Abstract

We have considered the paraxial vector erf-Gaussian beams with field distribution in the form of the error function that are shaped by the cone of plane waves with a fractional step of the azimuthal phase distribution modulated by the Gaussian envelope. We have revealed that the initial distributions of the transverse electric and transverse magnetic fields have a far from standard form but at the far diffraction field the field distributions recover nearly the symmetric form.

© 2012 Optical Society of America

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References

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  5. T. Fadeyeva, V. Shvedov, N. Shostka, C. Alexeyev, and A. Volyar, Opt. Lett. 35, 3787 (2010).
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  6. G. Yuan, S. Wei, and X.-C. Yuan, Opt. Lett. 36, 3479 (2011).
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  9. J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
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  10. I. Basisty, V. Pas’ko, V. Slyusar, M. Soskin, and M. Vasnetsov, J. Opt. A 6, S166 (2004).
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  11. S. R. Mishra, Opt. Commun. 85, 159 (1991).
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  12. A. P. Kiselev, Opt. Spectrosc. 102, 603 (2007).
    [CrossRef]
  13. D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
    [CrossRef]
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    [CrossRef]
  15. A. V. Volyar, V. G. Shvedov, and T. A. Fadeeva, Opt. Spectrosc. 90, 93 (2001).
    [CrossRef]

2011 (2)

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, Phys. Rev. Lett. 106, 123901 (2011).
[CrossRef]

G. Yuan, S. Wei, and X.-C. Yuan, Opt. Lett. 36, 3479 (2011).
[CrossRef]

2010 (2)

2009 (1)

2008 (1)

2007 (1)

A. P. Kiselev, Opt. Spectrosc. 102, 603 (2007).
[CrossRef]

2005 (1)

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

2004 (3)

J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

I. Basisty, V. Pas’ko, V. Slyusar, M. Soskin, and M. Vasnetsov, J. Opt. A 6, S166 (2004).
[CrossRef]

M. V. Berry, J. Opt. A 6, 259 (2004).
[CrossRef]

2001 (1)

A. V. Volyar, V. G. Shvedov, and T. A. Fadeeva, Opt. Spectrosc. 90, 93 (2001).
[CrossRef]

1997 (1)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

1995 (1)

I. Basisty, M. Soskin, and M. Vasnetsov, Opt. Commun. 119, 604 (1995).
[CrossRef]

1991 (1)

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

Alexeyev, C.

Basisty, I.

I. Basisty, V. Pas’ko, V. Slyusar, M. Soskin, and M. Vasnetsov, J. Opt. A 6, S166 (2004).
[CrossRef]

I. Basisty, M. Soskin, and M. Vasnetsov, Opt. Commun. 119, 604 (1995).
[CrossRef]

Berry, M. V.

M. V. Berry, J. Opt. A 6, 259 (2004).
[CrossRef]

Dholakia, K.

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

Fadeeva, T. A.

A. V. Volyar, V. G. Shvedov, and T. A. Fadeeva, Opt. Spectrosc. 90, 93 (2001).
[CrossRef]

Fadeyeva, T.

Garcia, H.

Gutierrez-Vega, J.

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Hnatovsky, C.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, Phys. Rev. Lett. 106, 123901 (2011).
[CrossRef]

Karimi, E.

Kiselev, A. P.

A. P. Kiselev, Opt. Spectrosc. 102, 603 (2007).
[CrossRef]

Kitamura, K.

Krolikowski, W.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, Phys. Rev. Lett. 106, 123901 (2011).
[CrossRef]

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Leach, J.

J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

Marrucci, L.

McGloin, D.

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

Mishra, S. R.

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

Noda, S.

Padgett, M. J.

J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

Pas’ko, V.

I. Basisty, V. Pas’ko, V. Slyusar, M. Soskin, and M. Vasnetsov, J. Opt. A 6, S166 (2004).
[CrossRef]

Piccirillo, B.

Rode, A.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, Phys. Rev. Lett. 106, 123901 (2011).
[CrossRef]

Sakai, K.

Santamato, E.

Sasada, H.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Shostka, N.

Shvedov, V.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, Phys. Rev. Lett. 106, 123901 (2011).
[CrossRef]

T. Fadeyeva, V. Shvedov, N. Shostka, C. Alexeyev, and A. Volyar, Opt. Lett. 35, 3787 (2010).
[CrossRef]

Shvedov, V. G.

A. V. Volyar, V. G. Shvedov, and T. A. Fadeeva, Opt. Spectrosc. 90, 93 (2001).
[CrossRef]

Slyusar, V.

I. Basisty, V. Pas’ko, V. Slyusar, M. Soskin, and M. Vasnetsov, J. Opt. A 6, S166 (2004).
[CrossRef]

Soskin, M.

I. Basisty, V. Pas’ko, V. Slyusar, M. Soskin, and M. Vasnetsov, J. Opt. A 6, S166 (2004).
[CrossRef]

I. Basisty, M. Soskin, and M. Vasnetsov, Opt. Commun. 119, 604 (1995).
[CrossRef]

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Vasnetsov, M.

I. Basisty, V. Pas’ko, V. Slyusar, M. Soskin, and M. Vasnetsov, J. Opt. A 6, S166 (2004).
[CrossRef]

I. Basisty, M. Soskin, and M. Vasnetsov, Opt. Commun. 119, 604 (1995).
[CrossRef]

Volyar, A.

Volyar, A. V.

A. V. Volyar, V. G. Shvedov, and T. A. Fadeeva, Opt. Spectrosc. 90, 93 (2001).
[CrossRef]

Wei, S.

Yao, E.

J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

Yuan, G.

Yuan, X.-C.

Contemp. Phys. (1)

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

J. Opt. A (2)

M. V. Berry, J. Opt. A 6, 259 (2004).
[CrossRef]

I. Basisty, V. Pas’ko, V. Slyusar, M. Soskin, and M. Vasnetsov, J. Opt. A 6, S166 (2004).
[CrossRef]

J. Opt. Soc. Am. A (1)

New J. Phys. (1)

J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

Opt. Commun. (2)

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

I. Basisty, M. Soskin, and M. Vasnetsov, Opt. Commun. 119, 604 (1995).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Opt. Spectrosc. (2)

A. V. Volyar, V. G. Shvedov, and T. A. Fadeeva, Opt. Spectrosc. 90, 93 (2001).
[CrossRef]

A. P. Kiselev, Opt. Spectrosc. 102, 603 (2007).
[CrossRef]

Phys. Rev. Lett. (2)

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, Phys. Rev. Lett. 106, 123901 (2011).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Evolution of the intensity distributions I(r,φ=0,z=const) and I(r=const,φ,z=const) in the erf-G beam with K=104, w0=150μm, λ=0.6328μm.

Fig. 2.
Fig. 2.

Phase diagram of the first type of erf-G beam near the axis with w0=150μm at z=0.

Fig. 3.
Fig. 3.

Sections xy and xz of the phase and intensity in the erf-G beam of the second type.

Fig. 4.
Fig. 4.

Structural transformation of the electric field in asymmetric TE and TM beams with K=i104 and w0=150μm against a background of the total beam intensity. The red dotted lines indicate the position x=y=0.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

H=×A,E=ikA+i(·A)/k,
Ψ=NF(X,Y)G(x,y,z),
(2/X2+2/Y2+K2)F=0.
Fp(R,φ)=02πexp{i[pφ+KRcos(φφ)]}dφ,
Ψ=eiσφ/2N{eR2/2erf(Rs)+σeR2/2erf(iRc)}G/R,
vA++uA=0andA+=uΨ,A=vΨ,
[D^,u(m)]=0,[D^,v(n)]=0,
E+=N[uFσ/2+ik(v/2Z)Fσ/2]G,
E=N[vFσ/2+ik(u/2Z)Fσ/2]G.
u(m)Fp=(iK/Z)mFpm,v(m)Fp=(iK/Z)mFp+m.

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