Directions in Electromagnetic Wave Modeling pp 87-100 | Cite as

# Complex Source Pulsed Beams: Propagation, Scattering and Applications

## Abstract

The excitation, propagation and diffraction of short pulse signals is receiving increased attention in a variety of fields. Due to the broad frequency spectra of such signals, the conventional route of inversion from the frequency domain is often less convenient, and physically less transparent, than direct treatment of time domain events. Analysis and synthesis of such wave solutions require use of source functions (e.g., time-dependent Green’s functions or plane waves). Important among source functions, for a variety of applications (some examples will be given below), are those which establish well focused fields. In the frequency domain, such fields take the form of transversely confined beams, the most favored among which have Gaussian-like profiles. In the time domain, such fields take the form of pulsed teams (PB), i.e. highly directed space-time wave packets. Several types of PB solutions of the wave equation have recently been introduced,^{1}“^{3} in particular in connection with long range focused energy transfer. Particular interest has been given to the focus wave modes (FWM)^{1} and the related wave functions,^{2} which are non diffracting or slowly diffracting free space wave packets. However, since these exact solutions comprise backward propagating spectral components, their role in modeling *physical* radiation is yet to be clarified.^{4}“^{6} Efforts have been made to minimize the backward propagating part in these exact solutions,^{7} but the effect of eliminating them completely has not yet been fully established.

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## References

- 1.J. B. Brittingham, Focus wave modes in homogeneous Maxwell’s equation,
*J. Appl. Phys., 54*, 1179–1189 (1983).ADSCrossRefGoogle Scholar - 2.R. W. Ziolkowsky, Localized transmission of electromagnetic energy,
*Phys. Rev. A, 39(4)*, 2005–2033 (1989).ADSCrossRefMathSciNetGoogle Scholar - 3.H. E. Moses and 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 imploding waves,
*IEEE Trans. Antennas Propagat., AP-34*, 188–196 (1986).ADSCrossRefzbMATHMathSciNetGoogle Scholar - 4.E. Heyman, B. Z. Steinberg and L. B. Felsen, Spectral analysis of focus wave modes (FWM),
*J. Opt. Soc. Am. A, 4*, 2084–2091 (1987).ADSMathSciNetGoogle Scholar - 5.E. Heyman and L. B. Felsen, Complex source pulsed beam fields,
*J. Opt. Soc. Am. A, 6*, 806–817 (1989).ADSCrossRefGoogle Scholar - 6.E. Heyman, The focus wave mode: A dilemma with causality,
*IEEE Trans. Antennas Propagat., AP-37*, 1604–1608 (1989).ADSCrossRefGoogle Scholar - 7.I. M. Besieries, A. M. Shaarawi and R. W. Zialkowski, A bidirectional ravelling plane wave representation of exact solutions of the scalar wave equation,
*J. Math. Phys., 30*, 1254 –1267 (1989).ADSCrossRefMathSciNetGoogle Scholar - 8.E. Heyman and L. B. Felsen, Propagating pulsed beam solutions by complex source parameter substitution,
*IEEE Trans. Antennas Propagat., AP-34*, 1062–1065 (1986).ADSCrossRefGoogle Scholar - 9.E. Heyman and B. Z. Steinberg, Spectral analysis of complex source pulsed beams,
*J. Opt. Soc. Am. A, 4*, 473–480 (1987).ADSCrossRefMathSciNetGoogle Scholar - 10.P. D. Einziger, and S. Raz, Wave solutions under complex space-time shifts,
*J. Opt. Soc. Am. A, 4*, 3–10 (1987).ADSCrossRefMathSciNetGoogle Scholar - 11.G. A. Deschamps, Gaussian beams as a bundle of complex rays,
*Electron. Lett., 7*, 684–685 (1971).CrossRefGoogle Scholar - 12.L. B. Felsen, Complex-source-point solutions of the field equations and their relation to the propagation and scattering of Gaussian beams, in
*Symp. Matemat. Instituto Nazionale di Alta Matematica, XVIII*, 40–56 Academic Press, London (1976).Google Scholar - 13.E. Heyman, B. Z. Steinberg and R. Ianconescu, Electromagnetic complex source pulsed beam,
*IEEE Trans. Antennas Propagat., AP-38*, 957–963, (1990).ADSCrossRefzbMATHGoogle Scholar - 14.E. Heyman and R. Ianconescu, Pulsed beam reflection and transmission at a dielectric interface: two dimensional fields,
*IEEE Trans, Antennas Propagat., AP-39*, Nov. (1990).Google Scholar - 15.E. Heyman, Pulsed beam expansion of transient radiation,
*Wave Motion, 11*, 337–349 (1989).CrossRefzbMATHMathSciNetGoogle Scholar - 16.B. Z. Steinberg, E. Heyman and L. B. Felsen, phase space beam summation for time-dependent radiation from large apertures: Continuous parametrization,
*J. Opt. Soc. Am. A*, in press (1991).Google Scholar - 17.V. Cerveny, M. M. Popov and I. Psencik, Computation of wave fields in inhomogeneous media — Gaussian beam approach,
*Geophys. J. R, astr. Soc, 70*, 109–128 (1982).CrossRefzbMATHGoogle Scholar - 318.C. H. Chapman, A new method for computing synthetic seismograms,
*Geophys. J. R. astr. Soc, 54*, 481–518 (1978).CrossRefzbMATHGoogle Scholar - 19.B. Z. Steinberg. E. Heyman and L. B. Felsen, phase space beam summation for time harmonic radiation from large apertures,
*J. Opt. Soc Am. A*, 7, Nov. (1990).Google Scholar - 20.S. Y. Shin and L. B. Felsen, Gaussian beam modes by multiples with complex source points,
*J. Opt. Soc Am., 67*, 699–700 (1977).ADSCrossRefGoogle Scholar - 21.E. Heyman and I. Beracha, Complex multiple pulsed beam expansion of transient radiation from well collimated apertures, in preparation.Google Scholar
- 22.E. Heyman and L. B. Felsen, Weakly dispersive spectral theory of transients. Part I: Formulation and interpretation,
*IEEE Trans. Antennas Propagat., AP-35*, 80–86 (1987).ADSCrossRefzbMATHMathSciNetGoogle Scholar - 23.E. Heyman and L. B. Felsen, Weakly dispersive spectral theory of transients. Part II: Evaluation of the spectral integral,
*IEEE Trans. Antennas Propagat., AP-35*, 574–580 (1987).ADSCrossRefzbMATHMathSciNetGoogle Scholar - 24.E. Heyman, Weakly dispersive spectral theory of transients. Part III: Applications,
*IEEE Trans. Antennas Propagat., AP-35*, 1258–1266 (1987).ADSCrossRefzbMATHMathSciNetGoogle Scholar