Abstract

It is shown that prominent measures of the helicity of chiral electromagnetic radiation have a common basis, in differences between the populations of optical modes associated with angular momenta of opposite sign. The analysis helps to develop the interpretation of chiroptical phenomena in which such metrics have been treated as representing physically distinct “superchiral” phenomena. Constructing theory with due cognizance of photonic character, it emerges only that the spin angular momentum of light is engaged in such observations. In consequence, the term “superchiral” is redundant.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, Nature Nanotechnol. 5, 783 (2010).
    [CrossRef]
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    [CrossRef]
  6. K. Y. Bliokh and F. Nori, Phys. Rev. A. 83, 021803 (2011).
    [CrossRef]
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    [CrossRef]
  8. D. S. Bradshaw and D. L. Andrews, Opt. Lett. 30, 3039 (2005).
    [CrossRef]
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    [CrossRef]
  10. A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
    [CrossRef]
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    [CrossRef]
  13. D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics (Dover, 1998), p. 36.
  14. G. Auletta, M. Fortunato, and G. Parisi, Quantum Mechanics (Cambridge University, 2009), pp. 26–28.
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    [CrossRef]
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    [CrossRef]
  17. F. Araoka, T. Verbiest, K. Clays, and A. Persoons, Phys. Rev. A 71, 055401 (2005).
    [CrossRef]
  18. W. Löffler, D. J. Broer, and J. P. Woerdman, Phys. Rev. A. 83, 065801 (2011).
    [CrossRef]
  19. G. N. Afansiev and Y. P. Stepanovsky, Nuovo Cimento A 109, 271 (1996).
    [CrossRef]
  20. S. Ragusa and M. Baylin, Nuovo Cimento B 107, 17 (1992).
    [CrossRef]
  21. J. E. S. Bergman, S. M. Mohammadi, L. K. S. Daldorff, B. Thidé, T. D. Carozzi, R. L. Karlsson, and M. Eriksson, “Conservation Laws in Generalized Riemann-Silberstein Electrodynamics” (2008), http://arxiv.org/abs/0803.2383 .
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    [CrossRef]

2011 (6)

N. Yang and A. E. Cohen, J. Phys. Chem. B. 115, 5304 (2011).
[CrossRef]

Y. Tang and A. E. Cohen, Science 332, 333 (2011).
[CrossRef]

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

A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[CrossRef]

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

W. Löffler, D. J. Broer, and J. P. Woerdman, Phys. Rev. A. 83, 065801 (2011).
[CrossRef]

2010 (2)

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

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, Nature Nanotechnol. 5, 783 (2010).
[CrossRef]

2009 (1)

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, Nano Lett. 9, 3016 (2009).
[CrossRef]

2005 (2)

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, Phys. Rev. A 71, 055401 (2005).
[CrossRef]

D. S. Bradshaw and D. L. Andrews, Opt. Lett. 30, 3039 (2005).
[CrossRef]

2004 (1)

D. L. Andrews, L. C. Dávila Romero, and M. Babiker, Opt. Commun. 237, 133 (2004).
[CrossRef]

1997 (1)

1996 (1)

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

1992 (2)

S. Ragusa and M. Baylin, Nuovo Cimento B 107, 17 (1992).
[CrossRef]

W. I. Fushchich and A. G. Nikitin, J. Phys. A: Math. Gen. 25, L231 (1992).
[CrossRef]

1979 (1)

V. Santarelli, Am. J. Phys. 47, 421 (1979).
[CrossRef]

1964 (1)

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

Afansiev, G. N.

G. N. Afansiev 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.

Andrews, D. L.

D. S. Bradshaw and D. L. Andrews, Opt. Lett. 30, 3039 (2005).
[CrossRef]

D. L. Andrews, L. C. Dávila Romero, and M. Babiker, Opt. Commun. 237, 133 (2004).
[CrossRef]

Araoka, F.

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, Phys. Rev. A 71, 055401 (2005).
[CrossRef]

Auletta, G.

G. Auletta, M. Fortunato, and G. Parisi, Quantum Mechanics (Cambridge University, 2009), pp. 26–28.

Babiker, M.

D. L. Andrews, L. C. Dávila Romero, and M. Babiker, Opt. Commun. 237, 133 (2004).
[CrossRef]

Barron, L. D.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, Nature Nanotechnol. 5, 783 (2010).
[CrossRef]

Baylin, M.

S. Ragusa and M. Baylin, Nuovo Cimento B 107, 17 (1992).
[CrossRef]

Bekshaev, A.

A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[CrossRef]

Bergman, J. E. S.

J. E. S. Bergman, S. M. Mohammadi, L. K. S. Daldorff, B. Thidé, T. D. Carozzi, R. L. Karlsson, and M. Eriksson, “Conservation Laws in Generalized Riemann-Silberstein Electrodynamics” (2008), http://arxiv.org/abs/0803.2383 .

Bliokh, K. Y.

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

A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[CrossRef]

Bradshaw, D. S.

Bretner, I.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, Nano Lett. 9, 3016 (2009).
[CrossRef]

Broer, D. J.

W. Löffler, D. J. Broer, and J. P. Woerdman, Phys. Rev. A. 83, 065801 (2011).
[CrossRef]

Carozzi, T. D.

J. E. S. Bergman, S. M. Mohammadi, L. K. S. Daldorff, B. Thidé, T. D. Carozzi, R. L. Karlsson, and M. Eriksson, “Conservation Laws in Generalized Riemann-Silberstein Electrodynamics” (2008), http://arxiv.org/abs/0803.2383 .

Carpy, T.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, Nature Nanotechnol. 5, 783 (2010).
[CrossRef]

Clays, K.

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, Phys. Rev. A 71, 055401 (2005).
[CrossRef]

Cohen, A. E.

N. Yang and A. E. Cohen, J. Phys. Chem. B. 115, 5304 (2011).
[CrossRef]

Y. Tang and A. E. Cohen, Science 332, 333 (2011).
[CrossRef]

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

Craig, D. P.

D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics (Dover, 1998), p. 36.

Daldorff, L. K. S.

J. E. S. Bergman, S. M. Mohammadi, L. K. S. Daldorff, B. Thidé, T. D. Carozzi, R. L. Karlsson, and M. Eriksson, “Conservation Laws in Generalized Riemann-Silberstein Electrodynamics” (2008), http://arxiv.org/abs/0803.2383 .

Dholakia, K.

Eriksson, M.

J. E. S. Bergman, S. M. Mohammadi, L. K. S. Daldorff, B. Thidé, T. D. Carozzi, R. L. Karlsson, and M. Eriksson, “Conservation Laws in Generalized Riemann-Silberstein Electrodynamics” (2008), http://arxiv.org/abs/0803.2383 .

Fortunato, M.

G. Auletta, M. Fortunato, and G. Parisi, Quantum Mechanics (Cambridge University, 2009), pp. 26–28.

Fushchich, W. I.

W. I. Fushchich and A. G. Nikitin, J. Phys. A: Math. Gen. 25, L231 (1992).
[CrossRef]

Gadegaard, N.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, Nature Nanotechnol. 5, 783 (2010).
[CrossRef]

Gorodetski, Y.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, Nano Lett. 9, 3016 (2009).
[CrossRef]

Hasman, E.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, Nano Lett. 9, 3016 (2009).
[CrossRef]

Hendry, E.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, Nature Nanotechnol. 5, 783 (2010).
[CrossRef]

Johnston, J.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, Nature Nanotechnol. 5, 783 (2010).
[CrossRef]

Kadodwala, M.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, Nature Nanotechnol. 5, 783 (2010).
[CrossRef]

Karlsson, R. L.

J. E. S. Bergman, S. M. Mohammadi, L. K. S. Daldorff, B. Thidé, T. D. Carozzi, R. L. Karlsson, and M. Eriksson, “Conservation Laws in Generalized Riemann-Silberstein Electrodynamics” (2008), http://arxiv.org/abs/0803.2383 .

Kelly, S. M.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, Nature Nanotechnol. 5, 783 (2010).
[CrossRef]

Kleiner, V.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, Nano Lett. 9, 3016 (2009).
[CrossRef]

Lapthorn, A. J.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, Nature Nanotechnol. 5, 783 (2010).
[CrossRef]

Lipkin, D.

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

Löffler, W.

W. Löffler, D. J. Broer, and J. P. Woerdman, Phys. Rev. A. 83, 065801 (2011).
[CrossRef]

Mandel, L.

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

Mikhaylovskiy, R. V.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, Nature Nanotechnol. 5, 783 (2010).
[CrossRef]

Milione, G.

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

Mohammadi, S. M.

J. E. S. Bergman, S. M. Mohammadi, L. K. S. Daldorff, B. Thidé, T. D. Carozzi, R. L. Karlsson, and M. Eriksson, “Conservation Laws in Generalized Riemann-Silberstein Electrodynamics” (2008), http://arxiv.org/abs/0803.2383 .

Nikitin, A. G.

W. I. Fushchich and A. G. Nikitin, J. Phys. A: Math. Gen. 25, L231 (1992).
[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 (2011).
[CrossRef]

Padgett, M. J.

Parisi, G.

G. Auletta, M. Fortunato, and G. Parisi, Quantum Mechanics (Cambridge University, 2009), pp. 26–28.

Persoons, A.

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, Phys. Rev. A 71, 055401 (2005).
[CrossRef]

Popland, M.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, Nature Nanotechnol. 5, 783 (2010).
[CrossRef]

Ragusa, S.

S. Ragusa and M. Baylin, Nuovo Cimento B 107, 17 (1992).
[CrossRef]

Romero, L. C. Dávila

D. L. Andrews, L. C. Dávila Romero, and M. Babiker, Opt. Commun. 237, 133 (2004).
[CrossRef]

Santarelli, V.

V. Santarelli, Am. J. Phys. 47, 421 (1979).
[CrossRef]

Shitrit, N.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, Nano Lett. 9, 3016 (2009).
[CrossRef]

Simpson, N. B.

Soskin, M.

A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[CrossRef]

Stepanovsky, Y. P.

G. N. Afansiev 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.

Y. Tang and A. E. Cohen, Science 332, 333 (2011).
[CrossRef]

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

Thidé, B.

J. E. S. Bergman, S. M. Mohammadi, L. K. S. Daldorff, B. Thidé, T. D. Carozzi, R. L. Karlsson, and M. Eriksson, “Conservation Laws in Generalized Riemann-Silberstein Electrodynamics” (2008), http://arxiv.org/abs/0803.2383 .

Thirunamachandran, T.

D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics (Dover, 1998), p. 36.

Verbiest, T.

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, Phys. Rev. A 71, 055401 (2005).
[CrossRef]

Woerdman, J. P.

W. Löffler, D. J. Broer, and J. P. Woerdman, Phys. Rev. A. 83, 065801 (2011).
[CrossRef]

Wolf, E.

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

Yang, N.

N. Yang and A. E. Cohen, J. Phys. Chem. B. 115, 5304 (2011).
[CrossRef]

Am. J. Phys. (1)

V. Santarelli, Am. J. Phys. 47, 421 (1979).
[CrossRef]

J. Math. Phys. (1)

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

J. Opt. (1)

A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[CrossRef]

J. Phys. A: Math. Gen. (1)

W. I. Fushchich and A. G. Nikitin, J. Phys. A: Math. Gen. 25, L231 (1992).
[CrossRef]

J. Phys. Chem. B. (1)

N. Yang and A. E. Cohen, J. Phys. Chem. B. 115, 5304 (2011).
[CrossRef]

Nano Lett. (1)

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, Nano Lett. 9, 3016 (2009).
[CrossRef]

Nature Nanotechnol. (1)

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, Nature Nanotechnol. 5, 783 (2010).
[CrossRef]

Nuovo Cimento A (1)

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

Nuovo Cimento B (1)

S. Ragusa and M. Baylin, Nuovo Cimento B 107, 17 (1992).
[CrossRef]

Opt. Commun. (1)

D. L. Andrews, L. C. Dávila Romero, and M. Babiker, Opt. Commun. 237, 133 (2004).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

F. Araoka, T. Verbiest, K. Clays, and A. Persoons, Phys. Rev. A 71, 055401 (2005).
[CrossRef]

Phys. Rev. A. (2)

W. Löffler, D. J. Broer, and J. P. Woerdman, Phys. Rev. A. 83, 065801 (2011).
[CrossRef]

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

Phys. Rev. Lett. (2)

Y. 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]

Science (1)

Y. Tang and A. E. Cohen, Science 332, 333 (2011).
[CrossRef]

Other (4)

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

D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics (Dover, 1998), p. 36.

G. Auletta, M. Fortunato, and G. Parisi, Quantum Mechanics (Cambridge University, 2009), pp. 26–28.

J. E. S. Bergman, S. M. Mohammadi, L. K. S. Daldorff, B. Thidé, T. D. Carozzi, R. L. Karlsson, and M. Eriksson, “Conservation Laws in Generalized Riemann-Silberstein Electrodynamics” (2008), http://arxiv.org/abs/0803.2383 .

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Equations (15)

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

J=ε0d3rr×(E×B),
L=ε0r^id3rEl(r×)i·Al,
S=ε0r^id3r(E×A)i.
A=k,η(2ε0ckV)12{e(η)(k)a(η)(k)eikz+h.c.},
S=k{N^(L)(k)N^(R)(k)}k^,
χ=ε02E·×E+12μ0B·×B,
χt+·φ=0,
φ=ε0c22[E×(×B)B×(×E)].
d3rχ=ckk2{N^(L)(k)N^(R)(k)}.
d3rχ=csin(2θ)sin(φ)kk2{N^(1)(k)N^(2)(k)},
A=k,η,l,p(2ε0ckV)12{el,p(η)(k)a(η)(k)fl,p(r)eikzilφ+h.c.},
Γ(+)Γ()=Im2ε0πρ3μα0(+)·mα0(+)×kk[N^(L)(k)N^(R)(k)],
Γ(+)Γ()=2ε0πρ3ckIm(μα0(+)·mα0(+))d3rχ.
C=d3rA·B,
χ=ε0c2k2C.

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