Abstract

It is observed that there exist two different classes of vector light beams that have the same first-order paraxial approximation. They are characterized by the axial and transverse orientations of a constant unit vector that comes from the constraint of transversality condition. Their vectorial structures in the nonparaxial regime and angular momentum properties are compared.

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2013 (1)

S.-Y. Yang and C.-F. Li, J. Opt. 15, 014016 (2013).
[CrossRef]

2009 (1)

2008 (2)

C.-F. Li, Phys. Rev. A 78, 063831 (2008).
[CrossRef]

A. April, Opt. Lett. 33, 1563 (2008).
[CrossRef]

2006 (1)

2005 (1)

2000 (2)

K. S. Youngworth and T. G. Brown, Opt. Express 7, 77 (2000).
[CrossRef]

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

1999 (1)

1990 (1)

1982 (1)

L. W. Davis and G. Patsakos, Phys. Rev. A 26, 3702 (1982).
[CrossRef]

1981 (1)

1980 (1)

D. N. Pattanayak and G. P. Agrawal, Phys. Rev. A 22, 1159 (1980).
[CrossRef]

1975 (1)

M. Lax, W. H. Lousisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

1966 (1)

1953 (1)

H. S. Green and E. Wolf, Proc. Phys. Soc. London Sect. A 66, 1129 (1953).
[CrossRef]

Agrawal, G. P.

D. N. Pattanayak and G. P. Agrawal, Phys. Rev. A 22, 1159 (1980).
[CrossRef]

Aït-Ameur, K.

Akhiezer, A. I.

A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics (Interscience Publishers, 1965).

April, A.

Berestetskii, V. B.

A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics (Interscience Publishers, 1965).

Bialynicki-Birula, I.

I. Bialynicki-Birula, Progress in Optics, E. Wolf, ed. (Elsevier, 1996), Vol. 36.

Blit, S.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Bomzon, Z.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Brown, T. G.

Chen, J.

Davidson, N.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Davis, L. W.

L. W. Davis and G. Patsakos, Phys. Rev. A 26, 3702 (1982).
[CrossRef]

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

de S. Denis, R.

Ford, D. H.

Friesem, A. A.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Green, H. S.

H. S. Green and E. Wolf, Proc. Phys. Soc. London Sect. A 66, 1129 (1953).
[CrossRef]

Guo, H.

Hasman, E.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Hierle, R.

Kimura, W. D.

Kogelnik, H.

Lax, M.

M. Lax, W. H. Lousisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Li, C.-F.

S.-Y. Yang and C.-F. Li, J. Opt. 15, 014016 (2013).
[CrossRef]

C.-F. Li, Phys. Rev. A 78, 063831 (2008).
[CrossRef]

C.-F. Li, “On the angular momentum of photons: effects of transversality condition on the quantization of radiation fields,” arXiv:1206.1668v4 (2013).

Li, T.

Lousisell, W. H.

M. Lax, W. H. Lousisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

McKnight, W. B.

M. Lax, W. H. Lousisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Oron, R.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Passilly, N.

Patsakos, G.

L. W. Davis and G. Patsakos, Phys. Rev. A 26, 3702 (1982).
[CrossRef]

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

Pattanayak, D. N.

D. N. Pattanayak and G. P. Agrawal, Phys. Rev. A 22, 1159 (1980).
[CrossRef]

Roch, J. F.

Saghafi, S.

Sheppard, C. J. R.

Tidwell, S. C.

Treussart, F.

Wolf, E.

H. S. Green and E. Wolf, Proc. Phys. Soc. London Sect. A 66, 1129 (1953).
[CrossRef]

Yang, S.-Y.

S.-Y. Yang and C.-F. Li, J. Opt. 15, 014016 (2013).
[CrossRef]

Youngworth, K. S.

Zhan, Q.

Zhuang, S.

Adv. Opt. Photon. (1)

Appl. Opt. (2)

Appl. Phys. Lett. (1)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

J. Opt. (1)

S.-Y. Yang and C.-F. Li, J. Opt. 15, 014016 (2013).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (4)

L. W. Davis and G. Patsakos, Phys. Rev. A 26, 3702 (1982).
[CrossRef]

D. N. Pattanayak and G. P. Agrawal, Phys. Rev. A 22, 1159 (1980).
[CrossRef]

M. Lax, W. H. Lousisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

C.-F. Li, Phys. Rev. A 78, 063831 (2008).
[CrossRef]

Proc. Phys. Soc. London Sect. A (1)

H. S. Green and E. Wolf, Proc. Phys. Soc. London Sect. A 66, 1129 (1953).
[CrossRef]

Other (3)

C.-F. Li, “On the angular momentum of photons: effects of transversality condition on the quantization of radiation fields,” arXiv:1206.1668v4 (2013).

A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics (Interscience Publishers, 1965).

I. Bialynicki-Birula, Progress in Optics, E. Wolf, ed. (Elsevier, 1996), Vol. 36.

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Figures (2)

Fig. 1.
Fig. 1.

Distribution of |E(1)|2 at the cross section.

Fig. 2.
Fig. 2.

Distribution of |E(2)|2|E(1)|2 at the cross section.

Equations (42)

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

ex=12(eR+eL)orey=i2(eReL),
er=excosϕ+eysinϕ=12(eiϕeR+eiϕeL),
eϕ=exsinϕ+eycosϕ=i2(eiϕeReiϕeL).
E(x,t)=1(2π)3/2(ωε0)1/2f(k)ei(k·xωt)d3k,
f=f1uI+f2vI,
uI=vI×w,vI=I×w|I×w|.
f=TIf˜,
f˜σw(k)=α˜σwf(k),
α˜+1=12(1i),α˜1=12(1i),
f˜σw,μ=Nα˜σwδ(ϱϱ0)δ(κκ0)eiμφ,
T1=(κkeϱϱkezeφ),
f+1,μ(1)=f0(ϱ,κ)eiμφ(κ0keϱϱ0kez+ieφ),
f+1,μ(1)f0eiμφ[eiφ(ex+iey)ϱ0kez]f+1,μ(1)
eϱ+ieφ=eiφ(ex+iey)
f1,μ(1)=f0(ϱ,κ)eiμφ(κ0keϱϱ0kezieφ).
f1,μ(1)f0eiμφ[eiφ(exiey)ϱ0kez]f1,μ(1),
eϱieφ=eiφ(exiey)
T2=C(ϱ,φ)k2(k2ϱ2cos2φ0ϱ2sinφcosφkκκϱcosφkϱsinφ),
C(ϱ,φ)=(1ϱ2k2cos2φ)1/2,
f+1,μ(2)=C(ϱ0,φ)f0(ϱ,κ)eiμφ[ex+iκ0keyϱ02k2cosφeϱϱ0k(κ0kcosφ+isinφ)ez].
f+1,μ(2)f0ei(μ+1)φ[eiφ(ex+iey)ϱ0kez]f+1,μ(2).
f1,μ(2)=C(ϱ0,φ)f0(ϱ,κ)eiμφ[exiκ0keyϱ02k2cosφeϱϱ0k(κ0kcosφisinφ)ez],
f1,μ(2)f0ei(μ1)φ[eiφ(exiey)ϱ0kez]f1,μ(2),
fσw,μ(1)=fσw,μσw(2).
12[f+1,μ(1)+f1,μ(1)]=f0eiμφ(κ0keϱϱ0kez),
12i[f+1,μ(1)f1,μ(1)]=f0eiμφeφ,
12[f+1,0(1)+f1,0(1)]=f0(κ0keϱϱ0kez),
12i[f+1,0(1)f1,0(1)]=f0eφ.
12[f+1,0(1)+f1,0(1)]f0eϱ,12i[f+1,0(1)f1,0(1)]=f0eφ,
12[f+1,1(2)+f1,1(2)]f02(eiφeR+eiφeL),
12i[f+1,1(2)f1,1(2)]if02(eiφeReiφeL),
12[f+1,1(2)+f1,1(2)]=Cf0[(1ϱ02k2cos2φ)eϱ(1κ0k)sinφeyϱ0k(κ0kcos2φ+sin2φ)ez].
12i[f+1,1(2)f1,1(2)]=Cf0[(κ0k+ϱ02k2sin2φ)eφ(1κ0kϱ02k2)sinφexϱ0k(1κ0k)sinφcosφez].
f+1,0(1)=f0[(1ϱ022k2)eϱ+ieφϱ0kez],
E(1)=J1(ϱ0r)[(1ϱ022k2)er+ieϕ]+iϱ0kJ0(ϱ0r)ez,
|E(1)|2=2J12+ϱ02k2(J02J12),
f+1,1(2)=f+1,0(1)+f0iϱ024k2(eϱ+ieφ)sin2φ,
E(2)=E(1)+ϱ028k2(J1e2iϕ+J3e2iϕ)(er+ieϕ),
|E(2)|2|E(1)|2=ϱ022k2J1(J1+J3)cos2ϕ,
J^=ik×+Σ^,
J^z=iφ+(0i0i00000),
J^zfσw,μ(1)=μfσw,μ(1),

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