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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 22, Iss. 6 — Jun. 1, 2005
  • pp: 1208–1215

Local spectrum analysis of field propagation in an anisotropic medium. Part II. Time-dependent fields

Igor Tinkelman and Timor Melamed  »View Author Affiliations


JOSA A, Vol. 22, Issue 6, pp. 1208-1215 (2005)
http://dx.doi.org/10.1364/JOSAA.22.001208


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Abstract

In Part I of this two-part investigation [J. Opt. Soc. Am. A 22, 1200 (2005)], we presented a theory for phase-space propagation of time-harmonic electromagnetic fields in an anisotropic medium characterized by a generic wave-number profile. In this Part II, these investigations are extended to transient fields, setting a general analytical framework for local analysis and modeling of radiation from time-dependent extended-source distributions. In this formulation the field is expressed as a superposition of pulsed-beam propagators that emanate from all space–time points in the source domain and in all directions. Using time-dependent quadratic-Lorentzian windows, we represent the field by a phase-space spectral distribution in which the propagating elements are pulsed beams, which are formulated by a transient plane-wave spectrum over the extended-source plane. By applying saddle-point asymptotics, we extract the beam phenomenology in the anisotropic environment resulting from short-pulsed processing. Finally, the general results are applied to the special case of uniaxial crystal and compared with a reference solution.

© 2005 Optical Society of America

OCIS Codes
(260.1180) Physical optics : Crystal optics
(270.5530) Quantum optics : Pulse propagation and temporal solitons
(350.5500) Other areas of optics : Propagation

History
Original Manuscript: December 21, 2004
Published: June 1, 2005

Citation
Igor Tinkelman and Timor Melamed, "Local spectrum analysis of field propagation in an anisotropic medium. Part II. Time-dependent fields," J. Opt. Soc. Am. A 22, 1208-1215 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-6-1208


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References

  1. I. Tinkelman, 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]
  2. 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]
  3. E. Heyman, L. B. Felsen, “Weakly dispersive spectraltheory of transients (STT), part II: evaluation of the spectral integral,” IEEE Trans. Antennas Propag. 35, 574–580 (1987). [CrossRef]
  4. T. B. Hansen, A. D. Yaghjian, “Planar near-field scanning in the time-domain. Part I: fomulation,” IEEE Trans. Antennas Propag. 42, 1280–1291 (1994). [CrossRef]
  5. T. Melamed, “Phase-space beam summation: a local spectrum analysis for time-dependent radiation,” J. Electromagn. Waves Appl. 11, 739–773 (1997). [CrossRef]
  6. E. Heyman, T. Melamed, “Space-time representation of ultra windband signals,” in Advances in Imaging and Electron Physics (Academic, San Diego, Calif., 1998), Vol. 103, pp. 3–63.
  7. E. Heyman, “Pulsed beam propagation in an inhomogeneous medium,” IEEE Trans. Antennas Propag. 42, 311–319 (1994). [CrossRef]

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