Abstract

The Sommerfeld–Maluzhinets theory for plasmons on a wedge surface with a small impedance ζ is used for the calculation of surface plasmon reflection, refraction, and transformation into photons. A methodologically simplified summary of the Sommerfeld–Maluzhinets theory, valid in the first order in ζ, is presented. The approach is satisfactory for highly conductive metals up to optical frequencies. Photon radiation takes place primarily in the direction of plasmon motion along the wedge surface. The angular distribution of the radiated photons has a Lorentzian form with width ζ. For a right-angle wedge, the reflection and refraction coefficients and the diffuse part of the photon radiation are also ζ.

© 2007 Optical Society of America

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  1. V.M.Agranovich and D.L.Mills, eds., Surface Polaritons (North Holland, 1982).
  2. S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
    [CrossRef] [PubMed]
  3. S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078 (2001).
    [CrossRef]
  4. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
    [CrossRef] [PubMed]
  5. M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg morrors," Phys. Rev. B 73, 155416 (2006).
    [CrossRef]
  6. H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762-1764 (2002).
    [CrossRef]
  7. R. F. Wallis, A. A. Maradudin, and G. I. Stegeman, "Surface polariton reflection and radiation at end faces," Appl. Phys. Lett. 42, 764-766 (1983).
    [CrossRef]
  8. K. Hasegawa, J. U. Nockel, and M. Deutsch, "Surface plasmon polariton propagation around bends at a metal-dielectric interface," Appl. Phys. Lett. 84, 1835-1837 (2004).
    [CrossRef]
  9. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
    [CrossRef]
  10. G. D. Maluzhinets, "Excitation, refraction and radiation of surface waves on a wedge with given impedances of the surfaces," Dokl. Akad. Nauk SSSR 121, 436-439 (1958).
  11. R. P. Starovoitova, M. S. Bobrovnikov, and V. N. Kislitsina, "Diffraction of surface waves on a break of impedance plane," Radiotekh. Elektron. (Moscow) 2, 250-259 (1962).
  12. N. G. Trenev, "Diffraction of surface electromagnetic waves on an impedance step," Radiotekh. Elektron. (Moscow) 3, 27-37 (1958).
  13. N. G. Trenev, "Diffraction of surface electromagnetic waves on a semifinite impedance plane," Radiotekh. Elektron. (Moscow) 3, 163-171 (1958).
  14. V. I. Talanov, "Surface electromagnetic waves on a rectangular impedance step in resonator," Izv. Vyssh. Uchebn. Zaved., Radiofiz. 1, 64-72 (1957).
  15. G. D. Maluzhinets, "Some generalizations of refraction method in the sinusoidal waves diffraction theory," Ph.D. dissertation (P. N. Lebedev Physical Institute Moscow, 1950).
  16. V. M. Babich, M. A. Lyalinov, and V. E. Grikurov, Sommerfeld-Malyuzhinets Approach for Diffraction Theory (Saint-Petersburg State U., 2004).
  17. V. M. Agranovich, "Crystal optics of surface polaritons and properties of surface," Usp. Fiz. Nauk 115, 199 (1975) V. M. Agranovich,[Sov. Phys. Usp. 18, 99 (1975)].
    [CrossRef]
  18. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, 1976).
  19. V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Pergamon, 1965).
  20. I. S. Gradstein and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, 1965), Eq. (8.412.6).
  21. L. A. Vainstein, Electromagnetic Waves (Radio i Svyaz, 1988).
  22. I. M. Brekhovskikh, Waves in Layered Media (Academic, 1960).

2006

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg morrors," Phys. Rev. B 73, 155416 (2006).
[CrossRef]

2005

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

2004

K. Hasegawa, J. U. Nockel, and M. Deutsch, "Surface plasmon polariton propagation around bends at a metal-dielectric interface," Appl. Phys. Lett. 84, 1835-1837 (2004).
[CrossRef]

2003

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

2002

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762-1764 (2002).
[CrossRef]

2001

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078 (2001).
[CrossRef]

1983

R. F. Wallis, A. A. Maradudin, and G. I. Stegeman, "Surface polariton reflection and radiation at end faces," Appl. Phys. Lett. 42, 764-766 (1983).
[CrossRef]

1975

V. M. Agranovich, "Crystal optics of surface polaritons and properties of surface," Usp. Fiz. Nauk 115, 199 (1975) V. M. Agranovich,[Sov. Phys. Usp. 18, 99 (1975)].
[CrossRef]

V. M. Agranovich, "Crystal optics of surface polaritons and properties of surface," Usp. Fiz. Nauk 115, 199 (1975) V. M. Agranovich,[Sov. Phys. Usp. 18, 99 (1975)].
[CrossRef]

1962

R. P. Starovoitova, M. S. Bobrovnikov, and V. N. Kislitsina, "Diffraction of surface waves on a break of impedance plane," Radiotekh. Elektron. (Moscow) 2, 250-259 (1962).

1958

N. G. Trenev, "Diffraction of surface electromagnetic waves on an impedance step," Radiotekh. Elektron. (Moscow) 3, 27-37 (1958).

N. G. Trenev, "Diffraction of surface electromagnetic waves on a semifinite impedance plane," Radiotekh. Elektron. (Moscow) 3, 163-171 (1958).

G. D. Maluzhinets, "Excitation, refraction and radiation of surface waves on a wedge with given impedances of the surfaces," Dokl. Akad. Nauk SSSR 121, 436-439 (1958).

1957

V. I. Talanov, "Surface electromagnetic waves on a rectangular impedance step in resonator," Izv. Vyssh. Uchebn. Zaved., Radiofiz. 1, 64-72 (1957).

Agranovich, V. M.

V. M. Agranovich, "Crystal optics of surface polaritons and properties of surface," Usp. Fiz. Nauk 115, 199 (1975) V. M. Agranovich,[Sov. Phys. Usp. 18, 99 (1975)].
[CrossRef]

V. M. Agranovich, "Crystal optics of surface polaritons and properties of surface," Usp. Fiz. Nauk 115, 199 (1975) V. M. Agranovich,[Sov. Phys. Usp. 18, 99 (1975)].
[CrossRef]

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, 1976).

Atwater, H. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Aussenegg, F. R.

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762-1764 (2002).
[CrossRef]

Babich, V. M.

V. M. Babich, M. A. Lyalinov, and V. E. Grikurov, Sommerfeld-Malyuzhinets Approach for Diffraction Theory (Saint-Petersburg State U., 2004).

Baudrion, A.-L.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg morrors," Phys. Rev. B 73, 155416 (2006).
[CrossRef]

Bobrovnikov, M. S.

R. P. Starovoitova, M. S. Bobrovnikov, and V. N. Kislitsina, "Diffraction of surface waves on a break of impedance plane," Radiotekh. Elektron. (Moscow) 2, 250-259 (1962).

Boltasseva, A.

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078 (2001).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078 (2001).
[CrossRef]

Brekhovskikh, I. M.

I. M. Brekhovskikh, Waves in Layered Media (Academic, 1960).

Dereux, A.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg morrors," Phys. Rev. B 73, 155416 (2006).
[CrossRef]

Deutsch, M.

K. Hasegawa, J. U. Nockel, and M. Deutsch, "Surface plasmon polariton propagation around bends at a metal-dielectric interface," Appl. Phys. Lett. 84, 1835-1837 (2004).
[CrossRef]

Devaux, E.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg morrors," Phys. Rev. B 73, 155416 (2006).
[CrossRef]

Ditlbacher, H.

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762-1764 (2002).
[CrossRef]

Ebbesen, T. W.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg morrors," Phys. Rev. B 73, 155416 (2006).
[CrossRef]

Erland, J.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Fock, V. A.

V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Pergamon, 1965).

González, M. U.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg morrors," Phys. Rev. B 73, 155416 (2006).
[CrossRef]

Gradstein, I. S.

I. S. Gradstein and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, 1965), Eq. (8.412.6).

Grikurov, V. E.

V. M. Babich, M. A. Lyalinov, and V. E. Grikurov, Sommerfeld-Malyuzhinets Approach for Diffraction Theory (Saint-Petersburg State U., 2004).

Harel, E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Hasegawa, K.

K. Hasegawa, J. U. Nockel, and M. Deutsch, "Surface plasmon polariton propagation around bends at a metal-dielectric interface," Appl. Phys. Lett. 84, 1835-1837 (2004).
[CrossRef]

Hvam, J. M.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Kik, P. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Kislitsina, V. N.

R. P. Starovoitova, M. S. Bobrovnikov, and V. N. Kislitsina, "Diffraction of surface waves on a break of impedance plane," Radiotekh. Elektron. (Moscow) 2, 250-259 (1962).

Koel, B. E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Krenn, J. R.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg morrors," Phys. Rev. B 73, 155416 (2006).
[CrossRef]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762-1764 (2002).
[CrossRef]

Leitner, A.

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762-1764 (2002).
[CrossRef]

Leosson, K.

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078 (2001).
[CrossRef]

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Lyalinov, M. A.

V. M. Babich, M. A. Lyalinov, and V. E. Grikurov, Sommerfeld-Malyuzhinets Approach for Diffraction Theory (Saint-Petersburg State U., 2004).

Maier, S. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Maluzhinets, G. D.

G. D. Maluzhinets, "Excitation, refraction and radiation of surface waves on a wedge with given impedances of the surfaces," Dokl. Akad. Nauk SSSR 121, 436-439 (1958).

G. D. Maluzhinets, "Some generalizations of refraction method in the sinusoidal waves diffraction theory," Ph.D. dissertation (P. N. Lebedev Physical Institute Moscow, 1950).

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

R. F. Wallis, A. A. Maradudin, and G. I. Stegeman, "Surface polariton reflection and radiation at end faces," Appl. Phys. Lett. 42, 764-766 (1983).
[CrossRef]

Meltzer, S.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, 1976).

Nockel, J. U.

K. Hasegawa, J. U. Nockel, and M. Deutsch, "Surface plasmon polariton propagation around bends at a metal-dielectric interface," Appl. Phys. Lett. 84, 1835-1837 (2004).
[CrossRef]

Requicha, A. A. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Ryzhik, I. M.

I. S. Gradstein and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, 1965), Eq. (8.412.6).

Schider, G.

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762-1764 (2002).
[CrossRef]

Skovgaard, P. M. W.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

Starovoitova, R. P.

R. P. Starovoitova, M. S. Bobrovnikov, and V. N. Kislitsina, "Diffraction of surface waves on a break of impedance plane," Radiotekh. Elektron. (Moscow) 2, 250-259 (1962).

Stegeman, G. I.

R. F. Wallis, A. A. Maradudin, and G. I. Stegeman, "Surface polariton reflection and radiation at end faces," Appl. Phys. Lett. 42, 764-766 (1983).
[CrossRef]

Stepanov, A. L.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg morrors," Phys. Rev. B 73, 155416 (2006).
[CrossRef]

Talanov, V. I.

V. I. Talanov, "Surface electromagnetic waves on a rectangular impedance step in resonator," Izv. Vyssh. Uchebn. Zaved., Radiofiz. 1, 64-72 (1957).

Trenev, N. G.

N. G. Trenev, "Diffraction of surface electromagnetic waves on an impedance step," Radiotekh. Elektron. (Moscow) 3, 27-37 (1958).

N. G. Trenev, "Diffraction of surface electromagnetic waves on a semifinite impedance plane," Radiotekh. Elektron. (Moscow) 3, 163-171 (1958).

Vainstein, L. A.

L. A. Vainstein, Electromagnetic Waves (Radio i Svyaz, 1988).

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078 (2001).
[CrossRef]

Wallis, R. F.

R. F. Wallis, A. A. Maradudin, and G. I. Stegeman, "Surface polariton reflection and radiation at end faces," Appl. Phys. Lett. 42, 764-766 (1983).
[CrossRef]

Weeber, J.-C.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg morrors," Phys. Rev. B 73, 155416 (2006).
[CrossRef]

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

Appl. Phys. Lett.

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078 (2001).
[CrossRef]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, "Two-dimensional optics with surface plasmon polaritons," Appl. Phys. Lett. 81, 1762-1764 (2002).
[CrossRef]

R. F. Wallis, A. A. Maradudin, and G. I. Stegeman, "Surface polariton reflection and radiation at end faces," Appl. Phys. Lett. 42, 764-766 (1983).
[CrossRef]

K. Hasegawa, J. U. Nockel, and M. Deutsch, "Surface plasmon polariton propagation around bends at a metal-dielectric interface," Appl. Phys. Lett. 84, 1835-1837 (2004).
[CrossRef]

Dokl. Akad. Nauk SSSR

G. D. Maluzhinets, "Excitation, refraction and radiation of surface waves on a wedge with given impedances of the surfaces," Dokl. Akad. Nauk SSSR 121, 436-439 (1958).

Izv. Vyssh. Uchebn. Zaved., Radiofiz.

V. I. Talanov, "Surface electromagnetic waves on a rectangular impedance step in resonator," Izv. Vyssh. Uchebn. Zaved., Radiofiz. 1, 64-72 (1957).

Nat. Mater.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Phys. Rep.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131-314 (2005).
[CrossRef]

Phys. Rev. B

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg morrors," Phys. Rev. B 73, 155416 (2006).
[CrossRef]

Phys. Rev. Lett.

S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, "Waveguiding in surface plasmon polariton band gap structures," Phys. Rev. Lett. 86, 3008-3011 (2001).
[CrossRef] [PubMed]

Radiotekh. Elektron. (Moscow)

R. P. Starovoitova, M. S. Bobrovnikov, and V. N. Kislitsina, "Diffraction of surface waves on a break of impedance plane," Radiotekh. Elektron. (Moscow) 2, 250-259 (1962).

N. G. Trenev, "Diffraction of surface electromagnetic waves on an impedance step," Radiotekh. Elektron. (Moscow) 3, 27-37 (1958).

N. G. Trenev, "Diffraction of surface electromagnetic waves on a semifinite impedance plane," Radiotekh. Elektron. (Moscow) 3, 163-171 (1958).

Usp. Fiz. Nauk

V. M. Agranovich, "Crystal optics of surface polaritons and properties of surface," Usp. Fiz. Nauk 115, 199 (1975) V. M. Agranovich,[Sov. Phys. Usp. 18, 99 (1975)].
[CrossRef]

Other

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, 1976).

V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Pergamon, 1965).

I. S. Gradstein and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, 1965), Eq. (8.412.6).

L. A. Vainstein, Electromagnetic Waves (Radio i Svyaz, 1988).

I. M. Brekhovskikh, Waves in Layered Media (Academic, 1960).

V.M.Agranovich and D.L.Mills, eds., Surface Polaritons (North Holland, 1982).

G. D. Maluzhinets, "Some generalizations of refraction method in the sinusoidal waves diffraction theory," Ph.D. dissertation (P. N. Lebedev Physical Institute Moscow, 1950).

V. M. Babich, M. A. Lyalinov, and V. E. Grikurov, Sommerfeld-Malyuzhinets Approach for Diffraction Theory (Saint-Petersburg State U., 2004).

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Figures (10)

Fig. 1
Fig. 1

Geometry of the problem in cylindrical coordinates.

Fig. 2
Fig. 2

Contour of integration in Eq. (13).

Fig. 3
Fig. 3

Contour of integration in Eq. (14).

Fig. 4
Fig. 4

Contour of integration in Eq. (16).

Fig. 5
Fig. 5

Angular distribution of the radiation for a rectangular wedge with impedance ζ = 0.015 i : solid curve is the directed radiation [absolute value of the function s ( θ + π ) ], the dashed curve is the diffuse radiation [the absolute value of the function s ( θ π ) ].

Fig. 6
Fig. 6

Same as Fig. 5, but for an impedance ζ = 0.15 i .

Fig. 7
Fig. 7

Near field for copper at distance k 0 r = 2 π . Solid curve corresponds to ζ = 0.0015 0.15 i ( ω = 2.8 × 10 15 s 1 ) , dashed curve corresponds to ζ = 0.0014 0.015 i ( ω = 2.8 × 10 14 s 1 ) .

Fig. 8
Fig. 8

Same as in Fig. 7 at distance k 0 r = 4 π .

Fig. 9
Fig. 9

Same as in Fig. 7 at distance k 0 r = 6 π .

Fig. 10
Fig. 10

Same as in Fig. 7 at distance k 0 r = 8 π .

Equations (59)

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E ( r , t ) = E 0 exp [ κ y + i ( k x ω t ) ] ,
B ( r , t ) = B 0 exp [ κ y + i ( k x ω t ) ] ,
χ = arccos ( k k 0 ) , Im χ < 0 .
k = k 0 ε 1 + ε .
ε ( ω ) = 1 4 π γ ω 2 + γ 2 ( 1 i γ ω ) σ 0 ,
ε 1 .
χ 1 ε .
Δ B + k 0 2 B = 0 ,
E 0 r = i k 0 r B θ , E 0 θ = i k 0 B r , E 0 z = 0 .
ζ 1 ε ,
[ E 0 r = ζ ± B , 1 r B θ = i k 0 ζ ± B ] θ = ± Φ .
χ ± ζ ± ,
B ν ( r , θ ) = J ν ( k 0 r ) ( s 1 ν e i ν θ + s 2 ν e i ν θ ) ,
J ν ( k r ) = 1 2 π π + i π + i e i k 0 r sin η + i ν η d η ,
B ν ( r , θ ) = 1 2 π π + i π + i e i k 0 r sin η [ s 1 ν e i ν ( η + θ ) + s 2 ν e i ν ( η θ ) ] d η .
B ν ( r , θ ) = 3 π 2 + i π 2 + i e i k 0 r cos η [ s 1 ν e i ν ( η + θ ) + s 2 ν e i ν ( η θ ) ] d η .
B ( r , θ ) = 3 π 2 + i π 2 + i e i k 0 r cos η [ s 1 ( θ + η ) + s 2 ( θ η ) ] d η .
B ( r , θ ) = 3 π 2 i π 2 i e i k 0 r cos η s 1 ( θ η ) d η + 3 π 2 + i π 2 + i e i k 0 r cos η s 2 ( θ η ) d η .
B ( r , θ ) = Γ e i k 0 r cos η s ( θ η ) d η .
Γ e i k 0 r cos η [ 1 r s ( η ± Φ ) ± i k 0 ζ ± s ( η ± Φ ) ] d η = 0 .
Γ e i k 0 r cos η ( sin η ± ζ ± ) s ( η ± Φ ) d η = 0 .
( sin η + ζ + ) s ( η + Φ ) = ( sin η + ζ + ) s ( η + Φ ) ,
( sin η ζ ) s ( η Φ ) = ( sin η ζ ) s ( η Φ ) .
s ( u ) = σ ( u ) Ψ ( u , ζ + ) Ψ ( u 3 π 2 , ζ ) , σ ( u ) = 2 3 cos 2 ϕ 0 3 sin 2 u 3 sin 2 ϕ 0 3 ,
Ψ ( v , ζ ) = ψ ( v + 5 π 4 ζ ) ψ ( v + π 4 + ζ ) ,
ψ ( w ) = 4 3 cos w π 6 cos w + π 6 sec w 6 ,
B ( r , θ ) = g 0 + g 1 + g 2 e i k 0 r cos η s ( θ η ) d η .
Re η < π , Im η Im χ .
η n = θ ( 1 ) n ϕ 0 3 π n 2 , n = 0 , ± 1 .
θ , Re ϕ 0 Φ ,
η 0 = θ ϕ 0 , η 1 = θ + ϕ 0 3 π 2 .
ϕ 0 = Φ χ + .
η 0 : π 4 Re χ + < θ < 3 π 4 ,
η 1 : π 4 + Re χ + < θ < 3 π 4 .
B 0 ( r , θ ) = A e i k 0 r cos ( θ Φ + χ + ) ,
A = 2 9 π i 3 4 cos 1 6 ( π 2 + ζ + χ + ) cos 1 6 ( 3 π 2 ζ χ + ) cos 1 6 ( 3 π 2 ζ + χ + ) cos 1 6 ( π 2 ζ χ + ) cos 1 6 ( π 2 ζ + χ + ) × cos 1 6 ( π 2 + ζ χ + ) cos 1 6 ( π ζ + χ + ) sin 1 6 ( ζ + + χ + ) cos 1 6 ( ζ + χ + ) cos 1 6 ( 2 π + ζ + χ + ) cos 1 6 ( 2 π ζ + χ + ) cos 1 6 ( π + ζ + χ + ) .
η ± = θ ( π + Φ + ζ ± ) .
η + : 3 π 4 + Re ζ + < θ 3 π 4 ,
η : 3 π 4 θ < 3 π 4 Re ζ .
ζ ± = δ i Z ± , δ > 0 , Z ± = Re ,
B + ( r , θ ) = T e i k 0 r cos ( θ Φ ζ + ) ,
T = 2 9 π i 3 4 cos 1 6 ( π + 2 ζ + ) sin 1 3 ζ + cos 1 6 ( π 2 + ζ + ζ ) cos 1 3 ( π + ζ + ) cos 1 6 ( 3 π 2 + ζ + ζ ) cos 1 6 ( π 2 + ζ + + ζ ) × sin 2 3 χ + cos 1 6 ( 5 π 2 + ζ + ζ ) cos 1 6 ( π 2 ζ + ζ ) cos 1 6 ( 3 π 2 + ζ + + ζ ) 1 2 cos 2 3 ζ + + 3 2 sin 2 3 ζ + + cos 2 3 χ + .
B ( r , θ ) = R e i k 0 r cos ( θ + Φ + ζ ) ,
R = 2 9 π i 3 4 cos 1 6 ( π + 2 ζ ) sin 1 3 ζ cos 1 6 ( π 2 ζ + + ζ ) cos 1 3 ( π + ζ ) cos 1 6 ( 3 π 2 ζ + + ζ ) cos 1 6 ( π 2 + ζ + + ζ ) × sin 2 3 χ + cos 1 6 ( 5 π 2 ζ + + ζ ) cos 1 6 ( π 2 ζ + ζ ) cos 1 6 ( 3 π 2 + ζ + + ζ ) 1 2 cos 2 3 ζ + 3 2 sin 2 3 ζ cos 2 3 χ + .
A = 2 8 π i 3 4 6 cos 1 6 ( π 2 + 2 ζ ) cos 1 6 ( 3 π 2 2 ζ ) cos 1 6 ( π 2 ζ ) sin 1 3 ζ cos 1 6 ( π 2 2 ζ ) cos 1 3 ( π ζ ) ,
T = 2 7 π i 3 4 2 cos 1 6 ( 3 π 2 + 2 ζ ) cos 1 6 ( π + 2 ζ ) cos 1 6 ( π 2 2 ζ ) sin 2 3 ζ sin 1 3 ζ cos 1 3 ( π + ζ ) cos 1 6 ( π 2 + 2 ζ ) ( 3 2 sin 2 3 ζ 1 2 cos 2 3 ζ ) ,
R = 2 7 π i 3 4 2 cos 1 6 ( 3 π 2 + 2 ζ ) cos 1 6 ( π + 2 ζ ) cos 1 6 ( π 2 2 ζ ) sin 2 3 ζ sin 1 3 ζ cos 1 3 ( π + ζ ) cos 1 6 ( π 2 + 2 ζ ) ( 3 2 sin 2 3 ζ + 3 2 cos 2 3 ζ ) .
R ( ζ ) 2 i Z 3 3 , T ( ζ ) 2 i Z 3 ,
ρ = k 0 r , f ( η ) = i cos ( η + π ) ,
F ( η ) = s ( θ η π ) .
cos ( η + π ) = 1 i x 2 .
d η = 2 i d x x 2 2 i ,
B g 1 ( r , θ ) = i 2 π k 0 r s ( θ π ) e i [ k 0 r + ( π 4 ) ] .
B g 2 ( r , θ ) = i 2 π k 0 r s ( θ + π ) e i [ k 0 r + ( π 4 ) ] .
D ( r , θ ) 1 2 π k 0 r e i [ k 0 r + ( π 4 ) ] θ θ 0 + ζ .
G = 2 Im ζ 2 ω ω p ,
P in = v 4 π A 2 0 e i k 0 r cos ( π 2 + i Z ) 2 d r v A 2 8 π k 0 Z .
P out = c 4 π A 2 2 π k 0 Φ Φ d θ θ θ 0 + ζ 2 c A 2 8 π k 0 Z .
v c ( 1 + ζ 2 2 ) .

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