Abstract

In this Letter we report on the generation of sub-diffraction-limited pure longitudinal magnetization in optomagnetic materials. The interaction between polarization singularities of cylindrically polarized beams and optical vortices in the tight focus of a high numerical-aperture objective as well as the induced magnetic fields through the inverse Faraday effect are investigated. A pure longitudinal magnetization distribution throughout the entire focal plane, which has a 15% reduction in the lateral full width at half-maximum, is achieved by tightly focusing an azimuthally polarized vortex beam.

© 2013 Optical Society of America

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  1. M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. M. Gu, Advanced Optical Imaging Theory (Springer, 2000).
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    [CrossRef]
  8. L. E. Helseth, Opt. Lett. 36, 987 (2011).
    [CrossRef]
  9. J. J. Yu, C. H. Zhou, and W. Jia, Opt. Commun. 283, 4171 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. Y. J. Zhang, Y. Okuno, and X. Xu, Optik 121, 2062 (2010).
    [CrossRef]
  16. Z. Gan, Y. Cao, R. A. Evans, and M. Gu, Nat. Commun. 4, 2061 (2013).
    [CrossRef]

2013 (1)

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, Nat. Commun. 4, 2061 (2013).
[CrossRef]

2012 (2)

X. Li, T. H. Lan, C. H. Tien, and M. Gu, Nat. Commun. 3, 998 (2012).
[CrossRef]

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, J. Opt. 14, 55704 (2012).
[CrossRef]

2011 (1)

2010 (3)

J. J. Yu, C. H. Zhou, and W. Jia, Opt. Commun. 283, 4171 (2010).
[CrossRef]

S. Ali, J. R. Davies, and J. T. Mendonca, Phys. Rev. Lett. 105, 035001 (2010).
[CrossRef]

Y. J. Zhang, Y. Okuno, and X. Xu, Optik 121, 2062 (2010).
[CrossRef]

2009 (1)

2007 (1)

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

2006 (1)

2005 (1)

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, Nature 435, 655 (2005).
[CrossRef]

2003 (1)

1988 (1)

M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).
[CrossRef]

1966 (1)

P. S. Pershan, J. P. van der Ziel, and L. D. Malmstrom, Phys. Rev. 143, 574 (1966).
[CrossRef]

1961 (1)

L. P. Pitaevskii, Sov. Phys. JETP-USSR 12, 1008 (1961).

Ali, S.

S. Ali, J. R. Davies, and J. T. Mendonca, Phys. Rev. Lett. 105, 035001 (2010).
[CrossRef]

Anbarasan, P. M.

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, J. Opt. 14, 55704 (2012).
[CrossRef]

Baibich, M. N.

M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).
[CrossRef]

Balbashov, A. M.

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, Nature 435, 655 (2005).
[CrossRef]

Broto, J. M.

M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).
[CrossRef]

Cao, Y.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, Nat. Commun. 4, 2061 (2013).
[CrossRef]

Chazelas, J.

M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).
[CrossRef]

Creuzet, G.

M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).
[CrossRef]

Davies, J. R.

S. Ali, J. R. Davies, and J. T. Mendonca, Phys. Rev. Lett. 105, 035001 (2010).
[CrossRef]

Eitenne, P.

M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).
[CrossRef]

Evans, R. A.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, Nat. Commun. 4, 2061 (2013).
[CrossRef]

Fert, A.

M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).
[CrossRef]

Friederich, A.

M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).
[CrossRef]

Gan, X.

Gan, Z.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, Nat. Commun. 4, 2061 (2013).
[CrossRef]

Ganic, D.

Gu, M.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, Nat. Commun. 4, 2061 (2013).
[CrossRef]

X. Li, T. H. Lan, C. H. Tien, and M. Gu, Nat. Commun. 3, 998 (2012).
[CrossRef]

D. Ganic, X. Gan, and M. Gu, Opt. Express 11, 2747 (2003).
[CrossRef]

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

Hansteen, F.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

Helseth, L. E.

Itoh, A.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

Jaroszewicz, Z.

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, J. Opt. 14, 55704 (2012).
[CrossRef]

Jia, W.

J. J. Yu, C. H. Zhou, and W. Jia, Opt. Commun. 283, 4171 (2010).
[CrossRef]

Kimel, A. V.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, Nature 435, 655 (2005).
[CrossRef]

Kirilyuk, A.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, Nature 435, 655 (2005).
[CrossRef]

Lan, T. H.

X. Li, T. H. Lan, C. H. Tien, and M. Gu, Nat. Commun. 3, 998 (2012).
[CrossRef]

Li, X.

X. Li, T. H. Lan, C. H. Tien, and M. Gu, Nat. Commun. 3, 998 (2012).
[CrossRef]

Malmstrom, L. D.

P. S. Pershan, J. P. van der Ziel, and L. D. Malmstrom, Phys. Rev. 143, 574 (1966).
[CrossRef]

Mendonca, J. T.

S. Ali, J. R. Davies, and J. T. Mendonca, Phys. Rev. Lett. 105, 035001 (2010).
[CrossRef]

Okuno, Y.

Pershan, P. S.

P. S. Pershan, J. P. van der Ziel, and L. D. Malmstrom, Phys. Rev. 143, 574 (1966).
[CrossRef]

Petroff, F.

M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).
[CrossRef]

Pillai, T. V. S.

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, J. Opt. 14, 55704 (2012).
[CrossRef]

Pisarev, R. V.

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, Nature 435, 655 (2005).
[CrossRef]

Pitaevskii, L. P.

L. P. Pitaevskii, Sov. Phys. JETP-USSR 12, 1008 (1961).

Rajesh, K. B.

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, J. Opt. 14, 55704 (2012).
[CrossRef]

Rasing, T.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, Nature 435, 655 (2005).
[CrossRef]

Ravi, V.

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, J. Opt. 14, 55704 (2012).
[CrossRef]

Stanciu, C. D.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

Suresh, P.

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, J. Opt. 14, 55704 (2012).
[CrossRef]

Tien, C. H.

X. Li, T. H. Lan, C. H. Tien, and M. Gu, Nat. Commun. 3, 998 (2012).
[CrossRef]

Tsukamoto, A.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

Usachev, P. A.

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, Nature 435, 655 (2005).
[CrossRef]

Van Dau, F. N.

M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).
[CrossRef]

van der Ziel, J. P.

P. S. Pershan, J. P. van der Ziel, and L. D. Malmstrom, Phys. Rev. 143, 574 (1966).
[CrossRef]

Xu, X.

Yu, J. J.

J. J. Yu, C. H. Zhou, and W. Jia, Opt. Commun. 283, 4171 (2010).
[CrossRef]

Zhan, Q.

Zhang, Y. J.

Zhou, C. H.

J. J. Yu, C. H. Zhou, and W. Jia, Opt. Commun. 283, 4171 (2010).
[CrossRef]

J. Opt. (1)

V. Ravi, P. Suresh, K. B. Rajesh, Z. Jaroszewicz, P. M. Anbarasan, and T. V. S. Pillai, J. Opt. 14, 55704 (2012).
[CrossRef]

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

Nat. Commun. (2)

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, Nat. Commun. 4, 2061 (2013).
[CrossRef]

X. Li, T. H. Lan, C. H. Tien, and M. Gu, Nat. Commun. 3, 998 (2012).
[CrossRef]

Nature (1)

A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, Nature 435, 655 (2005).
[CrossRef]

Opt. Commun. (1)

J. J. Yu, C. H. Zhou, and W. Jia, Opt. Commun. 283, 4171 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Optik (1)

Y. J. Zhang, Y. Okuno, and X. Xu, Optik 121, 2062 (2010).
[CrossRef]

Phys. Rev. (1)

P. S. Pershan, J. P. van der Ziel, and L. D. Malmstrom, Phys. Rev. 143, 574 (1966).
[CrossRef]

Phys. Rev. Lett. (3)

M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988).
[CrossRef]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, Phys. Rev. Lett. 99, 047601 (2007).
[CrossRef]

S. Ali, J. R. Davies, and J. T. Mendonca, Phys. Rev. Lett. 105, 035001 (2010).
[CrossRef]

Sov. Phys. JETP-USSR (1)

L. P. Pitaevskii, Sov. Phys. JETP-USSR 12, 1008 (1961).

Other (1)

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

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Figures (4)

Fig. 1.
Fig. 1.

Distribution of the light-induced magnetization in the focal plane of tightly focused LHC polarized beams with a topological charge of (a) 0, (b) +1, and (c) 1. Arrows indicate the orientation of the magnetization. (d)–(f) Cross-section plots of normalized longitudinal (Mz, blue curves), azimuthal (Mφ, red curves), and total magnetization (M, black curves). The radial magnetization field is null in the focal plane and not shown.

Fig. 2.
Fig. 2.

(a) Spatial distribution and (b) cross-section plot of light-induced magnetization by the IFE through tightly focusing radially polarized beams with a topologic charge of m=1.

Fig. 3.
Fig. 3.

(a) Distribution of magnetization induced by the IFE by tightly focusing an azimuthally polarized beam with a topological charge m=1. (b) Cross-section plots along the x axis (shown in the black solid line) and the z axis (shown in the blue dashed line). The azimuthal magnetization (Mφ) is zero in the focal vicinity.

Fig. 4.
Fig. 4.

(a) Cross-section plots of the normalized magnetization for LHC polarized (red curve), radially polarized (black curve), and azimuthally polarized (blue curve) beams when NA=0.95. (b) The lateral FWHMs of the magnetic field and (c) ratios of the longitudinal magnetic component (Mz/M), as a function of the NA of the objective.

Equations (7)

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

EL/RHC(ρs,φs,zs)=[EρEφEz]=imCei(m±1)φs[i[R1(m±1)A1(m±1)][R2(m±1)A2(m±1)]2R3(m±1)],
{R1(n)=0αP0(θ)sinθcosθ[Jn+1(kρssinθ)Jn1(kρssinθ)]*exp(ikzscosθ)dθ,R2(n)=0αP0(θ)sinθcosθ[Jn+1(kρssinθ)+Jn1(kρssinθ)]*exp(ikzscosθ)dθ,R3(n)=0αP0(θ)sin2θJn(kρssinθ)exp(ikzscosθ)dθ,A1(n)=0αP0(θ)sinθ[Jn+1(kρssinθ)+Jn1(kρssinθ)]*exp(ikzscosθ)dθ,A2(n)=0αP0(θ)sinθ[Jn+1(kρssinθ)Jn1(kρssinθ)]*exp(ikzscosθ)dθ,
M=iγE×E*,
MLHC(ρs,φs,zs)=[MρMφMz]=C[2Im[(R2(m+1)A2(m+1))*R3*(m+1)]2Re[(R1(m+1)A1(m+1))*R3*(m+1)]Re[(R1(m+1)A1(m+1))*(R2(m+1)A2(m+1))*]],
MRad(ρs,φs,zs)=[MρMφMz]=C[2Im[R2(m)*R3*(m)]2Re[R1(m)*R3*(m)]Re[R1(m)*R2*(m)]].
ERad(0,0,0)=[ExEyEz]=[02πcosφe±iφdφ02πsinφe±iφdφ0]=π[1±i0].
MAzi(ρs,φs,zs)=[MρMφMz]=C[00Re[A1(m)*A2*(m)]].

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