Abstract

The resonant-state expansion, a recently developed powerful method in electrodynamics, is generalized here for open optical systems containing magnetic, chiral, or bi-anisotropic materials. It is shown that the key matrix eigenvalue equation of the method remains the same, but the matrix elements of the perturbation now contain variations of the permittivity, permeability, and bi-anisotropy tensors. A general normalization of resonant states in terms of the electric and magnetic fields is presented.

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References

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    [Crossref]
  2. M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 87, 043827 (2013).
    [Crossref]
  3. M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 90, 013834 (2014).
    [Crossref]
  4. L. J. Armitage, M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 89, 053832 (2014).
    [Crossref]
  5. S. V. Lobanov, G. Zoriniants, W. Langbein, and E. A. Muljarov, Phys. Rev. A 95, 053848 (2017).
    [Crossref]
  6. K. S. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966).
    [Crossref]
  7. K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, 1993).
  8. G. Dhatt, G. Touzot, and E. Lefrançois, Finite Element Method (ISTE Ltd, 2012).
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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]
  17. E. A. Muljarov and W. Langbein, Phys. Rev. A 96, 017801 (2017).
    [Crossref]
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    [Crossref]
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    [Crossref]
  20. T. Weiss, M. Schäferling, H. Giessen, N. A. Gippius, S. G. Tikhodeev, W. Langbein, and E. A. Muljarov, Phys. Rev. B 96, 045129 (2017).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  25. M. L. Nesterov, X. Yin, M. Schäferling, H. Giessen, and T. Weiss, ACS Photon. 3, 578 (2016).
    [Crossref]

2017 (4)

S. V. Lobanov, G. Zoriniants, W. Langbein, and E. A. Muljarov, Phys. Rev. A 95, 053848 (2017).
[Crossref]

E. A. Muljarov and W. Langbein, Phys. Rev. A 96, 017801 (2017).
[Crossref]

T. Weiss, M. Schäferling, H. Giessen, N. A. Gippius, S. G. Tikhodeev, W. Langbein, and E. A. Muljarov, Phys. Rev. B 96, 045129 (2017).
[Crossref]

H. S. Sehmi, W. Langbein, and E. A. Muljarov, Phys. Rev. B 95, 115444 (2017).
[Crossref]

2016 (4)

M. L. Nesterov, X. Yin, M. Schäferling, H. Giessen, and T. Weiss, ACS Photon. 3, 578 (2016).
[Crossref]

E. A. Muljarov and W. Langbein, Phys. Rev. B 93, 075417 (2016).
[Crossref]

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

E. A. Muljarov and W. Langbein, Phys. Rev. B 94, 235438 (2016).
[Crossref]

2014 (2)

M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 90, 013834 (2014).
[Crossref]

L. J. Armitage, M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 89, 053832 (2014).
[Crossref]

2013 (1)

M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 87, 043827 (2013).
[Crossref]

2012 (2)

2010 (3)

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, IEEE J. Sel. Top. Quantum Electron. 16, 367 (2010).
[Crossref]

E. A. Muljarov, W. Langbein, and R. Zimmermann, Europhys. Lett. 92, 50010 (2010).
[Crossref]

M. Pisarenco, J. Maubach, I. Setija, and R. Mattheij, J. Opt. Soc. Am. A 27, 2423 (2010).
[Crossref]

2000 (1)

1996 (1)

1971 (1)

E. E. Shnol, Theor. Math. Phys. 8, 729 (1971).
[Crossref]

1966 (1)

K. S. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966).
[Crossref]

1939 (1)

A. J. F. Siegert, Phys. Rev. 56, 750 (1939).
[Crossref]

1928 (1)

G. Gamow, Zeitschrift für Physik 51, 204 (1928).
[Crossref]

Armitage, L. J.

L. J. Armitage, M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 89, 053832 (2014).
[Crossref]

Dhatt, G.

G. Dhatt, G. Touzot, and E. Lefrançois, Finite Element Method (ISTE Ltd, 2012).

Doost, M. B.

L. J. Armitage, M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 89, 053832 (2014).
[Crossref]

M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 90, 013834 (2014).
[Crossref]

M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 87, 043827 (2013).
[Crossref]

Fan, Z.

A. O. Govorov and Z. Fan, Chem. Phys. Chem. 13, 2551 (2012).
[Crossref]

Gamow, G.

G. Gamow, Zeitschrift für Physik 51, 204 (1928).
[Crossref]

Giessen, H.

T. Weiss, M. Schäferling, H. Giessen, N. A. Gippius, S. G. Tikhodeev, W. Langbein, and E. A. Muljarov, Phys. Rev. B 96, 045129 (2017).
[Crossref]

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

M. L. Nesterov, X. Yin, M. Schäferling, H. Giessen, and T. Weiss, ACS Photon. 3, 578 (2016).
[Crossref]

Gippius, N. A.

T. Weiss, M. Schäferling, H. Giessen, N. A. Gippius, S. G. Tikhodeev, W. Langbein, and E. A. Muljarov, Phys. Rev. B 96, 045129 (2017).
[Crossref]

Govorov, A. O.

A. O. Govorov and Z. Fan, Chem. Phys. Chem. 13, 2551 (2012).
[Crossref]

Hughes, S.

Kriegler, C. E.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, IEEE J. Sel. Top. Quantum Electron. 16, 367 (2010).
[Crossref]

Kristensen, P. T.

Kunz, K. S.

K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, 1993).

Lalanne, P.

Langbein, W.

S. V. Lobanov, G. Zoriniants, W. Langbein, and E. A. Muljarov, Phys. Rev. A 95, 053848 (2017).
[Crossref]

T. Weiss, M. Schäferling, H. Giessen, N. A. Gippius, S. G. Tikhodeev, W. Langbein, and E. A. Muljarov, Phys. Rev. B 96, 045129 (2017).
[Crossref]

H. S. Sehmi, W. Langbein, and E. A. Muljarov, Phys. Rev. B 95, 115444 (2017).
[Crossref]

E. A. Muljarov and W. Langbein, Phys. Rev. A 96, 017801 (2017).
[Crossref]

E. A. Muljarov and W. Langbein, Phys. Rev. B 94, 235438 (2016).
[Crossref]

E. A. Muljarov and W. Langbein, Phys. Rev. B 93, 075417 (2016).
[Crossref]

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

L. J. Armitage, M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 89, 053832 (2014).
[Crossref]

M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 90, 013834 (2014).
[Crossref]

M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 87, 043827 (2013).
[Crossref]

E. A. Muljarov, W. Langbein, and R. Zimmermann, Europhys. Lett. 92, 50010 (2010).
[Crossref]

Lefrançois, E.

G. Dhatt, G. Touzot, and E. Lefrançois, Finite Element Method (ISTE Ltd, 2012).

Leung, P. T.

Lindell, I.

I. Lindell, A. Sihvola, S. Tretyakov, and A. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, 1994).

Linden, S.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, IEEE J. Sel. Top. Quantum Electron. 16, 367 (2010).
[Crossref]

Lobanov, S. V.

S. V. Lobanov, G. Zoriniants, W. Langbein, and E. A. Muljarov, Phys. Rev. A 95, 053848 (2017).
[Crossref]

Luebbers, R. J.

K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, 1993).

Mattheij, R.

Maubach, J.

Mesch, M.

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

Muljarov, E. A.

E. A. Muljarov and W. Langbein, Phys. Rev. A 96, 017801 (2017).
[Crossref]

H. S. Sehmi, W. Langbein, and E. A. Muljarov, Phys. Rev. B 95, 115444 (2017).
[Crossref]

T. Weiss, M. Schäferling, H. Giessen, N. A. Gippius, S. G. Tikhodeev, W. Langbein, and E. A. Muljarov, Phys. Rev. B 96, 045129 (2017).
[Crossref]

S. V. Lobanov, G. Zoriniants, W. Langbein, and E. A. Muljarov, Phys. Rev. A 95, 053848 (2017).
[Crossref]

E. A. Muljarov and W. Langbein, Phys. Rev. B 93, 075417 (2016).
[Crossref]

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

E. A. Muljarov and W. Langbein, Phys. Rev. B 94, 235438 (2016).
[Crossref]

L. J. Armitage, M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 89, 053832 (2014).
[Crossref]

M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 90, 013834 (2014).
[Crossref]

M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 87, 043827 (2013).
[Crossref]

E. A. Muljarov, W. Langbein, and R. Zimmermann, Europhys. Lett. 92, 50010 (2010).
[Crossref]

Nesterov, M. L.

M. L. Nesterov, X. Yin, M. Schäferling, H. Giessen, and T. Weiss, ACS Photon. 3, 578 (2016).
[Crossref]

Pang, K. M.

Pisarenco, M.

Rill, M. S.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, IEEE J. Sel. Top. Quantum Electron. 16, 367 (2010).
[Crossref]

Schäferling, M.

T. Weiss, M. Schäferling, H. Giessen, N. A. Gippius, S. G. Tikhodeev, W. Langbein, and E. A. Muljarov, Phys. Rev. B 96, 045129 (2017).
[Crossref]

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

M. L. Nesterov, X. Yin, M. Schäferling, H. Giessen, and T. Weiss, ACS Photon. 3, 578 (2016).
[Crossref]

Sehmi, H. S.

H. S. Sehmi, W. Langbein, and E. A. Muljarov, Phys. Rev. B 95, 115444 (2017).
[Crossref]

Setija, I.

Shnol, E. E.

E. E. Shnol, Theor. Math. Phys. 8, 729 (1971).
[Crossref]

Siegert, A. J. F.

A. J. F. Siegert, Phys. Rev. 56, 750 (1939).
[Crossref]

Sihvola, A.

I. Lindell, A. Sihvola, S. Tretyakov, and A. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, 1994).

Silberstein, E.

Tikhodeev, S. G.

T. Weiss, M. Schäferling, H. Giessen, N. A. Gippius, S. G. Tikhodeev, W. Langbein, and E. A. Muljarov, Phys. Rev. B 96, 045129 (2017).
[Crossref]

Touzot, G.

G. Dhatt, G. Touzot, and E. Lefrançois, Finite Element Method (ISTE Ltd, 2012).

Tretyakov, S.

I. Lindell, A. Sihvola, S. Tretyakov, and A. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, 1994).

Viitanen, A.

I. Lindell, A. Sihvola, S. Tretyakov, and A. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, 1994).

Vlack, C. V.

Wegener, M.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, IEEE J. Sel. Top. Quantum Electron. 16, 367 (2010).
[Crossref]

Weiss, T.

T. Weiss, M. Schäferling, H. Giessen, N. A. Gippius, S. G. Tikhodeev, W. Langbein, and E. A. Muljarov, Phys. Rev. B 96, 045129 (2017).
[Crossref]

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

M. L. Nesterov, X. Yin, M. Schäferling, H. Giessen, and T. Weiss, ACS Photon. 3, 578 (2016).
[Crossref]

Yee, K. S.

K. S. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966).
[Crossref]

Yin, X.

M. L. Nesterov, X. Yin, M. Schäferling, H. Giessen, and T. Weiss, ACS Photon. 3, 578 (2016).
[Crossref]

Zimmermann, R.

E. A. Muljarov, W. Langbein, and R. Zimmermann, Europhys. Lett. 92, 50010 (2010).
[Crossref]

Zoriniants, G.

S. V. Lobanov, G. Zoriniants, W. Langbein, and E. A. Muljarov, Phys. Rev. A 95, 053848 (2017).
[Crossref]

ACS Photon. (1)

M. L. Nesterov, X. Yin, M. Schäferling, H. Giessen, and T. Weiss, ACS Photon. 3, 578 (2016).
[Crossref]

Chem. Phys. Chem. (1)

A. O. Govorov and Z. Fan, Chem. Phys. Chem. 13, 2551 (2012).
[Crossref]

Europhys. Lett. (1)

E. A. Muljarov, W. Langbein, and R. Zimmermann, Europhys. Lett. 92, 50010 (2010).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, IEEE J. Sel. Top. Quantum Electron. 16, 367 (2010).
[Crossref]

IEEE Trans. Antennas Propag. (1)

K. S. Yee, IEEE Trans. Antennas Propag. 14, 302 (1966).
[Crossref]

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

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

Opt. Lett. (2)

Phys. Rev. (1)

A. J. F. Siegert, Phys. Rev. 56, 750 (1939).
[Crossref]

Phys. Rev. A (5)

E. A. Muljarov and W. Langbein, Phys. Rev. A 96, 017801 (2017).
[Crossref]

M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 87, 043827 (2013).
[Crossref]

M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 90, 013834 (2014).
[Crossref]

L. J. Armitage, M. B. Doost, W. Langbein, and E. A. Muljarov, Phys. Rev. A 89, 053832 (2014).
[Crossref]

S. V. Lobanov, G. Zoriniants, W. Langbein, and E. A. Muljarov, Phys. Rev. A 95, 053848 (2017).
[Crossref]

Phys. Rev. B (4)

E. A. Muljarov and W. Langbein, Phys. Rev. B 93, 075417 (2016).
[Crossref]

T. Weiss, M. Schäferling, H. Giessen, N. A. Gippius, S. G. Tikhodeev, W. Langbein, and E. A. Muljarov, Phys. Rev. B 96, 045129 (2017).
[Crossref]

H. S. Sehmi, W. Langbein, and E. A. Muljarov, Phys. Rev. B 95, 115444 (2017).
[Crossref]

E. A. Muljarov and W. Langbein, Phys. Rev. B 94, 235438 (2016).
[Crossref]

Phys. Rev. Lett. (1)

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein, and E. A. Muljarov, Phys. Rev. Lett. 116, 237401 (2016).
[Crossref]

Theor. Math. Phys. (1)

E. E. Shnol, Theor. Math. Phys. 8, 729 (1971).
[Crossref]

Zeitschrift für Physik (1)

G. Gamow, Zeitschrift für Physik 51, 204 (1928).
[Crossref]

Other (3)

K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, 1993).

G. Dhatt, G. Touzot, and E. Lefrançois, Finite Element Method (ISTE Ltd, 2012).

I. Lindell, A. Sihvola, S. Tretyakov, and A. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, 1994).

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Equations (40)

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

× E = i k B , × H = i k D + 4 π c j ,
D = ϵ ^ E + ξ ^ H , B = μ ^ H + ζ ^ E ,
M ^ ( k , r ) F ( r ) = J ( r )
P ^ ( k , r ) = ( ϵ ^ η ^ η ^ T μ ^ ) , D ^ ( r ) = ( 0 × × 0 ) ,
F ( r ) = ( E i H ) and J ( r ) = ( J E i J H ) ,
M ^ ( k , r ) G ^ k ( r , r ) = I ^ δ ( r r ) ,
M ^ ( k n , r ) F n ( r ) = 0 ,
G ^ k ( r , r ) = n F n ( r ) F n ( r ) k k n ,
n k P ^ ( k , r ) k n P ^ ( k n , r ) k k n F n ( r ) F n ( r ) = I ^ δ ( r r ) .
P ^ ( r ) n F n ( r ) F n ( r ) = I ^ δ ( r r ) .
P ^ ( k , r ) = P ^ ( r ) + j Q ^ j ( r ) k Ω j ,
1 k k n ( k k Ω j k n k n Ω j ) = Ω j ( k Ω j ) ( k n Ω j ) ,
n [ P ^ ( r ) j Ω j Q ^ j ( r ) ( k Ω j ) ( k n Ω j ) ] F n ( r ) F n ( r ) = I ^ δ ( r r ) .
Q ^ j ( r ) n F n ( r ) F n ( r ) k n Ω j = 0
P ^ ( r ) n F n ( r ) F n ( r ) = I ^ δ ( r r ) ,
n P ^ ( k n , r ) F n ( r ) F n ( r ) = I ^ δ ( r r ) .
F ( k , r ) = n F n ( r ) k k n F n ( r ) · J ( r ) d r .
F n ( r ) · S ( r ) d r = 1 .
k F n · P ^ ( k ) F k n F · P ^ ( k n ) F n F n · D ^ F + F · D ^ F n = ( k k n ) F n · S ,
F n · D ^ F + F · D ^ F n = i · ( E n × H E × H n ) .
1 = V F n · [ k P ^ ( k ) ] F n d r + i S V ( E n × H n E n × H n ) · d S ,
F n = 1 k n ( r · ) F n ,
1 = V [ E n · ( k ϵ ^ ) E n + E n · ( k ξ ^ ) H n ] d r V [ H n · ( k ζ ^ ) E n + H n · ( k μ ^ ) H n ] d r + i k n S V [ E n × ( r · ) H n + H n × ( r · ) E n ] · d S .
1 = V E n · ( k ϵ ^ ) E n d r V H n · H n d r + i S V ( E n × H n E n × H n ) · d S ,
V H n · H n d r = i k n S V E n × H n · d S + V E n · ϵ ^ E n d r .
i S V ( E n × H n E n × H n ) · d S = i k n S V E n × H n · d S + 1 k n S V ( E n s · E n E n s · E n ) d S ,
1 = 2 V E n · ( k 2 ϵ ^ ) ( k 2 ) | k n E n d r + 1 k n S V ( E n s · E n E n s · E n ) d S ,
1 = E n · ( k 2 ϵ ^ ) ( k 2 ) | k n E n d r .
M ^ ( k , r ) F ( r ) = k Δ P ^ ( k , r ) F ( r ) ,
F ( r ) = k G ^ k ( r , r ) Δ P ^ ( k , r ) F ( r ) d r .
F ( r ) = n c n F n ( r ) ,
n c n F n ( r ) = k n F n ( r ) k k n m V n m c m ,
V n m = F n ( r ) · Δ P ^ ( r ) F m ( r ) d r .
( k k n ) c n = k m V n m c m ,
Δ P ^ ( k , r ) = Δ P ^ ( r ) + j Δ Q ^ j ( r ) k Ω j ,
F ( r ) = k G ^ k ( r , r ) Δ P ^ ( r ) F ( r ) d r k j G ^ k j ( r , r ) Δ Q ^ j ( r ) k Ω j F ( r ) d r ,
G ^ k j ( r , r ) = G ^ k ( r , r ) + Ω j k n F n ( r ) F n ( r ) k n Ω j .
( k k n ) c n = k m V n m ( ) c m + k n m [ V n m ( ) V n m ( k n ) ] c m ,
V n m ( k ) = F n ( r ) · Δ P ^ ( k , r ) F m ( r ) d r .
V n m ( k ) = V [ E n · Δ ϵ ^ ( k ) E m + E n · Δ ξ ^ ( k ) H m ] d r V [ H n · Δ ζ ^ ( k ) E m + H n · Δ μ ^ ( k ) H m ] d r .

Metrics