Abstract

By using the method of modal expansions of the independent transverse fields, a formula of vector plane wave spectrum (VPWS) of an arbitrary polarized electromagnetic wave in a homogenous medium is derived. In this formula VPWS is composed of TM- and TE-mode plane wave spectrum, where the amplitude and unit polarized direction of every plane wave are separable, which has more obviously physical meaning and is more convenient to apply in some cases compared to previous formula of VPWS. As an example, the formula of VPWS is applied to the well-known radially and azimuthally polarized beam. In addition, vector Fourier-Bessel transform pairs of an arbitrary polarized electromagnetic wave with circular symmetry are also derived.

© 2006 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  3. P. Varga and P. Török, “Exact and approximate solutions of Maxwell’s equations for a confocal cavity,” Opt. Lett. 21, 1523–1525 (1996).
    [CrossRef] [PubMed]
  4. S. R. Seshadri, “Electromagnetic Gaussian beam,” J. Opt. Soc. Am. A 15, 2712–2719 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. H. C. Kim and Y. H. Lee, “Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation,” Opt. Commun. 169, 9–16 (1999).
    [CrossRef]
  8. A. Ciattoni, B. Crosignani, and P. D. Porto, “Vectorial free-space optical propagation: a simple approach for generating all-order nonparaxial corrections,” Opt. Commun. 177, 9–13 (2000).
    [CrossRef]
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    [CrossRef]
  12. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), p. 21–31.
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    [CrossRef]
  14. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical- vector beams,” Opt. Express 7, 77–87 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-2-77.
    [CrossRef] [PubMed]

2001 (1)

2000 (3)

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical- vector beams,” Opt. Express 7, 77–87 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-2-77.
[CrossRef] [PubMed]

A. Ciattoni, B. Crosignani, and P. D. Porto, “Vectorial free-space optical propagation: a simple approach for generating all-order nonparaxial corrections,” Opt. Commun. 177, 9–13 (2000).
[CrossRef]

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

1999 (1)

H. C. Kim and Y. H. Lee, “Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation,” Opt. Commun. 169, 9–16 (1999).
[CrossRef]

1998 (2)

P. Varga and P. Török, “The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation,” Opt. Commun. 152, 108–118 (1998).
[CrossRef]

S. R. Seshadri, “Electromagnetic Gaussian beam,” J. Opt. Soc. Am. A 15, 2712–2719 (1998).
[CrossRef]

1997 (1)

A. Doicu and T. Wriedt, “Plane wave spectrum of electromagnetic beams,” Opt. Commun. 136, 114–124 (1997).
[CrossRef]

1996 (1)

1994 (1)

1979 (1)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–370 (1959).
[CrossRef]

Blit, S.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Bomzon, Z.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Bosch, S.

Brown, T. G.

Carnicer, A.

Ciattoni, A.

A. Ciattoni, B. Crosignani, and P. D. Porto, “Vectorial free-space optical propagation: a simple approach for generating all-order nonparaxial corrections,” Opt. Commun. 177, 9–13 (2000).
[CrossRef]

Crosignani, B.

A. Ciattoni, B. Crosignani, and P. D. Porto, “Vectorial free-space optical propagation: a simple approach for generating all-order nonparaxial corrections,” Opt. Commun. 177, 9–13 (2000).
[CrossRef]

Davidson, N.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Davis, L. W.

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

Doicu, A.

A. Doicu and T. Wriedt, “Plane wave spectrum of electromagnetic beams,” Opt. Commun. 136, 114–124 (1997).
[CrossRef]

Felsen, L. B.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Wave (IEEE PRESS, 1994), p. 183–252.

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), p. 21–31.

Friesem, A. A.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Hall, D. G.

Hasman, E.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Jordan, R. H.

Kim, H. C.

H. C. Kim and Y. H. Lee, “Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation,” Opt. Commun. 169, 9–16 (1999).
[CrossRef]

Lee, Y. H.

H. C. Kim and Y. H. Lee, “Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation,” Opt. Commun. 169, 9–16 (1999).
[CrossRef]

Marcuvitz, N.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Wave (IEEE PRESS, 1994), p. 183–252.

Martínez-Herrero, R.

Mejías, P. M.

Morse, P. M.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), p. 21–31.

Oron, R.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Porto, P. D.

A. Ciattoni, B. Crosignani, and P. D. Porto, “Vectorial free-space optical propagation: a simple approach for generating all-order nonparaxial corrections,” Opt. Commun. 177, 9–13 (2000).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–370 (1959).
[CrossRef]

Seshadri, S. R.

Török, P.

P. Varga and P. Török, “The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation,” Opt. Commun. 152, 108–118 (1998).
[CrossRef]

P. Varga and P. Török, “Exact and approximate solutions of Maxwell’s equations for a confocal cavity,” Opt. Lett. 21, 1523–1525 (1996).
[CrossRef] [PubMed]

Varga, P.

P. Varga and P. Török, “The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation,” Opt. Commun. 152, 108–118 (1998).
[CrossRef]

P. Varga and P. Török, “Exact and approximate solutions of Maxwell’s equations for a confocal cavity,” Opt. Lett. 21, 1523–1525 (1996).
[CrossRef] [PubMed]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–370 (1959).
[CrossRef]

Wriedt, T.

A. Doicu and T. Wriedt, “Plane wave spectrum of electromagnetic beams,” Opt. Commun. 136, 114–124 (1997).
[CrossRef]

Youngworth, K. S.

Appl. Phys. Lett. (1)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

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

Opt. Commun. (4)

P. Varga and P. Török, “The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation,” Opt. Commun. 152, 108–118 (1998).
[CrossRef]

H. C. Kim and Y. H. Lee, “Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation,” Opt. Commun. 169, 9–16 (1999).
[CrossRef]

A. Ciattoni, B. Crosignani, and P. D. Porto, “Vectorial free-space optical propagation: a simple approach for generating all-order nonparaxial corrections,” Opt. Commun. 177, 9–13 (2000).
[CrossRef]

A. Doicu and T. Wriedt, “Plane wave spectrum of electromagnetic beams,” Opt. Commun. 136, 114–124 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

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

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–370 (1959).
[CrossRef]

Other (2)

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), p. 21–31.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Wave (IEEE PRESS, 1994), p. 183–252.

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Equations (23)

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e i ( ρ ) = t Φ i ( ρ ) k ti ,
e i ( ρ ) = t Ψ i ( ρ ) k ti × z ̂ ,
h i ( ρ ) = z ̂ × t Φ i ( ρ ) k ti ,
h i ( ρ ) = t Ψ i ( ρ ) k ti ,
Φ i ( ρ ) = Ψ i ( ρ ) = 1 2 π exp [ j ( k xi x + k yi y ) ] ,
k ti 2 = k xi 2 + k yi 2 , < k xi < , < k yi < .
E t ( r ) = V ( z ) e ( ρ ) dk x dk y + V ( z ) e ( ρ ) dk x dk y ,
H t ( r ) = I ( z ) h ( ρ ) dk x dk y + I ( z ) h ( ρ ) dk x dk y
E z ( r ) = z ̂ 1 j 2 πωε I ( z ) k t exp [ j ( k x x + k y y ) ] dk x dk y ,
dV ( z ) dz = j k z ηI ( z ) ,
dI ( z ) dz = j k z η V ( z ) ,
I ( z ) = E ˜ TM exp ( j k z z ) ,
V ( z ) = k z ωε E ˜ TM exp ( j k z z ) ,
V ( z ) = E ˜ TE exp ( j k z z ) ,
E ( r ) = 1 4 π 2 [ k z k k t ( x ̂ k x + y ̂ k y ) z ̂ k t k ] E ˜ TM exp [ j ( k x x + k y y + k z z ) ] dk x dk y ,
1 4 π 2 ( x ̂ k y k t y ̂ k x k t ) E ˜ TE exp [ j ( k x x + k y y + k z z ) ] dk x dk y
E ˜ TM = k k t k z ( k x E x + k y E y ) exp [ j ( k x x + k y y + k z z ) ] dxdy ,
E ˜ TM = 1 k t ( k x E x k y E y ) exp [ j ( k x x + k y y + k z z ) ] dxdy .
E ( r ) = 1 2 π 0 k 1 k [ ρ ̂ j ( k 2 u 2 ) 1 2 J 1 ( ) + z ̂ u J 0 ( ) ] u
× E ˜ TM ( u ) exp [ j ( k 2 u 2 ) 1 2 z ] d u
φ ̂ j 1 2 π 0 k E ˜ TE ( u ) J 1 ( ) u exp [ j ( k 2 u 2 ) 1 2 z ] d u
E ˜ TM ( u ) = j 2 πk k 2 u 2 0 E ρ ( ρ ) J 1 ( ) ρ d ρ ,
E ˜ TE ( u ) = j 2 π 0 E φ ( ρ ) J 1 ( ) ρ d ρ ,

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