Abstract

The Hermite–Gauss and Laguerre–Gauss modes are well-known beam solutions of the scalar Helmholtz equation in the paraxial limit. As such, they describe linearly polarized fields or single Cartesian components of vector fields. The vector wave equation admits, in the paraxial limit, of a family of localized Bessel–Gauss beam solutions that can describe the entire transverse electric field. Two recently reported solutions are members of this family of vector Bessel–Gauss beam modes.

© 1996 Optical Society of America

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References

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  1. See, for example, H. Kogelnik, T. Li, Appl. Opt. 5, 50 (1966).
    [CrossRef]
  2. D. Pohl, Appl. Phys. Lett.20, 266 (1972).
    [CrossRef]
  3. J. J. Wynne, IEEE J. Quantum Electron. QE-10, 125 (1974).
  4. M. E. Marhic, E. Garmire, Appl. Phys. Lett. 38, 743 (1981).
    [CrossRef]
  5. T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. Anderson, M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).
  6. R. H. Jordan, D. G. Hall, Opt. Lett. 19, 427 (1994).
    [CrossRef] [PubMed]
  7. F. Gori, G. Guattari, C. Padovani, Opt. Commun. 64, 491 (1987).
    [CrossRef]
  8. See, for example,SnyderA. W.LoveJ. D., Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 250.
  9. M. Lax, W. H. Louisell, W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
    [CrossRef]
  10. J. E. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
    [CrossRef]
  11. J. E. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 54, 1499 (1987).
    [CrossRef]
  12. Z. Bouchal, M. Olivik, J. Mod. Opt. 42, 1555 (1995).
    [CrossRef]

1995 (1)

Z. Bouchal, M. Olivik, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

1994 (1)

1992 (1)

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. Anderson, M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).

1987 (3)

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

J. E. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. E. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 54, 1499 (1987).
[CrossRef]

1981 (1)

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

1975 (1)

M. Lax, W. H. Louisell, W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

1974 (1)

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

1966 (1)

Anderson, E.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. Anderson, M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).

Bouchal, Z.

Z. Bouchal, M. Olivik, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

Durnin, J. E.

J. E. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. E. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 54, 1499 (1987).
[CrossRef]

Eberly, J. H.

J. E. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 54, 1499 (1987).
[CrossRef]

Erdogan, T.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. Anderson, M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).

Garmire, E.

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

Gori, F.

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

Guattari, G.

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

Hall, D. G.

R. H. Jordan, D. G. Hall, Opt. Lett. 19, 427 (1994).
[CrossRef] [PubMed]

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. Anderson, M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).

Jordan, R. H.

King, O.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. Anderson, M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).

Kogelnik, H.

Lax, M.

M. Lax, W. H. Louisell, W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Li, T.

Louisell, W. H.

M. Lax, W. H. Louisell, W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Marhic, M. E.

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

McKnight, W. B.

M. Lax, W. H. Louisell, W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Miceli, J. J.

J. E. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 54, 1499 (1987).
[CrossRef]

Olivik, M.

Z. Bouchal, M. Olivik, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

Padovani, C.

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

Pohl, D.

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

Rooks, M. J.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. Anderson, M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).

Wicks, G. W.

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. Anderson, M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).

Wynne, J. J.

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

Appl. Opt. (1)

Appl. Phys. Lett. (2)

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

T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. Anderson, M. J. Rooks, Appl. Phys. Lett. 60, 1921 (1992).

IEEE J. Quantum Electron (1)

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

J. Mod. Opt. (1)

Z. Bouchal, M. Olivik, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

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

Opt. Commun. (1)

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

Opt. Lett. (1)

Phys. Rev. A (1)

M. Lax, W. H. Louisell, W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Phys. Rev. Lett. (1)

J. E. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 54, 1499 (1987).
[CrossRef]

Other (2)

See, for example,SnyderA. W.LoveJ. D., Optical Waveguide Theory (Chapman & Hall, London, 1983), p. 250.

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

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Equations (20)

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1 ρ ρ ( ρ f ρ ) + 1 ρ 2 2 f ϕ 2 + 2 i k f z = 0.
f ( ρ , z ) = w 0 w ( z ) exp [ i Φ ( z ) ] exp ( ρ 2 / w 0 1 + i z / L ) ,
× ×  E  k 2 E = 0,
E ( ρ , z) =  ϕ ^ F ( ρ , z ) exp [ i ( k z ω t ) ] .
1 ρ ρ ( ρ F ρ ) F ρ 2 + 2 i k F z = 0 ,
F ( ρ , z ) = A J 1 ( β ρ 1 + i z / L ) f ( ρ , z ) Q ( z ) ,
Q ( z ) = exp [ i β 2 z / ( 2 k ) 1 + i z / L ] .
E = F ( ρ , ϕ , z ) exp [ i ( k z ω t ) ] ,
F = ε ( ρ , ϕ , z ) f ( ρ , z ) ,
1 ρ ρ ( ρ ε ρ ρ ) 4 ρ / w 0 1 + i z / L ε ρ ρ + 1 ρ 2 2 ε ρ ϕ 2 1 ρ 2 ε ρ 2 ρ 2 ε ϕ ϕ + 2 i k ε ρ z = 0 ,
1 ρ ρ ( ρ ε ϕ ρ ) 4 ρ / w 0 1 + i z / L ε ϕ ρ + 1 ρ 2 2 ε ϕ ϕ 2 1 ρ 2 ε ϕ 2 ρ 2 ε ρ ϕ + 2 i k ε ϕ z = 0.
ε ρ , m ( ρ , ϕ , z ) = Q ( z ) [ a m J m 1 ( u ) + b m J m + 1 ( u ) ] [ or sin ( m ϕ ) cos ( m ϕ ) ] ,
ε ϕ , m ( ρ , ϕ , z ) = Q ( z ) [ a m J m 1 ( u ) b m J m + 1 ( u ) ] [ or cos ( m ϕ ) sin ( m ϕ ) ] ,
u = β ρ 1 + i z / L ,
ε ρ , m ( ρ , ϕ , z ) = a m Q ( z ) [ J m 1 ( u )    + J m + 1 ( u ) ] [ or sin ( m ϕ ) cos ( m ϕ ) ] ,
ε ϕ , m ( ρ , ϕ , z ) = a m Q ( z ) × [ J m 1 ( u ) J m + 1 ( u ) ] [ or cos ( m ϕ ) sin ( m ϕ ) ] .
m = 0 : E ( ρ , z ) = ϕ ^ 2 a 0 J 1 ( β ρ 1 + i z / L ) × f ( ρ , z ) Q ( z ) exp [ i ( k z ω t ) ] ,
m = 1 : E x ( ρ , ϕ , z ) = a 1 [ J 0 ( u ) + J 2 ( u ) cos ( 2 ϕ ) ] × f ( ρ , z ) Q ( z ) exp [ i ( k z ω t ) ] ,
E n ( ρ , ϕ , z ) = A n J n ( u ) f ( ρ , z ) Q ( z ) × cos ( n ϕ ) exp [ i ( k z ω t ) ] ,
m = 0 : H ( ρ , z ) = ϕ ^ 2 b 0 J 1 ( β ρ 1 + i z / L ) × f ( ρ , z ) Q ( z ) exp [ i ( k z ω t ) ] ,

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