Abstract

We formulate an efficient exact method of propagating optical wave packets (and cw beams) in isotropic and nonisotropic dispersive media. The method does not make the slowly varying envelope approximation in time or space and treats dispersion and diffraction exactly to all orders, even in the near field. It can also be used to determine the partial differential wave equation for pulses (and beams) to any order as a power series in the partial derivatives with respect to time and space. The method can treat extremely focused pulses and beams, e.g., from near-field scanning optical microscopy sources whose transverse spatial extent in smaller than a wavelength.

© 1997 Optical Society of America

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References

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  1. Y. B. Band and M. Trippenbach, Phys. Rev. Lett. 76, 1457 (1996).
    [CrossRef] [PubMed]
  2. M. Trippenbach and Y. B. Band, J. Opt. Soc. Am. B 13, 1403 (1996).
    [CrossRef]
  3. C. Radzewicz, J. S. Krasinski, M. J. la Grone, M. Trippenbach, and Y. B. Band, J. Opt. Soc. Am. B 14, 420 (1997).
    [CrossRef]
  4. C. Girard and A. Dereux, Phys. Rev. B 49, 11344 (1994).
    [CrossRef]
  5. O. J. F. Martin, C. Girard, and A. Dereux, Phys. Rev. Lett. 74, 526 (1995).
    [CrossRef] [PubMed]
  6. L. Novotny, D. W. Pohl, and P. Regli, J. Opt. Soc. Am. A 11, 1768 (1994).
    [CrossRef]
  7. R. Kopelman, A. Lewis, and K. Lieberman, J. Lumin. 45, 298 (1990); S. Shalom, K. Lieberman, A. Lewis, and S. R. Cohen, Rev. Sci. Instrum. 63, 4061 (1992); K. Lieberman, A. Lewis, G. Fish, T. Jovin, A. Schaper, and S. R. Cohen, Appl. Phys. Lett. 65, 648 (1994).
    [CrossRef]
  8. O. Marti and R. Moller, in Photons and Local Probes, Vol. 300 of NATO ASI Series E, Applied Sciences (Kluwer, Dordrecht, The Netherlands, 1995).
    [CrossRef]
  9. C. J. Bouwkamp, Rep. Prog. Phys. 17, 35 (1954).
    [CrossRef]
  10. C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
    [CrossRef]
  11. T. C. Scott, M. Trippenbach, and Y. B. Band, “An application of Maple to near-field optics,” MapleTech (to be published).
  12. J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Opt. 10, 129 (1976); M. D. Feit and J. A. Fleck, Appl. Opt. 17, 3390 (1978); Appl. Opt. 18, 2843 (1979).
    [CrossRef]

1997 (1)

1996 (3)

Y. B. Band and M. Trippenbach, Phys. Rev. Lett. 76, 1457 (1996).
[CrossRef] [PubMed]

M. Trippenbach and Y. B. Band, J. Opt. Soc. Am. B 13, 1403 (1996).
[CrossRef]

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

1995 (1)

O. J. F. Martin, C. Girard, and A. Dereux, Phys. Rev. Lett. 74, 526 (1995).
[CrossRef] [PubMed]

1994 (2)

1990 (1)

R. Kopelman, A. Lewis, and K. Lieberman, J. Lumin. 45, 298 (1990); S. Shalom, K. Lieberman, A. Lewis, and S. R. Cohen, Rev. Sci. Instrum. 63, 4061 (1992); K. Lieberman, A. Lewis, G. Fish, T. Jovin, A. Schaper, and S. R. Cohen, Appl. Phys. Lett. 65, 648 (1994).
[CrossRef]

1976 (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Opt. 10, 129 (1976); M. D. Feit and J. A. Fleck, Appl. Opt. 17, 3390 (1978); Appl. Opt. 18, 2843 (1979).
[CrossRef]

1954 (1)

C. J. Bouwkamp, Rep. Prog. Phys. 17, 35 (1954).
[CrossRef]

Band, Y. B.

C. Radzewicz, J. S. Krasinski, M. J. la Grone, M. Trippenbach, and Y. B. Band, J. Opt. Soc. Am. B 14, 420 (1997).
[CrossRef]

Y. B. Band and M. Trippenbach, Phys. Rev. Lett. 76, 1457 (1996).
[CrossRef] [PubMed]

M. Trippenbach and Y. B. Band, J. Opt. Soc. Am. B 13, 1403 (1996).
[CrossRef]

T. C. Scott, M. Trippenbach, and Y. B. Band, “An application of Maple to near-field optics,” MapleTech (to be published).

Bouwkamp, C. J.

C. J. Bouwkamp, Rep. Prog. Phys. 17, 35 (1954).
[CrossRef]

Dereux, A.

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

O. J. F. Martin, C. Girard, and A. Dereux, Phys. Rev. Lett. 74, 526 (1995).
[CrossRef] [PubMed]

C. Girard and A. Dereux, Phys. Rev. B 49, 11344 (1994).
[CrossRef]

Feit, M. D.

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Opt. 10, 129 (1976); M. D. Feit and J. A. Fleck, Appl. Opt. 17, 3390 (1978); Appl. Opt. 18, 2843 (1979).
[CrossRef]

Fleck, J. A.

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Opt. 10, 129 (1976); M. D. Feit and J. A. Fleck, Appl. Opt. 17, 3390 (1978); Appl. Opt. 18, 2843 (1979).
[CrossRef]

Girard, C.

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

O. J. F. Martin, C. Girard, and A. Dereux, Phys. Rev. Lett. 74, 526 (1995).
[CrossRef] [PubMed]

C. Girard and A. Dereux, Phys. Rev. B 49, 11344 (1994).
[CrossRef]

Kopelman, R.

R. Kopelman, A. Lewis, and K. Lieberman, J. Lumin. 45, 298 (1990); S. Shalom, K. Lieberman, A. Lewis, and S. R. Cohen, Rev. Sci. Instrum. 63, 4061 (1992); K. Lieberman, A. Lewis, G. Fish, T. Jovin, A. Schaper, and S. R. Cohen, Appl. Phys. Lett. 65, 648 (1994).
[CrossRef]

Krasinski, J. S.

la Grone, M. J.

Lewis, A.

R. Kopelman, A. Lewis, and K. Lieberman, J. Lumin. 45, 298 (1990); S. Shalom, K. Lieberman, A. Lewis, and S. R. Cohen, Rev. Sci. Instrum. 63, 4061 (1992); K. Lieberman, A. Lewis, G. Fish, T. Jovin, A. Schaper, and S. R. Cohen, Appl. Phys. Lett. 65, 648 (1994).
[CrossRef]

Lieberman, K.

R. Kopelman, A. Lewis, and K. Lieberman, J. Lumin. 45, 298 (1990); S. Shalom, K. Lieberman, A. Lewis, and S. R. Cohen, Rev. Sci. Instrum. 63, 4061 (1992); K. Lieberman, A. Lewis, G. Fish, T. Jovin, A. Schaper, and S. R. Cohen, Appl. Phys. Lett. 65, 648 (1994).
[CrossRef]

Marti, O.

O. Marti and R. Moller, in Photons and Local Probes, Vol. 300 of NATO ASI Series E, Applied Sciences (Kluwer, Dordrecht, The Netherlands, 1995).
[CrossRef]

Martin, O. J. F.

O. J. F. Martin, C. Girard, and A. Dereux, Phys. Rev. Lett. 74, 526 (1995).
[CrossRef] [PubMed]

Moller, R.

O. Marti and R. Moller, in Photons and Local Probes, Vol. 300 of NATO ASI Series E, Applied Sciences (Kluwer, Dordrecht, The Netherlands, 1995).
[CrossRef]

Morris, J. R.

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Opt. 10, 129 (1976); M. D. Feit and J. A. Fleck, Appl. Opt. 17, 3390 (1978); Appl. Opt. 18, 2843 (1979).
[CrossRef]

Novotny, L.

Pohl, D. W.

Radzewicz, C.

Regli, P.

Scott, T. C.

T. C. Scott, M. Trippenbach, and Y. B. Band, “An application of Maple to near-field optics,” MapleTech (to be published).

Trippenbach, M.

C. Radzewicz, J. S. Krasinski, M. J. la Grone, M. Trippenbach, and Y. B. Band, J. Opt. Soc. Am. B 14, 420 (1997).
[CrossRef]

Y. B. Band and M. Trippenbach, Phys. Rev. Lett. 76, 1457 (1996).
[CrossRef] [PubMed]

M. Trippenbach and Y. B. Band, J. Opt. Soc. Am. B 13, 1403 (1996).
[CrossRef]

T. C. Scott, M. Trippenbach, and Y. B. Band, “An application of Maple to near-field optics,” MapleTech (to be published).

Appl. Opt. (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Opt. 10, 129 (1976); M. D. Feit and J. A. Fleck, Appl. Opt. 17, 3390 (1978); Appl. Opt. 18, 2843 (1979).
[CrossRef]

J. Lumin. (1)

R. Kopelman, A. Lewis, and K. Lieberman, J. Lumin. 45, 298 (1990); S. Shalom, K. Lieberman, A. Lewis, and S. R. Cohen, Rev. Sci. Instrum. 63, 4061 (1992); K. Lieberman, A. Lewis, G. Fish, T. Jovin, A. Schaper, and S. R. Cohen, Appl. Phys. Lett. 65, 648 (1994).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

Phys. Rev. B (1)

C. Girard and A. Dereux, Phys. Rev. B 49, 11344 (1994).
[CrossRef]

Phys. Rev. Lett. (2)

O. J. F. Martin, C. Girard, and A. Dereux, Phys. Rev. Lett. 74, 526 (1995).
[CrossRef] [PubMed]

Y. B. Band and M. Trippenbach, Phys. Rev. Lett. 76, 1457 (1996).
[CrossRef] [PubMed]

Rep. Prog. Phys. (2)

C. J. Bouwkamp, Rep. Prog. Phys. 17, 35 (1954).
[CrossRef]

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

Other (2)

T. C. Scott, M. Trippenbach, and Y. B. Band, “An application of Maple to near-field optics,” MapleTech (to be published).

O. Marti and R. Moller, in Photons and Local Probes, Vol. 300 of NATO ASI Series E, Applied Sciences (Kluwer, Dordrecht, The Netherlands, 1995).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

3D surface and contour plot of Ax, y, z, t versus ct and x for a propagation distance of z=0.5 mm in the frame traveling with the z component of the group. The dashed contour plot ellipses show the second-order expansion result.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Ax, t=12π4-+d3KdωAK, ω×expiK-K0·x-ω-ω0t.
Ax, tz=12π4-+d3KdωAK, ωiK-K0·s0×expiK-K0·x-ω-ω0t.
KX2+KY2/ne2ω+KZ2/no2ω=ω2/c2.
Kz=12n2 sin2θ01ne2ω-1no2ωKx+ω2n2c2-n2ne2ωKy2-n4no2ωne2ωKx21/2,
Az=-β1At-i2β22At2+16β33At3+γxAx+iγtx2Atx+i2γxx2Ax2+i2γyy2Ay2+13γtxx3Ax2t+13γtyy3Ay2t+13γttx3At2x+….
γtxx=cω2n2n+ωnω-cω2n3n+2ωnω2nθ2-ωn3nωθ2+2cω2n4nθn+3ωnωnθ-2ωn2nωθ,

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