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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. 15, Iss. 5 — May. 1, 1998
  • pp: 1277–1284

Pulsed-beam propagation in lossless dispersive media. II. A numerical example

Timor Melamed and Leopold B. Felsen  »View Author Affiliations


JOSA A, Vol. 15, Issue 5, pp. 1277-1284 (1998)
http://dx.doi.org/10.1364/JOSAA.15.001277


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Abstract

In Part I of this two-part investigation we presented a theory for propagation of pulsed-beam wave packets in a homogeneous lossless dispersive medium with the generic dispersion relation k(ω). Emphasis was placed on the paraxial regime, and detailed studies were performed to parameterize the effect of dispersion in terms of specific physical footprints associated with the PB field and with properties of the k(ω) dispersion surface. Moreover, critical nondimensional combinations of these footprints were defined to ascertain the space–time range of applicability of the paraxial approximation. This was done by recourse to simple saddle-point asymptotics in the Fourier inversion integral from the frequency domain, with restrictions to the fully dispersive regime sufficiently far behind the wave front. Here we extend these studies by addressing the dispersive-to-nondispersive transition as the observer moves toward the wave front. It is now necessary to adopt a model for the dispersive properties to correct the nondispersive high-frequency limit k(ω)=ω/c with higher-order terms in (1/ω). A simple Lorentz model has been chosen for this purpose that allows construction of a simple uniform transition function which connects smoothly onto the near-wave-front-reduced generic k(ω) profile. This model is also used for assessing the accuracy of the various analytic parameterizations and estimates in part I through comparison with numerically generated reference solutions. It is found that both the asymptotics for the pulsed-beam field and the nondimensional estimators perform remarkably well, thereby lending confidence to the notion that the critical parameter combinations are well matched to the space–time wave dynamics.

© 1998 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(260.2030) Physical optics : Dispersion
(270.5530) Quantum optics : Pulse propagation and temporal solitons
(350.5500) Other areas of optics : Propagation

History
Original Manuscript: September 2, 1997
Revised Manuscript: January 15, 1998
Manuscript Accepted: December 2, 1997
Published: May 1, 1998

Citation
Timor Melamed and Leopold B. Felsen, "Pulsed-beam propagation in lossless dispersive media. II. A numerical example," J. Opt. Soc. Am. A 15, 1277-1284 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-5-1277


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References

  1. T. Melamed, L. B. Felsen, “Pulsed-beam propagation in lossless dispersive media. I. Theory,” J. Opt. Soc. Am. A 15, 1268–1276 (1998). [CrossRef]
  2. L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (IEEE, Piscataway, N.J., 1994). Classic reissue.
  3. K. E. Oughstun, G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics, Vol. 16 of Springer Series on Wave Phenomena (Springer, New York, 1997).
  4. W. Magnus, F. Oberhettinger, R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics (Springer-Verlag, New York, 1966).

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