Abstract

Making use of the complex-source-point method in cylindrical coordinates, an exact solution representing a cylindrical quasi-Gaussian beam of arbitrary waist w0 satisfying both the Helmholtz and Maxwell’s equations is introduced. The Cartesian components of the electromagnetic field are derived stemming from different polarizations of the magnetic and electric vector potentials based on Maxwell’s vectorial equations and Lorenz’s gauge condition, without any approximations. Computations illustrate the theory for tightly focused and quasi-collimated cylindrical beams. The results are particularly useful in beam-forming design using high-aperture or collimated cylindrical laser beams in imaging microscopy, particle manipulation, optical tweezers, and the study of scattering, radiation forces, and torque on cylindrical structures.

© 2013 Optical Society of America

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2013

F. G. Mitri, Optik 124, 1469 (2013).
[CrossRef]

F. G. Mitri, Eur. Phys. J. D 67, 1 (2013).
[CrossRef]

F. G. Mitri, Phys. Rev. A 88, 035804 (2013).
[CrossRef]

F. G. Mitri, Phys. Rev. A 87, 035804 (2013).
[CrossRef]

C. J. R. Sheppard, Appl. Opt. 52, 538 (2013).
[CrossRef]

F. G. Mitri, Opt. Lett. 38, 615 (2013).
[CrossRef]

2012

F. G. Mitri, Phys. Rev. A 85, 025801 (2012).
[CrossRef]

2011

2010

2003

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

2001

2000

1999

1998

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

1994

M. V. Berry, J. Phys. A 27, L391 (1994).
[CrossRef]

1990

E. Heyman, B. Z. Steinberg, and R. Iancunescu, IEEE Trans. Antennas Propag. 38, 957 (1990).
[CrossRef]

1987

1984

L. B. Felsen, Geophys. J. R. Astr. Soc. 79, 77 (1984).
[CrossRef]

J. S. Marsh, Am. J. Phys. 52, 152 (1984).
[CrossRef]

1981

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

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

1979

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

1976

1971

1967

Y. A. Kravtsov, Radiophys. Quantum Electron. 10, 719 (1967).
[CrossRef]

Barton, J. P.

Belanger, P. A.

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

Berry, M. V.

M. V. Berry, J. Phys. A 27, L391 (1994).
[CrossRef]

Brown, T.

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 366, 155 (1979).
[CrossRef]

Davis, L. W.

Deschamps, G. A.

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

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Durnin, J.

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

J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Felsen, L. B.

Gouesbet, G.

G. Gouesbet and G. Gréhan, Generalized Lorenz-Mie Theories, 1st ed. (Springer, 2011).

Gréhan, G.

G. Gouesbet and G. Gréhan, Generalized Lorenz-Mie Theories, 1st ed. (Springer, 2011).

Heyman, E.

Iancunescu, R.

E. Heyman, B. Z. Steinberg, and R. Iancunescu, IEEE Trans. Antennas Propag. 38, 957 (1990).
[CrossRef]

Jackson, J. D.

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

Keller, J. B.

Kozawa, Y.

Kravtsov, Y. A.

Y. A. Kravtsov, Radiophys. Quantum Electron. 10, 719 (1967).
[CrossRef]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Marsh, J. S.

J. S. Marsh, Am. J. Phys. 52, 152 (1984).
[CrossRef]

Miceli, J.

J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Mitri, F. G.

F. G. Mitri, Phys. Rev. A 88, 035804 (2013).
[CrossRef]

F. G. Mitri, Phys. Rev. A 87, 035804 (2013).
[CrossRef]

F. G. Mitri, Optik 124, 1469 (2013).
[CrossRef]

F. G. Mitri, Opt. Lett. 38, 615 (2013).
[CrossRef]

F. G. Mitri, Eur. Phys. J. D 67, 1 (2013).
[CrossRef]

F. G. Mitri, Phys. Rev. A 85, 025801 (2012).
[CrossRef]

F. G. Mitri, Opt. Lett. 36, 606 (2011).
[CrossRef]

Patsakos, G.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Saghafi, S.

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

Sato, S.

Sheppard, C. J. R.

C. J. R. Sheppard, Appl. Opt. 52, 538 (2013).
[CrossRef]

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

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Steinberg, B. Z.

E. Heyman, B. Z. Steinberg, and R. Iancunescu, IEEE Trans. Antennas Propag. 38, 957 (1990).
[CrossRef]

E. Heyman, B. Z. Steinberg, and L. B. Felsen, J. Opt. Soc. Am. A 4, 2081 (1987).
[CrossRef]

Streifer, W.

Youngworth, K.

Yu, P. K.

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

Am. J. Phys.

J. S. Marsh, Am. J. Phys. 52, 152 (1984).
[CrossRef]

Appl. Opt.

Electron. Lett.

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

Eur. Phys. J. D

F. G. Mitri, Eur. Phys. J. D 67, 1 (2013).
[CrossRef]

Geophys. J. R. Astr. Soc.

L. B. Felsen, Geophys. J. R. Astr. Soc. 79, 77 (1984).
[CrossRef]

IEEE Trans. Antennas Propag.

E. Heyman, B. Z. Steinberg, and R. Iancunescu, IEEE Trans. Antennas Propag. 38, 957 (1990).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. A

M. V. Berry, J. Phys. A 27, L391 (1994).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

F. G. Mitri, Optik 124, 1469 (2013).
[CrossRef]

Phys. Rev. A

F. G. Mitri, Phys. Rev. A 85, 025801 (2012).
[CrossRef]

F. G. Mitri, Phys. Rev. A 88, 035804 (2013).
[CrossRef]

F. G. Mitri, Phys. Rev. A 87, 035804 (2013).
[CrossRef]

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

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

Phys. Rev. Lett.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

J. Durnin, J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Proc. R. Soc. London

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

Radiophys. Quantum Electron.

Y. A. Kravtsov, Radiophys. Quantum Electron. 10, 719 (1967).
[CrossRef]

Other

A. E. Siegman, Lasers (University Science Books, 1986).

G. Gouesbet and G. Gréhan, Generalized Lorenz-Mie Theories, 1st ed. (Springer, 2011).

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

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Figures (3)

Fig. 1.
Fig. 1.

Planar cross-sectional plots of the modulus of the electric and magnetic fields’ components, in the transverse ( y , y ) , ( z , z ) and axial ( x , x ) configurations, denoted by (a)–(c), respectively, for a strongly focused beam with k w 0 = 0.1 and α = 0 . The lower panels display the cross-sectional plots for the power density with their one-line profiles at the center of the beam. The units along the axes are in millimeters.

Fig. 2.
Fig. 2.

Same as in Fig. 1, but α = 45 ° .

Fig. 3.
Fig. 3.

Same as in Fig. 1, but k w 0 = 4 and α = 45 ° .

Equations (33)

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ψ = ψ 0 H 0 ( 1 ) ( k ρ ρ ) e i ( k z z ω t ) ,
ψ = ψ 0 H 0 ( 1 ) ( k ρ ρ ) e i ( k z z ω t ) ,
x R = k w 0 2 / 2 .
ψ r = ψ 0 2 [ H 0 ( 1 ) ( k ρ ρ ) H 0 ( 1 ) ( k ρ ρ ) ] e i ( k z z ω t ) .
ψ r = ψ 0 J 0 ( k ρ ρ ) e i ( k z z ω t ) .
Ψ m , y = ψ 0 J 0 ( k ρ ρ + ) e i ( k z z ω t ) I 0 ( k ρ x R ) y .
× Ψ m , y = H m ε 1 / 2 ,
E m = i k [ Ψ m , y + ( · Ψ m , y ) / k 2 ] .
Ψ e , y = ψ 0 J 0 ( k ρ ρ + ) e i ( k z z ω t ) I 0 ( k ρ x R ) y .
× Ψ e , y = E e .
H e ε 1 / 2 = i k [ Ψ e , y + ( · Ψ e , y ) / k 2 ] .
E x ( y , y ) = i ψ 0 e i ( k z z ω t ) 2 k ρ + 3 I 0 ( k ρ x R ) [ ρ + ( k k z ρ + 2 k ρ 2 y X + ) J 0 ( k ρ ρ + ) + 2 k ρ y X + J 1 ( k ρ ρ + ) ] ,
E y ( y , y ) = i ψ 0 e i ( k z z ω t ) 2 k ρ + 3 I 0 ( k ρ x R ) { ρ + ( k ρ + k ρ y ) ( k ρ + + k ρ y ) J 0 ( k ρ ρ + ) k ρ [ ρ + 2 2 y 2 ] J 1 ( k ρ ρ + ) } ,
E z ( y , y ) = ψ 0 e i ( k z z ω t ) 2 ρ + I 0 ( k ρ x R ) k ρ J 1 ( k ρ ρ + ) ( X + + y sin α ) ,
H x ( y , y ) = i ψ 0 e i ( k z z ω t ) ε 2 k ρ + 3 I 0 ( k ρ x R ) [ ρ + ( k k z ρ + 2 + k ρ 2 y X + ) J 0 ( k ρ ρ + ) 2 k ρ y X + J 1 ( k ρ ρ + ) ] ,
H y ( y , y ) = ε E y ( y , y ) ,
H z ( y , y ) = ψ 0 e i ( k z z ω t ) ε 2 ρ + I 0 ( k ρ x R ) k ρ J 1 ( k ρ ρ + ) ( X + y sin α ) ,
E x ( z , z ) = ψ 0 e i ( k z z ω t ) 2 ρ + I 0 ( k ρ x R ) k ρ J 1 ( k ρ ρ + ) ( y + X + sin α ) ,
E y ( z , z ) = ε 1 2 H z ( y , y ) ,
E z ( z , z ) = i ψ 0 e i ( k z z ω t ) 2 I 0 ( k ρ x R ) k ρ J 1 ( k ρ ρ + ) cos α ,
H x ( z , z ) = ψ 0 e i ( k z z ω t ) ε 2 ρ + I 0 ( k ρ x R ) k ρ J 1 ( k ρ ρ + ) ( y X + sin α ) ,
H y ( z , z ) = ε E z ( y , y ) ,
H z ( z , z ) = ε E z ( z , z ) .
E x ( x , x ) = i ψ 0 e i ( k z z ω t ) 2 k ρ + 3 I 0 ( k ρ x R ) { ρ + ( k ρ + k ρ X + ) ( k ρ + + k ρ X + ) J 0 ( k ρ ρ + ) k ρ [ ρ + 2 2 X + 2 ] J 1 ( k ρ ρ + ) } ,
E y ( x , x ) = ψ 0 e i ( k z z ω t ) 2 k ρ + 3 I 0 ( k ρ x R ) { 2 i k ρ X + y J 1 ( k ρ ρ + ) ρ + ( i k k z ρ + 2 + i k ρ 2 X + y ) J 0 ( k ρ ρ + ) } ,
E z ( x , x ) = ψ 0 e i ( k z z ω t ) 2 ρ + I 0 ( k ρ x R ) k ρ ( y X + sin α ) J 1 ( k ρ ρ + ) ,
H x ( x , x ) = ε E x ( x , x ) ,
H y ( x , x ) = ψ 0 e i ( k z z ω t ) ε 2 k ρ + 3 I 0 ( k ρ x R ) { 2 i k ρ X + y J 1 ( k ρ ρ + ) + ρ + ( i k k z ρ + 2 i k ρ 2 X + y ) J 0 ( k ρ ρ + ) } ,
H z ( x , x ) = ψ 0 e i ( k z z ω t ) ε 2 ρ + I 0 ( k ρ x R ) k ρ ( y + X + sin α ) J 1 ( k ρ ρ + ) .
S = ( c / 8 π ) Re ( E × H * ) .
ψ r ( ) = ψ 0 ( ) J ( k ρ ρ ) e i ( k z z + θ ω t ) ,
ψ r , t ( ) = ψ 0 ( ) J ( k ρ ρ ) e i ( k z z ω t ) cos ( θ ) ,
θ = cos 1 [ ( x i x R ) / ρ ] .

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