Abstract

The scalar wave theory of nondiffracting electromagnetic (EM) high-order Bessel vortex beams of fractional type α has been recently explored, and their novel features and promising applications have been revealed. However, complete characterization of the properties for this new type of beam requires a vector analysis to determine the fields’ components in space because scalar wave theory is inadequate to describe such beams, especially when the central spot is comparable to the wavelength (kr/k1, where kr is the radial component of the wavenumber k). Stemming from Maxwell’s vector equations and the Lorenz gauge condition, a full vector wave analysis for the electric and magnetic fields is presented. The results are of particular importance in the study of EM wave scattering of a high-order Bessel vortex beam of fractional type α by particles.

© 2011 Optical Society of America

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Errata

F. G. Mitri, "Vector wave analysis of an electromagnetic high-order Bessel vortex beam of fractional type α: erratum," Opt. Lett. 38, 615-615 (2013)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-38-5-615

References

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2010

F. G. Mitri, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 395 (2010).
[CrossRef] [PubMed]

2008

2004

2003

2001

1996

1995

1991

S. R. Mishra, Opt. Commun. 85, 159 (1991).
[CrossRef]

1939

J. A. Stratton and L. J. Chu, Phys. Rev. 56, 99 (1939).
[CrossRef]

Burnham, D.

Chi, S.

Chu, L. J.

J. A. Stratton and L. J. Chu, Phys. Rev. 56, 99 (1939).
[CrossRef]

Guo, Q.

Gutierrez-Vega, J. C.

Hall, D. G.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999), p. 240.

Lee, W. M.

Lopez-Mariscal, C.

Marathay, A. S.

McCalmont, J. F.

McGloin, D.

Mishra, S. R.

S. R. Mishra, Opt. Commun. 85, 159 (1991).
[CrossRef]

Mitri, F. G.

F. G. Mitri, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 395 (2010).
[CrossRef] [PubMed]

Rudd, D.

Stratton, J. A.

J. A. Stratton and L. J. Chu, Phys. Rev. 56, 99 (1939).
[CrossRef]

Tao, S. H.

Yuan, X. C.

Appl. Opt.

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

F. G. Mitri, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 395 (2010).
[CrossRef] [PubMed]

J. Opt. A

J. C. Gutierrez-Vega and C. Lopez-Mariscal, J. Opt. A 10, 015009 (2008).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

S. R. Mishra, Opt. Commun. 85, 159 (1991).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

J. A. Stratton and L. J. Chu, Phys. Rev. 56, 99 (1939).
[CrossRef]

Other

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999), p. 240.

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Figures (3)

Fig. 1
Fig. 1

Theoretical magnitude cross-sectional profiles for the (a) electric and (b) magnetic field components along the axes x, y, and z (represented along each column) of an EM HOBVB- F α for α = 5 and k / k r = 2.3662 . When α becomes fractional ( = 5.5 ), the (c) electric and (d) magnetic field components exhibit specific patterns in which the symmetry is broken.

Fig. 2
Fig. 2

Same as in Fig. 1; however, k / k r = 1.1547 .

Fig. 3
Fig. 3

Comparison between the plots for the magnitudes of the energy density and the Poynting vector power density for α = 5 and α = 5.5 . Upper row, k / k r = 2.3662 ; lower row, k / k r = 1.1547 .

Equations (20)

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× E = i k ( H ε 1 / 2 ) ,
× ( H ε 1 / 2 ) = i k E ,
· E = 0 ,
· ( H ε 1 / 2 ) = 0 ,
× A p = H p ε 1 / 2 .
E p = i k [ A p + ( · A p ) / k 2 ] ,
( 2 + k 2 ) A p = 0.
A p = A 0 m = + { i ( α | m | ) sinc ( α m ) J | m | ( k r R ) exp [ i ( k z z + | m | ϕ ) ] } x ,
| m | = { m , if    m 0 , m , if    m < 0 ,
× A q = E q .
H q ε 1 / 2 = i k [ A q + ( · A q ) / k 2 ] .
A q = A 0 m = + { i ( α | m | ) sinc ( α m ) J | m | ( k r R ) exp [ i ( k z z + | m | ϕ ) ] } y .
E x = 1 2 E 0 m = + { i ( α | m | ) sinc ( α m ) exp [ i ( k z z + | m | ϕ ) ] × [ ( 1 + k z k k r 2 x 2 k 2 R 2 + | m | ( | m | 1 ) ( x i y ) 2 k 2 R 4 ) J | m | ( k r R ) k r ( y 2 x 2 2 i | m | x y ) k 2 R 3 J | m | + 1 ( k r R ) ] } ,
E y = 1 2 E 0 x y m = + { i ( α | m | ) sinc ( α m ) exp [ i ( k z z + | m | ϕ ) ] × [ ( | m | ( | m | 1 ) [ 2 + i ( x 2 y 2 ) / ( x y ) ] k r 2 R 2 k 2 R 4 ) J | m | ( k r R ) + k r [ 2 + i | m | ( y 2 x 2 ) / ( x y ) ] k 2 R 3 J | m | + 1 ( k r R ) ] } ,
E z = 1 2 i E 0 x k R ( 1 + k z k ) m = + { i ( α | m | ) sinc ( α m ) exp [ i ( k z z + | m | ϕ ) ] × [ ( | m | ( 1 i y / x ) R ) J | m | ( k r R ) k r J | m | + 1 ( k r R ) ] } ,
H x ε 1 / 2 = E y ,
H y ε 1 / 2 = 1 2 E 0 m = + { i ( α | m | ) sinc ( α m ) exp [ i ( k z z + | m | ϕ ) ] × [ ( 1 + k z k k r 2 y 2 k 2 R 2 + | m | ( | m | 1 ) ( y + i x ) 2 k 2 R 4 ) J | m | ( k r R ) k r ( x 2 y 2 + 2 i | m | x y ) k 2 R 3 J | m | + 1 ( k r R ) ] } ,
H z ε 1 / 2 = 1 2 i E 0 y k R ( 1 + k z k ) m = + { i ( α | m | ) sinc ( α m ) exp [ i ( k z z + | m | ϕ ) ] × [ ( | m | ( 1 + i x / y ) R ) J | m | ( k r R ) k r J | m | + 1 ( k r R ) ] } ,
ξ = [ ε ( E x 2 + E y 2 + E z 2 ) + ( H x 2 + H y 2 + H z 2 ) ] / 16 π ,
S = 1 2 Re [ ( E y H z * E z H y * ) x + ( E z H x * E x H z * ) y + ( E x H y * E y H x * ) z ] .

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