Abstract

The reciprocity of dissipative systems is usually justified by the microscopic reversibility of physical processes, i.e., relying on the time-reversal symmetry of physical laws at the microscopic level. Here, it is shown that it is unnecessary to invoke microscopic arguments to establish a direct link between the reciprocity of macroscopic systems and time-reversal invariance. It is demonstrated that lossy dielectrics have a hidden time-reversal symmetry, as the relevant dissipation channels can be mimicked by a distributed network of time-reversal invariant lossless transmission lines. It is proven that the reciprocity of lossy systems is fundamentally rooted on the hidden time-reversal invariance and linearity of the materials. Furthermore, it is demonstrated that the upper-half frequency plane response of dissipative materials can be approximated as much as desired by the response of some lossless material. The developed theory sheds new light on the link between dissipation, “open systems,” and interactions with a “bath” of oscillators.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. R. Feynman, R. Leighton, and M. Sands, The Feynman lectures on physics (California Institute of Technology, 1963).
  2. H. B. G. Casimir, “Reciprocity theorems and irreversible processes,” Proc. IEEE 51(11), 1570–1573 (1963).
    [Crossref]
  3. M. G. Silveirinha, “Time-reversal symmetry in antenna theory,” Symmetry (Basel) 11(4), 486 (2019).
    [Crossref]
  4. R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67(5), 717–754 (2004).
    [Crossref]
  5. C. Caloz, A. Alù, S. Tretyakov, D. Sounas, K. Achouri, and Z.-L. Deck-Léger, “Electromagnetic nonreciprocity,” Phys. Rev. Appl. 10(4), 047001 (2018).
    [Crossref]
  6. L. Onsager, “Reciprocal relations in irreversible processes I,” Phys. Rev. 37(4), 405–426 (1931).
    [Crossref]
  7. J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112(5), 1555–1567 (1958).
    [Crossref]
  8. A. O. Caldeira and A. J. Leggett, “Influence of dissipation on quantum tunneling in macroscopic systems,” Phys. Rev. Lett. 46(4), 211–214 (1981).
    [Crossref]
  9. A. O. Caldeira and A. J. Leggett, “Quantum tunnelling in a dissipative system,” Ann. Phys. 149(2), 374–456 (1983).
    [Crossref]
  10. B. Huttner and S. M. Barnett, “Quantization of the electromagnetic field in dielectrics,” Phys. Rev. A 46(7), 4306–4322 (1992).
    [Crossref] [PubMed]
  11. U. Vool and M. Devoret, “Introduction to quantum electromagnetic circuits,” Int. J. Circuit Theory Appl. 45(7), 897–934 (2017).
    [Crossref]
  12. W. E. I. Sha, A. Y. Liu, and W. C. Chew, “Dissipative quantum electromagnetics,” IEEE J. Multiscale Multiphys. Comput. Tech. 3, 198–213 (2018).
    [Crossref]
  13. D. C. Tzarouchis, N. Engheta, and A. Sihvola, “Resonant graded-index plasmonic nanoscatterers: enabling unusual light-matter interactions,” 12th International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials) (2018).
    [Crossref]
  14. J. B. Pendry, P. A. Huidobro, Y. Luo, and E. Galiffi, “Compacted dimensions and singular plasmonic surfaces,” Science 358(6365), 915–917 (2017).
    [Crossref] [PubMed]
  15. M. G. Silveirinha, “PTD symmetry protected scattering anomaly in optics,” Phys. Rev. B 95(3), 035153 (2017).
    [Crossref]
  16. A. Raman and S. Fan, “Photonic band structure of dispersive metamaterials formulated as a Hermitian eigenvalue problem,” Phys. Rev. Lett. 104(8), 087401 (2010).
    [Crossref] [PubMed]
  17. M. G. Silveirinha, “Chern invariants for continuous media,” Phys. Rev. B 92(12), 125153 (2015).
    [Crossref]
  18. M. G. Silveirinha, “Topological classification of Chern-type insulators by means of the photonic Green function,” Phys. Rev. B 97(11), 115146 (2018).
    [Crossref]
  19. M. G. Silveirinha, “Modal expansions in dispersive material systems with application to quantum optics and topological photonics”, chapter to appear in Advances in Mathematical Methods for Electromagnetics, (edited by Paul Smith, Kazuya Kobayashi) IET, (available in arXiv:1712.04272).
  20. D. E. Fernandes and M. G. Silveirinha, “Asymmetric transmission and isolation in nonlinear devices: why they are different,” IEEE Antennas Wirel. Propag. Lett. 17(11), 1953–1957 (2018).
    [Crossref]
  21. J. B. Pendry, “Time reversal and negative refraction,” Science 322(5898), 71–73 (2008).
    [Crossref] [PubMed]
  22. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of continuous media, vol. 8 of Course on Theoretical Physics, (Butterworth-Heinemann, 2004).

2019 (1)

M. G. Silveirinha, “Time-reversal symmetry in antenna theory,” Symmetry (Basel) 11(4), 486 (2019).
[Crossref]

2018 (4)

C. Caloz, A. Alù, S. Tretyakov, D. Sounas, K. Achouri, and Z.-L. Deck-Léger, “Electromagnetic nonreciprocity,” Phys. Rev. Appl. 10(4), 047001 (2018).
[Crossref]

W. E. I. Sha, A. Y. Liu, and W. C. Chew, “Dissipative quantum electromagnetics,” IEEE J. Multiscale Multiphys. Comput. Tech. 3, 198–213 (2018).
[Crossref]

M. G. Silveirinha, “Topological classification of Chern-type insulators by means of the photonic Green function,” Phys. Rev. B 97(11), 115146 (2018).
[Crossref]

D. E. Fernandes and M. G. Silveirinha, “Asymmetric transmission and isolation in nonlinear devices: why they are different,” IEEE Antennas Wirel. Propag. Lett. 17(11), 1953–1957 (2018).
[Crossref]

2017 (3)

U. Vool and M. Devoret, “Introduction to quantum electromagnetic circuits,” Int. J. Circuit Theory Appl. 45(7), 897–934 (2017).
[Crossref]

J. B. Pendry, P. A. Huidobro, Y. Luo, and E. Galiffi, “Compacted dimensions and singular plasmonic surfaces,” Science 358(6365), 915–917 (2017).
[Crossref] [PubMed]

M. G. Silveirinha, “PTD symmetry protected scattering anomaly in optics,” Phys. Rev. B 95(3), 035153 (2017).
[Crossref]

2015 (1)

M. G. Silveirinha, “Chern invariants for continuous media,” Phys. Rev. B 92(12), 125153 (2015).
[Crossref]

2010 (1)

A. Raman and S. Fan, “Photonic band structure of dispersive metamaterials formulated as a Hermitian eigenvalue problem,” Phys. Rev. Lett. 104(8), 087401 (2010).
[Crossref] [PubMed]

2008 (1)

J. B. Pendry, “Time reversal and negative refraction,” Science 322(5898), 71–73 (2008).
[Crossref] [PubMed]

2004 (1)

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67(5), 717–754 (2004).
[Crossref]

1992 (1)

B. Huttner and S. M. Barnett, “Quantization of the electromagnetic field in dielectrics,” Phys. Rev. A 46(7), 4306–4322 (1992).
[Crossref] [PubMed]

1983 (1)

A. O. Caldeira and A. J. Leggett, “Quantum tunnelling in a dissipative system,” Ann. Phys. 149(2), 374–456 (1983).
[Crossref]

1981 (1)

A. O. Caldeira and A. J. Leggett, “Influence of dissipation on quantum tunneling in macroscopic systems,” Phys. Rev. Lett. 46(4), 211–214 (1981).
[Crossref]

1963 (1)

H. B. G. Casimir, “Reciprocity theorems and irreversible processes,” Proc. IEEE 51(11), 1570–1573 (1963).
[Crossref]

1958 (1)

J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112(5), 1555–1567 (1958).
[Crossref]

1931 (1)

L. Onsager, “Reciprocal relations in irreversible processes I,” Phys. Rev. 37(4), 405–426 (1931).
[Crossref]

Achouri, K.

C. Caloz, A. Alù, S. Tretyakov, D. Sounas, K. Achouri, and Z.-L. Deck-Léger, “Electromagnetic nonreciprocity,” Phys. Rev. Appl. 10(4), 047001 (2018).
[Crossref]

Alù, A.

C. Caloz, A. Alù, S. Tretyakov, D. Sounas, K. Achouri, and Z.-L. Deck-Léger, “Electromagnetic nonreciprocity,” Phys. Rev. Appl. 10(4), 047001 (2018).
[Crossref]

Barnett, S. M.

B. Huttner and S. M. Barnett, “Quantization of the electromagnetic field in dielectrics,” Phys. Rev. A 46(7), 4306–4322 (1992).
[Crossref] [PubMed]

Caldeira, A. O.

A. O. Caldeira and A. J. Leggett, “Quantum tunnelling in a dissipative system,” Ann. Phys. 149(2), 374–456 (1983).
[Crossref]

A. O. Caldeira and A. J. Leggett, “Influence of dissipation on quantum tunneling in macroscopic systems,” Phys. Rev. Lett. 46(4), 211–214 (1981).
[Crossref]

Caloz, C.

C. Caloz, A. Alù, S. Tretyakov, D. Sounas, K. Achouri, and Z.-L. Deck-Léger, “Electromagnetic nonreciprocity,” Phys. Rev. Appl. 10(4), 047001 (2018).
[Crossref]

Casimir, H. B. G.

H. B. G. Casimir, “Reciprocity theorems and irreversible processes,” Proc. IEEE 51(11), 1570–1573 (1963).
[Crossref]

Chew, W. C.

W. E. I. Sha, A. Y. Liu, and W. C. Chew, “Dissipative quantum electromagnetics,” IEEE J. Multiscale Multiphys. Comput. Tech. 3, 198–213 (2018).
[Crossref]

Deck-Léger, Z.-L.

C. Caloz, A. Alù, S. Tretyakov, D. Sounas, K. Achouri, and Z.-L. Deck-Léger, “Electromagnetic nonreciprocity,” Phys. Rev. Appl. 10(4), 047001 (2018).
[Crossref]

Devoret, M.

U. Vool and M. Devoret, “Introduction to quantum electromagnetic circuits,” Int. J. Circuit Theory Appl. 45(7), 897–934 (2017).
[Crossref]

Engheta, N.

D. C. Tzarouchis, N. Engheta, and A. Sihvola, “Resonant graded-index plasmonic nanoscatterers: enabling unusual light-matter interactions,” 12th International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials) (2018).
[Crossref]

Fan, S.

A. Raman and S. Fan, “Photonic band structure of dispersive metamaterials formulated as a Hermitian eigenvalue problem,” Phys. Rev. Lett. 104(8), 087401 (2010).
[Crossref] [PubMed]

Fernandes, D. E.

D. E. Fernandes and M. G. Silveirinha, “Asymmetric transmission and isolation in nonlinear devices: why they are different,” IEEE Antennas Wirel. Propag. Lett. 17(11), 1953–1957 (2018).
[Crossref]

Galiffi, E.

J. B. Pendry, P. A. Huidobro, Y. Luo, and E. Galiffi, “Compacted dimensions and singular plasmonic surfaces,” Science 358(6365), 915–917 (2017).
[Crossref] [PubMed]

Hopfield, J. J.

J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112(5), 1555–1567 (1958).
[Crossref]

Huidobro, P. A.

J. B. Pendry, P. A. Huidobro, Y. Luo, and E. Galiffi, “Compacted dimensions and singular plasmonic surfaces,” Science 358(6365), 915–917 (2017).
[Crossref] [PubMed]

Huttner, B.

B. Huttner and S. M. Barnett, “Quantization of the electromagnetic field in dielectrics,” Phys. Rev. A 46(7), 4306–4322 (1992).
[Crossref] [PubMed]

Leggett, A. J.

A. O. Caldeira and A. J. Leggett, “Quantum tunnelling in a dissipative system,” Ann. Phys. 149(2), 374–456 (1983).
[Crossref]

A. O. Caldeira and A. J. Leggett, “Influence of dissipation on quantum tunneling in macroscopic systems,” Phys. Rev. Lett. 46(4), 211–214 (1981).
[Crossref]

Liu, A. Y.

W. E. I. Sha, A. Y. Liu, and W. C. Chew, “Dissipative quantum electromagnetics,” IEEE J. Multiscale Multiphys. Comput. Tech. 3, 198–213 (2018).
[Crossref]

Luo, Y.

J. B. Pendry, P. A. Huidobro, Y. Luo, and E. Galiffi, “Compacted dimensions and singular plasmonic surfaces,” Science 358(6365), 915–917 (2017).
[Crossref] [PubMed]

Onsager, L.

L. Onsager, “Reciprocal relations in irreversible processes I,” Phys. Rev. 37(4), 405–426 (1931).
[Crossref]

Pendry, J. B.

J. B. Pendry, P. A. Huidobro, Y. Luo, and E. Galiffi, “Compacted dimensions and singular plasmonic surfaces,” Science 358(6365), 915–917 (2017).
[Crossref] [PubMed]

J. B. Pendry, “Time reversal and negative refraction,” Science 322(5898), 71–73 (2008).
[Crossref] [PubMed]

Potton, R. J.

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67(5), 717–754 (2004).
[Crossref]

Raman, A.

A. Raman and S. Fan, “Photonic band structure of dispersive metamaterials formulated as a Hermitian eigenvalue problem,” Phys. Rev. Lett. 104(8), 087401 (2010).
[Crossref] [PubMed]

Sha, W. E. I.

W. E. I. Sha, A. Y. Liu, and W. C. Chew, “Dissipative quantum electromagnetics,” IEEE J. Multiscale Multiphys. Comput. Tech. 3, 198–213 (2018).
[Crossref]

Sihvola, A.

D. C. Tzarouchis, N. Engheta, and A. Sihvola, “Resonant graded-index plasmonic nanoscatterers: enabling unusual light-matter interactions,” 12th International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials) (2018).
[Crossref]

Silveirinha, M. G.

M. G. Silveirinha, “Time-reversal symmetry in antenna theory,” Symmetry (Basel) 11(4), 486 (2019).
[Crossref]

M. G. Silveirinha, “Topological classification of Chern-type insulators by means of the photonic Green function,” Phys. Rev. B 97(11), 115146 (2018).
[Crossref]

D. E. Fernandes and M. G. Silveirinha, “Asymmetric transmission and isolation in nonlinear devices: why they are different,” IEEE Antennas Wirel. Propag. Lett. 17(11), 1953–1957 (2018).
[Crossref]

M. G. Silveirinha, “PTD symmetry protected scattering anomaly in optics,” Phys. Rev. B 95(3), 035153 (2017).
[Crossref]

M. G. Silveirinha, “Chern invariants for continuous media,” Phys. Rev. B 92(12), 125153 (2015).
[Crossref]

Sounas, D.

C. Caloz, A. Alù, S. Tretyakov, D. Sounas, K. Achouri, and Z.-L. Deck-Léger, “Electromagnetic nonreciprocity,” Phys. Rev. Appl. 10(4), 047001 (2018).
[Crossref]

Tretyakov, S.

C. Caloz, A. Alù, S. Tretyakov, D. Sounas, K. Achouri, and Z.-L. Deck-Léger, “Electromagnetic nonreciprocity,” Phys. Rev. Appl. 10(4), 047001 (2018).
[Crossref]

Tzarouchis, D. C.

D. C. Tzarouchis, N. Engheta, and A. Sihvola, “Resonant graded-index plasmonic nanoscatterers: enabling unusual light-matter interactions,” 12th International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials) (2018).
[Crossref]

Vool, U.

U. Vool and M. Devoret, “Introduction to quantum electromagnetic circuits,” Int. J. Circuit Theory Appl. 45(7), 897–934 (2017).
[Crossref]

Ann. Phys. (1)

A. O. Caldeira and A. J. Leggett, “Quantum tunnelling in a dissipative system,” Ann. Phys. 149(2), 374–456 (1983).
[Crossref]

IEEE Antennas Wirel. Propag. Lett. (1)

D. E. Fernandes and M. G. Silveirinha, “Asymmetric transmission and isolation in nonlinear devices: why they are different,” IEEE Antennas Wirel. Propag. Lett. 17(11), 1953–1957 (2018).
[Crossref]

IEEE J. Multiscale Multiphys. Comput. Tech. (1)

W. E. I. Sha, A. Y. Liu, and W. C. Chew, “Dissipative quantum electromagnetics,” IEEE J. Multiscale Multiphys. Comput. Tech. 3, 198–213 (2018).
[Crossref]

Int. J. Circuit Theory Appl. (1)

U. Vool and M. Devoret, “Introduction to quantum electromagnetic circuits,” Int. J. Circuit Theory Appl. 45(7), 897–934 (2017).
[Crossref]

Phys. Rev. (2)

L. Onsager, “Reciprocal relations in irreversible processes I,” Phys. Rev. 37(4), 405–426 (1931).
[Crossref]

J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev. 112(5), 1555–1567 (1958).
[Crossref]

Phys. Rev. A (1)

B. Huttner and S. M. Barnett, “Quantization of the electromagnetic field in dielectrics,” Phys. Rev. A 46(7), 4306–4322 (1992).
[Crossref] [PubMed]

Phys. Rev. Appl. (1)

C. Caloz, A. Alù, S. Tretyakov, D. Sounas, K. Achouri, and Z.-L. Deck-Léger, “Electromagnetic nonreciprocity,” Phys. Rev. Appl. 10(4), 047001 (2018).
[Crossref]

Phys. Rev. B (3)

M. G. Silveirinha, “PTD symmetry protected scattering anomaly in optics,” Phys. Rev. B 95(3), 035153 (2017).
[Crossref]

M. G. Silveirinha, “Chern invariants for continuous media,” Phys. Rev. B 92(12), 125153 (2015).
[Crossref]

M. G. Silveirinha, “Topological classification of Chern-type insulators by means of the photonic Green function,” Phys. Rev. B 97(11), 115146 (2018).
[Crossref]

Phys. Rev. Lett. (2)

A. Raman and S. Fan, “Photonic band structure of dispersive metamaterials formulated as a Hermitian eigenvalue problem,” Phys. Rev. Lett. 104(8), 087401 (2010).
[Crossref] [PubMed]

A. O. Caldeira and A. J. Leggett, “Influence of dissipation on quantum tunneling in macroscopic systems,” Phys. Rev. Lett. 46(4), 211–214 (1981).
[Crossref]

Proc. IEEE (1)

H. B. G. Casimir, “Reciprocity theorems and irreversible processes,” Proc. IEEE 51(11), 1570–1573 (1963).
[Crossref]

Rep. Prog. Phys. (1)

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67(5), 717–754 (2004).
[Crossref]

Science (2)

J. B. Pendry, “Time reversal and negative refraction,” Science 322(5898), 71–73 (2008).
[Crossref] [PubMed]

J. B. Pendry, P. A. Huidobro, Y. Luo, and E. Galiffi, “Compacted dimensions and singular plasmonic surfaces,” Science 358(6365), 915–917 (2017).
[Crossref] [PubMed]

Symmetry (Basel) (1)

M. G. Silveirinha, “Time-reversal symmetry in antenna theory,” Symmetry (Basel) 11(4), 486 (2019).
[Crossref]

Other (4)

R. Feynman, R. Leighton, and M. Sands, The Feynman lectures on physics (California Institute of Technology, 1963).

M. G. Silveirinha, “Modal expansions in dispersive material systems with application to quantum optics and topological photonics”, chapter to appear in Advances in Mathematical Methods for Electromagnetics, (edited by Paul Smith, Kazuya Kobayashi) IET, (available in arXiv:1712.04272).

D. C. Tzarouchis, N. Engheta, and A. Sihvola, “Resonant graded-index plasmonic nanoscatterers: enabling unusual light-matter interactions,” 12th International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials) (2018).
[Crossref]

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of continuous media, vol. 8 of Course on Theoretical Physics, (Butterworth-Heinemann, 2004).

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Figures (1)

Fig. 1
Fig. 1 (a) Dissipative RL circuit. (b) Equivalent time-reversal invariant lossless circuit where the resistor is implemented with a semi-infinite transmission line.

Equations (22)

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

× E = B t , × H = j + D t .
E ( r , t ) T E TR = E ( r , t ) , H ( r , t ) T H TR = H ( r , t ) .
E ω ( r ) T E ω TR = E ω * ( r ) , H ω ( r ) T H ω TR = H ω * ( r ) , j ω ( r ) T j ω TR = j ω * ( r ) .
R i ( t ) + L d i ( t ) d t = v ( t ) .
v ( t ) T v ( t ) , i ( t ) T i ( t ) .
ε ( ω ) = 1 + Ω 0 2 ω 0 2 ω 2 i Γ ω .
2 P t 2 + Γ P t + ω 0 2 P = ε 0 Ω 0 2 E .
2 P t 2 + 2 Γ A Z 0 V u = 0 + ω 0 2 P = ε 0 Ω 0 2 E ,
V u u = L I u t , I u u = C V u t + A P t δ ( u ) .
× E = μ 0 H / t , × H = j + P / t + ε 0 E / t .
Re { [ S ( E ω , H ω * ) ] P e x t ( E ω , j ω * ) } = 0 ,
Re { [ S ( E ω , H ω * ) + S ( E ω * , H ω ) ] P ext ( E ω , j ω * ) P ext ( E ω * , j ω ) } = 0 .
Re { e i ϕ [ [ S ( E ω , H ω ) + S ( E ω , H ω ) ] + P ext ( E ω , j ω ) P ext ( E ω , j ω ) ] } = 0 .
[ S ( E ω , H ω ) + S ( E ω , H ω ) ] = P ext ( E ω , j ω ) + P ext ( E ω , j ω ) ,
[ S ( E ω , H ω ) + S ( E ω , H ω ) ] = P ext ( E ω , j ω ) + P ext ( E ω , j ω ) + P d ( V ω , u = 0 , δ I ω , u = 0 ) P d ( V ω , u = 0 , δ I ω , u = 0 )
( D ω B ω ) = ( ε 0 ε ¯ 1 c ξ ¯ 1 c ζ ¯ μ 0 μ ¯ ) M ( ω ) ( E ω H ω ) .
M TR ( ω ) = σ z M * ( ω ) σ z , with σ z = ( 1 3 × 3 0 0 1 3 × 3 ) .
M TR ( ω ) = σ z M T ( ω ) σ z , for ω real valued .
ε ( ω ) = 1 + n Ω n ω ω p , n = 1 + Re { ω p , n } > 0 ( Ω n ω ω p , n + Ω n * ω + ω p , n * ) .
ε ( ω ) = 1 n Ω n ( 1 ω ω n + i γ n + 1 ω + ω n + i γ n ) .
1 ω ω n + i γ n = 1 π + d ξ γ n γ n 2 + ( ξ ω n ) 2 1 ω ξ .
ε ( ω ) = 1 + + d ξ χ ξ ( ω ) , χ ξ ( ω ) = 1 π ( 1 ω ξ 1 ω + ξ ) n Ω n γ n γ n 2 + ( ξ ω n ) 2 .

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