Abstract

For both paraxial and nonparaxial light, numerous electromagnetic quantities are expressible in terms of photon annihilation and creation operators. Accordingly, measures of energy, angular momentum, and chirality acquire a consistent interpretation. From the photonic nature of light, it emerges that an infinite hierarchy of spin-type measures depend on a difference in number operators for modes of opposing helicity, with pure circular polarization giving maximal values. Measures of orbital angular momentum are determined by a sum of corresponding number operators. Analysis of the electric and magnetic fields in the reflection of circular polarizations reveals regions of prominent chiral interference.

© 2013 Optical Society of America

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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]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. D. L. Andrews and M. M. Coles, Opt. Lett. 37, 3009 (2012).
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2012 (4)

S. M. Barnett, R. P. Cameron, and A. M. Yao, Phys. Rev. A 86, 013845 (2012).
[CrossRef]

M. M. Coles and D. L. Andrews, Phys. Rev. A 85, 063810 (2012).
[CrossRef]

R. P. Cameron, S. M. Barnett, and A. M. Yao, New J. Physics 14, 053050 (2012).
[CrossRef]

D. L. Andrews and M. M. Coles, Opt. Lett. 37, 3009 (2012).
[CrossRef]

2011 (3)

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

K. Y. Bliokh and F. Nori, Phys. Rev. A 83, 021803(R) (2011).
[CrossRef]

I. Bialynicki-Birula and Z. Bialynicka-Birula, J. Opt. 13, 064014 (2011).
[CrossRef]

2010 (1)

Y. Q. Tang and A. E. Cohen, Phys. Rev. Lett. 104, 163901 (2010).
[CrossRef]

2006 (1)

F. S. Roux, Opt. Commun. 268, 15 (2006).
[CrossRef]

1996 (2)

G. N. Afanasiev and Y. P. Stepanovsky, Nuovo Cimento A 109, 271 (1996).
[CrossRef]

J. L. Trueba and A. F. Rañada, Eur. J. Phys. 17, 141 (1996).
[CrossRef]

1994 (1)

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

1964 (1)

D. M. Lipkin, J. Math. Phys. 5, 696 (1964).
[CrossRef]

1936 (1)

R. A. Beth, Phys. Rev. 50, 115 (1936).
[CrossRef]

Afanasiev, G. N.

G. N. Afanasiev and Y. P. Stepanovsky, Nuovo Cimento A 109, 271 (1996).
[CrossRef]

Alfano, R. R.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Allen, L.

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

Andrews, D. L.

D. L. Andrews and M. M. Coles, Opt. Lett. 37, 3009 (2012).
[CrossRef]

M. M. Coles and D. L. Andrews, Phys. Rev. A 85, 063810 (2012).
[CrossRef]

D. L. Andrews, Structured Light and its Applications(Academic, 2008).

Aspect, A.

G. Grynberg, A. Aspect, and C. Fabre, Introduction to Quantum Optics (Cambridge University, 2010).

Auletta, G.

G. Auletta, M. Fortunato, and G. Parisi, Quantum Mechanics (Cambridge University, 2009).

Barnett, S. M.

R. P. Cameron, S. M. Barnett, and A. M. Yao, New J. Physics 14, 053050 (2012).
[CrossRef]

S. M. Barnett, R. P. Cameron, and A. M. Yao, Phys. Rev. A 86, 013845 (2012).
[CrossRef]

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

Beth, R. A.

R. A. Beth, Phys. Rev. 50, 115 (1936).
[CrossRef]

Bialynicka-Birula, Z.

I. Bialynicki-Birula and Z. Bialynicka-Birula, J. Opt. 13, 064014 (2011).
[CrossRef]

Bialynicki-Birula, I.

I. Bialynicki-Birula and Z. Bialynicka-Birula, J. Opt. 13, 064014 (2011).
[CrossRef]

Bliokh, K. Y.

K. Y. Bliokh and F. Nori, Phys. Rev. A 83, 021803(R) (2011).
[CrossRef]

Cameron, R. P.

R. P. Cameron, S. M. Barnett, and A. M. Yao, New J. Physics 14, 053050 (2012).
[CrossRef]

S. M. Barnett, R. P. Cameron, and A. M. Yao, Phys. Rev. A 86, 013845 (2012).
[CrossRef]

Cohen, A. E.

Y. Q. Tang and A. E. Cohen, Phys. Rev. Lett. 104, 163901 (2010).
[CrossRef]

Coles, M. M.

D. L. Andrews and M. M. Coles, Opt. Lett. 37, 3009 (2012).
[CrossRef]

M. M. Coles and D. L. Andrews, Phys. Rev. A 85, 063810 (2012).
[CrossRef]

Craig, D. P.

D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics (Dover Publications1998).

Fabre, C.

G. Grynberg, A. Aspect, and C. Fabre, Introduction to Quantum Optics (Cambridge University, 2010).

Fortunato, M.

G. Auletta, M. Fortunato, and G. Parisi, Quantum Mechanics (Cambridge University, 2009).

Grynberg, G.

G. Grynberg, A. Aspect, and C. Fabre, Introduction to Quantum Optics (Cambridge University, 2010).

Lipkin, D. M.

D. M. Lipkin, J. Math. Phys. 5, 696 (1964).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Milione, G.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Nolan, D. A.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Nori, F.

K. Y. Bliokh and F. Nori, Phys. Rev. A 83, 021803(R) (2011).
[CrossRef]

Parisi, G.

G. Auletta, M. Fortunato, and G. Parisi, Quantum Mechanics (Cambridge University, 2009).

Rañada, A. F.

J. L. Trueba and A. F. Rañada, Eur. J. Phys. 17, 141 (1996).
[CrossRef]

Roux, F. S.

F. S. Roux, Opt. Commun. 268, 15 (2006).
[CrossRef]

Stepanovsky, Y. P.

G. N. Afanasiev and Y. P. Stepanovsky, Nuovo Cimento A 109, 271 (1996).
[CrossRef]

Sztul, H. I.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Tang, Y. Q.

Y. Q. Tang and A. E. Cohen, Phys. Rev. Lett. 104, 163901 (2010).
[CrossRef]

Thirunamachandran, T.

D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics (Dover Publications1998).

Trueba, J. L.

J. L. Trueba and A. F. Rañada, Eur. J. Phys. 17, 141 (1996).
[CrossRef]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Yao, A. M.

R. P. Cameron, S. M. Barnett, and A. M. Yao, New J. Physics 14, 053050 (2012).
[CrossRef]

S. M. Barnett, R. P. Cameron, and A. M. Yao, Phys. Rev. A 86, 013845 (2012).
[CrossRef]

Eur. J. Phys. (1)

J. L. Trueba and A. F. Rañada, Eur. J. Phys. 17, 141 (1996).
[CrossRef]

J. Math. Phys. (1)

D. M. Lipkin, J. Math. Phys. 5, 696 (1964).
[CrossRef]

J. Opt. (1)

I. Bialynicki-Birula and Z. Bialynicka-Birula, J. Opt. 13, 064014 (2011).
[CrossRef]

New J. Physics (1)

R. P. Cameron, S. M. Barnett, and A. M. Yao, New J. Physics 14, 053050 (2012).
[CrossRef]

Nuovo Cimento A (1)

G. N. Afanasiev and Y. P. Stepanovsky, Nuovo Cimento A 109, 271 (1996).
[CrossRef]

Opt. Commun. (2)

F. S. Roux, Opt. Commun. 268, 15 (2006).
[CrossRef]

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

R. A. Beth, Phys. Rev. 50, 115 (1936).
[CrossRef]

Phys. Rev. A (3)

S. M. Barnett, R. P. Cameron, and A. M. Yao, Phys. Rev. A 86, 013845 (2012).
[CrossRef]

M. M. Coles and D. L. Andrews, Phys. Rev. A 85, 063810 (2012).
[CrossRef]

K. Y. Bliokh and F. Nori, Phys. Rev. A 83, 021803(R) (2011).
[CrossRef]

Phys. Rev. Lett. (2)

Y. Q. Tang and A. E. Cohen, Phys. Rev. Lett. 104, 163901 (2010).
[CrossRef]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Other (5)

G. Grynberg, A. Aspect, and C. Fabre, Introduction to Quantum Optics (Cambridge University, 2010).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

G. Auletta, M. Fortunato, and G. Parisi, Quantum Mechanics (Cambridge University, 2009).

D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics (Dover Publications1998).

D. L. Andrews, Structured Light and its Applications(Academic, 2008).

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Figures (1)

Fig. 1.
Fig. 1.

Electric (top) and magnetic (bottom) field vectors of reflected circularly polarized light. Superposition (c,f) of the input (a,d) and reflected (b,e) beams results in states with minima and maxima in different locations for the electric and magnetic fields.

Equations (12)

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

J=ε0d3r[r×(E×B)],
L=ε0d3rEi(r×)Ai,
S=ε0d3r(E×A),
A=k,η(2ε0ckV)12{e(η)(k)a(η)(k)ei(k·r)+h.c.},
E(x)=eilϕ0kdκE(κ)eikzz×{(αuex+αvey)Jl(κρ)+ezκ2kz[(iαuαv)eiϕJl1(κρ)(iαu+αv)eiϕJl+1(κρ)]},
αu/v±12[a(L)(k)±a(R)(k)],
n|aaaa|nnr|ns,
α|aaaa|α=α¯rαs,
H=12d3r(A·BC·E),S=ε012d3r(E×A+B×C),
e(1)=sinθi^+eiϕcosθj^,e(2)=cosθi^eiϕsinθj^,
A=k,η,l,p(2ε0ckV)12{el,p(η)(k)a(η)(k)fl,p(r)eikzilφ+h.c.},
L=k,l,plk^[N^lp(1)(k)+N^lp(2)(k)].

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