B. Felsen, “Asymptotic theory for inhomogeneous waves,” IEEE Trans. Antennas Propag. 21, 827–842 (1973).
[CrossRef]

A. E. Siegman, “Hermite–Gaussian functions of complex argument as optical-beam eigenfunctions,” J. Opt. Soc. Am. 63, 1093–1094 (1973).
[CrossRef]

1972 (1)

G. A. Deschamps, “Ray techniques in electromagnetics,” Proc. IEEE 60, 1022–1035 (1972).
[CrossRef]

1971 (2)

J. B. Keller, W. Streifer, “Complex rays with an application to Gaussian beams,” J. Opt. Soc. Am. 61, 40–43 (1971).
[CrossRef]

G. A. Deschamps, “Gaussian beams as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
[CrossRef]

1968 (1)

Yu. A. Kravtsov, “Two new asymptotic techniques for the theory of wave propagation in inhomogeneous media,” Sov. Phys. Acoust. 14, 1–17 (1968).

1967 (1)

Yu. A. Kravtsov, “Complex rays and complex caustics,” Radiophys. Quantum Electron. 10, 719–730 (1967).
[CrossRef]

1966 (1)

H. Kogelnik, T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983).
[CrossRef]

Arnold, J. M.

J. M. Arnold, “Spectral synthesis of uniform wave functions,” Wave Motion 8, 135–150 (1986).
[CrossRef]

J. M. Arnold, L. B. Felsen, “Rigorous asymptotic theory of evanescent waves for guided propagation,” J. Acoust. Soc. Am. 67, 757–763 (1980).
[CrossRef]

J. M. Arnold, L. B. Felsen, “Rigorous evanescent wave theory for guided modes in graded index optical fibers,” IEEE Trans. Microwave Theory Tech. 28, 996–999 (1980).
[CrossRef]

Asatryan, A. A.

Yu. A. Kravtsov, G. W. Forbes, A. A. Asatryan, “Theory and applications of complex rays,” in Vol. 39 of Progress in Optics Series (Elsevier, Amsterdam, 1999).

Babic, V. M.

V. M. Babič, V. S. Buldyrev, Short-Wavelength Diffraction Theory: Asymptotic Methods, E. F. Kuester, translator (Springer-Verlag, Berlin, 1990) [Russian edition: Asymptotic Methods in Short-Wavelength Diffraction Problems: The Model Problem Method (Nauka, Moscow, 1972)].

V. M. Babič, N. Y. Kirpičnikova, The Boundary Layer Method in Diffraction Theory, E. F. Kuester, translator (Springer-Verlag, Berlin, 1979).

Barrett, H. H.

Bastiaans, M. J.

M. J. Bastiaans, “The expansion of an optical signal into a discrete set of Gaussian beams,” Optik 57, 95–102 (1980).

M. J. Bastiaans, “Signal descriptions by means of a local frequency spectrum,” in Transformation in Optical Signal Processing, W. T. Rhodes, ed., Proc. SPIE373, 49–62 (1981).
[CrossRef]

Bayliss, A.

B. S. White, A. Noris, A. Bayliss, R. Burridge, “Some remarks on the Gaussian beam summation method,” Geophys. J. R. Astron. Soc. 89, 579–636 (1987).
[CrossRef]

Bélanger, P. A.

M. Couture, P. A. Bélanger, “From Gaussian beam tocomplex-source-point spherical wave,” Phys. Rev. A 24, 355–359 (1981).
[CrossRef]

Beracha, I.

Bertoni, H.

J. W. Ra, H. Bertoni, L. B. Felsen, “Reflection and transmission of beams at dielectric interfaces,” SIAM J. Appl. Math. 24, 396–412 (1973).
[CrossRef]

Bertoni, H. L.

Besieris, I. M.

Boersma, J.

E. Heyman, A. G. Tijhuis, J. Boersma, “Spherical and collimated pulsed fields in conducting media,” in Proceedings of the Union Radio-Scientifique Internationale Trianum International Symposium on Electromagnetic Theory (Union Radio-Scientifique Internationale, Gent, Belgium, 1995), pp. 643–645.

Bogush, A. J.

A. J. Bogush, R. E. Elkins, “Gaussian beam expansions for large aperture antennas,” IEEE Trans. Antennas Propag. 34, 228–243 (1986).
[CrossRef]

Borghi, R.

M. A. Porras, R. Borghi, M. Santarsiero, “Few-optical-cycles Bessel–Gauss pulsed beams in free space,” Phys. Rev. E 62, 5729–5737 (2000).
[CrossRef]

Brittingham, J. N.

J. N. Brittingham, “Focus wave modes in homogeneous Maxwell’s equations: transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
[CrossRef]

Buldyrev, V. S.

V. M. Babič, V. S. Buldyrev, Short-Wavelength Diffraction Theory: Asymptotic Methods, E. F. Kuester, translator (Springer-Verlag, Berlin, 1990) [Russian edition: Asymptotic Methods in Short-Wavelength Diffraction Problems: The Model Problem Method (Nauka, Moscow, 1972)].

Burkholder, R. J.

R. J. Burkholder, P. H. Pathak, “Analysis of EM penetration into and scattering by electrically large open waveguide cavities using Gaussian beam shooting,” Proc. IEEE 79, 1401–1412 (1991).
[CrossRef]

H. T. Chou, P. H. Pathak, R. J. Burkholder, “Novel Gaussian beam method for the rapid analysis of large reflector antennas,” IEEE Trans. Antennas Propag. (to be published).

Burridge, R.

S. Zeroug, F. E. Stanke, R. Burridge, “A complex-transducer-point model for finite emitting and receiving ultrasonic transducers,” Wave Motion 24, 21–40 (1996).
[CrossRef]

B. S. White, A. Noris, A. Bayliss, R. Burridge, “Some remarks on the Gaussian beam summation method,” Geophys. J. R. Astron. Soc. 89, 579–636 (1987).
[CrossRef]

C?ervený, V.

V. C̆ervený, “Gaussian beam synthetic seismograms,” J. Geophys. Res. 58, 44–72 (1985).

V. C̆ervený, M. M. Popov, I. Ps̆enc̆hik, “Computation of wave films in inhomogeneous media—Gaussian beam approach,” Geophys. J. R. Astron. Soc. 70, 109–128 (1982).
[CrossRef]

Carin, L.

B. Rao, L. Carin, “Beam-tracing-based inverse scattering for general aperture antennas,” J. Opt. Soc. Am. A 16, 2219–2231 (1999).
[CrossRef]

B. Rao, L. Carin, “Hybrid (parabolic equation) (Gaussian beam) algorithm for wave propagation through large inhomogeneous regions,” IEEE Trans. Antennas Propag. 46, 700–709 (1998).
[CrossRef]

Castañon, D.

V. Galdi, D. Castañon, L. B. Felsen are preparing a paper titled “Reconstruction of moderately rough interfaces via quasi-ray Gaussian beams” for publication.

V. Galdi, D. Castañon, L. B. Felsen, “Quasi-ray Gaussian beam algorithms for time-harmonic two-dimensional scattering by moderately rough interfaces,” IEEE Trans. Antennas Propag. (to be published).

Chapman, C. H.

C. J. Thompson, C. H. Chapman, “An introduction to Maslov’s asymptotic method,” Geophys. J. R. Astron. Soc. 83, 143–168 (1985).
[CrossRef]

Cheung, H. D.

H. D. Cheung, E. V. Jull, “Scattering of antenna beams by local cylinders,” J. Electromagn. Waves Appl. 13, 1315–1331 (1999).
[CrossRef]

Chimenti, D. E.

T. J. Cloutier, A. Safaeincili, D. E. Chimenti, S. Zeroug, L. B. Felsen, “Ultrasonic beam reflection from fluid-loaded cylindrical shells,” J. Appl. Phys. 83, 2408–2419 (1998).
[CrossRef]

Chou, H. T.

H. T. Chou, P. H. Pathak, R. J. Burkholder, “Novel Gaussian beam method for the rapid analysis of large reflector antennas,” IEEE Trans. Antennas Propag. (to be published).

Choudhary, S.

S. Choudhary, L. B. Felsen, “Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking,” Proc. IEEE 62, 1530–1541 (1974).
[CrossRef]

S. Choudhary, L. B. Felsen, “Asymptotic theory for inhomogeneous waves,” IEEE Trans. Antennas Propag. 21, 827–842 (1973).
[CrossRef]

Cloutier, T. J.

T. J. Cloutier, A. Safaeincili, D. E. Chimenti, S. Zeroug, L. B. Felsen, “Ultrasonic beam reflection from fluid-loaded cylindrical shells,” J. Appl. Phys. 83, 2408–2419 (1998).
[CrossRef]

Couture, M.

M. Couture, P. A. Bélanger, “From Gaussian beam tocomplex-source-point spherical wave,” Phys. Rev. A 24, 355–359 (1981).
[CrossRef]

Cullen, A. L.

A. L. Cullen, P. K. Yu, “Complex source-point theory of the electromagnetic open resonator,” Proc. R. Soc. London, Ser. A 366, 155–171 (1979).
[CrossRef]

Deschamps, G. A.

R. W. Ziolkowski, G. A. Deschamps, “The asymptotic evaluation of high-frequency fields near a caustic: an introduction to Maslov’s method,” Radio Sci. 19, 1001–1025 (1984).
[CrossRef]

W. D. Wang, G. A. Deschamps, “Application of complex ray tracing to scattering problems,” Proc. IEEE 62, 1541–1551 (1974).
[CrossRef]

G. A. Deschamps, “Ray techniques in electromagnetics,” Proc. IEEE 60, 1022–1035 (1972).
[CrossRef]

G. A. Deschamps, “Gaussian beams as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
[CrossRef]

Dezhong, Y.

Y. Dezhong, “Complex source representation of time harmonic radiation from a plane aperture,” IEEE Trans. Antennas Propag. 43, 720–723 (1995).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction free beam,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction free beam,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Einziger, P. D.

P. D. Einziger, S. Raz, M. Shapira, “Gabor representation and aperture theory,” J. Opt. Soc. Am. A 3, 508–522 (1986).
[CrossRef]

P. D. Einziger, L. B. Felsen, “Evanescent waves and complex rays,” IEEE Trans. Antennas Propag. 30, 594–604 (1982).
[CrossRef]

Elkins, R. E.

A. J. Bogush, R. E. Elkins, “Gaussian beam expansions for large aperture antennas,” IEEE Trans. Antennas Propag. 34, 228–243 (1986).
[CrossRef]

Ergin, A. A.

A. A. Ergin, B. Shanker, E. Michielssen, “The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena,” IEEE Trans Antennas Propag. 41, 39–52 (1999).
[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]

Felsen, L. B.

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

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

T. J. Cloutier, A. Safaeincili, D. E. Chimenti, S. Zeroug, L. B. Felsen, “Ultrasonic beam reflection from fluid-loaded cylindrical shells,” J. Appl. Phys. 83, 2408–2419 (1998).
[CrossRef]

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

S. Zeroug, L. B. Felsen, “Nonspecular reflection of two- and three-dimensional acoustic beams from fluid-immersed plane-layered elastic structures,” J. Acoust. Soc. Am. 95, 3075–3089 (1994).
[CrossRef]

S. Zeroug, L. B. Felsen, “Nonspecular reflection of beams forms liquid–solid interfaces,” J. Nondestruct. Eval. 11, 263–278 (1992).
[CrossRef]

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

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

J. J. Maciel, L. B. Felsen, “Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers: I—plane layer,” IEEE Trans. Antennas Propag. 38, 1607–1617 (1990).
[CrossRef]

J. J. Maciel, L. B. Felsen, “Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers: II—circular layer,” IEEE Trans. Antennas Propag. 38, 1618–1624 (1990).
[CrossRef]

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

J. J. Maciel, L. B. Felsen, “Systematic study of fields due to extended apertures by Gaussian beam discretization,” IEEE Trans. Antennas Propag. 37, 884–892 (1989).
[CrossRef]

E. Heyman, L. B. Felsen, “Real and complex spectra—an alternative view of WKBJ seismograms,” Geophys. J. R. Astron. Soc. 91, 1087–1126 (1987).
[CrossRef]

I. T. Lu, L. B. Felsen, Y. Z. Ruan, “Spectral aspects of the Gaussian beam method: reflection from homogeneous half space,” Geophys. J. R. Astron. Soc. 89, 915–922 (1987).
[CrossRef]

E. Heyman, L. B. Felsen, “Weakly dispersive spectral theory of transients (STT). Part I: formulation and interpretation,” IEEE Trans. Antennas Propag. 35, 80–86 (1987).
[CrossRef]

E. Heyman, L. B. Felsen, “Weakly dispersive spectral theory of transients (STT). Part II: evaluation of the spectral integral,” IEEE Trans. Antennas Propag. 35, 574–580 (1987).
[CrossRef]

E. Heyman, B. Z. Steinberg, L. B. Felsen, “Spectral analysis of focus wave modes,” J. Opt. Soc. Am. A 4, 2081–2091 (1987).
[CrossRef]

Y. Z. Ruan, L. B. Felsen, “Reflection and transmission of beams at a curved interface,” J. Opt. Soc. Am. A 3, 566–579 (1986).
[CrossRef]

E. Heyman, L. B. Felsen, “Propagating pulsed beam solution by complex source parameter substitution,” IEEE Trans. Antennas Propag. 34, 1062–1065 (1986).
[CrossRef]

L. B. Felsen, “Real spectra, complex spectra, compact spectra,” J. Opt. Soc. Am. A 3, 486–496 (1986).
[CrossRef]

X. J. Gao, L. B. Felsen, “Complex ray analysis of beam transmission through two-dimensional radomes,” IEEE Trans. Antennas Propag. 33, 963–975 (1985).
[CrossRef]

G. Ghione, I. Montrosset, L. B. Felsen, “Complex ray analysis of radiation from large apertures with tapered illumination,” IEEE Trans. Antennas Propag. 32, 689–693 (1984).
[CrossRef]

P. D. Einziger, L. B. Felsen, “Evanescent waves and complex rays,” IEEE Trans. Antennas Propag. 30, 594–604 (1982).
[CrossRef]

J. V. Hasselmann, L. B. Felsen, “Asymptotic analysis of parabolic reflector antennas,” IEEE Trans. Antennas Propag. 30, 677–685 (1982).
[CrossRef]

J. M. Arnold, L. B. Felsen, “Rigorous evanescent wave theory for guided modes in graded index optical fibers,” IEEE Trans. Microwave Theory Tech. 28, 996–999 (1980).
[CrossRef]

J. M. Arnold, L. B. Felsen, “Rigorous asymptotic theory of evanescent waves for guided propagation,” J. Acoust. Soc. Am. 67, 757–763 (1980).
[CrossRef]

A. C. Green, H. L. Bertoni, L. B. Felsen, “Properties of the shadow cast by a half-screen when illuminated by a Gaussian beam,” J. Opt. Soc. Am. 69, 1503–1508 (1979).
[CrossRef]

S. Y. Shin, L. B. Felsen, “Gaussian beam modes by multipoles with complex source points,” J. Opt. Soc. Am. 67, 699–700 (1977).
[CrossRef]

L. B. Felsen, “Rays, modes, and beams in optical fiber waveguides,” Opt. Quantum Electron. 9, 189–195 (1977).
[CrossRef]

S. Y. Shin, L. B. Felsen, “Lateral shifts of totally reflected Gaussian beams,” Radio Sci. 12, 551–564 (1977).
[CrossRef]

L. B. Felsen, “Evanescent waves,” J. Opt. Soc. Am. 66, 751–760 (1976).
[CrossRef]

S. Choudhary, L. B. Felsen, “Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking,” Proc. IEEE 62, 1530–1541 (1974).
[CrossRef]

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

S. Choudhary, L. B. Felsen, “Asymptotic theory for inhomogeneous waves,” IEEE Trans. Antennas Propag. 21, 827–842 (1973).
[CrossRef]

J. W. Ra, H. Bertoni, L. B. Felsen, “Reflection and transmission of beams at dielectric interfaces,” SIAM J. Appl. Math. 24, 396–412 (1973).
[CrossRef]

V. Galdi, D. Castañon, L. B. Felsen, “Quasi-ray Gaussian beam algorithms for time-harmonic two-dimensional scattering by moderately rough interfaces,” IEEE Trans. Antennas Propag. (to be published).

L. B. Felsen, “Complex-source-point solutions of the field equations and their relation to the propagation and scattering of Gaussian beams,” in Symposia Matematica, Istituto Nazionale di Alta Matematica (Academic, London, 1976), Vol. XVIII, pp. 40–56.

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973); for a new printing see the IEEE Press Series on Electromagnetic Waves (Institute of Electrical and Electronics Engineers, New York, 1994).

V. Galdi, D. Castañon, L. B. Felsen are preparing a paper titled “Reconstruction of moderately rough interfaces via quasi-ray Gaussian beams” for publication.

Feng, S.

Forbes, G. W.

Yu. A. Kravtsov, G. W. Forbes, A. A. Asatryan, “Theory and applications of complex rays,” in Vol. 39 of Progress in Optics Series (Elsevier, Amsterdam, 1999).

Fukumitsu, O.

Galdi, V.

V. Galdi, D. Castañon, L. B. Felsen are preparing a paper titled “Reconstruction of moderately rough interfaces via quasi-ray Gaussian beams” for publication.

V. Galdi, D. Castañon, L. B. Felsen, “Quasi-ray Gaussian beam algorithms for time-harmonic two-dimensional scattering by moderately rough interfaces,” IEEE Trans. Antennas Propag. (to be published).

Gao, X. J.

X. J. Gao, L. B. Felsen, “Complex ray analysis of beam transmission through two-dimensional radomes,” IEEE Trans. Antennas Propag. 33, 963–975 (1985).
[CrossRef]

Ghione, G.

G. Ghione, I. Montrosset, L. B. Felsen, “Complex ray analysis of radiation from large apertures with tapered illumination,” IEEE Trans. Antennas Propag. 32, 689–693 (1984).
[CrossRef]

Goldsmith, P. F.

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications, Chapman and Hall Series on Microwave Technology and Techniques (Institute of Electrical and Electronics Engineers, New York, 1998).

Gori, F.

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Gozani, J.

Green, A. C.

Greenleaf, J. F.

J.-Y. Lu, J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free space scalar wave equations and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19–31 (1992).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Hansen, T. B.

A. N. Norris, T. B. Hansen, “Exact complex source representations of time-harmonic radiation,” Wave Motion 25, 127–141 (1997).
[CrossRef]

T. B. Hansen, A. N. Norris, “Exact complex source representations of transient radiation,” Wave Motion 26, 101–115 (1997).
[CrossRef]

T. B. Hansen, A. D. Yaghjian, “Planar near field scanning in the time domain. Part II: sampling theorem and computation schemes,” IEEE Trans. Antennas Propag. 42, 1292–1300 (1994).
[CrossRef]

T. B. Hansen, A. D. Yaghjian, “Planar near field scanning in the time domain. Part I: formulation,” IEEE Trans. Antennas Propag. 42, 1280–1291 (1994).
[CrossRef]

T. B. Hansen, A. D. Yaghjian, Plane-Wave Theory of Time-Domain Fields: Near-Field Scanning Applications, IEEE Press Series on Electromagnetic Wave Theory (Institute of Electrical and Electronics Engineers, New York, 1999).

Hasselmann, J. V.

J. V. Hasselmann, L. B. Felsen, “Asymptotic analysis of parabolic reflector antennas,” IEEE Trans. Antennas Propag. 30, 677–685 (1982).
[CrossRef]

Heyman, E.

E. Heyman, V. Lomakin, G. Kaiser, “Physical source realization of complex source pulsed beams,” J. Acoust. Soc. Am. 107, 1880–1891 (2000).
[CrossRef] [PubMed]

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

J. Oz, E. Heyman, “Modal theory for the two-frequency mutual coherence function in random media. Beam waves,” Waves Random Media 8, 159–174 (1998).
[CrossRef]

T. Melamed, E. Heyman, “Spectral analysis of time-domain diffraction tomography,” Radio Sci. 32, 593–604 (1997).
[CrossRef]

E. Heyman, “Transient plane wave spectrum representation for radiation from volume source distribution,” J. Math. Phys. 37, 658–681 (1996).
[CrossRef]

E. Heyman, R. Ianconescu, “Pulsed beam diffraction by a perfectly conducting wedge. Part II: local scattering models,” IEEE Trans. Antennas Propag. 43, 519–528 (1995).
[CrossRef]

R. Ianconescu, E. Heyman, “Pulsed beam diffraction by a perfectly conducting wedge. Part I: exact solution,” IEEE Trans. Antennas Propag. 42, 1377–1385 (1994).
[CrossRef]

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

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

E. Heyman, R. Strachielevitz, D. Koslof, “Pulsed beam reflection and transmission at a planar interface: exact solutions and approximate local models,” Wave Motion 18, 315–343 (1993).
[CrossRef]

B. Z. Steinberg, E. Heyman, “The local Radon transform and variable scale resolution with application to time-dependent radiation,” SIAM J. Appl. Math 53, 381–400 (1993).
[CrossRef]

E. Heyman, I. Beracha, “Complex multipole pulsed beams and Hermite pulsed beams: a novel expansion scheme for transient radiation from well-collimated apertures,” J. Opt. Soc. Am. A 9, 1779–1793 (1992).
[CrossRef]

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

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

B. Z. Steinberg, E. Heyman, “Phase-space beam summation for time-dependent radiation from large apertures: discretized parameterization,” J. Opt. Soc. Am. A 8, 959–966 (1991).
[CrossRef]

E. Heyman, B. Z. Steinberg, R. Ianconescu, “Electromagnetic complex source pulsed beam fields,” IEEE Trans. Antennas Propag. 38, 957–963 (1990).
[CrossRef]

E. Heyman, “The focus wave mode: a dilemma with causality,” IEEE Trans. Antennas Propag. 37, 1604–1608 (1989).
[CrossRef]

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

E. Heyman, “Complex source pulsed beam expansion of transient radiation,” Wave Motion 11, 337–349 (1989).
[CrossRef]

E. Heyman, “Weakly dispersive spectral theory of transients (STT). Part III: applications,” IEEE Trans. Antennas Propag. 35, 1258–1266 (1987).
[CrossRef]

E. Heyman, L. B. Felsen, “Weakly dispersive spectral theory of transients (STT). Part I: formulation and interpretation,” IEEE Trans. Antennas Propag. 35, 80–86 (1987).
[CrossRef]

E. Heyman, L. B. Felsen, “Real and complex spectra—an alternative view of WKBJ seismograms,” Geophys. J. R. Astron. Soc. 91, 1087–1126 (1987).
[CrossRef]

E. Heyman, L. B. Felsen, “Weakly dispersive spectral theory of transients (STT). Part II: evaluation of the spectral integral,” IEEE Trans. Antennas Propag. 35, 574–580 (1987).
[CrossRef]

E. Heyman, B. Z. Steinberg, “A spectral analysis of complex-source pulsed beams,” J. Opt. Soc. Am. A 4, 473–480 (1987).
[CrossRef]

E. Heyman, B. Z. Steinberg, L. B. Felsen, “Spectral analysis of focus wave modes,” J. Opt. Soc. Am. A 4, 2081–2091 (1987).
[CrossRef]

E. Heyman, L. B. Felsen, “Propagating pulsed beam solution by complex source parameter substitution,” IEEE Trans. Antennas Propag. 34, 1062–1065 (1986).
[CrossRef]

E. Heyman, A. G. Tijhuis, J. Boersma, “Spherical and collimated pulsed fields in conducting media,” in Proceedings of the Union Radio-Scientifique Internationale Trianum International Symposium on Electromagnetic Theory (Union Radio-Scientifique Internationale, Gent, Belgium, 1995), pp. 643–645.

E. Heyman, T. Melamed, “Space–time representation of ultra-wideband signals,” in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, New York, 1998), pp. 1–66, 103.

Ianconescu, R.

E. Heyman, R. Ianconescu, “Pulsed beam diffraction by a perfectly conducting wedge. Part II: local scattering models,” IEEE Trans. Antennas Propag. 43, 519–528 (1995).
[CrossRef]

R. Ianconescu, E. Heyman, “Pulsed beam diffraction by a perfectly conducting wedge. Part I: exact solution,” IEEE Trans. Antennas Propag. 42, 1377–1385 (1994).
[CrossRef]

E. Heyman, B. Z. Steinberg, R. Ianconescu, “Electromagnetic complex source pulsed beam fields,” IEEE Trans. Antennas Propag. 38, 957–963 (1990).
[CrossRef]

Jull, E. V.

H. D. Cheung, E. V. Jull, “Scattering of antenna beams by local cylinders,” J. Electromagn. Waves Appl. 13, 1315–1331 (1999).
[CrossRef]

G. A. Suedan, E. V. Jull, “Beam diffraction by planar and parabolic reflectors,” IEEE Trans. Antennas Propag. 39, 521–527 (1991).
[CrossRef]

G. A. Suedan, E. V. Jull, “3-dimensional scalar beam diffraction by a half plane,” Comput. Phys. Commun. 68, 346–352 (1991).
[CrossRef]

Kaiser, G.

E. Heyman, V. Lomakin, G. Kaiser, “Physical source realization of complex source pulsed beams,” J. Acoust. Soc. Am. 107, 1880–1891 (2000).
[CrossRef] [PubMed]

Keller, J. B.

Kirpicnikova, N. Y.

V. M. Babič, N. Y. Kirpičnikova, The Boundary Layer Method in Diffraction Theory, E. F. Kuester, translator (Springer-Verlag, Berlin, 1979).

Kogelnik, H.

H. Kogelnik, T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966).
[CrossRef]

Koslof, D.

E. Heyman, R. Strachielevitz, D. Koslof, “Pulsed beam reflection and transmission at a planar interface: exact solutions and approximate local models,” Wave Motion 18, 315–343 (1993).
[CrossRef]

Kravtsov, Yu. A.

Yu. A. Kravtsov, “Two new asymptotic techniques for the theory of wave propagation in inhomogeneous media,” Sov. Phys. Acoust. 14, 1–17 (1968).

Yu. A. Kravtsov, “Complex rays and complex caustics,” Radiophys. Quantum Electron. 10, 719–730 (1967).
[CrossRef]

Yu. A. Kravtsov, G. W. Forbes, A. A. Asatryan, “Theory and applications of complex rays,” in Vol. 39 of Progress in Optics Series (Elsevier, Amsterdam, 1999).

Landesman, B. T.

Lax, M.

G. P. Agrawal, M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983).
[CrossRef]

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Letrou, C.

D. Lugara, C. Letrou, “Alternative to Gabor’s representation of plane aperture radiation,” Electron. Lett. 34, 2286–2287 (1998).
[CrossRef]

Li, T.

H. Kogelnik, T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966).
[CrossRef]

Lomakin, V.

E. Heyman, V. Lomakin, G. Kaiser, “Physical source realization of complex source pulsed beams,” J. Acoust. Soc. Am. 107, 1880–1891 (2000).
[CrossRef] [PubMed]

Louisell, W. H.

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Lu, I. T.

I. T. Lu, L. B. Felsen, Y. Z. Ruan, “Spectral aspects of the Gaussian beam method: reflection from homogeneous half space,” Geophys. J. R. Astron. Soc. 89, 915–922 (1987).
[CrossRef]

Lu, J.-Y.

J.-Y. Lu, J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free space scalar wave equations and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19–31 (1992).
[CrossRef]

Lugara, D.

D. Lugara, C. Letrou, “Alternative to Gabor’s representation of plane aperture radiation,” Electron. Lett. 34, 2286–2287 (1998).
[CrossRef]

Maciel, J. J.

J. J. Maciel, L. B. Felsen, “Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers: I—plane layer,” IEEE Trans. Antennas Propag. 38, 1607–1617 (1990).
[CrossRef]

J. J. Maciel, L. B. Felsen, “Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers: II—circular layer,” IEEE Trans. Antennas Propag. 38, 1618–1624 (1990).
[CrossRef]

J. J. Maciel, L. B. Felsen, “Systematic study of fields due to extended apertures by Gaussian beam discretization,” IEEE Trans. Antennas Propag. 37, 884–892 (1989).
[CrossRef]

Marcuvitz, N.

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973); for a new printing see the IEEE Press Series on Electromagnetic Waves (Institute of Electrical and Electronics Engineers, New York, 1994).

McKnight, W. B.

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Melamed, T.

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

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

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

T. Melamed, E. Heyman, “Spectral analysis of time-domain diffraction tomography,” Radio Sci. 32, 593–604 (1997).
[CrossRef]

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

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

E. Heyman, T. Melamed, “Space–time representation of ultra-wideband signals,” in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, New York, 1998), pp. 1–66, 103.

Miceli, J. J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction free beam,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Michielssen, E.

A. A. Ergin, B. Shanker, E. Michielssen, “The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena,” IEEE Trans Antennas Propag. 41, 39–52 (1999).
[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]

Montrosset, I.

G. Ghione, I. Montrosset, L. B. Felsen, “Complex ray analysis of radiation from large apertures with tapered illumination,” IEEE Trans. Antennas Propag. 32, 689–693 (1984).
[CrossRef]

Moses, H. E.

H. E. Moses, R. T. Prosser, “Acoustic and electromagnetic bullets. New exact solutions of the acoustic and Maxwell’s equation,” SIAM J. Appl. Math. 50, 1325–1340 (1990).
[CrossRef]

H. E. Moses, R. T. Prosser, “Initial conditions, sources, and currents for prescribed time-dependent acoustic and electromagnetic fields in three dimensions. Part I: the inverse initial value problem. Acoustic and electromagnetic ‘bullets,’ expanding waves, and implodidng waves,” IEEE Trans. Antennas Propag. 34, 188–196 (1986).
[CrossRef]

Noris, A.

B. S. White, A. Noris, A. Bayliss, R. Burridge, “Some remarks on the Gaussian beam summation method,” Geophys. J. R. Astron. Soc. 89, 579–636 (1987).
[CrossRef]

Norris, A. N.

T. B. Hansen, A. N. Norris, “Exact complex source representations of transient radiation,” Wave Motion 26, 101–115 (1997).
[CrossRef]

A. N. Norris, T. B. Hansen, “Exact complex source representations of time-harmonic radiation,” Wave Motion 25, 127–141 (1997).
[CrossRef]

A. N. Norris, “Complex point-source representation of real sources and the Gaussian beam summation method,” J. Opt. Soc. Am. A 3, 2005–2010 (1986).
[CrossRef]

Oughstun, K.

K. Oughstun, “The angular spectrum representation and the Sherman expansion of pulsed EM fields in dispersive attenuative media,” Pure Appl. Opt. 7, 1059–1078 (1998).
[CrossRef]

Oz, J.

J. Oz, E. Heyman, “Modal theory for the two-frequency mutual coherence function in random media. Beam waves,” Waves Random Media 8, 159–174 (1998).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Pathak, P. H.

R. J. Burkholder, P. H. Pathak, “Analysis of EM penetration into and scattering by electrically large open waveguide cavities using Gaussian beam shooting,” Proc. IEEE 79, 1401–1412 (1991).
[CrossRef]

H. T. Chou, P. H. Pathak, R. J. Burkholder, “Novel Gaussian beam method for the rapid analysis of large reflector antennas,” IEEE Trans. Antennas Propag. (to be published).

Popov, M. M.

V. C̆ervený, M. M. Popov, I. Ps̆enc̆hik, “Computation of wave films in inhomogeneous media—Gaussian beam approach,” Geophys. J. R. Astron. Soc. 70, 109–128 (1982).
[CrossRef]

M. M. Popov, “A new method of computation of wave fields using Gaussian beams,” Wave Motion 4, 85–95 (1982).
[CrossRef]

Porras, M. A.

M. A. Porras, R. Borghi, M. Santarsiero, “Few-optical-cycles Bessel–Gauss pulsed beams in free space,” Phys. Rev. E 62, 5729–5737 (2000).
[CrossRef]

M. A. Porras, “Nonsinusoidal few-cycle pulsed light beams in free space,” J. Opt. Soc. Am. B 16, 1468–1474 (1999).
[CrossRef]

M. A. Porras, “Ultrashort pulsed Gaussian light beams,” Phys. Rev. E 58, 1086–1093 (1998).
[CrossRef]

Prosser, R. T.

H. E. Moses, R. T. Prosser, “Acoustic and electromagnetic bullets. New exact solutions of the acoustic and Maxwell’s equation,” SIAM J. Appl. Math. 50, 1325–1340 (1990).
[CrossRef]

H. E. Moses, R. T. Prosser, “Initial conditions, sources, and currents for prescribed time-dependent acoustic and electromagnetic fields in three dimensions. Part I: the inverse initial value problem. Acoustic and electromagnetic ‘bullets,’ expanding waves, and implodidng waves,” IEEE Trans. Antennas Propag. 34, 188–196 (1986).
[CrossRef]

Ps?enc?hik, I.

V. C̆ervený, M. M. Popov, I. Ps̆enc̆hik, “Computation of wave films in inhomogeneous media—Gaussian beam approach,” Geophys. J. R. Astron. Soc. 70, 109–128 (1982).
[CrossRef]

Ra, J. W.

J. W. Ra, H. Bertoni, L. B. Felsen, “Reflection and transmission of beams at dielectric interfaces,” SIAM J. Appl. Math. 24, 396–412 (1973).
[CrossRef]

Rao, B.

B. Rao, L. Carin, “Beam-tracing-based inverse scattering for general aperture antennas,” J. Opt. Soc. Am. A 16, 2219–2231 (1999).
[CrossRef]

B. Rao, L. Carin, “Hybrid (parabolic equation) (Gaussian beam) algorithm for wave propagation through large inhomogeneous regions,” IEEE Trans. Antennas Propag. 46, 700–709 (1998).
[CrossRef]

Raz, S.

Ruan, Y. Z.

I. T. Lu, L. B. Felsen, Y. Z. Ruan, “Spectral aspects of the Gaussian beam method: reflection from homogeneous half space,” Geophys. J. R. Astron. Soc. 89, 915–922 (1987).
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Y. Z. Ruan, L. B. Felsen, “Reflection and transmission of beams at a curved interface,” J. Opt. Soc. Am. A 3, 566–579 (1986).
[CrossRef]

Safaeincili, A.

T. J. Cloutier, A. Safaeincili, D. E. Chimenti, S. Zeroug, L. B. Felsen, “Ultrasonic beam reflection from fluid-loaded cylindrical shells,” J. Appl. Phys. 83, 2408–2419 (1998).
[CrossRef]

Santarsiero, M.

M. A. Porras, R. Borghi, M. Santarsiero, “Few-optical-cycles Bessel–Gauss pulsed beams in free space,” Phys. Rev. E 62, 5729–5737 (2000).
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A. A. Ergin, B. Shanker, E. Michielssen, “The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena,” IEEE Trans Antennas Propag. 41, 39–52 (1999).
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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).
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Shapira, M.

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S. Y. Shin, L. B. Felsen, “Gaussian beam modes by multipoles with complex source points,” J. Opt. Soc. Am. 67, 699–700 (1977).
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S. Y. Shin, L. B. Felsen, “Lateral shifts of totally reflected Gaussian beams,” Radio Sci. 12, 551–564 (1977).
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S. Y. Shin, L. B. Felsen, “Gaussian beams in anisotropic media,” Appl. Phys. 5, 239–250 (1974).
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S. Zeroug, F. E. Stanke, R. Burridge, “A complex-transducer-point model for finite emitting and receiving ultrasonic transducers,” Wave Motion 24, 21–40 (1996).
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Steinberg, B. Z.

Strachielevitz, R.

E. Heyman, R. Strachielevitz, D. Koslof, “Pulsed beam reflection and transmission at a planar interface: exact solutions and approximate local models,” Wave Motion 18, 315–343 (1993).
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G. A. Suedan, E. V. Jull, “3-dimensional scalar beam diffraction by a half plane,” Comput. Phys. Commun. 68, 346–352 (1991).
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Takenaka, T.

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C. J. Thompson, C. H. Chapman, “An introduction to Maslov’s asymptotic method,” Geophys. J. R. Astron. Soc. 83, 143–168 (1985).
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E. Heyman, A. G. Tijhuis, J. Boersma, “Spherical and collimated pulsed fields in conducting media,” in Proceedings of the Union Radio-Scientifique Internationale Trianum International Symposium on Electromagnetic Theory (Union Radio-Scientifique Internationale, Gent, Belgium, 1995), pp. 643–645.

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B. S. White, A. Noris, A. Bayliss, R. Burridge, “Some remarks on the Gaussian beam summation method,” Geophys. J. R. Astron. Soc. 89, 579–636 (1987).
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Winful, H. G.

Wünsche, A.

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T. B. Hansen, A. D. Yaghjian, “Planar near field scanning in the time domain. Part I: formulation,” IEEE Trans. Antennas Propag. 42, 1280–1291 (1994).
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T. B. Hansen, A. D. Yaghjian, “Planar near field scanning in the time domain. Part II: sampling theorem and computation schemes,” IEEE Trans. Antennas Propag. 42, 1292–1300 (1994).
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T. B. Hansen, A. D. Yaghjian, Plane-Wave Theory of Time-Domain Fields: Near-Field Scanning Applications, IEEE Press Series on Electromagnetic Wave Theory (Institute of Electrical and Electronics Engineers, New York, 1999).

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Yu, P. K.

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Zauderer, E.

Zeroug, S.

T. J. Cloutier, A. Safaeincili, D. E. Chimenti, S. Zeroug, L. B. Felsen, “Ultrasonic beam reflection from fluid-loaded cylindrical shells,” J. Appl. Phys. 83, 2408–2419 (1998).
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S. Zeroug, F. E. Stanke, R. Burridge, “A complex-transducer-point model for finite emitting and receiving ultrasonic transducers,” Wave Motion 24, 21–40 (1996).
[CrossRef]

S. Zeroug, L. B. Felsen, “Nonspecular reflection of two- and three-dimensional acoustic beams from fluid-immersed plane-layered elastic structures,” J. Acoust. Soc. Am. 95, 3075–3089 (1994).
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S. Zeroug, L. B. Felsen, “Nonspecular reflection of beams forms liquid–solid interfaces,” J. Nondestruct. Eval. 11, 263–278 (1992).
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Ziolkowski, R. W.

A. M. Shaarawi, I. M. Besieris, R. W. Ziolkowski, S. M. Sedky, “Generation of approximate focus-wave-mode pulses from wide-band dynamic Gaussian apertures,” J. Opt. Soc. Am. A 12, 1954–1964 (1995).
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R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,” J. Math. Phys. 26, 861–863 (1985).
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R. W. Ziolkowski, G. A. Deschamps, “The asymptotic evaluation of high-frequency fields near a caustic: an introduction to Maslov’s method,” Radio Sci. 19, 1001–1025 (1984).
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Appl. Phys. (1)

S. Y. Shin, L. B. Felsen, “Gaussian beams in anisotropic media,” Appl. Phys. 5, 239–250 (1974).
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Comput. Phys. Commun. (1)

G. A. Suedan, E. V. Jull, “3-dimensional scalar beam diffraction by a half plane,” Comput. Phys. Commun. 68, 346–352 (1991).
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Geophys. J. R. Astron. Soc. (5)

B. S. White, A. Noris, A. Bayliss, R. Burridge, “Some remarks on the Gaussian beam summation method,” Geophys. J. R. Astron. Soc. 89, 579–636 (1987).
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I. T. Lu, L. B. Felsen, Y. Z. Ruan, “Spectral aspects of the Gaussian beam method: reflection from homogeneous half space,” Geophys. J. R. Astron. Soc. 89, 915–922 (1987).
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E. Heyman, L. B. Felsen, “Real and complex spectra—an alternative view of WKBJ seismograms,” Geophys. J. R. Astron. Soc. 91, 1087–1126 (1987).
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IEEE Trans Antennas Propag. (1)

A. A. Ergin, B. Shanker, E. Michielssen, “The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena,” IEEE Trans Antennas Propag. 41, 39–52 (1999).
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IEEE Trans. Antennas Propag. (27)

T. Melamed, E. Heyman, L. B. Felsen, “Local spectral analysis of short-pulse-excited scattering from weakly inhomogeneous media. Part I: forward scattering,” IEEE Trans. Antennas Propag. 47, 1208–1217 (1999).
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T. Melamed, E. Heyman, L. B. 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).
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T. B. Hansen, A. D. Yaghjian, “Planar near field scanning in the time domain. Part II: sampling theorem and computation schemes,” IEEE Trans. Antennas Propag. 42, 1292–1300 (1994).
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G. A. Suedan, E. V. Jull, “Beam diffraction by planar and parabolic reflectors,” IEEE Trans. Antennas Propag. 39, 521–527 (1991).
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S. Choudhary, L. B. Felsen, “Asymptotic theory for inhomogeneous waves,” IEEE Trans. Antennas Propag. 21, 827–842 (1973).
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J. V. Hasselmann, L. B. Felsen, “Asymptotic analysis of parabolic reflector antennas,” IEEE Trans. Antennas Propag. 30, 677–685 (1982).
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G. Ghione, I. Montrosset, L. B. Felsen, “Complex ray analysis of radiation from large apertures with tapered illumination,” IEEE Trans. Antennas Propag. 32, 689–693 (1984).
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X. J. Gao, L. B. Felsen, “Complex ray analysis of beam transmission through two-dimensional radomes,” IEEE Trans. Antennas Propag. 33, 963–975 (1985).
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A. J. Bogush, R. E. Elkins, “Gaussian beam expansions for large aperture antennas,” IEEE Trans. Antennas Propag. 34, 228–243 (1986).
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P. D. Einziger, L. B. Felsen, “Evanescent waves and complex rays,” IEEE Trans. Antennas Propag. 30, 594–604 (1982).
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E. Heyman, L. B. Felsen, “Propagating pulsed beam solution by complex source parameter substitution,” IEEE Trans. Antennas Propag. 34, 1062–1065 (1986).
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E. Heyman, B. Z. Steinberg, R. Ianconescu, “Electromagnetic complex source pulsed beam fields,” IEEE Trans. Antennas Propag. 38, 957–963 (1990).
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E. Heyman, T. Melamed, “Certain considerations in aperture synthesis for ultrawideband/short-pulsed fields,” IEEE Trans. Antennas Propag. 42, 518–525 (1994).
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E. Heyman, “Pulsed beam propagation in an inhomogeneous medium,” IEEE Trans. Antennas Propag. 42, 311–319 (1994).
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R. Ianconescu, E. Heyman, “Pulsed beam diffraction by a perfectly conducting wedge. Part I: exact solution,” IEEE Trans. Antennas Propag. 42, 1377–1385 (1994).
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E. Heyman, R. Ianconescu, “Pulsed beam diffraction by a perfectly conducting wedge. Part II: local scattering models,” IEEE Trans. Antennas Propag. 43, 519–528 (1995).
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E. Heyman, L. B. Felsen, “Weakly dispersive spectral theory of transients (STT). Part I: formulation and interpretation,” IEEE Trans. Antennas Propag. 35, 80–86 (1987).
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E. Heyman, L. B. Felsen, “Weakly dispersive spectral theory of transients (STT). Part II: evaluation of the spectral integral,” IEEE Trans. Antennas Propag. 35, 574–580 (1987).
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E. Heyman, “Weakly dispersive spectral theory of transients (STT). Part III: applications,” IEEE Trans. Antennas Propag. 35, 1258–1266 (1987).
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B. Rao, L. Carin, “Hybrid (parabolic equation) (Gaussian beam) algorithm for wave propagation through large inhomogeneous regions,” IEEE Trans. Antennas Propag. 46, 700–709 (1998).
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J. J. Maciel, L. B. Felsen, “Systematic study of fields due to extended apertures by Gaussian beam discretization,” IEEE Trans. Antennas Propag. 37, 884–892 (1989).
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J. J. Maciel, L. B. Felsen, “Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers: I—plane layer,” IEEE Trans. Antennas Propag. 38, 1607–1617 (1990).
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J. J. Maciel, L. B. Felsen, “Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers: II—circular layer,” IEEE Trans. Antennas Propag. 38, 1618–1624 (1990).
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Y. Dezhong, “Complex source representation of time harmonic radiation from a plane aperture,” IEEE Trans. Antennas Propag. 43, 720–723 (1995).
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E. Heyman, “The focus wave mode: a dilemma with causality,” IEEE Trans. Antennas Propag. 37, 1604–1608 (1989).
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H. E. Moses, R. T. Prosser, “Initial conditions, sources, and currents for prescribed time-dependent acoustic and electromagnetic fields in three dimensions. Part I: the inverse initial value problem. Acoustic and electromagnetic ‘bullets,’ expanding waves, and implodidng waves,” IEEE Trans. Antennas Propag. 34, 188–196 (1986).
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IEEE Trans. Microwave Theory Tech. (1)

J. M. Arnold, L. B. Felsen, “Rigorous evanescent wave theory for guided modes in graded index optical fibers,” IEEE Trans. Microwave Theory Tech. 28, 996–999 (1980).
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IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

J.-Y. Lu, J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free space scalar wave equations and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19–31 (1992).
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J. Acoust. Soc. Am. (3)

J. M. Arnold, L. B. Felsen, “Rigorous asymptotic theory of evanescent waves for guided propagation,” J. Acoust. Soc. Am. 67, 757–763 (1980).
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T. J. Cloutier, A. Safaeincili, D. E. Chimenti, S. Zeroug, L. B. Felsen, “Ultrasonic beam reflection from fluid-loaded cylindrical shells,” J. Appl. Phys. 83, 2408–2419 (1998).
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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).
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T. Melamed, “Phase space beam summation: a local spectrum analysis of time dependent radiation,” J. Electromagn. Waves Appl. 11, 739–773 (1997).
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V. C̆ervený, “Gaussian beam synthetic seismograms,” J. Geophys. Res. 58, 44–72 (1985).

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R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,” J. Math. Phys. 26, 861–863 (1985).
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S. Zeroug, L. B. Felsen, “Nonspecular reflection of beams forms liquid–solid interfaces,” J. Nondestruct. Eval. 11, 263–278 (1992).
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J. Opt. Soc. Am. (5)

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A. Wünsche, “Transition from the paraxial approximation to exact solutions of the wave equation and application to Gaussian beams,” J. Opt. Soc. Am. A 9, 765–774 (1992).
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T. Melamed, L. B. Felsen, “Pulsed beam propagation in lossless dispersive media. II. A numerical example,” J. Opt. Soc. Am. A 15, 1277–1284 (1998).
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L. B. Felsen, “Real spectra, complex spectra, compact spectra,” J. Opt. Soc. Am. A 3, 486–496 (1986).
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P. D. Einziger, S. Raz, M. Shapira, “Gabor representation and aperture theory,” J. Opt. Soc. Am. A 3, 508–522 (1986).
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Y. Z. Ruan, L. B. Felsen, “Reflection and transmission of beams at a curved interface,” J. Opt. Soc. Am. A 3, 566–579 (1986).
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A. N. Norris, “Complex point-source representation of real sources and the Gaussian beam summation method,” J. Opt. Soc. Am. A 3, 2005–2010 (1986).
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E. Heyman, B. Z. Steinberg, “A spectral analysis of complex-source pulsed beams,” J. Opt. Soc. Am. A 4, 473–480 (1987).
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E. Heyman, B. Z. Steinberg, L. B. Felsen, “Spectral analysis of focus wave modes,” J. Opt. Soc. Am. A 4, 2081–2091 (1987).
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B. T. Landesman, H. H. Barrett, “Gaussian amplitude functions that are exact solutions to the scalar Helmholtz equation,” J. Opt. Soc. Am. A 5, 1610–1619 (1988).
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B. Z. Steinberg, E. Heyman, L. B. Felsen, “Phase-space beam summation for time-harmonic radiation from large apertures,” J. Opt. Soc. Am. A 8, 41–59 (1991).
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B. Z. Steinberg, E. Heyman, L. B. Felsen, “Phase-space beam summation for time-dependent radiation from large apertures: continuous parameterization,” J. Opt. Soc. Am. A 8, 943–958 (1991).
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B. Z. Steinberg, E. Heyman, “Phase-space beam summation for time-dependent radiation from large apertures: discretized parameterization,” J. Opt. Soc. Am. A 8, 959–966 (1991).
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E. Heyman, I. Beracha, “Complex multipole pulsed beams and Hermite pulsed beams: a novel expansion scheme for transient radiation from well-collimated apertures,” J. Opt. Soc. Am. A 9, 1779–1793 (1992).
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A. M. Shaarawi, I. M. Besieris, R. W. Ziolkowski, S. M. Sedky, “Generation of approximate focus-wave-mode pulses from wide-band dynamic Gaussian apertures,” J. Opt. Soc. Am. A 12, 1954–1964 (1995).
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J. Opt. Soc. Am. B (1)

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Opt. Quantum Electron. (1)

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Optik (1)

M. J. Bastiaans, “The expansion of an optical signal into a discrete set of Gaussian beams,” Optik 57, 95–102 (1980).

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Phys. Rev. E (2)

M. A. Porras, R. Borghi, M. Santarsiero, “Few-optical-cycles Bessel–Gauss pulsed beams in free space,” Phys. Rev. E 62, 5729–5737 (2000).
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M. A. Porras, “Ultrashort pulsed Gaussian light beams,” Phys. Rev. E 58, 1086–1093 (1998).
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Proc. R. Soc. London, Ser. A (1)

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Radio Sci. (3)

S. Y. Shin, L. B. Felsen, “Lateral shifts of totally reflected Gaussian beams,” Radio Sci. 12, 551–564 (1977).
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T. Melamed, E. Heyman, “Spectral analysis of time-domain diffraction tomography,” Radio Sci. 32, 593–604 (1997).
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R. W. Ziolkowski, G. A. Deschamps, “The asymptotic evaluation of high-frequency fields near a caustic: an introduction to Maslov’s method,” Radio Sci. 19, 1001–1025 (1984).
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T. B. Hansen, A. N. Norris, “Exact complex source representations of transient radiation,” Wave Motion 26, 101–115 (1997).
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S. Zeroug, F. E. Stanke, R. Burridge, “A complex-transducer-point model for finite emitting and receiving ultrasonic transducers,” Wave Motion 24, 21–40 (1996).
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J. M. Arnold, “Spectral synthesis of uniform wave functions,” Wave Motion 8, 135–150 (1986).
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Waves Random Media (1)

J. Oz, E. Heyman, “Modal theory for the two-frequency mutual coherence function in random media. Beam waves,” Waves Random Media 8, 159–174 (1998).
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E. Heyman, A. G. Tijhuis, J. Boersma, “Spherical and collimated pulsed fields in conducting media,” in Proceedings of the Union Radio-Scientifique Internationale Trianum International Symposium on Electromagnetic Theory (Union Radio-Scientifique Internationale, Gent, Belgium, 1995), pp. 643–645.

H. T. Chou, P. H. Pathak, R. J. Burkholder, “Novel Gaussian beam method for the rapid analysis of large reflector antennas,” IEEE Trans. Antennas Propag. (to be published).

Yu. A. Kravtsov, G. W. Forbes, A. A. Asatryan, “Theory and applications of complex rays,” in Vol. 39 of Progress in Optics Series (Elsevier, Amsterdam, 1999).

L. B. Felsen, “Complex-source-point solutions of the field equations and their relation to the propagation and scattering of Gaussian beams,” in Symposia Matematica, Istituto Nazionale di Alta Matematica (Academic, London, 1976), Vol. XVIII, pp. 40–56.

V. M. Babič, V. S. Buldyrev, Short-Wavelength Diffraction Theory: Asymptotic Methods, E. F. Kuester, translator (Springer-Verlag, Berlin, 1990) [Russian edition: Asymptotic Methods in Short-Wavelength Diffraction Problems: The Model Problem Method (Nauka, Moscow, 1972)].

V. M. Babič, N. Y. Kirpičnikova, The Boundary Layer Method in Diffraction Theory, E. F. Kuester, translator (Springer-Verlag, Berlin, 1979).

J. Fox, ed., Proceedings of the Symposium on Quasi-Optics (Polytechnic, Brooklyn, 1964).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications, Chapman and Hall Series on Microwave Technology and Techniques (Institute of Electrical and Electronics Engineers, New York, 1998).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973); for a new printing see the IEEE Press Series on Electromagnetic Waves (Institute of Electrical and Electronics Engineers, New York, 1994).

T. B. Hansen, A. D. Yaghjian, Plane-Wave Theory of Time-Domain Fields: Near-Field Scanning Applications, IEEE Press Series on Electromagnetic Wave Theory (Institute of Electrical and Electronics Engineers, New York, 1999).

E. Heyman, T. Melamed, “Space–time representation of ultra-wideband signals,” in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, New York, 1998), pp. 1–66, 103.

M. J. Bastiaans, “Signal descriptions by means of a local frequency spectrum,” in Transformation in Optical Signal Processing, W. T. Rhodes, ed., Proc. SPIE373, 49–62 (1981).
[CrossRef]

V. Galdi, D. Castañon, L. B. Felsen, “Quasi-ray Gaussian beam algorithms for time-harmonic two-dimensional scattering by moderately rough interfaces,” IEEE Trans. Antennas Propag. (to be published).

V. Galdi, D. Castañon, L. B. Felsen are preparing a paper titled “Reconstruction of moderately rough interfaces via quasi-ray Gaussian beams” for publication.

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Figures (11)

Fig. 1
Fig. 1

GB parameters: z0 is the waist plane, zR is the Rayleigh distance, R is the phase-front radius of curvature, and Θ is the angular beam spread. In Section 4 these wave objects are used to synthesize fields with the time-harmonic or the time-dependent forms u^0(x)exp(-iωt) and u0(x, t), respectively, in extended aperture sources located in the z=0 plane.

Fig. 2
Fig. 2

Oblate spheroidal coordinate systems for the source and the beam definitions of expressions (2.3). All dimensions are normalized with respect to the collimation distance b. Motion along either sr or si is continuous everywhere except across the branch cuts (the wavy lines): Tracking is continuous along the sr ellipses but is discontinuous along the si hyperbolae for (a) the source case, whereas the opposite is true for (b) the beam case. The dashed curves outline the transverse half-amplitude contours of a CSPB whose location at time ct/b=1.4 is depicted by the short solid curve. The corresponding CSPB parameters in Eq. (2.13) are f+(t)=δ+[t-(i/2)T] [see Eq. (2.21)], with cT/b=10-2, giving, through Eq. (2.23), a waist width of w010-1.

Fig. 3
Fig. 3

Snapshots of the CSPB of Eq. (2.13) for a pulse of f+(t)=-exp(iα)δ+(1)[t-i(1/2)T], see Eq. (2.21), with α=π/3. The plots show cross-sectional cuts of the axially symmetric field in the (z, ρ) plane, where ρ=(x12+x2)1/2. All length scales are normalized with respect to b. Observation times are (a) ct/b=0.2, (b) ct/b=1, (c) ct/b=2, (d) ct/b=1. The PB parameters are (a)–(c) cT/b=10-3 for collimated PB’s and (d) cT/b=10-1 for noncollimated PB’s. Note that in (d) the scales are different.

Fig. 4
Fig. 4

PB propagation schematic in an inhomogeneous medium with the definitions of the ray-based coordinates (see Subsection 3.B).

Fig. 5
Fig. 5

PB shown in Fig. 4 is impinging on a curved interface S (see Subsection 3.C).

Fig. 6
Fig. 6

Radiation from extended planar aperture distributions: plane-wave representation of the radiated field. Shown are (a) the SST of the initial data u0 in the three-dimensional (x0, t) domain [see Eq. (4.7a)] and (b) the radiated field for z>0 that was synthesized by the angular superposition of Eqs. (4.9) and (4.10) of the time-dependent plane waves u˜0(ξ, τ) as shown, propagating in the direction κ of Eq. (4.4).

Fig. 7
Fig. 7

Parameterization schematic of the asymptotic SST. The main contribution to the SST for a given ξ arises from a point xs, where the plane wave ξ is locally matched to the source distribution through the stationary delay condition of Eqs. (4.14). The corresponding value of τ is determined by the Legendre transform in Eq. (4.16).

Fig. 8
Fig. 8

Radiation from the extended planar aperture distributions: phase-space beam (or PB) superposition. The arrows form a schematic of the beam propagators; the long arrows represent beams that are strongly excited by the local features of the distribution [as described by the Lagrange manifold in Eq. (4.14)].

Fig. 9
Fig. 9

Configuration-space coordinates of the beam propagator Bˆ in expression (4.29) or B in expression (4.40). For a given X the beam axis zb originates at the point x0=x¯ in the z=0 plane and is aligned along κ¯ of Eq. (4.26). The transverse coordinates xb=(xb1, xb2) are rotated such that xb1 lies in the plane (ξ¯, κ¯), whereas xb2 is orthogonal to xb1 and thus lies in the z=0 plane.

Fig. 10
Fig. 10

Local (PB) spectrum: (a) the local SST of the initial field u0(x0, t) [cf. Fig. 6(a)] and (b) the corresponding PB propagator.  

Fig. 11
Fig. 11

Lagrange manifold constraint in Eqs. (4.37) for the geometrical-optics-enhanced regions in the phase space Y described by the local SST function U0(Y) that corresponds to the time-dependent distribution in Eq. (4.13b). The constraint describes the geometrically enhanced PB propagators shown in Fig. 8. If the aperture has end points at xe, then U0(Y) also enhances the PB propagators that emanate from x¯=xe in all directions ξ¯ described by the diffraction constraints.

Equations (118)

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uˆ(r)=[q(z)]-1expikz+12|x|2q(z),
q(z)=z-z0-izR,zR>0,
1q(z)=1R(z)+iλπw2(z),
R(z)=(z-z0)+zR2/(z-z0),
w(z)=w0[1+(z-z0)2/zR2]1/2,
w0=(zRλ/π)1/2=w|z=z0.
Θ=λ/πw0=(λ/πzR)1/21
uˆ(r)=det Γ(z)det Γ(0)1/2exp{ik[z+12xtΓ(z)x]},
Γ(z)=[Γ-1(0)+zI]-1,
r=r0+ib,
r0=0,b=bz˚,i.e., r=(0, 0, ib).
s(r)=[(x-x)2+(y-y)2+(z-z)]1/2
=[ρ2+(z-ib)2]1/2,
Re[s(r)]0,
Im[s(r)]0.
E0={r : x2+y2b2, z=0},
Esr: x2+y2b2+sr2+z2sr2=1,sr>0.
Hsi: x2+y2b2-si2-z2si2=1,-bsib.
(ρ, z)=b-1[(b2+sr2)1/2(b2-si2)1/2, -srsi],sr>0,-b<si<b.
uˆ(r)=s-1exp(iks)=s-1exp(iksr-ksi),k=ω/c,
s±z-ib+12 ρ2/(z-ib),z0
uˆ(r)=(z-ib)-1expikz+12ρ2z-ib×exp(kb)z>0-(z-ib)-1exp-ikz+12ρ2z-ib×exp[-(kb)]z<0.
u+(r, t)=1π0dω exp[-iω(t-t)]fˆ(ω)s-1exp(iks),
Im(t) |Im(r)|/c=b/c,
t=ib/c.
u+(r, t)=s-1f+(τ),τ=t-γ.
γ(r)=γr+iγi=t+s/c=sr/c+i(b+si)/c,
fγi(t)=Re[f+(t-iγi)],
f¯γi(t)=Im[f+(t-iγi)],tR.
u=Re(u+)=|s|-2{srfγi(t-γr)+sif¯γi(t-γr)},
u+(z-ib)-1f+[t-z/c-ρ2/2c(z-ib)].
R(z)=z+b2/z,I(z)=b[1+(z/b)2],
γr=z/c+ρ2/[2cR(z)],γi=ρ2/[2cI(z)],
u=[zfγi(t-γr)-bf¯γi(t-γr)]/(z2+b2),
f+(t)=δ+(n)(τ)dndτn δ+(τ)=(-)nn!πi(τ)n+1,
τ=t-i2 T,T>0.
fγi(t)=π-1T/2+γit2+(T/2+γi)2,
f¯γi(t)=π-1-tt2+(T/2+γi)2.
w(z)=w0[1+(z/b)2]1/2,w0=2(cTb)1/2.
Θ2=4cT/b=(w0/b)21.
(12+22+z2-c-2t2)u(r, t)=0,
u(r, t)=U(r, τ),τ=t-z/c.
(x12+x22-2c-1zτ2)U=0.
u+(r, t)=det Γ(z)det Γ(0)1/2f+t-z/c-12cxtΓ(z)x,
u(r, t)=[c0(σ)]1/2U(x, σ, τ),τ=t-0σdσc0(σ),
(12+22-2c0-1στ-c0-3xtC2xτ2)U=0,
u+(r, t)=c0(σ)c0(0)detQ(0)detQ(σ)1/2f+t-0σdσc0(σ)-12c0(σ)xtΓ(σ)x,
Q=c0P,P=-c0-2C2Q
u+(r, t)=Aαcα(σα)det Qα(0)cα(0)det Qα(σα)1/2f+t-0σαdσcα(σ)-12cα(σα)xαtΓα(σα)xα,
Γr(0)=J[Γi(0)-2Θi-1KΘi-1cos θi]J,
c1-1[ΘitΓi(0)Θi-Kcos θi]=c2-1[ΘttΓt(0)Θt-Kcos θt],
J=100-1
Θα=100cos θα,Θr=JΘi.
xc2-1xσ2=ABCD xc1-1xσ1,
c2-1Γ2=[C+c1-1DΓ1][A+c1-1BΓ1]-1.
B=0,A=D-1=Θi-1Θt=100cos θtcos θi
uˆ(r)=d2x0 2u^0(x0)z0Gˆ(r, r0),
u(r, t)=d2x02(z/R)4πR [R-1u0(x0, t-R/c)+c-1u0(x0, t-R/c)],
u˜^0(ξ)=d2x0exp(-ikξx0)u^0(x0),
u^0(x0)=k2π2d2ξ exp(ikξx0)u˜^0(ξ),
κ=(ξ, ζ)=(cos θ1, cos θ2, cos θz),|κ| =1,
ζ=(1-|ξ|2)1/2,Im(ζ)0
u˜0(ξ, τ)=12π-dω exp(-iωτ)u˜^0(ξ, ω).
u˜0(ξ, τ)=12π-dωd2x0 u^0(x0)×exp[-iω(τ+c-1ξ  x0)].
u˜0(ξ, τ)=d2x0 u0(x0, τ+c-1ξ  x0),
u0(r, t)=-(2πc)-2d2ξ t2u˜(ξ, t-c-1ξ  x),
uˆ(r)=k2π2d2ξ u˜^0(ξ)exp[ik(ξ  x+ζz)],
u+(r, t)=1π0dω exp(-iωt)k2π2d2ξ u˜^0(ξ)×exp[ik(ξx+ζz],
u+(r, t)=-(2πc)-2d2ξ t2u˜+0[ξ, t-c-1(ξ  x+ζz)],
uprop(r, t)
=-(2πc)-2|ξ|<1d2ξ t2u˜0[ξ, t-c-1(ξ  x+ζz)],
uev(r, t)=-(2πc)-Re|ξ|>1d2ξ t2u˜+[ξ, t-c-1(ξ  x+ζz)],ζ=i|ζ|.
u0(x0, t)u^0(x0, ω)Eq. (4.3a) u˜^0(ξ, ω)Eq. (A.1) u˜+(ξ, τ)
u˜+(ξ, τ)=1πid2x0dt u0(x0, t+c-1ξ  x0)τ-t,
Im(τ)<0.
u^0(x0, ω)=a^0(x0, ω)exp[iωt0(x0)],
u0(x0, t)=a0[x0, t-t0(x0)].
ξ=c0t0(xs),xs=xs(ξ).
u˜^0(ξ, ω)=a˜^0(ξ, ω)exp[iωτ0(ξ)],
u˜0(ξ, τ)=a˜0[ξ, τ-τ0(ξ)],
τ0(ξ)=[t0(xs)-c-1ξ  xs],xs=xs(ξ),
a˜ˆ(ξ, ω)=-2πω-1[det ij2t0(xs)]-1/2a^0(xs),
a˜+(ξ, τ)=2π[det ij2t0(xs)]-1/2τ(-1)ia+(xs, τ),
x0=-cξτ0(ξs),at ξs=ξs(x0).
U^0(X)=d2x0 u^0(x0)W^*(x0; X),
U^0(X)=k2π2d2ξ u˜ˆ(ξ)W˜^*(ξ; X),
Δx=N^-1d2x0 |x0|2|wˆ(x0)|21/2,
Δξ=N^-1k2πd2ξ |ξ|2|w˜ˆ(ξ)|21/2,
Nˆ=d2x0 |wˆ(x0)|21/2=k2πd2ξ |w˜ˆ(ξ)|21/2
u^0(x0)=k2π2N^-2d4X U^0(X)Wˆ(x0; X).
uˆ(r)=k2π2N^-2d4X U^0(X)Bˆ(r; X),
Bˆ(r; X)
=k2π2d2ξ w˜ˆ(ξ-ξ¯)exp{ik[ξ  (x-x¯)+ζz]}.
κ¯=(ξ¯, ζ¯),ζ¯=(1-|ξ¯|2)1/2.
(x-x¯)/R¯=ξ¯,R¯(z2+|x-x¯|2)1/2.
wˆ(x0)=exp(-k|x0|2/2β),
w˜ˆ(ξ)=2πβk-1exp (-kβ|ξ|2/2),
Bˆ(r; X)-Z1-iF1zb-Z1-iF1-Z2-iF2zb-Z2-iF21/2×expikzb+xb12/2zb-Z1-iF1+xb22/2zb-Z2-iF2,
U0(Y)=12π-dω U^0(X; ω)exp(-iωt¯),
U0(Y)=d2x0dt u0(x0, t)W(x0, t; Y),
W(x0, t; Y)=w[x0-x¯, t-t¯-c-1ξ¯  (x0-x¯)],
u0(x0, t)
=-(2πc)-2t2N(t)  d5Y U0(Y)W(x0, t; Y),
u(r, t)=-(2πc)-2t2N(t)  d5Y U0(Y)B(r, t; Y),
B+(r, t; Y)=-(2πc)-2t2d2ξ w˜+(ξ-ξ¯, t-{t¯-c-1[ξ  (x-x¯)+ζz)]}),
(x-x¯)/R¯=ξ¯,t=t¯+R¯/v,
ξ¯=ct0(x¯),t¯=t0(x¯),
w(x0, t)=Re[exp(iα)]δ+(n)[t-i2 Tβ-i|x0|2/2βc],
w˜+(ξ, τ)=-i2πβc exp(iα)δ+(n-1)[τ-(i2Tβ-iβ|ξ|2/2c)].
B+exp(iα)-Z1-iF1zb-(Z1-iF1)-Z2-iF2zb-(Z2-iF2)1/2×δ+(l)t-t¯-zbc-xb12/2czb-Z1-iF1-xb22/2czb-Z2-iF2-i2Tβ,
f+(τ)=1π0dω exp(-iωτ)fˆ(ω),Im(τ)0.
f+(τ)=1πi-dt f(t)τ-t,τC-.
f+(t)=f(t)+if-(t),tR,
f-(t)=-1π-dtPf(t)t-t,tR
δ+(t)=1/πitIm(t)<0δ(t)+P/πitIm(t)=0,
δ+(n)(τ)=τnδ+(τ)=(-1)nn!πiτn+1,n0,
δ+(-1)(τ)=-τdτδ+(τ)=1+1πiln τ,
f+(τ)=δ+(μ)(τ)exp(-iωcτ)=iπΓ(μ+1)(-τ)μ+1exp(-iωcτ),

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