Abstract

Generation of a nondiffracting transversally polarized beam by means of transmitting an azimuthally polarized beam through a multibelt spiral phase hologram and then highly focusing by a high-NA lens is presented. A relatively long depth of focus (4.84λ) of the electric field with only radial and azimuthal components is achieved. The polarization of the wavefront near the focal plane is analyzed in detail by calculating the Stokes polarization parameters. It is found that the polarization is spatially varying and entirely transversally polarized, and the polarization singularity disappears at the beam center, which makes the central bright channel possible.

© 2011 Optical Society of America

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References

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2011 (2)

2010 (1)

2008 (1)

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

2006 (3)

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and C. T. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Z. Bomzon, M. Gu, and J. Shamir, Appl. Phys. Lett. 89, 241104 (2006).
[CrossRef]

M. A. Golub, V. Shurman, and I. Grossinger, Appl. Opt. 45, 144 (2006).
[CrossRef] [PubMed]

2004 (1)

2000 (1)

1991 (1)

1987 (1)

1954 (1)

Bomzon, Z.

Z. Bomzon, M. Gu, and J. Shamir, Appl. Phys. Lett. 89, 241104 (2006).
[CrossRef]

Brown, T. G.

Chong, C. T.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and C. T. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Collet, E.

E. Collet, Polarized Light (Dekker, 1993).

Davidson, N.

Durnin, J.

Flores, A.

Friesem, A. A.

Golub, M. A.

Grossinger, I.

Gu, M.

Z. Bomzon, M. Gu, and J. Shamir, Appl. Phys. Lett. 89, 241104 (2006).
[CrossRef]

Hao, X.

Hasman, E.

Kuang, C. F.

Li, Y. D.

Lin, J.

Liu, X.

Lukyanchuk, B.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

McLeod, J. H.

Miao, X. S.

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and C. T. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Pu, P. X.

Shamir, J.

Z. Bomzon, M. Gu, and J. Shamir, Appl. Phys. Lett. 89, 241104 (2006).
[CrossRef]

Sheppard, C.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

Shi, L. P.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and C. T. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Shurman, V.

Tan, J. B.

Tan, W. L.

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and C. T. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Tian, B.

Wang, H. F.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and C. T. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

Wang, M. R.

Wang, T. T.

Yang, J. J.

Yin, K.

Youngworth, K. S.

Yuan, G. Q.

H. F. Wang, L. P. Shi, G. Q. Yuan, X. S. Miao, W. L. Tan, and C. T. Chong, Appl. Phys. Lett. 89, 171102 (2006).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic configuration of the setup: azimuthally polarized Bessel–Gaussian beam passes through a multibelt spiral phase hologram and is subsequently focused by a high-NA lens.

Fig. 2
Fig. 2

(a) Theoretical and (c) FDTD results of electric field component intensity distributions in the radial direction, (b) theoretical and (d) FDTD results of contour plot of the total electric field intensity in the focal plane using an ordinary spiral phase hologram with charge + 1 . λ = 0.633 μm , NA = 0.95 . The inset shows the experimental result.

Fig. 3
Fig. 3

(a)  | E r | 2 + | E ϕ | 2 , (b)  | E r | 2 , and (c)  | E ϕ | 2 distributions in the y z plane after phase modulation by a five-belt spiral phase hologram. (d) Normalized axial intensity with multibelt phase hologram (solid red curve) and ordinary phase hologram (dashed black curve). Inset shows the total transverse electric field intensity distribution at z = 0 .

Fig. 4
Fig. 4

(a) Cross section of the ellipticity of local polarization ellipses at different observation planes and (b) the azimuthal angle distribution in the first quadrant at the focal plane.

Equations (6)

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E ( r , ϕ , z ) = [ E r E ϕ E z ] = [ A e i ϕ ( I 0 + I 2 ) i A e i ϕ ( I 0 I 2 ) 0 ] ,
I n = 0 θ m cos θ 1 / 2 sin θ f ( θ ) l 0 ( θ ) e i k 0 z cos θ J n ( k 0 r sin θ ) d θ .
l 0 ( θ ) = exp [ ( sin θ / sin θ m ) 2 ] J 1 ( 2 sin θ / sin θ m ) .
θ 1 = 14.3 ° , θ 2 = 26.5 ° , θ 3 = 58.5 ° , θ 4 = 67.26 ° .
tan 2 ψ = S 2 / S 1 = tan [ 2 ϕ + arg ( I 0 * I 2 ) ] ,
sin 2 χ = S 3 / S 0 = ( | I 0 | 2 | I 2 | 2 ) / ( | I 0 | 2 + | I 2 | 2 ) ,

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