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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. 11, Iss. 4 — Apr. 1, 1994
  • pp: 1471–1490

Body-of-revolution finite-difference time-domain modeling of space–time focusing by a three-dimensional lens

David B. Davidson and Richard W. Ziolkowski  »View Author Affiliations


JOSA A, Vol. 11, Issue 4, pp. 1471-1490 (1994)
http://dx.doi.org/10.1364/JOSAA.11.001471


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Abstract

We introduce a body-of-revolution finite-difference time-domain simulation capability that can be applied to rotationally symmetric linear-optics problems. This simulator allows us to reduce a computationally intractable, three-dimensional problem to a numerically solvable two-dimensional one. It is used to model the propagation of a pulsed Gaussian beam through a thin dielectric lens and the focusing of the resulting pulsed beam. Analytic results for such a lens-focused, pulsed Gaussian beam are also derived. It is shown that, for the same input energy, one can design ultrawide-bandwidth driving signals to achieve a significantly larger intensity enhancement than is possible with equivalent many-cycle, monochromatic signals. Several specially engineered (designer) pulses are introduced that illustrate how one can achieve these intensity enhancements. The simulation results confirm that intensity enhancements can be realized with properly designed ultrawide-bandwidth pulses.

© 1994 Optical Society of America

History
Original Manuscript: June 21, 1993
Revised Manuscript: November 15, 1993
Manuscript Accepted: November 18, 1993
Published: April 1, 1994

Citation
David B. Davidson and Richard W. Ziolkowski, "Body-of-revolution finite-difference time-domain modeling of space–time focusing by a three-dimensional lens," J. Opt. Soc. Am. A 11, 1471-1490 (1994)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-11-4-1471


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References

  1. R. W. Ziolkowski, J. B. Judkins, “Full-wave vector Maxwell equation modelling of the self-focusing of ultrashort optical pulses in a nonlinear Kerr medium exhibiting a finite response time,” J. Opt. Soc. Am. B 10, 186–198 (1993). [CrossRef]
  2. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equation in isotropic media,” IEEE Trans. Antennas Propag., AP-14302–307 (1966).
  3. W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990).
  4. A. Taflove, K. R. Umashankar, “The finite-difference time-domain method for numerical modelling of electromagnetics wave interactions with arbitrary structures,” in Finite Element and Finite Difference Methods in Electromagnetic Scattering, M. A. Morgan, ed., Vol. 2 of Progress in Electromagnetic Research (Elsevier, New York, 1990).
  5. D. E. Merewether, R. Fisher, “Finite difference solution of Maxwell’s equation for EMP applications,” Rep. EMA-79–R-4 (Defense Nuclear Agency, Washington, D.C., 1980).
  6. A. C. Cangellaris, R. Lee, “On the accuracy of numerical wave simulations based on finite methods,” J. Electromagn. Waves Appl. 6, 1635–1653 (1992). [CrossRef]
  7. R. W. Ziolkowski, J. B. Judkins, “Propagation characteristics of ultrawide-bandwidth pulsed Gaussian beams,” J. Opt. Soc. Am. A 9, 2021–2030 (1992). [CrossRef]
  8. D. B. Davidson, “A parallel processing tutorial,” IEEE Antennas Propag. Mag. 32(4), 6–19 (1990). [CrossRef]
  9. D. B. Davidson, “Parallel processing revisited: a second tutorial,” IEEE Antennas Propag. Mag. 34(10), 9–21 (1992). [CrossRef]
  10. R. F. Harrington, Field Computation by Moment Methods, 2nd ed. (Krieger, Malabar, Fla., 1982).
  11. A. Taflove, K. R. Umashankar, “Advanced numerical modeling of microwave penetration and coupling for complex structures—final report,” final Rep. UCRL-15960, Contract 6599805 (Lawrence Livermore National Laboratory, Livermore, Calif., 1987).
  12. J. Bailey, “Implementing fine-grained scientific algorithms on the Connection Machine supercomputer,” Thinking Machines Tech. Rep. Ser. TR90-1 (Thinking Machines Corporation, Cambridge, Mass., 1990).
  13. R. W. Ziolkowski, “Properties of electromagnetic beams generated by ultra-wide bandwidth pulse-driven arrays,” IEEE Trans. Antennas Propag. 40, 888–905 (1992). [CrossRef]
  14. R. W. Ziolkowski, I. M. Besieris, A. M. Shaarawi, “Aperture realizations of exact solutions to homogeneous wave equations,” J. Opt. Soc. Am. A 10, 75–87 (1993). [CrossRef]
  15. G. C. Sherman, “Short pulses in the focal region,” J. Opt. Soc. Am. A 6, 1382–1387 (1989). [CrossRef]
  16. Z. Bor, Z. L. Horváth, “Distortion of femtosecond laser pulse in lenses. Wave optical description,” Opt. Commun. 94, 249–258 (1992). [CrossRef]
  17. J. J. Stamnes, Waves in Focal Regions (Hilger, London, 1986).
  18. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).
  19. I. S. Gradshteyn, I. M. Ryzhik, eds., Tables of Integrals, Series and Products (Academic, New York, 1965).

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