Abstract

The interaction of an electromagnetic wave with a noncentrosymmetric crystal is not necessarily time reversible, and the departure from reversality may be seen in nonlocal (wave-vector linear) phenomena. However, relativistic symmetry with respect to simultaneous time and space inversion is always preserved in optics.

© 1995 Optical Society of America

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  1. It has been proved that chemical interactions of a chiral molecule are not necessarily T invariant and that any analysis of dynamic processes involving molecules that exist in two enantiomeric forms must be based on the validity of PT invariance. SeeE. M. Lifshitz, L. P. Pitaevskii, Physical Kinetics (Pergamon, Oxford, 1981), p. 6L. D. Barron, Science 226, 1491 (1994).
  2. V. I. Belinicher, B. I. Sturman, Sov. Phys. Usp. 23, 1299 (1980).
    [CrossRef]
  3. J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, Reading, Mass., 1994), pp. 255–256.
  4. A. R. Bungay, S. V. Popov, Yu. P. Svirko, N. I. Zheludev, Chem. Phys. Lett. 218, 249 (1994).
    [CrossRef]
  5. N. I. Zheludev, S. V. Popov, Yu. P. Svirko, A. Malinowski, D. Yu. Paraschuk, Phys. Rev. B 50, 11508 (1994).
    [CrossRef]
  6. V. B. Berestetskii, E. M. Lifshitz, L. P. Pitaevskii, Quantum Electrodynamics (Permagon, Oxford, 1982).
  7. L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, Cambridge, 1982).
  8. M. Lax, Symmetry Principles in Solids State and Molecular Physics (Wiley, New York, 1974).
  9. Several years ago a search for quasi-particles with fractional statistics in superconductors began. Fractional statistics of the carriers may lead to broken time reversality of the crystal Hamiltonian itself [seeB. G. Levi, Phys. Today 44(2), 17 (1991)]. Weak interactions of optical electrons with the nucleus lead to breakage parity. Here we exclude these special cases from our consideration.
  10. Note that complete relativistic invariance requires symmetry with respect to CPT, where C is the charge-conjugation operation. Optics is, however, evidently symmetric with respect to C, making it obligatory for optical interactions to be PT invariant.
  11. L. D. Barron, A. D. Buckingham, J. Phys. B 6, 1295 (1973).
    [CrossRef]
  12. L. Onsager, Phys. Rev. 37, 405 (1031)H. G. B. Casimir, Rev. Mod. Phys. 17, 345 (1945).
    [CrossRef]
  13. L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, Oxford, 1984).
  14. A. R. Bungay, Yu. P. Svirko, N. I. Zheludev, Phys. Rev. B 47, 16141 (1993).
    [CrossRef]

1994

A. R. Bungay, S. V. Popov, Yu. P. Svirko, N. I. Zheludev, Chem. Phys. Lett. 218, 249 (1994).
[CrossRef]

N. I. Zheludev, S. V. Popov, Yu. P. Svirko, A. Malinowski, D. Yu. Paraschuk, Phys. Rev. B 50, 11508 (1994).
[CrossRef]

1993

A. R. Bungay, Yu. P. Svirko, N. I. Zheludev, Phys. Rev. B 47, 16141 (1993).
[CrossRef]

1991

Several years ago a search for quasi-particles with fractional statistics in superconductors began. Fractional statistics of the carriers may lead to broken time reversality of the crystal Hamiltonian itself [seeB. G. Levi, Phys. Today 44(2), 17 (1991)]. Weak interactions of optical electrons with the nucleus lead to breakage parity. Here we exclude these special cases from our consideration.

1980

V. I. Belinicher, B. I. Sturman, Sov. Phys. Usp. 23, 1299 (1980).
[CrossRef]

1973

L. D. Barron, A. D. Buckingham, J. Phys. B 6, 1295 (1973).
[CrossRef]

1031

L. Onsager, Phys. Rev. 37, 405 (1031)H. G. B. Casimir, Rev. Mod. Phys. 17, 345 (1945).
[CrossRef]

Barron, L. D.

L. D. Barron, A. D. Buckingham, J. Phys. B 6, 1295 (1973).
[CrossRef]

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, Cambridge, 1982).

Belinicher, V. I.

V. I. Belinicher, B. I. Sturman, Sov. Phys. Usp. 23, 1299 (1980).
[CrossRef]

Berestetskii, V. B.

V. B. Berestetskii, E. M. Lifshitz, L. P. Pitaevskii, Quantum Electrodynamics (Permagon, Oxford, 1982).

Buckingham, A. D.

L. D. Barron, A. D. Buckingham, J. Phys. B 6, 1295 (1973).
[CrossRef]

Bungay, A. R.

A. R. Bungay, S. V. Popov, Yu. P. Svirko, N. I. Zheludev, Chem. Phys. Lett. 218, 249 (1994).
[CrossRef]

A. R. Bungay, Yu. P. Svirko, N. I. Zheludev, Phys. Rev. B 47, 16141 (1993).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, Oxford, 1984).

Lax, M.

M. Lax, Symmetry Principles in Solids State and Molecular Physics (Wiley, New York, 1974).

Levi, B. G.

Several years ago a search for quasi-particles with fractional statistics in superconductors began. Fractional statistics of the carriers may lead to broken time reversality of the crystal Hamiltonian itself [seeB. G. Levi, Phys. Today 44(2), 17 (1991)]. Weak interactions of optical electrons with the nucleus lead to breakage parity. Here we exclude these special cases from our consideration.

Lifshitz, E. M.

It has been proved that chemical interactions of a chiral molecule are not necessarily T invariant and that any analysis of dynamic processes involving molecules that exist in two enantiomeric forms must be based on the validity of PT invariance. SeeE. M. Lifshitz, L. P. Pitaevskii, Physical Kinetics (Pergamon, Oxford, 1981), p. 6L. D. Barron, Science 226, 1491 (1994).

L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, Oxford, 1984).

V. B. Berestetskii, E. M. Lifshitz, L. P. Pitaevskii, Quantum Electrodynamics (Permagon, Oxford, 1982).

Malinowski, A.

N. I. Zheludev, S. V. Popov, Yu. P. Svirko, A. Malinowski, D. Yu. Paraschuk, Phys. Rev. B 50, 11508 (1994).
[CrossRef]

Onsager, L.

L. Onsager, Phys. Rev. 37, 405 (1031)H. G. B. Casimir, Rev. Mod. Phys. 17, 345 (1945).
[CrossRef]

Paraschuk, D. Yu.

N. I. Zheludev, S. V. Popov, Yu. P. Svirko, A. Malinowski, D. Yu. Paraschuk, Phys. Rev. B 50, 11508 (1994).
[CrossRef]

Pitaevskii, L. P.

It has been proved that chemical interactions of a chiral molecule are not necessarily T invariant and that any analysis of dynamic processes involving molecules that exist in two enantiomeric forms must be based on the validity of PT invariance. SeeE. M. Lifshitz, L. P. Pitaevskii, Physical Kinetics (Pergamon, Oxford, 1981), p. 6L. D. Barron, Science 226, 1491 (1994).

V. B. Berestetskii, E. M. Lifshitz, L. P. Pitaevskii, Quantum Electrodynamics (Permagon, Oxford, 1982).

L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, Oxford, 1984).

Popov, S. V.

A. R. Bungay, S. V. Popov, Yu. P. Svirko, N. I. Zheludev, Chem. Phys. Lett. 218, 249 (1994).
[CrossRef]

N. I. Zheludev, S. V. Popov, Yu. P. Svirko, A. Malinowski, D. Yu. Paraschuk, Phys. Rev. B 50, 11508 (1994).
[CrossRef]

Sakurai, J. J.

J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, Reading, Mass., 1994), pp. 255–256.

Sturman, B. I.

V. I. Belinicher, B. I. Sturman, Sov. Phys. Usp. 23, 1299 (1980).
[CrossRef]

Svirko, Yu. P.

A. R. Bungay, S. V. Popov, Yu. P. Svirko, N. I. Zheludev, Chem. Phys. Lett. 218, 249 (1994).
[CrossRef]

N. I. Zheludev, S. V. Popov, Yu. P. Svirko, A. Malinowski, D. Yu. Paraschuk, Phys. Rev. B 50, 11508 (1994).
[CrossRef]

A. R. Bungay, Yu. P. Svirko, N. I. Zheludev, Phys. Rev. B 47, 16141 (1993).
[CrossRef]

Zheludev, N. I.

A. R. Bungay, S. V. Popov, Yu. P. Svirko, N. I. Zheludev, Chem. Phys. Lett. 218, 249 (1994).
[CrossRef]

N. I. Zheludev, S. V. Popov, Yu. P. Svirko, A. Malinowski, D. Yu. Paraschuk, Phys. Rev. B 50, 11508 (1994).
[CrossRef]

A. R. Bungay, Yu. P. Svirko, N. I. Zheludev, Phys. Rev. B 47, 16141 (1993).
[CrossRef]

Chem. Phys. Lett.

A. R. Bungay, S. V. Popov, Yu. P. Svirko, N. I. Zheludev, Chem. Phys. Lett. 218, 249 (1994).
[CrossRef]

J. Phys. B

L. D. Barron, A. D. Buckingham, J. Phys. B 6, 1295 (1973).
[CrossRef]

Phys. Rev.

L. Onsager, Phys. Rev. 37, 405 (1031)H. G. B. Casimir, Rev. Mod. Phys. 17, 345 (1945).
[CrossRef]

Phys. Rev. B

A. R. Bungay, Yu. P. Svirko, N. I. Zheludev, Phys. Rev. B 47, 16141 (1993).
[CrossRef]

N. I. Zheludev, S. V. Popov, Yu. P. Svirko, A. Malinowski, D. Yu. Paraschuk, Phys. Rev. B 50, 11508 (1994).
[CrossRef]

Phys. Today

Several years ago a search for quasi-particles with fractional statistics in superconductors began. Fractional statistics of the carriers may lead to broken time reversality of the crystal Hamiltonian itself [seeB. G. Levi, Phys. Today 44(2), 17 (1991)]. Weak interactions of optical electrons with the nucleus lead to breakage parity. Here we exclude these special cases from our consideration.

Sov. Phys. Usp.

V. I. Belinicher, B. I. Sturman, Sov. Phys. Usp. 23, 1299 (1980).
[CrossRef]

Other

J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, Reading, Mass., 1994), pp. 255–256.

Note that complete relativistic invariance requires symmetry with respect to CPT, where C is the charge-conjugation operation. Optics is, however, evidently symmetric with respect to C, making it obligatory for optical interactions to be PT invariant.

V. B. Berestetskii, E. M. Lifshitz, L. P. Pitaevskii, Quantum Electrodynamics (Permagon, Oxford, 1982).

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, Cambridge, 1982).

M. Lax, Symmetry Principles in Solids State and Molecular Physics (Wiley, New York, 1974).

It has been proved that chemical interactions of a chiral molecule are not necessarily T invariant and that any analysis of dynamic processes involving molecules that exist in two enantiomeric forms must be based on the validity of PT invariance. SeeE. M. Lifshitz, L. P. Pitaevskii, Physical Kinetics (Pergamon, Oxford, 1981), p. 6L. D. Barron, Science 226, 1491 (1994).

L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, Oxford, 1984).

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Equations (4)

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H = p 2 2 m + e V - e 2 8 m 2 c 2 2 V + e 4 m 2 c 2 [ V × p ] · σ .
H int = - e m c p · A ( r , t ) + e 2 2 m c 2 A 2 ( r , t ) - e 2 4 m 2 c 3 [ V × A ( r , t ) ] · σ - μ · B ( r , t ) .
Δ H int = H int - T { H int } = - 2 3 c k α q α β t A β ( 0 ) sin ( ω t ) - 2 m · [ k × A ( 0 ) ] sin ( ω t ) - e 2 2 m 2 c 3 { ( r · V ) ( σ · [ k × A ( 0 ) ] ) - ( r · σ ) ( V · [ k × A ( 0 ) ] ) } sin ( ω t ) .
Δ H int , odd = - e 2 2 m 2 c 3 { ( r · V odd ) ( σ · [ k × A ( 0 ) ] ) - ( r · σ ) ( V odd · [ k × A ( 0 ) ] ) } sin ( ω t ) .

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