Abstract

An intuitive argument is presented for the phase anomaly, that is, the 180° phase shift of a light wave in passing through a focus. The treatment is based on the geometrical properties of Gaussian light beams, and suggests a new viewpoint for understanding the origin of the phase shift. Generalizing the argument by including higher-order modes of the light field allows the case of a spherical wave to be treated.

© 1980 Optical Society of America

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  1. Gouy, C. R. Acad. Sci. Paris 110, 1251–1253 (1890).
  2. Gouy, Ann. Chim. Phys. 6, XXIV, 145–213 (1891).
  3. P. Debye, Ann. Phys. 30, 755 (1909). A discussion of Debye's work can be found in J. Picht, Optische Abbildung (Vieweg & Sohn, Braunschweig, 1931). References to much of the early work in this field, including that of F. Reiche and K. Schwarzschild, can also be found in this book.
  4. A. Rubinowicz, "On the anomalous propagation of phase in the focus," Phys. Rev. 54, 931–936 (1938).
  5. E. H. Linfoot and E. Wolf, "Phase Distribution near Focus in an Aberration-free Diffraction Image," Proc. Phys. Soc. London 69, 823–832 (1956).
  6. Due to an algebraic error, the original paper states that the wavelength is decreased by this factor (E. Wolf, private communication).
  7. H. Kogelnik and T. Li, "Laser Beams and Resonators," Appl. Opt. 5, 1550–1567 (1966).
  8. P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists (Springer-Verlag, Berlin, 1954), p. 3.
  9. M. Abramowitz and I. A. Segen, Handbook of Mathematical Functions (Dover, New York, 1965), Eqs. (17.3.11) and (17.3.12).
  10. N. N. Lebedev, Special Functions and their Applications (Dover, New York, 1972), p. 88.

1966 (1)

1956 (1)

E. H. Linfoot and E. Wolf, "Phase Distribution near Focus in an Aberration-free Diffraction Image," Proc. Phys. Soc. London 69, 823–832 (1956).

1938 (1)

A. Rubinowicz, "On the anomalous propagation of phase in the focus," Phys. Rev. 54, 931–936 (1938).

Abramowitz, M.

M. Abramowitz and I. A. Segen, Handbook of Mathematical Functions (Dover, New York, 1965), Eqs. (17.3.11) and (17.3.12).

Byrd, P. F.

P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists (Springer-Verlag, Berlin, 1954), p. 3.

Debye, P.

P. Debye, Ann. Phys. 30, 755 (1909). A discussion of Debye's work can be found in J. Picht, Optische Abbildung (Vieweg & Sohn, Braunschweig, 1931). References to much of the early work in this field, including that of F. Reiche and K. Schwarzschild, can also be found in this book.

Friedman, M. D.

P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists (Springer-Verlag, Berlin, 1954), p. 3.

Kogelnik, H.

Lebedev, N. N.

N. N. Lebedev, Special Functions and their Applications (Dover, New York, 1972), p. 88.

Li, T.

Linfoot, E. H.

E. H. Linfoot and E. Wolf, "Phase Distribution near Focus in an Aberration-free Diffraction Image," Proc. Phys. Soc. London 69, 823–832 (1956).

Rubinowicz, A.

A. Rubinowicz, "On the anomalous propagation of phase in the focus," Phys. Rev. 54, 931–936 (1938).

Segen, I. A.

M. Abramowitz and I. A. Segen, Handbook of Mathematical Functions (Dover, New York, 1965), Eqs. (17.3.11) and (17.3.12).

Wolf, E.

E. H. Linfoot and E. Wolf, "Phase Distribution near Focus in an Aberration-free Diffraction Image," Proc. Phys. Soc. London 69, 823–832 (1956).

Appl. Opt. (1)

Phys. Rev. (1)

A. Rubinowicz, "On the anomalous propagation of phase in the focus," Phys. Rev. 54, 931–936 (1938).

Proc. Phys. Soc. London (1)

E. H. Linfoot and E. Wolf, "Phase Distribution near Focus in an Aberration-free Diffraction Image," Proc. Phys. Soc. London 69, 823–832 (1956).

Other (7)

Due to an algebraic error, the original paper states that the wavelength is decreased by this factor (E. Wolf, private communication).

Gouy, C. R. Acad. Sci. Paris 110, 1251–1253 (1890).

Gouy, Ann. Chim. Phys. 6, XXIV, 145–213 (1891).

P. Debye, Ann. Phys. 30, 755 (1909). A discussion of Debye's work can be found in J. Picht, Optische Abbildung (Vieweg & Sohn, Braunschweig, 1931). References to much of the early work in this field, including that of F. Reiche and K. Schwarzschild, can also be found in this book.

P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists (Springer-Verlag, Berlin, 1954), p. 3.

M. Abramowitz and I. A. Segen, Handbook of Mathematical Functions (Dover, New York, 1965), Eqs. (17.3.11) and (17.3.12).

N. N. Lebedev, Special Functions and their Applications (Dover, New York, 1972), p. 88.

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