Abstract

Transverse-electric and transverse-magnetic beam modes are considered based on a theory in which complex dipole sources and sinks are oriented along the beam axis; the theory is similar to one that was previously presented for transverse dipoles. The field in the region of the waist is explored. Modes with such polarization have been reported from a wide range of laser types.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
    [CrossRef]
  2. J. J. Wynne, IEEE J. Quantum Electron. QE-10, 125 (1974).
    [CrossRef]
  3. Y. Mushiake, K. Matsumura, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
    [CrossRef]
  4. M. E. Marhic and E. Garmire, Appl. Phys. Lett. 38, 743 (1981).
    [CrossRef]
  5. T. Erdogan, O. King, G. W. Wicks, D. G. Hall, K. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
    [CrossRef]
  6. H. Kogelnik and T. Li, Proc. IEEE 54, 1312 (1966).
    [CrossRef]
  7. L. W. Davis and G. Patsakos, Opt. Lett. 6, 22 (1981).
    [CrossRef] [PubMed]
  8. L. W. Davis and G. Patsakos, Phys. Rev. A 26, 3702 (1982).
    [CrossRef]
  9. C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
    [CrossRef]
  10. F. Gori, G. Guatteri, and C. Padovani, Opt. Commun. 64, 491 (1987).
    [CrossRef]
  11. R. H. Jorden and D. G. Hall, Opt. Lett. 19, 427 (1994).
    [CrossRef]
  12. D. G. Hall, Opt. Lett. 21, 9 (1996).
    [CrossRef] [PubMed]
  13. P. L. Greene and D. G. Hall, J. Opt. Soc. Am. A 13, 962 (1996).
    [CrossRef]
  14. A. A. Tovar and G. H. Clark, J. Opt. Soc. Am. A 14, 3333 (1997).
    [CrossRef]
  15. S. R. Seshadri, J. Opt. Soc. Am. A 15, 2712 (1998).
    [CrossRef]
  16. P. L. Greene and D. G. Hall, Opt. Express 4, 411 (1999) http://epubs.osa.org/opticsexpress .
    [CrossRef] [PubMed]
  17. G. A. Deschamps, Electron. Lett. 7, 684 (1971).
    [CrossRef]
  18. A. L. Cullen and P. K. Yu, Proc. R. Soc. London Ser. A 366, 155 (1979).
    [CrossRef]
  19. C. J. R. Sheppard and S. Saghafi, Phys. Rev. A 57, 2971 (1998).
    [CrossRef]
  20. C. J. R. Sheppard and S. Saghafi, J. Opt. Soc. Am. A 16, 1381 (1999).
    [CrossRef]
  21. C. J. R. Sheppard and S. Saghafi, “Electric and magnetic dipole beam modes beyond the paraxial approximation,” Optik (to be published).
  22. M. Couture and P.-A. Belanger, Phys. Rev. A 24, 355 (1981).
    [CrossRef]

1999 (2)

1998 (2)

S. R. Seshadri, J. Opt. Soc. Am. A 15, 2712 (1998).
[CrossRef]

C. J. R. Sheppard and S. Saghafi, Phys. Rev. A 57, 2971 (1998).
[CrossRef]

1997 (1)

1996 (2)

1994 (1)

1992 (1)

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, K. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
[CrossRef]

1987 (1)

F. Gori, G. Guatteri, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

1982 (1)

L. W. Davis and G. Patsakos, Phys. Rev. A 26, 3702 (1982).
[CrossRef]

1981 (3)

M. E. Marhic and E. Garmire, Appl. Phys. Lett. 38, 743 (1981).
[CrossRef]

L. W. Davis and G. Patsakos, Opt. Lett. 6, 22 (1981).
[CrossRef] [PubMed]

M. Couture and P.-A. Belanger, Phys. Rev. A 24, 355 (1981).
[CrossRef]

1979 (1)

A. L. Cullen and P. K. Yu, Proc. R. Soc. London Ser. A 366, 155 (1979).
[CrossRef]

1978 (1)

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
[CrossRef]

1974 (1)

J. J. Wynne, IEEE J. Quantum Electron. QE-10, 125 (1974).
[CrossRef]

1972 (2)

Y. Mushiake, K. Matsumura, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
[CrossRef]

1971 (1)

G. A. Deschamps, Electron. Lett. 7, 684 (1971).
[CrossRef]

1966 (1)

H. Kogelnik and T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Anderson, K.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, K. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
[CrossRef]

Belanger, P.-A.

M. Couture and P.-A. Belanger, Phys. Rev. A 24, 355 (1981).
[CrossRef]

Clark, G. H.

Couture, M.

M. Couture and P.-A. Belanger, Phys. Rev. A 24, 355 (1981).
[CrossRef]

Cullen, A. L.

A. L. Cullen and P. K. Yu, Proc. R. Soc. London Ser. A 366, 155 (1979).
[CrossRef]

Davis, L. W.

L. W. Davis and G. Patsakos, Phys. Rev. A 26, 3702 (1982).
[CrossRef]

L. W. Davis and G. Patsakos, Opt. Lett. 6, 22 (1981).
[CrossRef] [PubMed]

Deschamps, G. A.

G. A. Deschamps, Electron. Lett. 7, 684 (1971).
[CrossRef]

Erdogan, T.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, K. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
[CrossRef]

Garmire, E.

M. E. Marhic and E. Garmire, Appl. Phys. Lett. 38, 743 (1981).
[CrossRef]

Gori, F.

F. Gori, G. Guatteri, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Greene, P. L.

Guatteri, G.

F. Gori, G. Guatteri, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Hall, D. G.

Jorden, R. H.

King, O.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, K. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
[CrossRef]

Kogelnik, H.

H. Kogelnik and T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Li, T.

H. Kogelnik and T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Marhic, M. E.

M. E. Marhic and E. Garmire, Appl. Phys. Lett. 38, 743 (1981).
[CrossRef]

Matsumura, K.

Y. Mushiake, K. Matsumura, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Mushiake, Y.

Y. Mushiake, K. Matsumura, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Nakajima, N.

Y. Mushiake, K. Matsumura, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Padovani, C.

F. Gori, G. Guatteri, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Patsakos, G.

L. W. Davis and G. Patsakos, Phys. Rev. A 26, 3702 (1982).
[CrossRef]

L. W. Davis and G. Patsakos, Opt. Lett. 6, 22 (1981).
[CrossRef] [PubMed]

Pohl, D.

D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
[CrossRef]

Rooks, M. J.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, K. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
[CrossRef]

Saghafi, S.

C. J. R. Sheppard and S. Saghafi, J. Opt. Soc. Am. A 16, 1381 (1999).
[CrossRef]

C. J. R. Sheppard and S. Saghafi, Phys. Rev. A 57, 2971 (1998).
[CrossRef]

C. J. R. Sheppard and S. Saghafi, “Electric and magnetic dipole beam modes beyond the paraxial approximation,” Optik (to be published).

Seshadri, S. R.

Sheppard, C. J. R.

C. J. R. Sheppard and S. Saghafi, J. Opt. Soc. Am. A 16, 1381 (1999).
[CrossRef]

C. J. R. Sheppard and S. Saghafi, Phys. Rev. A 57, 2971 (1998).
[CrossRef]

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
[CrossRef]

C. J. R. Sheppard and S. Saghafi, “Electric and magnetic dipole beam modes beyond the paraxial approximation,” Optik (to be published).

Tovar, A. A.

Wicks, G. W.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, K. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
[CrossRef]

Wilson, T.

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
[CrossRef]

Wynne, J. J.

J. J. Wynne, IEEE J. Quantum Electron. QE-10, 125 (1974).
[CrossRef]

Yu, P. K.

A. L. Cullen and P. K. Yu, Proc. R. Soc. London Ser. A 366, 155 (1979).
[CrossRef]

Appl. Phys. Lett. (3)

D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
[CrossRef]

M. E. Marhic and E. Garmire, Appl. Phys. Lett. 38, 743 (1981).
[CrossRef]

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, K. Anderson, and M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
[CrossRef]

Electron. Lett. (1)

G. A. Deschamps, Electron. Lett. 7, 684 (1971).
[CrossRef]

IEE J. Microwaves Opt. Acoust. (1)

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. J. Wynne, IEEE J. Quantum Electron. QE-10, 125 (1974).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Commun. (1)

F. Gori, G. Guatteri, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (3)

L. W. Davis and G. Patsakos, Phys. Rev. A 26, 3702 (1982).
[CrossRef]

C. J. R. Sheppard and S. Saghafi, Phys. Rev. A 57, 2971 (1998).
[CrossRef]

M. Couture and P.-A. Belanger, Phys. Rev. A 24, 355 (1981).
[CrossRef]

Proc. IEEE (2)

Y. Mushiake, K. Matsumura, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

H. Kogelnik and T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

A. L. Cullen and P. K. Yu, Proc. R. Soc. London Ser. A 366, 155 (1979).
[CrossRef]

Other (1)

C. J. R. Sheppard and S. Saghafi, “Electric and magnetic dipole beam modes beyond the paraxial approximation,” Optik (to be published).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Variation in time-averaged electric-energy density along the axes for an electric-dipole sink–source combination oriented along the z axis (TM01 mode). For large values of kz0 the beam has a dark center.

Fig. 2
Fig. 2

Phase variation along the axis for an electric-dipole sink–source combination oriented along the z axis (TM01 mode).

Fig. 3
Fig. 3

Contours of constant time-averaged electric-energy density in an azimuthal plane, for an electric-dipole sink–source combination oriented along the z axis, for two different values of kz0 (TM01 mode).

Fig. 4
Fig. 4

Variation in the time-averaged electric-energy density (in arbitrary units) in the waist for a magnetic-dipole sink–source combination oriented along the z axis (TE01 mode).

Fig. 5
Fig. 5

Contours of constant intensity in an azimuthal plane for magnetic-dipole sink–source combination oriented along the z axis, for kz0=2 (TE01 mode).

Equations (6)

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

E=fkR-gkRz-iz0xi+yjR2+fkRz-iz02R2+gkRx2+y2R2k,
fkR=j0kR+j2kR=-3cos kRkR3-sin kRkR3,gkR=j0kR-12j2kR=32sin kRkR+cos kRkR2-sin kRkR3,
R=x2+y2+z-iz021/2.
E=fkRk,
H=ε0μ0fkRyRi-xRj,
E=-i2fkRkyi-kxj,

Metrics