Abstract

The longitudinal component of a focused beam is split into two parts along the optical axis to obtain a longitudinally polarized long focal depth using amplitude filtering based on Euler transformation and a radially polarized Bessel–Gaussian beam. Numerical results indicate that long focal depth and FWHM can be easily achieved with 9λ and 0.8λ, respectively. A radially polarized beam can be converted into a longitudinally polarized beam with a conversion efficiency of 51.0%. It can therefore be believed that the proposed scheme can be widely used to generate a longitudinally polarized beam for particle acceleration, laser cutting, and optical trapping.

© 2011 Optical Society of America

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References

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2010 (2)

2008 (2)

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, Appl. Phys. Lett. 92, 233106 (2008).
[CrossRef]

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

2003 (1)

2002 (1)

T. Grosjean, D. Courjon, and M. Spajer, Opt. Commun. 203, 1 (2002).
[CrossRef]

1991 (1)

Chang, C.-K.

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, Appl. Phys. Lett. 92, 233106 (2008).
[CrossRef]

Chen, C.-H.

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, Appl. Phys. Lett. 92, 233106 (2008).
[CrossRef]

Cheng, T.-D.

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, Appl. Phys. Lett. 92, 233106 (2008).
[CrossRef]

Chong, C. T.

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

Courjon, D.

T. Grosjean, D. Courjon, and M. Spajer, Opt. Commun. 203, 1 (2002).
[CrossRef]

Davidson, N.

Friesem, A. A.

Grosjean, T.

T. Grosjean, D. Courjon, and M. Spajer, Opt. Commun. 203, 1 (2002).
[CrossRef]

Hasman, E.

Huang, K.

Kang, X.-L.

Kitamura, K.

Lee, C.-K.

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, Appl. Phys. Lett. 92, 233106 (2008).
[CrossRef]

Li, Y.-P.

Lin, D.-Z.

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, Appl. Phys. Lett. 92, 233106 (2008).
[CrossRef]

Liu, C.-K.

Lukyanchuk, B.

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

Noda, S.

Sakai, K.

Sheppard, C.

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

Shi, L.

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

Shi, P.

Spajer, M.

T. Grosjean, D. Courjon, and M. Spajer, Opt. Commun. 203, 1 (2002).
[CrossRef]

Sun, C.-C.

Wang, H.

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

Yeh, C.-S.

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, Appl. Phys. Lett. 92, 233106 (2008).
[CrossRef]

Zhang, X.

Appl. Phys. Lett. (1)

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, Appl. Phys. Lett. 92, 233106 (2008).
[CrossRef]

Nat. Photon. (1)

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

Opt. Commun. (1)

T. Grosjean, D. Courjon, and M. Spajer, Opt. Commun. 203, 1 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

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Figures (3)

Fig. 1
Fig. 1

Schematic of setup with radially polarized BG beam, filter, and high-NA lens.

Fig. 2
Fig. 2

(a) Amplitude transmittance for N = 1 , M = 0.9 , (b) corresponding intensity distribution in the y z plane. The DOF obtained is 2.2 λ . Points A and B are the centers of individual focusing with predicted focus points z M and z + M .

Fig. 3
Fig. 3

(a), (c), and (e) are the amplitude transmittance spectra for ( N = 2 , M = 0.7 ), ( N = 3 , M = 0.7 ), and ( N = 4 , M = 0.7 ), respectively; (b), (d), and (f) are the corresponding intensity distributions in the y z plane. The DOF values in (b), (d), and (f) are 3.8 λ , 6.6 λ , and 9.5 λ , respectively.

Tables (1)

Tables Icon

Table 1 Comparison of Amplitude Filtering Function with Other Filtering

Equations (7)

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E r ( r , z ) = A 0 α cos 1 2 θ sin ( 2 θ ) l ( θ ) J 1 ( k r sin θ ) e i k z cos θ d θ ,
l ( θ ) = exp [ ( β sin θ sin α ) 2 ] J 1 ( 2 γ sin θ sin α ) ,
T R N ( θ ) = p = 1 N cos [ 2 M π ( 2 p 1 ) cos θ ] ,
T N ( θ ) = T R N ( θ ) / max [ T R N ( θ ) ] .
T 1 ( θ ) = cos ( ϕ ) = 1 2 [ exp ( i ϕ ) + exp ( i ϕ ) ] ,
E r ( r , z ) = 1 2 A 0 α cos 1 2 θ sin ( 2 θ ) l ( θ ) J 1 ( k r sin θ ) × ( e i k ( z M ) cos θ + e i k ( z + M ) cos θ ) d θ .
E r ( r , z ) = E r ( r , z M ) + E r ( r , z + M ) .

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